CHAMP-3.0.1-Manual

CHAMP User’s Manual

Copyright ©2002-2012

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CHAMP User’s Manual

CHAMP Version 3.0.1

December 2012

TABLE OF CONTENTS

1. Welcome 1

2. Overview of the CHAMP Program 2

3. Getting Started with CHAMP - the Wizards 4

3.1 Horn Wizard 4

3.2 Ring-focus / Axially Displaced Reflector wizard 15

3.3 Wizard analysis 19

4. The CHAMP Program Lay-out 21

4.1 The CHAMP Bar and the CHAMP Tabs 22

4.2 The Geometry Tab 23

4.3 The Analysis Tab 25

4.4 Launching the Analysis 27

4.5 The Results Tab - Part I (Analysis) 28

4.6 The Optimisation Tab 32

4.7 Launching the Optimisation 36

4.8 The Results Tab - Part II (Optimisation) 41

5. Project and File Organization 43

6. Tutorial Examples 45

6.1 Potter Horn 46

6.2 Linear Sections Horn 55

6.3 Horn with Slanted Corrugations 63

6.4 Reflector Wizard followed by Horn Wizard 73

6.5 Reflector with Corrugated Horn 79

6.6 Optimisation of reflector system 89

6.7 Horn with Lens 98

6.8 Shroud Case 108

7. Batch-Mode Operation 124

8. CHAMP3 for CHAMP2 Users 126

9. Technical Description 130

9.1 Analysis Methods 130

9.2 Input Definitions 134

9.3 Output Definitions 138

10.Reference Section 141

10.1 Alphabetical List of Classes and Command Types 142

10.2 Classes 147

10.3 Command Types 334

10.4 Applicable Units and the dB-Scale 354

10.5 File Extensions 356

10.6 File Formats 358

List of References 380

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1. Welcome

Welcome to the CHAMP User’s Manual. The present document provides adescription of the CHAMP software and a series of tutorial examples.

In Chapter 2 a general overview of the CHAMP software is first given. TwoWizards are available which assist the user in setting up a horn geometry ora reflector geometry in terms of few input parameters, and thus provides aneasy way of getting started with the program. The wizards are introduced inChapter 3. Next, the main features of the CHAMP Graphical User Interface(GUI), are described in Chapter 4, and it is demonstrated how to perform anRF-analysis as well as a simple optimisation of the horn or antenna. Finally,the CHAMP project and file handling is presented in Chapter 5. Thus, followingChaptes 5, the user should be able to set-up, and analyze /optimise a widerange of horn and antenna geometries.

A number of more detailed Tutorial Examples are presented Chapter 6 in orderto demonstrate the software features and capabilities.

While the previous chapters have focused on the usage of the software usingthe CHAMP GUI, the experienced user may find it beneficial to run the softwarein batch mode, as described in Chapter 7.

Chapter 8 is for all users who are already familiar with the previous version ofthe program, CHAMP2, and wish to know the main differences with CHAMP3.

A short introduction of the modelling techniques used in CHAMP as well asmathematical definitions of the applied terms, explanations of the appliedgeometries and electromagnetic models as well as output data capabilities isgiven in the CHAMP Technical Description, Chapter 9.

A complete and detailed description of all classes, commands and input/outputfile formats of CHAMP is found in the Reference Section in Chapter 10.

To take full advantage of the present manual, it is recommended you have aversion of CHAMP running.

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2. Overview of the CHAMPProgram

CHAMP is a general software tool for design and analysis of a rotationallysymmetric feed horn possibly illuminating rotationally symmetric reflectorsand scattering structures.

Most types of conical horn may be modelled, e.g. smooth-walled horns andhorns with axial, radial or ring-loaded corrugations. Note however, that CHAMPcurrently does not support modelling of coaxial-moded horns.

The program models the influence of any metallic, dielectric, or compositemetallic/dielectic, rotationally symmetric structure in the close vicinity of andco-aligned with the feed horn.

CHAMP offers optimization capabilities for feed, sub- and main reflectors. Thishas been made possible by introducing a new, fast analysis algorithm, com-bined with an approach to defining any geometrical parameter as a possiblevariable to the optimisation.

CHAMP thus allows a fast and accurate design and analysis of any rotationallysymmetric antenna with a feed horn as the illuminating source, ranging fromlarge Earth telescopes to compact terminals.

The electromagnetic models which may be applied for the analysis are:

• Mode matching (MM) for the horn interior

• Higher-order Method of Moments for Body of Revolutions (BOR-MoM) forthe scattering structures

It is assumed that the user has an engineering understanding of the advan-tages and limitations of these methods. For more details, please see theChapter 9.

CHAMP consists of two main components: A Graphical User Interface (GUI)and a back-end module.

The GUI assists the user in:

1. Defining the antenna geometry, manually or by using one of the wizards.

2. Setting up the horn excitation mode and control variables to the analysis.

3. Launching the computation invoking the back-end module

4. Visualizing the results computed by the back-end module

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5. Defining the variables and performance goals to an optimisation of theantenna geometry

6. Launching the optimisaiton.

The back-end module performs the antenna analysis and optimisation as wellas a number of tasks related to project management, i.e. logging, file in-put/output, 3D drawing, and license management.

In the installation directory, the GUI is the "CHAMP.exe" and the back-endmodule is the "CHAMP-analysis.exe" executables. To launch CHAMP, click onthe CHAMP-Icon or navigate to the directory in which CHAMP is installed anddouble-click on the "CHAMP.exe" program. This will open the GUI. The analysismodule can be used for batch-mode operation without the GUI, as explainedin Chapter 7. We will assume in this document that CHAMP is launched withthe GUI.

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3. Getting Started with CHAMP -the Wizards

The CHAMP welcome dialogue provides different options for getting started.Most users will initially select the Wizard, which facilitates the definition ofcorrugated horns and/or dual-reflector terminals. It implements many engi-neering design tools in a simple and easy-to-use fashion and with the aid ofthe wizard it is possible to design fairly complex systems from surprisingly fewinput parameters. It should be recognized, though, that the wizard only catersfor but a few of the many, many different horn types that can be designedwith CHAMP.

The Wizard can also be activated from the Tools pull-down menu.

3.1 Horn Wizard

The horn wizard applies to the design of smooth-walled horn and radiallycorrugated horns with an optional mode-converter, and the design equationsare appropriate for narrow flare angle horns, typically less than 20◦. Theprincipal input parameters are the frequency band and desired gain roll-off ata given angle. If the assumption about the narrow-flare angle is not fulfilledin the final design, the CHAMP analysis is still correct but may reveal that thegain roll-off is not as expected.

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3.1.1 The frequency menu

3.1.1.1 Input parameters required from the user:

Lower frequency the lowest frequency of operation.

Upper frequency the highest frequency of operation.

3.1.1.2 Derived data, that may be modified by the expert designer:

Design frequency

Multiplier

Output frequency

3.1.1.3 Remarks:

The design and the output frequency are used later to define a corrugatedhorn according to the rules-of-thumb given in the paper by C. Granet & G.James [1]. The design formulas are quite complex and the reader is referredto the paper for details, but with some modifications the depth of the slotschanges from being approximately 1/4λ deep at the design frequency at thethroat of the horn, to approximately 1/4λ deep at the output frequency at theaperture.

The frequencies are derived from the formulas below:

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Multiplier Design fre-quency

Output fre-quency

Upper fre-quency ≤ 1.44x (lower fre-quency)

1.025 Square rootof (lower fre-quency x upperfrequency)

Multiplier x de-sign frequency

Upper fre-quency > 1.44x (lower fre-quency)

1.100 1.2 x lower fre-quency

Multiplier x de-sign frequency

It is noted that the experienced horn designer is free to change the designfrequency and the output frequency at large, just as these parameters maylater be selected as optimization variables if the designer wants to explorethe possibility of further improving the initial design.

3.1.2 The feeding waveguide set-up menu


None.

3.1.2.2 Derived data, that may be modified by the expert de-signer:

Waveguide radius

7

3.1.2.3 Remarks:

The wizard proposes an input radius of 1.5/π times the free-space wavelengthat the design frequency. This choice will ensure that the fundamental modewill propagate and that the return loss is typically better than 15 dB.

The size may be adjusted to meet mechanical or interfacing requirements.When adjusting the parameter, the wizard reports at the bottom if there areany problems with the particular choice, either that the fundamental modecannot propagate or if the next higher-order mode (TM11) can propagate.

Another consideration that the user should make is that in case the horn willalso be used for tracking modes (TE01, TM01 or TE21) the input guide mustof course be sufficiently wide to support those.

3.1.3 Selection of horn type

This menu is very simple and offers the choice between two of the severalhorn types that CHAMP includes.

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3.1.3.1 Single-depth corrugated horn set up

3.1.3.1.1 Aperture size and flare angle

Input parameters required from the user:

Pattern taper value the desired gain-roll off measured in dB relative to on-axis gain.

Pattern taper angle the angle at which the Pattern taper value applies.

Derived data, that may be modified by the expert de-signer:

None.

Remarks:

From the given input data, taper value and taper angle, the wizard proposesdimensions for the horn, based on fairly simple rules given in Johnson & Jasik[2]. There are different ways in which to achieve the requirements, and thisleads to a trade-off between horn aperture size and length:

• A small aperture must radiate with high efficiency to meet a given taper.This implies a small aperture phase error, which in turn implies a narrowflare angle and longer over-all length of the horn

• A large aperture may give the same taper with a less efficient aperturedistribution, i.e. with larger phase error, and can be achieved with awider flare angle and shorter horn

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The table parameterizes this trade-off by the aperture phase error ∆ shownto the left. Since the design equations are under the assumption of a narrowflare angle, the wizard will show flare angles larger than 20◦ in red color. Thisdoes not mean that the horn cannot be used, but it may not behave exactlyas expected from the rules of thumb. The succeeding CHAMP analysis willalways predict the correct performance.

3.1.3.1.2 Mode-converter design and corrugation details

Input data required from the user

None


Section exit radius: the horn aperture radius, as determined from the de-sired taper

Section length: overall length of the horn, including the mode-converter

Corrugation pitch: the size of a corrugation, measured as the width of aslot and the thickness of a tooth

Number of corrugations: total number of corrugations throughout the horn

Number of mode converter corrugations: the portion of the number ofcorrugations that to which the mode converter design rules are applied

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Width to pitch ratio: the ratio between the width of a single corrugationslot and the corrugation pitch (per definition < 1)

Mode converter percentage factor: a number between 40% and 50% thatis used in the design of the mode converter, see re-marks

Mode converter slot type: offers the choice between "Variable depth slots","Ring loaded slots" and "Width to pitch slots"

Profile: offers the choice between different horn profiles

Remarks

It is in general not possible to obtain a good return loss at the circular waveg-uide input to a corrugated horn, if the corrugations are designed to be approx-imately λ/4 throughout the horn. Therefore, the wizard offers the capabilityof designing a mode converter which gradually changes the depth of thecorrugations from λ/2 to λ/4.

If the aperture radius is changed from the one proposed by the wizard, thehorn geometry will change depending on the setting of the radio button:

Radio button selects:User changes: Section length Corrugation

pitchNo. of corruga-tions

Section exit ra-dius:

Horn flare an-gle changes

Section lengthand no. ofcorrugationchange, tokeep flareangle constant

Section lengthand no. ofcorrugationchange, tokeep flareangle constant

Section length: No. of corruga-tions changes

Corrugationpitch change

Corrugationpitch:

No. of corruga-tions changes,and pitch ad-justed

Section lengthchanges

No. of corruga-tions:

Corrugationpitch changes

Section lengthchanges

The mode converter is implemented by applying the mode-converter corru-gation design rules from the earlier given reference (Granet & James) [1] tothe first part of the corrugations of the feed, 16 in the example shown. Ifthe horn is very short, this number may be lower for the given pitch size. Abetter return loss can be achieved by increasing the number of slots in themode converter, but this may impede the cross-polarization performance ofthe horn.

The mode converter percentage factor is a number between 40% and 50%and determines the depth of the first slot relative to the wavelength at thedesign frequency.

11

There are 8 different choice available for the horn profile, linear, sinusoid, hy-perbolic, exponential, asymmetric sine-square, tangential, simple polynomialand polynomial. The wizard default is the linear profile and it is left to theuser to experiment with different profiles to assess if, for a given application,there are advantages of one profile over another. It is noted that once thehorn is defined, it is possible in the CHAMP GUI to convert the profile to acubic spline expansion, where the expansion coefficients can be applied asvariables in an optimization.

Figure 3-1 Definition of various horn profiles (from [1])

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3.1.3.1.3 Horn design, when a mode converter is not included

With the obvious exception of parameters related to the mode converter, thismenu offers the same choices as the one described in the previous paragraph.

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3.1.3.2 Smooth horn set up

3.1.3.2.1 Aperture size


Pattern taper value: the desired gain-roll off measured in dB relative toon-axis gain

Pattern taper angle: the angle at which the Pattern taper value applies


None.

Remarks:

The aperture radius r of the smooth horn is chosen from the very simpleapproximation r/λ = 0.362 x Square root ( taper value / sin(taper angle))

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3.1.3.2.2 Smooth horn profile set up


None.

Derived data, that may be modified by the expert designer:

Section exit radius: the horn output aperture size

Flare angle: the angle between the horn axis and the straight line connect-ing the input flange to the output flange of the horn

Section length: the total length of the horn measured along the horn axis

Profile: offers a choice between different horn profiles

Remarks:

Changing the section end radius affects the length of the horn but not theflare angle; changing the flare angle changes the horn length and vice versa.The same 8 profiles are available as for the corrugation horn.

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3.2 Ring-focus / Axially Displaced Reflector wizard

3.2.1 Frequency set-up


Lower frequency: the lowest frequency of operation

Upper frequency: the highest frequency of operation


None.

3.2.1.3 Remarks:

The wizard defines the centre frequency as the arithmetic mean of the twoinput frequencies.

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3.2.2 Reflectors set-up


Mode: selects one of two possible dual reflector configurations: Gregorian orCassegrain Ring-focus

Main reflector diameter: the diameter of the outer boundary of the mainreflector

Use relative or absolute values: choice between two different ways of spec-ifying the geometry

If relative:

Main reflector f/D: the ratio between the main reflector diameter and thefocal length of the offset parabola used as generating curve for the mainreflector

Sub reflector diameter relative to main reflector diameter: as the namesays

If absolute:

Focal length: the focal length of the offset parabola used as generatingcurve for the main reflector

Sub reflector diameter: the size of the sub reflector

All:

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Half-angle subtended by the sub reflector at the feed: half of the an-gle under which the sub reflector rim is seen when viewed from thecenter of the feed aperture


None.

3.2.2.3 Remarks:

The geometry is often referred to as a ring-focus or an axially displaced re-flector system. It’s generated by taking as starting point the cross section ofa standard offset system of either the Gregorian (elliptical sub reflector) orCassegrain (hyperbolical sub reflector) type. This system is rotated aroundan axis parallel to the boresight axis and through the focal point of the subreflector. Such system offers the advantages of non-offset systems withoutthe scattering issues due to blockage and direct coupling back to the feedfrom the sub reflector.

Detailed description of the geometry may be found in the paper by Moreiraand Prata [4].

3.2.3 Horn interior set up


None.

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Waveguide diameter: diameter of the simple, open-ended waveguide beingused as feed

Waveguide length: length of the initial waveguide

3.2.3.3 Remarks:

In the absence of general tools for choosing a feed system for the antennaconfiguration, the wizard proposes an open-ended wave-guide where the di-ameter is determined such that the far-field pattern from the aperture willhave a taper of -12 dB at an angle corresponding the to the half-subtendedangle of the sub reflector.

The user will in general have to add a more advanced horn once the wizardhas set up the entire system in CHAMP, since the choice of an open-endedwaveguide would very rarely be an optimum choice. Moreover, it will oftenbe the case that the proposed size of the waveguide is such that it maysupport several higher-order modes and it will therefore be a better solutionto design a flared horn with the same aperture dimension, and with an inputguide that only supports the fundamental mode. In this way, the generationof higher-order modes throughout the horn is accurately calculated by CHAMP.

The length of the waveguide has no influence on the horn pattern, and canbe chosen for illustration purposes.

If the user does not alter the waveguide diameter, and returns to the previ-ous menu to change some of the parameters, a new value for the diameterwill be computed when entering this menu again. If the user has made amodification, the automatic re-calculation is suspended and the user’s choicegets priority.

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3.2.4 Horn exterior set up


None.


Horn wall thickness: material thickness of the horn

3.2.4.3 Remarks:

The horn is modeled with a flange around the aperture, corresponding to thechosen material thickness. From this flange, an outer cylinder is defined whichextends to the main reflector surface. The material thickness is calculated bythe wizard as a tenth of the wavelength at the centre frequency, and can bechanged by the user to reflector the actual choice based on mechanical aswell as electrical considerations.

3.3 Wizard analysis

When the wizard is completed, the chosen geometry is shown in the CHAMPGUI and can be analyzed immediately using the standard procedure. Thedefault set up, which may be modified by the user to reflect the desiredconfiguration, is as below:

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The analysis is carried out at three frequencies equidistantly spaced fromthe lower to the upper, and with the fundamental TE11 mode as excitation.The polarization is linear along the horn x-axis, and the exterior geometry,including the reflectors, are included in the analysis using standard settingsfor the moment-method analysis. As always, it is recommended to perform aconvergence analysis to ensure that the standard parameters are appropriate.

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4. The CHAMP Program Lay-out

After closing the wizard, the main window of CHAMP looks like Figure 4-1, andconsists of the following parts:

• At the top: the CHAMP Menus in the form of a top line with all theCHAMP menus needed to manipulate the project, open the wizards andgenerate objects (File, Edit, ..), and a number of icons for the mostcommonly used functionalities.

• To the left: the CHAMP Bar which is a vertical bar with four icons atthe top which allow the user to switch between the four CHAMP Tabs,i.e. different steps in the RF-modellling as well as two icons at thebottom which allow the user to launch the horn analysis and the hornoptimisation.

• To the right: the CHAMP User Area which is the largest part of thewindow with a lay-out which changes depending on the selected CHAMPTabs. As an example, when the Geometry Tab is selected, the CHAMPUser Area shows:

– To the left: a 2D-rendering of the horn antenna geometry.

– To the right: an editor with all the data used to define the geometry.

Figure 4-1 The main window of CHAMP after finalizing theReflector Wizard.

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4.1 The CHAMP Bar and the CHAMP Tabs

The four icons in the CHAMP Bar are the CHAMP Tabs which guide the userthrough different steps in the RF-modellling of the horn antenna. Selectingone of the CHAMP Tabs changes the contents and lay-out of the CHAMP UserArea and the CHAMP Menus. The following CHAMP Tabs are available:

• The Geometry Tab for specification of the horn antenna geometry.

• The Analysis Tab for specification of the horn excitation, the frequen-cies used in the analyses, as well as a number of control settings for theanalysis.

• The Optimisation Tab for specification of the optimisation variablesand the optimisation goals, i.e. the performance measures which theoptimisation should try to reach.

• The Results Tab for viewing results obtained in the RF-modelling of thehorn antenna.

Further, below the CHAMP Tabs, two icons are shown:

• The Analysis Button in the form of a blue triangle, or a ’play’ button,which launches the horn analysis.

• The Optimisation Button, in the form of two blue triangles, or a ’fastforward’ button, which launches the horn optimisation.

The horn analysis and the horn optimisation may also be started via theAnalysis menu item. There is no icon for the tolerance analysis, and thistolerance analysis can only be started via the menu item Analysis.

In the following, the four CHAMP Tabs are described in details in order toexemplify the use of the different parts of the program. We will perform ananalysis and an optimisation of the single reflector antenna defined by one ofthe Wizards in Chapter 3.

It is assumed that the program has been launched, and the Reflector Wizardhas been completed using the suggested default values. The top line of theCHAMP window shows the name of the CHAMP project and the program name:

Untitled* TICRA CHAMP.

The project name is currently "Untitled", and the asterisk indicates that theproject has not been saved. We start by saving the project clicking on SaveProject As... in the File menu. We select the project name MyReflectorand the project is saved in a suitable folder location, e.g. C:/ticra/Test.When the save procedure is executed, the top line in the CHAMP windowshows the project name. The asterisk has disappeared as all changes havebeen saved.

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4.2 The Geometry Tab

The Geometry Tab is used to specify the horn antenna geometry. The Tab isavailable by clicking the Geometry icon in the CHAMP Bar.

The CHAMP User Area shows:

• To the left: a 2D-rendering of the horn antenna geometry, the so-calledGeometry View.

• To the right: an editor with all the data used to define geometry. Thiseditor is denoted the Property Editor.

Figure 4-2 The lay-out of the Geometry Tab.

The data defining the horn antenna geometry may be changed in the Geom-etry View using the mouse, whereby the corresponding values are updatedin the Property Editor. The data may also be edited in the Property Editor,whereby the drawing is updated. It is possible to click on a point on the draw-ing, and if the point is given directly in terms of the (z, ρ)-coordinates, thesecoordinates are highlighted in the Property Editor, and vice versa. The twoparts of the CHAMP User Area are described in the following two sections.

4.2.1 The Geometry View

The Geometry View shows a cut (parallel projection) through the horn in oneof the symmetry planes. As CHAMP is restricted to handling a rotationallysymmetric geometry, the Geometry View provides a full description of thegeometry. It is possible to obtain a complete 3D-view of the horn (or a slicehereof) using the item View -> 3D available as a menu item and as an iconin the CHAMP Menus.

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The border of the Geometry View shows a ruler, with labels shown in theuser-selected default length unit. This default length unit may be changed bythe user in the Units tab of the Application Preferences menu availableby selecting File > Preferences.... The default length unit is a user settingthat will be used for the user’s other CHAMP projects.

It is possible to zoom in the plot using the mouse wheel or the ’+’- and ’-’-keyson the keyboard. It is also possible to zoom to a region, by first selecting theZoom Region icons in the CHAMP Menus, and then using the mouse. Finally,it is possible to pan the plot, by first selecting the Pan icons in the CHAMPMenus, and then using the mouse.

4.2.2 The Property Editor

The Property Editor provides an overview as well as editing access to all theuser input data which defines the antenna geometry.

The contents of the Editor are sorted in three main categories, namely HornInterior, Exterior Geometry, and Variables. Each of the of these maincategories may contain a number of objects. The names of the object andthe object class are shown in the top header row. The objects are sortedaccording to the order also used in the Create menu. Each of the entriesmay be expanded or collapsed using the ’+’ or ’-’ in the header row.

The data contained in an object may be edited using a single-click by themouse. The data may be in the form of integer values, real values, or char-acter strings. Data may also be in the form of so-called variables.

4.2.3 Real Variables

CHAMP introduces the concept of ’Real Variables’. The user may assign asymbolic name for any real valued quantity in CHAMP, and reference thissymbolic name elsewhere in the geometry set-up (either directly or throughthe most commonly used mathematical functions). This allows the user tointroduce a number of design parameters which influence not only a singlebut several of the input fields in the program. A new Real Variable may bedefined in three different ways:

• an existing real value, e.g. 0.8, in the Property Editor is replaced by asymbolic name, e.g. ’my_var’. The Real Variable is assigned the realvalue, my_var = 0.8.

• an existing real value, e.g. 0.8, in the Property Editor is replaced byan expression using the Real variable, e.g. ’1.0*cos(my_var)’. The RealVariable is assigned the value zero.

• selecting Real Variable in the Create menu. A name for the variableshall be specified, e.g. ’my_var’ and it is assigned the value zero.

The symbolic name may subsequently be used in all other input fields in theProperty Editor. More details about the algebraic and trigonometric expres-sions allowed may be found in the Section Real Variable in the ReferenceSection of Chapter 10.

25

4.3 The Analysis Tab

The Analysis Tab is used to specify the horn excitation, the frequencies usedin the analysis, as well as a number of control settings for the analysis. TheTab is available by selecting the Analysis icon in the CHAMP Bar.


• At the top: The Analysis Section with the List of Analyses specified bythe user.

• At the bottom: The Settings for Analysis Section with a number ofuser input fields specifying the frequencies and analysis control settingsfor the user-defined analysis selected in the List of Analyses. The inputfields are divided in five groups:

– The Frequency group defining the frequencies used

– The Excitation group defining the horn excitation

– The Additional Analysis group defining the amount of output calcu-lated in each analysis

– The Horn Interior Analysis Accuracy group defining control settingsfor the mode matching modelling

– The Exterior Geometry Analysis Accuracy group defining control set-tings for the Method of Moments modelling

Figure 4-3 The lay-out of the Analysis Tab.

The horn excitation may be either the fundamental mode or one of threetracking modes. When adding a new Analysis to CHAMP, the user must spec-ify an Analysis Name as well as choose between Fundamental Mode or

26

Tracking Mode excitation. The analysis name is used in CHAMP as a shortreference to the frequencies and control settings for this Analysis.

Each analysis is performed for a Number of frequencies equidistantlyspaced from the Start frequency to the End frequency. The resultingfrequency step is shown as information.

In each CHAMP Analysis, the horn antenna is excited by a single mode at thehorn throat. If the fundamental mode has been selected, the user may choosebetween four polarisations as well as a polarisation ratio. If the tracking modehas been selected, the user may choose between one of the modes, TE21,TM01, or TE01, as well as a possible rotation of the mode relative to thex-axis. The precise definition of the horn excitation is available in Chapter 9.

CHAMP models the horn interior in terms of a segmented geometry using so-called elementary modules, c.f. Section 9.1.1.2. It is possible to get a previewof this segmented geometry by clicking Preview Segmentation.

Note: The convergence of the modelling should always be checked,by launching additional analyses with more stringent requirementsto the modelling until no changes are observed in the results. Themodelling accuracy is controlled by the four analysis control settings’Additional Modes’, ’Interior Segmentation’, ’Exterior Expansion Accu-racy’ and ’Maximum Mesh Length’, which are further described in theCorrugated Horn Mode Matching section. In summary, the accuracysettings should be checked in the following cases:

• ’Additional Modes’: Always.

• ’Exterior Expansion Accuracy’: Always.

• ’Interior Segmentation’: If the horn has a smooth-walled hornsection.

• ’Maximum Mesh Length’: If the exterior geometry has scattererswith a highly curved profile.

It is not necessary to check these parameters independently. A singlerun with all parameters increased will be sufficient. When convergedresults are obtained, it is highly recommended to restore the analysiscontrol settings with the lowest value for which convergence is ob-tained, in order to keep the computation time as low as possible infuture analyses.

In the case considered, the Reflector Wizard has set up a single Analysisnamed "TE11_Band1" with three frequencies in a frequency band from 7.5 GHzto 8.5 GHz. The fundamental mode is linearly polarised along the x-axis. Thecontrol settings have their default values. As the Wizard has guided the Userin the set-up of the geometry as well as the frequencies and control settings,we are now ready to perform the actual modelling of the horn.

27

4.4 Launching the Analysis

The analysis of the horn antenna is launched by clicking on the AnalysisButton (or selecting the corresponding menu item).

The user is first warned that the project must be saved before starting ananalysis. The program will create a number of files and file folders for thepresent project, as will be further described in Chapter 5. When the userhas selected first OK and subsequently a project file name and folder, theCHAMP - Analysis Launcher dialog appears, c.f. Figure 4-4.

Figure 4-4 The CHAMP - Analysis Launcher dialog.

The dialog contains three different parts:

• At the top: The Analysis Name, which is a unique name of this analysiswithin the CHAMP project. The program will suggest a default name,"Analysis_XXXX", for the analysis, where "XXXX" is an unused number.

• At the centre: The Analyses Summary Table with a summary of theindividual analysis specifications used in the present analysis. It is pos-sible to modify the number of frequency steps, and it is possible to omitindividual analysis specifications from the analysis.

• At the bottom: The Comment Field which is a user-defined text associ-ated with the current analysis. The text will be saved in the project andcan be viewed and/or edited in the Results Manager.

In the case considered, add a comment, e.g. "My first analysis", in the Com-ment Field and then press OK. The analysis now starts and the CHAMP -progress window appears, c.f. Figure 4-5.

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Figure 4-5 The CHAMP - progress window.

The progress window contains information issued by the CHAMP backgroundmodule during the modelling, as well as information about the overall progressof the modelling.

4.5 The Results Tab - Part I (Analysis)

The Results Tab is used to view results obtained in the RF-modelling of thehorn antenna. The Tab is available by clicking the Results icon in the CHAMPBar.


• To the left: The Results Tree with a branch for each modelling per-formed, i.e. for each Analysis, Optimisation or Tolerance Analysis launchedby the user. Under each branch, a number of entries are available forfast access to the modelling results.

• To the right: The Results Plot Area where plots of the modelling resultsare shown.

An example of the Results Tab lay-out is shown in Figure 4-6.

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Figure 4-6 The lay-out of the Results Tab.

Following the analysis of the horn antenna presented in the previous section,the Results Tree has only one single top branch, and the Results Plot Area isempty.

Expand the "TE11_Band1" branch, and double click on the Return Loss entryto obtain the plot in Figure 4-7 of the return loss at the 3 frequencies. Notethat the lay-out of the Return Loss plot to some extent may be controlled usingthe settings in the Results Manager tab of the Application Preferencesmenu available by selecting File > Preferences....

Figure 4-7 Return loss for the first analysis (3 frequencies).

Next, expand the Pattern Cuts branch and double click on the "8.0 GHz"entry to obtain the plot in Figure 4-8 of the radiated pattern at the centre fre-

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quency, 8.0 GHz. Six curves are plotted, namely the co- and cross-polarisationin the planes φ = 0◦ (E-plane), φ = 45◦, and φ = 90◦ (H-plane). The cross po-larisation is zero in the E- and H-planes, so only four of the six curves arevisible.

Figure 4-8 Radiation pattern at 8.0lGHz.

By default, the pattern cuts are calculated from θ = 0◦ to θ = 180◦. The usermay change the θ-range via the Analysis tab of the Application Prefer-ences menu available by selecting File > Preferences.... For the plot ofthe Radiation Pattern, it may be difficult to see details around the main beamand the first side-lobes. Even after changing the plot range of the x-axis fromθ = 0◦ to θ = 30◦ degrees, there are too few data points to provide a plot ofproper quality. Naturally, it is possible to change the default θ-range and thenlaunch a new analysis. A faster way is, however, to use the RecalculateCuts functionality available as an icon in the menu line at the top of the plotwindow. Clicking on this icon produces the dialog in Figure 4-9.

Figure 4-9 The Recalculate Cuts dialog.

Enter the desired values of θ and select OK. A new pattern cut is calculatedand the plot is updated with the new data values, as shown in Figure 4-10.

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Figure 4-10 Radiation Pattern at 8.0 GHz after the Recalculate Cutsfunctionality.

The Recalculate Cuts functionality is only available for pattern cuts. If a plotwith more frequency points is needed for e.g. the return loss, a new analysismust be launched. Increase the number of frequencies from 3 to 51 in theAnalysis Tab, and launch this new analysis via the Analysis Button. Whenthe analysis is finalized, a new top-branch is available in the Results Tree onthe Results Tab. Double-clicking on the Return Loss entry leads to the plotof the return loss in Figure 4-11.

Figure 4-11 Return loss for the second analysis (51 frequencies).

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4.6 The Optimisation Tab

The Optimisation Tab is used to specify the optimisation variables and theoptimisation goals, the latter being the performance measures, which theoptimisation should try to reach. The Tab is available by clicking the Optimi-sation icon in the CHAMP Bar.


• At the top: The Variables Section, where the user selects and des-elects optimisation variables from a list of all variables defined. TheVariable Section is divided in two halves with the deselected variablesto the left and the selected variables to the right. The user selectsor deselects optimisation variables using the arrows between the twohalves.

• At the bottom: The Goals Section with a table of the optimisation goalsused in the optimisation. New goals may be added or existing goalsedited via the buttons to the right of the table or by double-clicking ina table row.

An example of the Optimisation Tab lay-out is shown in Figure 4-12.

Figure 4-12 The lay-out of the Optimisation Tab.

In the case considered, the Wizard sets up a dual-reflector system with asingle variable, "z_focal_length". The geometry is defined in such a way thatwhen this variable is zero, the focal point of the reflector system is at thehorn aperture, z = 0. If "z_focal_length" is changed both the subreflector andthe main reflector are displaced, and the length of the horn exterior geometrychanged, so that 1) the horn and main reflector remain connected, and 2) thefocal point of the reflector system is at z equal to z_focal_length.

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We will select the "z_focal_length" as optimisation variable in the VariablesSection.

In the Goals Sections, it is possible to add an arbitrary number of optimisationgoals. When selecting Add Goal, the Goal Wizard appears. On the first page,the Select goal type page, the user selects the type of optimisation goal.A variety of goal types is available as seen in Figure 4-13. Each goal typerepresents different RF-properties, which may be the goal of the optimisation.Some of the RF-properties relate to the beam pattern radiated by a hornexcited by the fundamental mode, while others relate to the tracking beampattern radiated by a horn excited by one of the tracking modes.

Figure 4-13 Selection of optimisation goal type.

For the case considered, we will select the Return Loss goal type.

On the second page, the Select analysis page, the user selects one of theavailable analysis specifications to be used by the optimisation goal. A goalspecification can only reference one analysis specification, but several opti-misation goals of the same type may be defined. As an example, if the userhas an analysis specification for the Tx-band and another analysis specifica-tion for the Rx-band, and wants to obtain a return loss better than 25 dB inboth bands, then two goals must be set-up, one for the Tx-band and anotherfor the Rx-band. In the case considered, we will select the only availableanalysis, "TE11_Band1".

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Figure 4-14 Selection of analysis used by the optimisation goal.

On the third and final page, the Add return loss goal page, the userspecifies the goal values for the optimisation goal. It is also possible to assigna weight to the goals which allows the user to control the importance of thegoal in the optimisation. In the case considered, we will optimise to improvethe return loss in Figure 4-7 to be better than 25 dB.

Figure 4-15 Selection of values for the optimisation goal.

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Select Finish, and the optimisation goal to the return loss has been defined.

Only a single optimisation variable, "z_focal_length", has been defined, whichwill display the sub- and main reflector relative to the feeding waveguide.Hence, if only the return loss should be improved, then the optimisation willtend to move the subreflector away from the horn aperture to minimise theenergy reflected into the horn. However, this will result in a poorer illumina-tion of the main reflector, and thus a reduction in the antenna directivity.

Therefore, we will add a second optimisation goal, namely a goal to the on-axis directivity, as will be described in the following. First, return to theResults Tab and double-click on the On-axis Directivity entry in the BeamParameters vs. Frequency branch for "Analysis_0002". This leads to theplot of the on-axis directivity vs. the frequency in Figure 4-16.

Figure 4-16 On-axis directivity vs. frequency for the secondanalysis.

This plot is used to define the goal value of the new optimisation goal. Thechallenge is to select the proper value, as the frequency variation of theon-axis directivity is significant, c.f. Figure 4-16. With a single optimisationvariable, we do not have sufficient degrees of freedom to increase the direc-tivity to the same level independent of frequency. Therefore, we specify thenew optimisation goal only to the center frequency. This is done by:

• on the Analysis Tab, add a new analysis using the center frequency only.

• on the Optimisation Tab, add a new optimisation goal. Select the On-axis directivity type, the new analysis, and specify a value of 40.5 dBias the goal value for the on-axis directivity.

The Optimisation Tab should then look like Figure 4-12.

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4.7 Launching the Optimisation

The optimisation of the horn antenna is launched by clicking on the Optimi-sation Button (or selecting the corresponding menu item).

The user is first alerted that the project must be saved before starting anoptimisation. If the project has not been saved before, the program will createa number of files and file folders for the present project, as will be furtherdescribed in Chapter 5. After selecting OK (and possibly subsequently aproject file name and folder), the CHAMP - Optimisation Launcher dialogappears, c.f. Figure 4-17.

Figure 4-17 The CHAMP - Optimisation Launcher dialog.

The dialog contains four different parts:

• At the top: The Optimisation Name, which is the unique name ofthis Optimisation within the CHAMP project. The program will suggest adefault name, "Optimisation_XXXX" where XXXX is an unused number.

• Below the Optimisation Name: The Analysis Section, which shows thename of the analysis specifications within the CHAMP project. It is pos-sible to change the number of frequencies used from this dialog.

• Below the Analysis section: The Optimisation Settings Section, withthe choice of optimisation algorithm and control settings to the optimi-sation.

• At the bottom: The Comment Field which is a user-defined text whichis associated with the current optimisation. The text will be saved in theproject and can be viewed and/or edited in the Results Manager.

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In the case considered, it will be sufficient to optimise the antenna at a fewfrequencies. We will therefore change the number of frequencies used in the"TE11_Band1" analysis from 51 to 3. In the Optimisation Settings section,the optimisation algorithm is specified to minmax, i.e. an algorithm whichtries to minimise the maximum residual. In each optimisation iteration, theanalyses listed in the Analysis Section are performed Nvar + 1 times, whereNvar is the number of optimisation variables. The maximum number of iter-ations is set to 200 by default. The optimisation algorithm will typically stopbefore, when no further improvements are obtained. It may also be stoppedby the user via the buttons at the lower left. We will keep the default opti-misation settings, add a Comment, e.g. "My first optimisation" and then clickOK. The optimisation now starts and the CHAMP - Optimisation progresswindow appears, c.f. Figure 4-18.

Figure 4-18 The CHAMP - Optimisation progress window.

The CHAMP - Optimisation progress shows the progress of the analy-ses performed in each iteration of the optimisation. After each iteration, thescreen is cleared and the currently best value of the optimisation objectivefunction is reported.

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Figure 4-19 The Log tab in the CHAMP - Optimisationprogress window.

Figure 4-20 The Residuals tab in the CHAMP - Optimisationprogress window.

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Figure 4-21 The Variables tab in the CHAMP - Optimisationprogress window.

The "Optimise_0001" has completed in 9 iterations. In the Results Tab, anew entry "Optimise_0001" has been added to the tree, with the summarizedresults from the optimisation (more detailed described in Section 4.8). In theGeometry Tab, the geometry has been updated with the optimum value of"z_focal_point" of (approximately) 2.05, i.e. the reflectors have been movedto the right.

From the behaviour of the residuals in Figure 4-20 it is observed that in Itera-tion 0, the initial geometry, the worst return loss residual was dominating, andthat the minmax-algorithm focuses on reducing this residual. This is obtainedby moving the subreflector further away from the feed horn.

We now want to perform a second optimisation where we relax on the returnloss requirement compared to the on-axis directivity requirement. This can beachieved either by specifying a less stringent goal value, or by reducing theweight of the return loss goal. In the following, the latter solution is selected.

We prefer to restart from the initial geometry instead of the current geometrywhich is the result of the first optimisation. Hence, we need to restore theinitial geometry which is most easily done using the Results Tab. In the ResultTree, right-click on the "Optimise_0001" branch, and select Revert to designbefore optimisation. The initial geometry (with "z_focal_point" equal tozero) has now been restored.

In the Optimisation Tab change the weight of the return loss goal from 1.0 to0.1. This can be done directly in the right-most column of the table in theGoal Section. Next, launch the second optimisation.

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Figure 4-22 The Residuals tab in the CHAMP - Optimisationprogress window for the second optimisation.

Figure 4-23 The Variables tab in the CHAMP - Optimisationprogress window for the second optimisation.

The "Optimise_0002" has completed in 8 iterations. In the Results Tab a newentry, "Optimise_0002", with the summarized results from the optimisationhas been added to the tree. In the Geometry Tab the geometry has beenupdated with the optimum value of "z_focal_point" of approximately -2.06,i.e. the reflectors have been moved to the left.

Following the optimisation we will need to analyse the optimised configura-

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tion. The analysis is launched in the same way as described in Section 4.4. Wewill perform the analysis at 51 frequencies. When the analysis is completes,we return to the Results Tab and double-click on the On-axis Directivityentry in the Beam Parameters vs. Frequency branch for "Analysis_0003".In the plot we add the corresponding curve from Analysis_0002 in the follow-ing way: First right-click on the return loss curve in the Analysis_0002-plotand select copy. Then right-click in the new plot and select paste (or usectrl-c and ctrl-v). This leads to the plot of the on-axis directivity vs. frequencyin Figure 4-24.

Figure 4-24 On-axis directivity vs. frequency for "Analysis_0003"(black curve) compared to "Analysis_0002" (greencurve).

It is observed that we have gained approximately 0.7 dB in the central part ofthe band simply by moving the reflectors relative to the fundamental modewaveguide.

Clearly, the optimisation problem considered is relatively simple. More de-grees of freedom could be added to the optimisation. Examples of morecomplicated optimisation scenarios are presented in Chapter 6.

4.8 The Results Tab - Part II (Optimisation)

Following the optimisations of the horn antenna presented in the previoussection, the Results Tree has a top branch for each of the optimisations per-formed.

Under each of these branches, five entries are shown.

• The Optimisation Summary entry. Displays a text-file with summaryinformation about the optimisation.

• Three Geometry entries. Displays a plot of either the original geometry,the optimised geometry or both in a simple SVG-format.

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• The Optimisation Iteration Plots. Displays the plot of the residualsand variables versus the iteration number. This is the same plot asshown during the optimisation, c.f. Figure 4-22 and Figure 4-23.

The optimisation summary file describes details about the horn interior ge-ometry before and after the optimisation, as well as information about theindividual optimisation variables and residuals. An example of the Optimisa-tion Summary file is shown in Figure 4-25.

Figure 4-25 The optimisation summary file generated from thesecond optimisation.

This completes the description of the general CHAMP lay-out. In the followingchapter, the CHAMP project and file organization is described and in Chapter 6a number of Tutorial Examples are presented.

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5. Project and File Organization

CHAMP saves a project in a file structure that requires no user intervention.However, some information about the organization of the files may be usefuland will be presented in the following.

Let us consider a CHAMP project MyReflector saved in a file folder namedTest. The file folder, Test, contains the CHAMP project file MyReflec-tor.champ and a sub-folder named MyReflector.champ_data, as shownin Figure 5-1.

Figure 5-1 A CHAMP project has a project file and a file folderwith all information about the project.

The CHAMP project file, MyReflector.champ, holds information about thelatest version of the project including information about the plots openedwhen the project was last saved. The format of the project file will not bedescribed in the User’s Manual, as the project file is intended for the GraphicalUser Interface (GUI) only.

The sub-folder MyReflector.champ_data contains all data defined by theuser as well as all results obtained in the RF-modelling. More precisely, thefolder always contains a file, geometry.tor, as well as a sub-folder for eachRF-modelling of horn performed by the user, c.f. Figure 5-2.

Figure 5-2 An example of the file folders in theMyReflector.champ folder.

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When the project is saved, e.g. using Save Project, the changes made bythe user are saved in the tor-file named geometry.tor. This file alwayscontains the most recent definition of the geometry and the most recentanalysis and optimisation settings. This is the file read by the GUI when aCHAMP project is opened.

When an RF-modelling is executed, the GUI first creates the sub-folder for thepresent RF-modelling. Hence, a sub-folder is present for each RF-modellingperformed, i.e. when selecting "Analyse Horn...", "Analyse Tolerances...", or"Optimise...". By default the GUI suggests the names "Analysis_0001", "Tol-erance_0001", and "Optimisation_0001" for the RF-modelling but the usermay select another name. The folder will have the same name as the RF-modelling.

The GUI first stores a geometry.tor-file and a geometry.tci-file in thisfolder (in the case of an optimisation, the tor-file is named geometry_orig.tor).Next, the program execution is performed in this directory and all data filesarising from the program execution are stored in the folder.

When the user selects the Revert to ... functionality in the Results tab theGUI re-reads the geometry.tor-file stored in the relevant sub-folder. The tor-and tci-files may also be used as a starting point for further analyses usingbatch mode operation, as further described in Chapter 7.

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6. Tutorial Examples

In order to demonstrate the capabilities of CHAMP, a number of tutorial exam-ples is here presented. The antenna configurations represent cases which arecommonly encountered in practice; however, they are sufficiently advancedto demonstrate numerous complex features.

The files associated with these tutorial examples are provided as Tutorial Ex-amples files delivered with the CHAMP-package. They may be accessed fromthe welcome menu of the CHAMP Graphical User Interface.

It is noted that the main focus of the present chapter is to present the tutorialexamples from a program input/output point-of-view, not from a theoretical orapplication point-of-view. It is assumed that the user has a basic knowledge ofthe Wizards, the program main layout and basic usage, as well as the projectand file organisation, as described in the Chapters 3,4 and 5.

The following Tutorial Examples are present:

Contents

6.1 Potter Horn 46

6.2 Linear Sections Horn 55

6.3 Horn with Slanted Corrugations 63

6.4 Re�ector Wizard followed by Horn Wizard 73

6.5 Re�ector with Corrugated Horn 79

6.6 Optimisation of re�ector system 89

6.7 Horn with Lens 98

6.8 Shroud Case 108

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6.1 Potter Horn

A relative simple approach to a horn feed with low sidelobes, coincidenceof the phase centers in the E- and H-plane patterns and a high degree ofsymmetry of the principal-plane patterns (= low cross polarization) was pro-posed by Potter in 1963, see [5]. It’s fundamental part is an input waveguidesupporting the TE11 mode, followed by a step to a wider waveguide wherethe TM11 mode can propagate. The wider waveguide, the phasing section, issucceeded by a flare section that provides the transition to free space withthe appropriate aperture size.

Figure 6-1 Principal sketch of Potter horn design.

6.1.1 Analysis of the original Potter horn

6.1.1.1 Set up of geometry

Design data for three horns with different aperture sizes can be found in theoriginal paper by Potter. Horn no. 2 is selected for further analysis here.

Frequency(GHz)

Input ra-dius

Phasingsectionradius

Phasingsectionlength

Flare an-gle

Apertureradius

Length ofphasingand flaresections

9.600 0.625” 0.80” 0.40” 6.25◦ 2.635” 17.155”

To set up this geometry, we start CHAMP and choose to design manually.Since Potter’s paper lists the geometrical parameters in inches, we select thisas the default unit underFile - Preferences - Units.

The frequency is set to 9.6 GHz in the top toolbar. The step section is createdby the menus:Create - Horn Interior - Waveguide Step

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Figure 6-2 Principal sketch of Potter horn design.

The values used to generate the step are not in any way representative for aPotter horn, and the values therefore needs to be changed in the right pane.Input and output radii as well as the length of the phasing section (L2) aregiven in the table above. L1 is not given, and is the length on the inputfeeding guide. Since CHAMP will assume a single TE11 mode in this section,it’s length has no impact on the predicted performance and can be selectedby the user.

The flare section is created by:Create - Horn Interior - Smooth Walled Section (linear_profile)which is attached to the right-hand end of the waveguide step. Again, thevalues of the flare section need to be changed to reflect the true Potter de-sign.

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6.1.1.2 Use of variables

CHAMP implements a very powerful feature by which all parameters can beexpressed as variables. This is useful for optimization purposes, but can alsobe used as an efficient tool in the geometry set up.

We introduce variables for the output section of the step, i.e. the radius andthe length. The output aperture of the horn is also expressed by a variable.These variables are simply introduced by selecting the parameter value in theright pane, and overwrite it with an alphanumeric expression:

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The variables are given initial values that correspond to the parameters theyare allocated to. Changing a parameter to a variable will therefore not changethe design until the value of this variable is changed.

CHAMP’s module for the flared section requires the input and output radii, aswell as the length. Potter’s design does not specify the length but the flareangle. An elegant way of utilizing variables is to introduce the flare angle asa new variable and express the flare length by the flare angle. This is doneby selecting

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Create - Variables - Real Variable and give it the name "flare_angle".Once this is done, it can be assigned a value in radians in the right pane. Theflare length is now given as the difference between the input and output radiiof the flare section, divided by the tangent to the flare angle.

6.1.1.3 Performing analysis

Next, the desired analysis must be specified. This is done by selecting theAnalysis window and adding an analysis:

Since the Potter is fairly narrow-band by nature, we select a bandwidth of 10%and analyze the horn in 201 frequency steps when excited by the fundamentalTE11 waveguide mode, linearly polarized along x. Note even though we havenot defined an exterior horn geometry, the analysis is still specified to includea method-of-moment solution. By doing this, the coupling from the modes inthe horn aperture to free space is computed more accurately than by a simpleaperture integration of the modal field.

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After saving the project an analysis can be executed by pushing the play-button.

6.1.1.4 Viewing results

The data can be inspected in the Results window, where several options areavailable. Double clicking on Return Loss gives the VSWR as a function offrequency.

A plot of the E- and H-planes and the 45-degree plane at the design frequency,9.6 GHz, shows a high degree of symmetry and, consequently, low crosspolarization

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The Results window gives an option for plotting various beam parameters vs.frequency. Of special interest here are the maximum cross polar component,the beam widths and the best-fit phase centers.

For both the beam widths and the best fit phase centers, it is necessary tospecify which part of the beam to be used for these computations. Sincethe Potter horn will often be used as feed in a reflector antenna system weconsider the -12 dB level relative to peak as defining the beam.

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All three sets of curves clearly demonstrate that the Potter horn is very well-designed for the center frequency of 9.6 GHz. Potter lists the full half-power(-3 dB) beamwidth to be 16.0 degrees, while the results from CHAMP showthat it is closer to 17.0 degrees, see below, but this seems to be a minordiscrepancy.

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6.2 Linear Sections Horn

A smooth-walled horn composed solely of linear sections is shown in Figure 6-3.

Figure 6-3 Sketch of horn composed of smooth-walled linearsections.

This horn is much simpler to manufacture than a corrugated horn especially ifthe horn is small as it becomes if the frequency is high. It is in fact possible tomanufacture such a horn simply by direct drilling in a block of aluminum usinga properly shaped machine tool, see [3]. The performance is not as good asthat of a corrugated horn, but if the angles and positions of the linear sectionsare properly optimised a bandwidth of up to 20% can be obtained.

In this example we consider a horn with three sections as shown in Figure 6-4defined by the radii R1, R2, R3 and R4 and the lengths L1, L2 and L3.

Figure 6-4 A cross-section sketch of the linear section horn.

A centre frequency of 300 GHz is selected corresponding to a wavelengthclose to 1 mm.

The following design data are used:

Centre frequency: 300 GHzFrequency band: 270 — 330 GHz , corresponding to 20%Waveguide radius: R1 = 0.5 mmAperture radius: R4 = 3.0 mmTotal length: L = 20.0 mm

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The four variables to be optimised are R2, R3, L1 and L2. The remainingvariable L3 can be computed from the relation L = L1 + L2 + L3. Instead ofoptimising R2 and R3 it is, however, convenient to define the variables d1 andd2

d1 = R2 −R1

d2 = R3 −R1 − d1(6.1)

These variables can be given a lower bound of zero to prevent the profile ofcrossing the axis of the horn.

6.2.1 Set up of geometry

The initial geometry is set up without the use of the design wizard. As shownin Figure 6-5 the design consists of three linear sections which are createdby means of the menu point Create - Horn Interior - Smooth WalledSection.

Figure 6-5 Set up of initial geometry.

The variables to be optimised are chosen (more or less at random) as

d1 = 0.5 mmd2 = 0.5 mmL1 = L2 = 1.0 mm

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and the fixed variables as

R1 = 0.5 mmR4 = 3.0 mmL = 20.0 mm

From these variables the input and output radii and profile lengths can bespecified as shown in Figure 6-5.

6.2.2 Initial analysis

In the Analysis tab seven frequencies from 270 to 330 GHz are specified asshown in Figure 6-6

Figure 6-6 Specification of analysis. Seven freqencies from 270 to330 GHz.

Pushing the Play - button will now execute the initial analysis and the resultscan be viewed in the Results tab as shown in Figure 6-7. It is seen that theside-lobes and cross polarisation are high and that optimisation of the designis clearly needed.

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Figure 6-7 Initial analysis at 330 GHz.

6.2.3 Defining variables

In the Optimistion tab the variables L1, L2, d1 and d2 are selected with lowerbound zero and with no upper bound as shown in Figure 6-8.

Figure 6-8 Selection of variables for optimisation.

In this way the horn radius will never become less than R1 and the lengthsL1 and L2 cannot become negative.

6.2.4 Defining goals

In the Optimisation tab the goals of the optimisation are also specified. Inthis example it is first attempted to bring down the cross-polar level. This isdone by selecting the goal Maximum cx-polar to peak and specifying agoal of −25 dB as shown in Figure 6-9.

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Figure 6-9 Specifying cross-polar goal.

Reducing cross-polar will automatically also make the E- and H-plane patternsmore equal since only m = 1 modes are present in the horn.

6.2.5 Optimisation with cross-polar and beam circularity constraints

The optimisation is activated by pushing the "Double-Arrow" optimise button.The progress is monitored in the optimisation window as shown in Figure 6-10.It is seen that the optimisation is stopped after the 15th iteration and that nosignificant improvement is obtained after the 10th iteration. The maximumresidue is below zero which means that the cross-polar is now more than25 dB below the co-polar peak at all frequencies.

Figure 6-10 Iteration sequence for cross-polar optimisation.

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In the Results tab the optimised design can be compared to the start point,see Figure 6-11, which shows that the profile has become more smooth.

Figure 6-11 Horn cross-section before (black) and after (red)optimisation.

The worst case is again the upper frequency, 330 GHz (see Figure 6-12), butit has improved much compared to the initial result in Figure 6-7

Figure 6-12 Horn pattern at 330 GHz after cross-polarisationminimization.

The return loss remains very good (35 dB), but the circularity of the beammay still be improved by specifying goals of the type Directivity variation

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with azimuthal angle. In the corresponding menu (see figure 6-13) a goalof 0 dB is selected, i.e. no azimuthal variation, and Aim below the goaland a theta angle of 5 degrees. This is repeated for a number of other thetaangles e.g. 10, 15, 16, 17 and 18 degrees.

Figure 6-13 Specifying circularity constraints.

The optimisation converges within 6 iterations and results in further improve-ments as seen in Figure 6-14.

Figure 6-14 Horn pattern at 330 GHz after optimisation withcross-polar and circularity constraints.

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The additional constraint on beam circularity does, however, increase thecross-polar level in most of the frequency band as seen in Figure 6-15. It isa characteristic behaviour that if additional goals are introduced they tend toworsen the compliance of the other goals.

Figure 6-15 Comparison of cross-polar level below peak foroptimisation of cross-polarisation alone (black) andcombined cross-polar and beam circularityoptimisation (red).

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6.3 Horn with Slanted Corrugations

Wide-angle corrugated horns may be designed with the corrugations perpen-dicular to the horn profile rather than to the horn axis.

The mode matching in CHAMP is not able to handle corrugations slanted withrespect to the horn axis, as the slanted corrugations cannot be represented bythe elementary modules described in Section 9.1.1.2. However, the Methodof Moments in CHAMP can handle slanted corrugations. Hence, this type ofcorrugations can be modelled in CHAMP considering the corrugations as partof the horn exterior geometry.

This tutorial example presents the CHAMP modelling of a horn with slantedcorrugations.

6.3.1 The horn geometry

We will use a design of a horn presented in a 1974 Master-thesis, [6], byO. Sørensen from the Electromagnetics Institute, Technical University of Den-mark (now DTU-Elektro). The horn geometry is shown in Figure 6-16.

Figure 6-16 A drawing from [6] of the horn modelled in the presentTutorial Example. Used with permission.

The horn has been used in several R&D-studies. It was designed to radiatea field with a relatively small edge taper, namely 5-6 dB taper at θ = 18◦, at

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the design frequency of 10.0 GHz. A horn flare angle of 15◦ was chosen inthe design.

From the drawing in Figure 6-16, the following design parameters have beenidentified1:

Design Parameter ValueFlange outer diameter 70.0 mmFlange thickness 7.5 mmWaveguide diameter 26.65 mmWaveguide thickness 7.5 mmWaveguide outer length 22.3 mmWaveguide skirt length 7.7 mm

Total length of horn 151.2 mmAperture outer diameter 116.4 mmAperture cover diameter 106 mmAperture inner diameter 86 mmAperture cover thickness 3.0 mmHorn neck length 22.0 mm

Corrugation pitch 6.0 mmCorrugation width 3.85 mmCorrugation depth 9.4 mmWall thickness 5.0 mm

Table 6.1 Design parameters derived from Figure 6-16.

The waveguide skirt and the horn neck both form an angle of 45◦ with thehorn axis. In the modelling, we will neglect the four holes in the flange (atρ = 70.0 mm) as well as the aperture cover.

It is not clear from the drawing if the intersection between the waveguidesection and the conical section is at the same z-value on the horn interiorand exterior. Also, the drawing does not include the horn flare angle of 15◦.

6.3.2 CHAMP modelling

In our CHAMP modelling, we use the flare angle as a design parameter and weassume that the intersection between the waveguide section and the flaredsection is at the same z-value on the horn interior and exterior. Consequently,in order not to overspecify the CHAMP model, we do not use the waveguideskirt length and the horn total length.

We must define the interface between the mode matching (horn interior) andMethod of Moments (horn exterior). As described previously, the mode match-ing in CHAMP is not able to handle corrugations slanted with respect to the

1The drawing shows a horn neck length of 25.0 mm, but this length includes the aperturecover thickness

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horn axis, as the slanted corrugations cannot be represented by the elemen-tary modules described in Section 9.1.1.2.

Therefore, the horn interior must start at the horn throat and end before thefirst of the slanted corrugations, i.e. the horn interior may be the waveguidesection only, or the waveguide section plus the very first part of the conicalsection. For simplicity, we choose the waveguide section only and as a con-sequence, the horn will be placed with the interface between the waveguideand the conical horn section at z = 0. In CHAMP terms, the conical hornsection with the slanted corrugations is part of the horn exterior geometry.

In CHAMP, the horn interior is set up using a Waveguide Section with theproper radius and length. The entire exterior geometry (including the slantedcorrugations) is set-up using a single Horn Exterior object. This is a piece-wise linear representation of the geometry, and thus all corner points of thehorn must be provided as input to the program.

We will use the CHAMP ’real variables’ to set up the geometry.

6.3.3 The horn without corrugations

In the present section, we will set up the horn without corrugations. First,launch CHAMP and choose Design Manually in the welcome dialog.

As one of the design variables is the flare angle, we will start by introducing avariable, ’dtr’, for use in the trigonometric functions, converting angles fromdegrees to radians.

dtr = 0.01745329 (=π/180)

We introduce the variable ’flare’ for the horn flare angle in degrees as well asthe cosine and tangent of this angle

flare = 15.0 (flare angle in degrees)flare_cos = cos(flare*dtr)flare_tan = tan(flare*dtr)

Next, a number of variables are defined for the waveguide and flange sectiondesign parameters:

adapter_r = 35.0 (half flange outer diameter)adapter_l = 7.5 (flange thickness)wg_r = 13.325 (half waveguide diameter)wg_thickness = 7.5 (waveguide thickness)wg_tube = 22.3 (waveguide outer length)

There are three lines in the horn geometry which make an angle of 15◦ withthe horn axis, namely 1) the line defined by the corrugation teeth, 2) the linedefined by the bottom of the corrugations, and 3) the conical, outer part ofthe horn, c.f. Figure 6-17. The three lines may be expressed as:

ρ = flare_tan ∗ z + bi , i = 1, 2, 3 (6.2)

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where the unknown b1 is equal to the waveguide radius, and b2 and b3 aregiven simply in terms of the corrugation depth, the wall thickness and b1.

Figure 6-17 The helping lines used in the definition of the hornexterior.

We introduce variables for the corrugation design parameters:

pitch = 6.0 (corrugation pitch)groove_d = 9.4 (corrugation depth)groove_w = 3.85 (corrugation width)wall_thickness = 5.0 (wall thickness)

Now, the three unknowns from (6.2) may be created as variables

b_1 = wg_rb_2 = b_1 + groove_d / flare_cosb_3 = b_2 + wall_thickness / flare_cos

It is also possible to calculate the height (ρ-dimension) of the waveguideshoulder as

wg_shoulder = b_3 - wg_r - wg_thickness

Similarly, there are two lines in the drawing which make an angle of 45◦ withthe horn axis, namely 4) the line defining the horn shoulder and 5) the linedefining the waveguide shoulder. These lines may be expressed as:

ρ = z + bi , i = 4, 5 (6.3)

In order to calculate b4, we will find the coordinates, (neck_r, neck_z), of theinterface between the horn shoulder and the horn neck. We will need tointroduce variables for the design parameters close to the horn aperture.

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ap_r = 43.0 (half aperture inner diameter)window_r = 53.0 (half aperture cover diameter)window_l = 3.0 (aperture cover thickness)neck_r = 58.2 (half aperture outer diameter)neck_l = 25.0 (horn neck length plus

aperture cover thickness)

From these variables, it is possible to find first the z-coordinate, ap_z, of thehorn inner diameter, and subsequently neck_z.

ap_z = (ap_r - wg_r) / flare_tanneck_z = ap_z + window_l - neck_l

The point (neck_r, neck_z) is located on line 4, and the interface between thewaveguide shoulder and the flared section is located on line 5. Inserting thecoordinates of these point in (6.3) leads to

b_4 = neck_r - neck_cb_5 = wg_r + wg_thickness + wg_shoulder

As a final step, we will introduce variables for the z- and ρ-coordinates of thefollowing intersections: A) ’P34’ between line 3 and 4 , B) ’P35’ between line3 and 5, and C) ’P5wg’ between line 5 and the outer part of the waveguidesection. The expressions derived from (6.2) and (6.3) are:

P34_z = (b_3 - b_4) / (1 - flare_tan)P34_r = P34_z + b_4P35_z = (b_3 - b_5) / (1 - flare_tan)P35_r = P35_z + b_5P5wg_z = P35_z - wg_shoulderP5wg_r = P35_r - wg_shoulder

This completes the definition of real variables in CHAMP. We have introduced16 variables defined directly in terms of a real number, namely 14 of the16 design variables of Table 6.1, the flare angle and a factor for convertingdegrees to radians. In addition, we have introduced 17 variables defined interms of other variables.

We will now use the variables in the definition of the horn exterior. We usethe snap-to-aperture functionality, and then specify the remaining 12 cornerpoints of the horn exterior geometry. The definition is available in the TutorialExample delivered together with the CHAMP package. The Figure 6-18 showsthe Geometry Tab for the present example.

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Figure 6-18 The CHAMP geometry of the horn without corrugations.

The CHAMP variables directly related to the design parameters may now bechanged, and for small changes of the variables, the horn geometry remainsconnected. As an example, Figure 6-19 shows the horn geometry when theflare angle has been changed from 15◦ to 17◦, the horn neck length from25 mm to 15 mm, and the aperture cover thickness from 3 mm to 0 mm.

Figure 6-19 The CHAMP geometry of the horn without corrugationsand with three of the design parameters changed.

Note however, that no bounds on the variable can be defined in the set-up of

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the geometry. Hence, it is possible to obtain non-realizable designs.

In the Analysis Tab, we define an analysis specification with the horn excitedwith the fundamental TE11-mode polarized along the x-axis. The frequencyband is centered around 10.0 GHz, namely from 9.5 GHz to 10.5 GHz in 21steps.

The return loss, the pattern cut at 10.0 GHz, and the level of the cross-polarisation relative to the on-axis peak are shown in Figures 6-20, 6-21, and6-22, respectively. The horn has an excellent return loss over the band butradiates a beam with different beam widths in the E- and H-planes and thusa high cross-polarisation.

Figure 6-20 Return loss for the horn without corrugations.

Figure 6-21 Pattern cut at 10 GHz for the horn withoutcorrugations.

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Figure 6-22 The level of the maximum cross-polarisation relativeto the on-axis peak directivity for the horn withoutcorrugations.

It has been demonstrated that a detailed horn geometry can be set up inCHAMP in terms of the design parameters using the so-called variables. Next,we will add the corrugation layout.

6.3.4 The corrugation lay-out

The horn has 18 corrugations. We will include these corrugations in the hornexterior defined in the previous section. We thus introduce the 4 points foreach corrugation. The details will not be described here, but may be seenin the Tutorial Example delivered with the CHAMP package. The resultinggeometry is shown in Figure 6-23.

Figure 6-23 The CHAMP geometry of the horn with corrugations.

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The return loss, the pattern cut at 10.0 GHz, and the level of the cross-polarisation relative to the on-axis peak are shown in Figures 6-24, 6-25, and6-26, respectively. The return loss is significantly degraded compared to thehorn without corrugations. However, the corrugations result in a radiatedbeam with almost identical E- and H-planes and thus a low cross-polarisationlevel.

Figure 6-24 Return loss for the horn with corrugations.

Figure 6-25 Pattern cut at 10 GHz for the horn with corrugations.

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Figure 6-26 The level of the maximum cross-polarisation relativeto the on-axis peak directivity for the horn withcorrugations.

This concludes the analysis of the horn with slanted corrugations. We willleave it to the user to optimise the horn with the aim of improving the returnloss, e.g. by optimising the depth of the first corrugations.

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6.4 Reflector Wizard followed by Horn Wizard

This example describes how to combine the reflector wizard and the hornwizard for the design of a particular antenna with an aperture diameter of 1m and operating at 29-31 GHz in right hand circular polarisation.

6.4.1 Reflector wizard

Open the reflector wizard and select the following values

• 29-31 GHz

• Gregorian ring focus design

• Main reflector diameter D = 1000 mm

• Focal length f, f/D = 0.3

• Subreflector diameter d, d/D = 0.15

• Half angle subtended by subreflector at feed = 30◦

The wizard and the associated geometry is shown in Figure 6-27.

Figure 6-27 Reflector wizard.

Press the next button and select Insert an open ended wave-guide. Se-lect 19.5 mm for the waveguide diameter and accept the default value for

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the length. Press the next button and select the option Insert a hornexterior. Select 1 mm for the horn wall thickness and press Finish. Thisgenerates the geometry shown in Figure 6-28. One will notice that, comparedto Figure 6-27, the main reflector has been extended automatically towardsthe axis such that it coincides with the exterior section of the feeding waveg-uide. In the property editor this is expressed by the fact that node(2) of theExterior geometry is identical to node(1) of the main reflector.

Figure 6-28 Reflector surface generated by the reflector wizard.

The waveguide feed created above is not acceptable and a new feed shall bedesigned by the horn wizard. The coordinates for the main and subreflectorare generated under the assumption that the focus on the axis is located atz = 0. However, it is possible to translate both reflectors along the axis bymeans of the real variable z_focal_point.

6.4.2 Horn wizard

Open the horn wizard and select the following values

• 29-31 GHz and accept the design and output frequencies

• Accept the default waveguide radius

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• Select single depth, corrugated horn

• Select the taper to -12 dB at 30◦ and select the horn parameters corre-sponding to ∆/λ = 0.2

• Use a mode converter and accept all the default values

• Terminate the horn wizard by pressing Finish

The last action generates a blue bar on the drawing and its position indicateswhere the horn will be inserted. By means of the mouse the blue bar can belocated either in the front or in the back of the previously defined waveguide.Here we wish to insert the horn in the front end of the waveguide and byclicking on the blue bar in this position the horn is inserted.

The blue bar is now replaced by a red bar between the front end of thewaveguide and the rear end of the horn. The red bar indicates that thereis a geometrical mismatch between the section to the left and to the rightof the red bar. By right clicking on the bar one can either adjust the leftsection to the right section or vice versa, or one can insert a step betweenthe two sections. In this case we wish to adjust the waveguide diameter tothe horn and we choose adjust left section and the waveguide radiuschanges immediately to the input radius of the horn. The horn is shown inFigure 6-29.

Figure 6-29 Feed horn designed by the horn wizard.

It is clear from Figure 6-29 that the external structure no longer fits with thenew horn design. This problem is most easily solved by adding one more

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point to the external structure and then specifying the coordinates of the twofirst nodes directly in the Property Editor, as shown in Figure 6-30.

Figure 6-30 Top: Property editor specification of the externalstructure. Bottom: resulting feed horn .

6.4.3 Calculated results

To start the analyses of the antenna a first calculation, "Analysis_0001", isperformed at the centre frequency, 30 GHz, and with RHCP excitation of thefeed. The reason for doing this is partly to check that the antenna behavesas expected and partly to save the antenna design including both horn andreflectors. The peak directivity is found to 48.75 dBi and the return loss is39 dB.

The horn aperture is located at z = 0 which is also the location of the reflectorfocus. However, the best fit focal point for the horn is located some distanceinside the horn. It is therefore necessary to make a separate analysis of thehorn itself. This is done in "Analysis_0002" by removing the main and subre-flector such that only the horn and the horn exterior remain. The results show

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that the return loss is 40.6 dB, and the best-fit phase centre, corresponding toa taper of -12 dB, is located 3.5 mm behind the horn aperture. The antennamust therefore be modified according to this information.

In the Results tab right click on "Analysis_0001" and select Revert to thisdesign. This will bring back the reflectors which were removed in "Analy-sis_0002". The parameter z_focal_point, which may be found in the Prop-erty Editor is now changed from 0 to -3.5 mm and the antenna is rununder "Analysis_0003". The peak directivity is now 48.91 dBi whereas thereturn loss remains almost unchanged at 42.8 dB.

It is expected that the return loss is to some degree affected by interferencebetween the horn and the subreflector. When analysing the antenna in thewhole band from 29 to 31 GHz it is therefore necessary to use a fairly smallspacing in the frequency. In "Analysis_0004" a spacing of 0.05 GHz is used.

The radiation pattern at 30 GHz is shown in Figure 6-31.

Figure 6-31 Radiation pattern at 30 GHz.

The peak directivity across the band is shown in Figure 6-32 and the returnloss is depicted in Figure 6-33.

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Figure 6-32 Peak directivity from 29 to 31 GHz.

Figure 6-33 Return loss from 29 to 31 GHz.

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6.5 Reflector with Corrugated Horn

In this example we will analyse a corrugated horn, both the horn alone andwith the horn inserted in a Cassegrain reflector antenna geometry. TheCHAMP analysis result will be compared to an analysis using GRASP.

Figure 6-34 shows a screen dump from CHAMP with the complete geometry.

Figure 6-34 CHAMP screen dump showing horn/reflector geometry.Please note for later use that the z-Offset values ofsub and main reflector are -2.98 m.

In Table 6.2 the parameters are listed.

Parameter ValueMain reflector diameter 50 m

Main reflector focal length 20 mSub reflector diameter 10 m

Sub reflector eccentricity 1.73Sub reflector interfoci distance 17, 02 m

Sub reflector magnification 3.74Frequencies 0.8, 0.9, 1.0 GHz

Table 6.2 Cassegrain reflector geometry.

The diameter of the main reflector is 133λ at the lowest frequency. Witha reflector of this order of magnitude the interaction between feed and subreflector is assumed to be insignificant so the result obtained with GRASP(which does not take into account this effect) should be quite similar to theresult obtained by CHAMP.

First step in this exercise consists in an analysis of the horn without reflectors.Figure 6-35 is a screen dump from CHAMP showing the data of the horn andthe exterior wall to the right.

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Figure 6-35 CHAMP screen dump showing horn geometry.

An analysis of the horn has been done at the frequencies listed in Table 6.2.The result is shown in Figure 6-36.

Figure 6-36 Corrugated horn pattern (diagonal plane, co and X) at0.8 (black), 0,9 (red) and 1.0 (green) GHz.

The horn analysis has been done using the centre of the horn aperture asphase reference point. It is beneficial to the performance to locate the best-fit phase centre as close as possible to the external focus of the hyperboloidalsub reflector. The best-fit phase centre relative to the horn aperture is foundfrom the analysis and visualised as shown in Figure 6-37.

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Figure 6-37 Best-fit phase centre relative to horn aperture in0◦-plane (black), 45◦-plane (red) and 90◦-plane(green).

As expected the phase centre migrates into the horn for increasing frequency.

For the right location of the horn in the antenna a compromise among thephase-centre displacement values in Figure 6-37 must be chosen. It has beendecided to move the horn towards the sub reflector by 0.6 m.

Figure 6-38 CHAMP screen dump showing horn/reflector geometry.Please note that now the z-Offset values of sub andmain reflector are -3.58 m.

In figure 6-38 the full geometry is shown. The change in z-Offset from Fig-ure 6-34 to Figure 6-38 means that sub and main reflector have been moved

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backwards by 0.6 m, hence, the feed has been moved towards the sub re-flector by this amount.

An analysis of the full geometry is now done and the result in terms of coand cross polar patterns in the diagonal plane at the 3 frequencies is shownin Figure 6-39.

Figure 6-39 Co and cross polar pattern in the diagonal plane at 0.8(black), 0,9 (red) and 1.0 (green) GHz.

The co polar component has of course the maximum level at θ=0◦ where thecross polar component is zero. Furthermore, the co polar pattern has a peakat θ=23.8◦ which is the feed spill-over beyond the subreflector. At θ=110◦

the cross polar component has a peak and this is the sub reflector spill-overbeyond the main reflector. The reason why this spill-over appears in thecross polar component is because the sub reflector radiates in the directionopposite to the z-axis of the field coordinate system and is a consequence ofthe Ludwig-3 polarisation definition. This happens only in the diagonal plane.

It could be of interest to compare this very detailed and accurate analysisin CHAMP (using mode matching inside the horn and method of momentson the horn exterior and reflectors) to the faster but more simple PhysicalOptics analysis method in our reflector antenna analysis tool, GRASP. For thisreason the reflector geometry has been imported in GRASP and the feed isrepresented by a set of spherical wave expansion coefficients generated byCHAMP (Figure 6-35).

In Figure 6-40 the geometry as in appears in GRASP is shown.

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Figure 6-40 3D view of reflector geometry in GRASP

The advantage in CHAMP is that the mutual interaction between feed struc-ture, sub reflector and main reflector is completely described in one analysisstep. It is not possible to do this in GRASP. Here the steps must be doneone-by one, in the simplest case it is:

• Feed field → Calculate currents on sub

• Currents on sub → Calculate currents on main

• Feed + currents on main and sub → Far field

• Feed field → Calculate currents on main(2)

• Currents on main(2) → Add to far field above

This command sequence can be illustrated by the ray path shown in Figure6-41.

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Figure 6-41 Ray path corresponding to command sequence above.

In Figure 6-42 the CHAMP and GRASP analyses have been compared using thesimple command sequence fro GRASP above. It is obvious that substancialdifferences exist even close to main beam. The peak level of the CHAMPanalysis is 50.60 dBi whereas the GRASP analysis shows a peak level of 51.07dBi, a difference of 0.47 dB.

Figure 6-42 Co and cross polar pattern in the diagonal plane at 0.8GHz. Black is CHAMP (Figure 6-39), red is GRASP(command sequence above),

The GRASP analysis can be made more precise by adding another sub-main

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loop as follows:




• Currents on main → Calculate currents on sub(2)

• Currents on sub(2) → Calculate currents on main(2)

• Currents on sub(2) and main(2) → Add to far field above



The command sequence is illustrated by the ray path shown in Figure 6-43.


In Figure 6-44 the CHAMP and GRASP analyses have been compared using thisextended command sequence. The correlation is considerably better than theone in Figure 6-42. The peak level of the CHAMP and GRASP analyses are now50.60 dBi and 50.29 dBi, a difference of 0.31 dB.

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The effect of one more sub-main loop in GRASP has been examined:




• Currents on main → Calculate currents on sub(2)



• Currents on main(2) → Calculate currents on sub(3)





The command sequence is illustrated by the ray path shown in Figure 6-45.

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In Figure 6-46 the CHAMP and GRASP analyses have been compared usingthis extended command sequence. The correlation is slightly better than theone in Figure 6-44. The peak level of the CHAMP and GRASP analyses arenow 50.60 dBi and 50.53 dBi, a difference of 0.07 dB.


The CHAMP result has been compared to the most precise GRASP result inthe total range from 0◦ to 180◦. The result is shown in Figure 6-47.

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Figure 6-47 Co and cross polar pattern in the diagonal plane at 0.8GHz. Black is CHAMP (Figure 6-39), red is GRASP(Figure 6-46).

Finally, in Figure 6-48 the impact on the return loss of adding the sub andmain reflectors to the horn is shown. With a Cassegrain geometry of thissize (main reflector diameter of 133λ at lowest frequency) the horn-reflectorinteraction is not significant.

Figure 6-48 Return loss for horn alone (black) and horn includingreflectors (red).

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6.6 Optimisation of reflector system

To get started, CHAMP3 is opened and the button ’Use Wizard’ is chosen.Since the purpose is to design a top-hat antenna, we choose the option ’Ringfocus / Axially Displaced Reflector wizard’ and press ’Next’. Since we plan todesign the system at 25 GHz we enter this value as both ’Lower Frequency’and ’Upper Frequency’. Then click on ’Info’ to fill the box with ’Centre Fre-quency’ and press ’Next’. In the next window we have the choice betweena ’Gregorian Ring-focus’ and a ’Cassegrain Ring-focus’ design. Strictly speak-ing these options refer to a ’Displaced-axis Gregorian, single offset’ and a’Displaced-axis Cassegrain, single offset’ design (double offset designs are notimplemented). We choose ’Gregorian Ring-focus’, and now have to choose a’Main reflector diameter’, a ’Main reflector f/D’, a ’Subreflector diameter rela-tive to main reflector diameter’, and ’Half angle subtended by subreflector atfeed’. The first value is chosen as 750.0 mm based on operational consider-ation, and the two next as 0.25 and 0.1 to get a reasonably compact design,and the last as 40 deg. (i.e. the feed taper at 40 deg. is -12 dB). (The mainreflector diameter is chosen as 750 mm, not e.g. 75 cm, since this choiceof units will lead to all data pertaining to the reflectors to be presented inmm, which will facilitate the merger with a feed horn, also measured in mm).The last box is left as ’Relative’. Then press ’Next’. In the next window it ispossible to either include an open ended waveguide as the feed model, or toskip the inclusion of a feed model. Since we assume that we have alreadyoptimised a corrugated feed in another CHAMP3 project named ’horn2des’,we shall import this design at a later stage, so for now select ’Skip this step’and press ’Next’. In the next window we have to decide whether to include ahorn exterior structure. Omitting such a structure will result in an open holein the main reflector leading to excessive radiation in the 180 deg. direction.For now we omit the exterior structure, but will remember to include it afterimporting the horn model. We can now press ’Finish’.

We should now be presented with the window shown in Figure 6-49.

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Figure 6-49 CHAMP3 start window.

We are now ready to import the feed horn, so we select ’File→Import→HornGeometry...’. In the ’Choose a file’ window, we select ’horn_geometry.tor’ file.This should promt a window ’Select Horn Geometry’, cf. Figure 6-50, fromwhich we select ’horn’. Since the horn is presumerably optimised in anotherproject, the horn data will include ’Variables’ used as optimisation parameters.Since such variables cannot at present be imported, they must be replacedby their numerical values in the horn CHAMP project before the import of thehorn is possible.

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Figure 6-50 Horn select window.

From the analysis of the horn model it is known that the best fit phase centrelies at z=36.16 mm, so we set the ’z_focal_point’ to 36.16 mm, see Figure6-51.

Figure 6-51 Input of z_focal_point

The two reflector surfaces are by default represented by rotationally symmet-ric surfaces defined by a profile modelled by a number of splines. Since weshall be optimising the reflectors below, we first replace the z-values of the 10nodes of each reflector by a symbolic name, which can be used as optimisa-tion variables. This is done by simply typing the names into the appropriateboxes in the right hand panel, as shown in Figure 6-52. For simplicity wechoose the names mz1,...,mz10 for the main reflector and sz1,...,sz10 for thesubreflector.

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Figure 6-52 Definition of symbolic names for spline nodes ofreflectors.

The final step in the preparation of the design, is to modify the horn exteriorstructure such that it connects with the main reflector. To do this we firstmodify the ρ value of the node Node(1) on the main reflector to align it withthe rear cylinder of the horn exterior structure (radius 10.0 mm, see Node(17)in the ’Horn Exterior’). i.e. the value of ρ=37.5 mm in Node(1) is replaced by10.0 mm. Next the node closing the horn exterior to the rear, Node(18), ismodified to coincide with Node(1) on the main reflector, i.e. (z, ρ)=(-5.0, 0.)mm is replaced by (z, ρ)=(mz1+z_focal_point, 10.0) mm. (If the main reflectorhad been defined in units different from mm, this substitution would havebeen slightly different, since the symbolic variables represent pure numberswithout units). We have now established galvanic contact between the hornexterior and the main reflector and the geometry should look as in Figure6-53.

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Figure 6-53 Geometry of support structure of horn.

We must now define a set of goals that the final design must achieve. Weshall define 4 goals: 1) A gain of more than 40 dB at boresight, 2) A returnloss better than 20 dB, 3) A specific template (co_template) that the co-polarbeam must lie under everywhere, and 4) A specific template (cx_template)for the cross polarised beam. More precisely, the co-polar template is definedin (6.4), and the cross polar template is defined in (6.5).

29.0− 25.0 log θ dBi, 1.5o <= θ <= 7.0o

8.0 dBi, 7.0o <= θ <= 9.2o [6.4]

32.0− 25.0 log θ dBi, 9.2o <= θ <= 48.0o

−10.0 dBi, 48.0o <= θ <= 180.0o

19.0− 25.0 log θ dBi, 1.8o <= θ <= 7.0o

−2.0 dBi, 7.0o <= θ <= 9.2o [6.5]

To enter these goals into CHAMP, we first press the Analysis symbol in theleft hand panel. We next ’Add...’ an analysis, which we denote ’Tx’ and setboth ’Start frequency’ and ’End frequency’ to 25.0 GHz and the ’Number offrequencies’ to 1. The ’Polarisation’ is set to ’rhc’. Next press the Optimi-sation symbol in the left hand panel. Since we plan to use all the splinenode z-coordinates on both sub- and main reflector as variables, we mark’mz1’,...,’mz10’ and ’sz1’,...,’sz10’ in the left hand top window, and press thegreen arrow (⇒). Next we press ’Add goal...’ and define the return loss and,after again pressing ’Add goal...’, the On-axis directivity.

To define the two templates we again press ’Add goal...’ and select ’Co-polarpattern template’. It may be necessary to cancel the window and repeatto press ’Add goal...’, if the bullet ’Co-polar pattern template’ does not ap-pear. Press ’next’ twice and select the bullet ’Aim below the goal (minimise)’and choose ’<Edit templates...>’ as ’Template reference’. Press ’Create’ andselect ’Piecewise logarithmic template’. Enter the name, ’co_template’ andpress ’OK’. We now enter the θ values from the first line of (6.4) and enterthe dBi values 29.0 and -25.0 as ’A’ and ’B’. Then click on the green ’+’ andenter the values from the second line. Proceed until all 4 lines have beenentered. The box should now look as in Figure 6-54.

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Figure 6-54 Definition of co_template.

We press ’OK’ and subsequently ’Finish’ to end the definition of ’co_template’.Now repeat the procedure for the cross polar template (cx_template) definedin (6.5). After pressing ’Add goal...’ now select ’Cx-polar pattern template’and repeat the above procedure with data from (6.5). The ’Goals’ windowshould now look like Figure 6-55.

Figure 6-55 Definition of goals for optimisation.

Before starting the optimisation, we perform an analysis of the system wehave defined by pressing the play-button in the left hand panel. The returnloss is 22.8 dB, the on-axis gain 43.8 dBi and the radiation pattern (RHC andLHC) are shown in Figures 6-56 and 6-57, where also the two templates havebeen included via the button ’Add Pattern Template’ (notice that the figuresare identical, except for the abscissa axis).

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Figure 6-56 Radiation pattern before optimisation.

Figure 6-57 Radiation pattern before optimisation, expanded.

Close to the main beam the co-polar pattern is almost in agreement with thetemplate (except for a 4 dB overshoot at 1.7o, whereas around 52o the co-polar pattern exceeds the template by app. 9. dB. The cross polar patternexceeds the template around 3o and 5o by app. 7. dB.

We are now ready to perform an optimisation, and press the "Double-Arrow"optimise button in the left hand panel. We choose the ’Optimisation algo-rithm’ as ’minmax’ and choose the ’Max. iterations’ as 20.

The result of the optimisation is: return loss: 18.8 dB, on-axis directivity:44.5 dBi and the radiation pattern shown in Figures 6-58 and 6-59.

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Figure 6-58 Radiation pattern after optimisation.

Figure 6-59 Radiation pattern after optimisation, expanded.

In Figures 6-60 and 6-61 the main reflector, resp. subreflector, is comparedbefore and after optimisation. Evidently the main reflector is subject to verylimited modifications, whereas the subreflector is changed significantly.

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Figure 6-60 Main reflector before and after optimisation.

Figure 6-61 Subreflector before and after optimisation.

From the optimised figures it is evident that except for some minor exceptions,both the co-polar and cross-polar radiation patterns are within the prescribedtemplates.

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6.7 Horn with Lens

It is sometimes desirable to insert a focusing dielectric lens in the aperture ofa corrugated horn in order to increase the directivity. In this way the horn canbe made relatively short as needed in certain applications with constraintson the available space. A drawback is that reflections in the lens surfaceswill increase the return loss as well as cross polarisation. The type of lensnormally used for this purpose is plano-convex with focal length equal to theaxial length of the horn. Design formulas for such a lens can be found in [2]Chapter 16.

A drawing of a horn with a plano-convex lens in the aperture is shown inFigure 6-62.

Figure 6-62 Corrugated horn with plano-convex lens.

6.7.1 Set up of horn geometry

The following frequency band and geometry parameters of the horn are used:

Centre frequency: 50 GHzFrequency band: 42.5 — 57.5 GHzWaveguide radius: 3.0 mmAperture radius: 30.0 mmHorn length: 80.0 mm

In CHAMP the Geometry tab is selected and the frequency 50 GHz is insertedin the upper icon bar. Hereafter Create - Horn Interior - Single DepthSection with Mode Converter is selected and the parameters listed aboveare inserted, see Figure 6-63. For all other parameters the default values areretained.

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Figure 6-63 Horn parameters.

6.7.2 Initial analysis

To perform an initial horn analysis the Analysis tab is selected and a newanalysis with seven frequencies in the interval 42.5 — 57.5 GHz is inserted asshown in Figure 6-64.

Figure 6-64 Analysis specification.

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When the Play button is pressed the analysis is performed and the patternshown in Figure 6-65 is obtained.

Figure 6-65 Horn pattern at 50 GHz.

It is seen that the pattern is rather broad due to the large flare angle of thehorn. A more narrow pattern with higher directivity can be obtained by useof an aperture lens without much increase in the overall length of the horn.This is illustrated in the following section.

6.7.3 Horn with smooth lens

A plano-convex lens is used (see [2]) with the parameters:

Dielectric constant: 2.00Focal length: 88.888 mmCentre thickness: 16.25 mm

The lens is defined by selecting Create - Exterior Geometry - BoR Meshby which a general Body of Revolution can be created. It is now required tospecify a BoR mesh by means of Regions, Nodes, Linear Segments andCubic Segments. First the Regions will be considered, see Figure 6-66.

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Figure 6-66 Defining the dielectric region of the lens.

In this dialog box a number of homogeneous regions of constant permitivityand permeability can be defined. Only the dielectric material of the lensneeds to be defined since free space is the default region and need not to bespecified. The dielectrics is denoted region No. 1 with a dielectric constant of2.0 and no loss tangent.

The next item to be considered is the table of Nodes, see Figure 6-67.

Figure 6-67 Nodes defining the dielectric lens and outer hornsurface.

It is helpful to compare this table with the sketch in Figure 6-68 in which thenumbering of the first nodes is shown.

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Figure 6-68 Numbering of the first nodes.

It is seen that node No. 1 is located on the axis of revolution in the distance3.0 mm in front of the horn aperture. Together with node No. 2 it definesthe inner surface of the lens. The inner surface my be located directly on theaperture as long as it is made up of only one type of material. This is the casehere, but for a lens with grooves (which will be considered next) it will not besatisfied. For this reason the lens is moved a short distance (3 mm) aheadof the aperture. The next node, No. 3, connects the outer horn structure tothe corrugated section. The metallic (perfectly conducting) part of this outerstructure is defined by nodes No. 2, 3, 4 and 5. After this the outer rim of thelens is defined by nodes No. 4, 6 and 7 and hereafter follows the nodes No. 8to No. 37 on the outer curved surface of the lens.

The segments connecting the nodes No. 1 to 7 are all linear so therefore thefollowing 6 linear segments are defined, see Figure 6-69.

Figure 6-69 Linear segments.

It is seen that the first segment that connects node No. 1 and 2 separatesregion No. 0 and region No. 1. This means that it separates free space(default region No. 0) from the dielectric region No. 1. The order in which theregions are specified is not important such that Region 1 may instead be set to

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1 and Region 2 to 0 without any change in the geometry. Surface impedance isnot relevant for a dielectric interface which is indicated by setting the surfaceimpedance equal to Zs = −1 + 0i, i.e. real part of −1 and zero imaginarypart. Hereafter follows segment No. 2 which is a metallic connection ofthe outer horn structure to the corrugated section. Both regions are hereset to 0 and the surface impedance is also set to 0 because the segment isperfectly conducting. The third segment is defined by nodes No. 2 and 4 andseparates metal from dielectrics. One region is therefore set to 0 and theother to 1. Again the segment is perfectly conducting with impedance equalto 0. Segment No. 4 is metallic and defines the outer conical surface of thehorn. Segments No. 5 and 6 separates free space from dielectrics and arethus of the same type as segment No. 1.

The outer surface of the lens is curved and is conveniently represented bycubic segments. This is illustrated in Figure 6-70.

Figure 6-70 Cubic segments.

The horn is now ready for analysis and looks as shown in Figure 6-71.

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Figure 6-71 Horn with smooth lens.

Analysis of the smooth lens gives the pattern shown in Figure 6-72, which canbe compared to Figure 6-65. It is seen that the lens focus the beam such thatit becomes more narrow and more directive.

Figure 6-72 Radiation pattern at 50 GHz for horn with smooth lens.

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6.7.4 Horn with grooved lens

The lens considered in the previous section makes the horn more directive,but it also increases the return loss due to reflections in the surfaces of thelens. This phenomenon can be reduced by inserting a matching layer onboth the inner and outer lens surface. Ideally the matching layer should bemade of a dielectric material with dielectric constant equal to the square rootof that of the lens and a thickness of a quarter of the wavelength in thematching material. It may, however, be difficult to find a material with theneeded dielectric constant and also problematic to shape it correctly and glueit together with the lens. Instead a similar effect can be achieved by cuttingcircular groves in the lens as shown in Figure 6-73.

Figure 6-73 Upper part of horn with grooved lens.

The nodes of the mesh are illustrated in the figure above. All groves aremade up of linear segments, whereas the ridges on the outer surface arecubic segments with four nodes on each. The radiation pattern at 50 GHz isshown in Figure 6-74

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Figure 6-74 Radiation pattern at 50 GHz for horn with grooved lens.

In order to compare the performance in more detail the following figures showthe peak gain, return loss and cross-polarisation of the horn without lens aswell as with the smooth and grooved lens.

Figure 6-75 Comparison of peak directivity.Without lens(black), with smooth lens (blue), withgrooved lens (red).

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Figure 6-76 Comparison of return loss.Without lens(black), with smooth lens (blue), withgrooved lens (red).

Figure 6-77 Comparison of cross polarisation.Without lens(black), with smooth lens (blue), withgrooved lens (red).

It is clearly seen in Figure 6-75 that the directivity is increased by the lens.On the other hand the return loss becomes higher as seen in Figure 6-76, butit can be reduced almost to the level of the uncovered horn by means of thegrooves. A drawback of the grooves is, however, that the cross-polar level isincreased at some frequencies as shown in Figure 6-77.

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6.8 Shroud Case

Shrouds are very often used to increase the Front to Back ratio, F/B, anddecrease the radiation in the backward half sphere of the reflector antenna.The following describes the analysis of the RF effect of a cylindrical shroudmounted on a front fed paraboloid reflector and an optimization of the shroudlength. The antenna geometry in the analysis is shown in Figure 6-78.

• Paraboloid: D = 2 m, f/D = 0.333

• Shrouds: R = 1. m, L = 1.2 m

• Frequency: 10 GHz

• Feed: Fundamental mode circular waveguide.

Figure 6-78 Geometry of shroud mounted antenna

The influence of the shroud is shown in Figure 6-79, where the far-fields fromthe reflector only and from the shroud mounted system are compared.

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Figure 6-79 Far field from reflector without and with 1.2 m shroud.

The set up for the CHAMP analysis is shown in the next sections together withan optimization of the length of the shroud for a maximum F/B ratio within alength limit of 1.2 meters.

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6.8.1 Analysis of the original shroud antenna

6.8.1.1 Set up of geometry

To set up this geometry, we start CHAMP and choose to design manually. Thecircular waveguide is created by the menus:Create - Horn Interior - Smooth_walled_section

and select linear_profile

Figure 6-80 Smooth walled horn section.

The Input and output radii are set to 10 mm and the length is set to 100 mm.Since CHAMP will assume a single TE11 mode in this section, it’s length hasno impact on the predicted performance and can be selected by the user.

In order to have a realistic illumination of the shroud the horn must have anaperture thickness. This exterior part of the horn is created by the menus:Create - Exterior geometry - Horn Exterior

Click on the drawing to add two nodes and then click on Accept. Correct thenode data to the ones on the screen dump.

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Figure 6-81 Exterior horn section.

The paraboloid reflector is created by the menus:Create - Exterior geometry - Reflectors - Tabulated Reflector

In the import subreflector window browse for the tabulated reflector file “re-flector.rsf”, and change the z-offset to 666. mm. In the Tabulated Reflectormenu change the length units for rho and z to m and the z-Factor to -1, inorder to turn the paraboloid. A drawing of the reflector is now created byView - Fit to Window

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Figure 6-82 Single paraboloid reflector section.

The shroud is created by the menus:Create - Exterior geometry - Reflectors - Piecewise Linear Reflec-tor

Click on the drawing to add a node near the top reflector edge and a nodein the end of the shroud, then click on Accept. Correct the node data to theones on the screen dump.

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Figure 6-83 Shroud section.

6.8.1.2 Use of variables

CHAMP implements a very powerful feature by which geometric parameterscan be expressed as variables. This is useful for optimization purposes, butcan also be used as an efficient tool in the geometry set up.

We introduce variables for the shroud section, i.e. the radius and the length.These variables are simply introduced by selecting the parameter value in theright pane, and overwrite it with an alphanumeric expression:

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Figure 6-84 Setup of variables.

The variables are given initial values that correspond to the parameters theyare allocated to. Changing a parameter to a variable will therefore not changethe design until the value of this variable is changed.

6.8.1.3 Performing analysis

Next, the desired analysis must be specified. This is done by selecting the“Analysis” window and adding an analysis:

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Figure 6-85 Fundamental TE11 mode for analysis.

The antenna is analyzed at one frequency, 10 GHz, and excited by the funda-mental TE11 waveguide mode, linearly polarized along x. Due to the definedexterior horn geometry, the method-of-moment solution is included on theanalysis and the expansion accuracy is set to high.

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Figure 6-86 Frequency input.

After saving the project an analysis can be executed by pushing the “play”-

button.

6.8.1.4 Viewing results

The data can be inspected in the “Results” window by the menus:Results - 1200 - shroud_antenna - Pattern Cuts - 10.0 GHz

where a plot of the E- and H-planes and the 45-degree plane is available.

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Figure 6-87 Pattern cuts for 10 GHz and shroud length 1200 mm.

A large peak above 40 dBi in the θ=180◦ direction is observed. This is actuallythe reflector main beam direction, because the patterns always have θ=0◦ inthe feed direction. So the reflector Front direction is in θ= 180◦ and thereflector Back radiation is in θ=0◦. The dB values for the curve can be foundby a click on the curve by the right mouse button. This gives an option to“Quick View the Data for Curves”, wherein the Front radiation (θ=180◦) isfound to 44.8 dBi and the Back radiation (θ=0◦) to -17.2 dBi. This gives aF/B ratio of 62 dB. The largest field value in the back half sphere is found inθ=90◦ direction to -17.5 dBi.

6.8.2 Optimization of the shroud length

6.8.2.1 Set up of optimization

The Back radiation is generated by the currents near the shroud opening.These currents can be visualized by selecting:Results - 1200 - shroud_antenna - Additional Data - Surface Cur-rents - 3D-view - 10.0 GHz

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Figure 6-88 Illumination of shroud.

The currents are seen to fluctuate relative to the shroud length giving thepossibility to optimize this length for lower back radiation. The large illumina-tion from 300 mm to 500 mm is due to a the double scattered rays in Figure6-89.

Figure 6-89 Ray scattering (Generated by GRASP).

Therefore, the shroud length must be larger than 500 mm. By visualization alength of 720 mm is chosen where the current levels are very low. The valueis inserted in the geometry scheme for variables, dL = 720.

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The goal for the optimization is set to a F/B ratio of 60 dB in the optimizationmenu by clicking the “Add Goal” button and choosing “Directivity in specificdirections” and press next.

Figure 6-90 Goal specification for optimization.

The θ value is set to 180 because this is actually the forward direction whichhas to be 60 dB or more larger than the Back direction (θ=0◦). Now theoptimization button is activated.

Figure 6-91 Minmax optimization.

The minmax optimization routine is selected. After optimization a summary

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can be found underResults - from720 - Optimisation Summary

Figure 6-92 Optimization results from 720 mm shroud length start.

The optimized F/B ratio is found to 80 dB for a shroud length of 716.5 mm.The resulting patterns after an analysis is runned show very low back radiationin the interval θ = 90◦ to 180◦.

Figure 6-93 Pattern cuts for optimized shroud length 716.5 mm.

One must notice that this result may be very sensitive for frequency variation.Therefore, a frequency band of ±200 MHz is introduced and analyzed.

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Figure 6-94 Setup of frequency band using 5 frequencies.

The resulting patterns in E-plane are copy and pasted from the individualfrequency patterns.

Figure 6-95 Pattern cuts for optimized shroud length 716.5 mm.

The F/B ratio is increased for all off center frequencies to a maximum of50.6 dB at 9.8 GHz. Due to a lot of local maxima for the F/B ratio the GeneticAlgorithm must be used instead of the minmax optimization in order to findthe best shroud length inside the interval 716 mm to 1200 mm.

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Figure 6-96 Set up of Genetic Algorithm optimization from shroudlength 1020 mm.

Using this scheme a F/B ratio maximum of 60.1 dB is found for a shroud lengthof 1026 mm. In order to find the best local maximum a minmax optimizationmust be performed after a genetic algorithm optimization. After a minmaxoptimization with a frequency interval of 0.05 GHz the shroud length is foundto 1025 mm and the F/B ratio is reduced to 58.2 dB for 9.85 GHz.

Figure 6-97 Pattern cuts for optimized shroud length 1025 mm.

In order to get a F/B ratio of 60 dB for all frequencies in the frequency band

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the feed must be redesigned to give a larger directivity.

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7. Batch-Mode Operation

The CHAMP analysis module can be executed from the command line by fol-lowing the step-by-step instructions below.

1. Prepare a CHAMP project. It is recommended to use the CHAMP GUIto prepare a valid CHAMP project containing the correct geometry, theanalysis definitions, and optionally the optimization goals and the opti-mization variables. Run an analysis once from inside the GUI to generatethe required project files and directories.

2. Locate the project files and create a copy of the relevant directory. Forinstance, if the CHAMP project is named "MyProject", the relevant direc-tory is:

MyProject.champ_data\Analysis_0001.

This directory contains a file called geometry.tor with the objects forthe horn antenna geometry data and a file called geometry.tci includingcommands for the actions to be carried out analyzing or optimization ofthe antenna.

Place the copy of this directory outside the MyProject.champ_datadirectory.

Note: It is not recommended to perform batch-mode computa-tions in a directory containing a project managed by the CHAMPGUI. Doing so may result in a malfunction of the GUI if projectfiles or result files are modified in an unexpected way. Instead,the batch-mode computation should be performed in a dedicateddirectory.

3. Open a command prompt and navigate to the dedicated batch modedirectory created in the previous item.

4. Add the location of the CHAMP executable to the PATH by executing thefollowing command:

PATH = %PATH%;<installation_directory>\bin

where <installation_directory> is typically

C:\Program Files\TICRA\CHAMP-3.0.0

This step can be avoided if the directory has been added to the system-wide PATH variable.

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5. Run the analysis by executing the following command:

champ-analysis <name1>.tci <name2>.out <name3>.log

where the tci-file is an input file, and the out- and log-files are outputfiles. All files are ASCII-files and the names (name1, name2, and name3)may differ or be identical. As an example: champ-analysis.exe geome-try.tci my_job.out my_job.log

6. Subsequent batch runs can be performed by repeating the last stepoutlined above.

7. The analysis may be stopped by pressing the CTRL C keys.

The contents of the tor-file can be modified using a standard text editor orby creating automated scripts, e.g., using Matlab. The tor-file contains anarbitrary number of objects - each object is of a certain class and contains anumber of parameters. A detailed description of the classes and the associ-ated parameters are included in the Classes section.

The tci-file contains a number of commands executed sequentially by CHAMP.A detailed description of the available commands is included in the Com-mand Types section. A typical tci-file contains one or more instances of theGet Modes, Get Optimum, Get Field, Get SWE, and Export STEP commands.In addition to these commands the following two commands are useful forreading and writing tor-files:

1. files read all <tor file>. This command reads the tor-file contain-ing the objects. Additional files read all commands can be addedby advanced users if it is desirable to split the project in multiple torfiles.

2. files write <tor file>. This command writes the object to thespecified tor-file. This can be used to update a tor-file with the optimisedgeometry.

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8. CHAMP3 for CHAMP2 Users

This section is intended for those who are familiar with CHAMP2 and wishto know the main differences between CHAMP2 and CHAMP3. The generalchanges will be described in the following.

Real Variables

CHAMP3 introduces the concept of ’Real Variables’. The user may assign asymbolic name for any real valued quantity in CHAMP, and reference thissymbolic name elsewhere in the geometry set-up (either directly or throughthe most commonly used mathematical functions). This allows the user tointroduce a number of design parameters which influence not only a singlebut several of the input fields in the program.

As an example, the user may introduce a Real Variable for the corrugationdepth and another Real Variable for the horn wall thickness, and define theradius of the horn exterior in terms of these two variables. If the corruga-tion depth is optimised, the radius of the horn exterior will automatically beupdated to insure that the wall thickness is kept at a fixed value.

In CHAMP2, optimisation variables were defined in a similar way. Thus, theenhancement from CHAMP2 to CHAMP3 is the generalization of the use ofvariables from the optimisation to the the geometry set-up.

The Real Variables are defined in the Geometry Tab, e.g. by specifying asymbolic name directly in the Property Editor.

Changed definition of optimisation variables

Any Real Variable defined may be selected as optimisation variable.

Thus, the specification of optimisation variables has been chanded to a simpleselection from a list of all Real Variables available. Optimisation bounds maystill be defined for all optimisation variables.

When reading a CHAMP2 project into the CHAMP3 GUI, the old definition ofoptimisation variables is automatically converted to the new definition. Theuser will be warned to accept this conversion. The converted CHAMP3 projectcannot be read by CHAMP2.

Changed program lay-out

The CHAMP3 Graphical User Interface (GUI) is very similar to that of CHAMP2.The GUI has a number of so-called CHAMP Tabs which guide the user throughdifferent steps in the RF-modellling of the horn antenna. Selecting one of the

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CHAMP Tabs changes the contents and lay-out of the main user area and themenu. Compared to CHAMP2, the Variables Tab and the Goals Tabs havebeen combined into a single tab, Optimisation. Hence, the new CHAMPhas 4 tabs instead of 5, namely: Geometry, Analysis, Optimisation, andResults, as shown in the leftmost bar of Figure 8-1.

Figure 8-1 The lay-out of the Optimisation Tab.

The new tab, Optimisation, is used to specify optimisation variables as wellas optimisation goals. The reason for the change, is the introduction of theReal Variables described above, which has removed many functionalities pre-viously needed in the specification of the optimisation variables. In CHAMP3,the user simply selects the optimisation variable from a list of all availableReal Variables.

Enhanced Method of Moments algorithm

CHAMP has been enhanced with a completely redesigned Method-of-Momentssolver for general bodies of revolution. The new solver employs an efficientdiscretization scheme using electrically large curved patches, which impliesthat the modeling speed is improved at least by a factor of 10 when comparedto the previous version. In addition, the new solver allows greater modelingflexibility by allowing dielectric materials and infinitely thin conductors.

The new BoR-MoM employs a higher-order formulation based on hierarchicalbasis functions and smooth curvilinear patches, which imply that even largestructures can be handled with very few unknowns. The typical runtime fora full-wave analysis of a 40λ reflector system is 1-2 seconds per frequencypoint on a laptop. In comparison, the previous CHAMP version used 30-60seconds per frequency point for a similar reflector.

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The new Method of Moments algorithm also enables the analysis of hornexterior and reflectors for tracking-mode excitation of the horn, which wasnot available in the previous versions of CHAMP.

From horn antenna to reflector program

CHAMP has been extended to allow fast and accurate design of rotationallysymmetric reflector systems. In order to facilitate an easy initial design, theCHAMP wizard has been extended with a new option for defining axially dis-placed reflector systems. The wizard will generate the sub- and main reflectordefinition, as well as optional placeholders for the feed horn and the connec-tion between the horn and the main reflector. The user must then design asuitable horn and refine the design to reach the required performance. Thisincludes reshaping of the reflector surfaces as well as definition of appropriatesupport structures.

Often, the pattern radiated by rotationally symmetric reflector systems is re-quired to follow stringent pattern envelopes. Therefore, a new "Pattern Tem-plate" optimization goal has been added to CHAMP, which offers a convenientway of specifying the piecewise linear or piecewise logarithmic templates tothe optimisation.

In addition, it is now possible to overlay the defined pattern templates in theplot of pattern cuts in the Results Tab.

New scattering structures

The previous version of CHAMP allowed a subreflector to be defined. CHAMP3allows an arbitrary number of scatterers, such as reflectors, support struc-tures, lenses, or a radome.

A number of new classes are available:

• New spline-based reflectors. A new class, "Spline Reflector", has beenintroduced. The Spline Reflector class is a convenient way of definingcurved reflectors using a very low number of data points. In addition,the spline reflector option allows reflector shaping by including the datapoints in the list of optimization variables

• New "BoR Mesh" geometry definition A new class, "BoR Mesh" has beenintroduced. This class allows definition of arbitrary rotationally symmet-ric structures. The user defines a number of nodes and specifies how thenodes should be connected to form curve segments. These curve seg-ments define the generatrix of the body of revolution to be analyzed.The curve segments may define conducting surfaces or interfaces be-tween two homogeneous dielectric regions. Curve segments can bestraight or curved, and any number of dielectric regions is allowed. Thisnew class provides a flexible way of defining complex support structures,lenses, or radomes.

• New "Dielectric Support Tube" definition A new class, "Dielectric SupportTube", has been introduced. This class provides a convenient way of

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defining a hollow dielectric tube, which is connected to the exterior ofthe horn at one end and to a subreflector at the other end. The tubemay be inserted into a recess at one or both ends. For more complexdielectric support structures, the "BoR Mesh" option must be used.

In the previous versions of CHAMP, all reflectors were required to have a finitethickness which leads to a significant overhead. This is no longer required andthe "Grow Thickness" setting has therefore been removed. Reflectors may stillbe defined with a finite thickness, if required.

Changed default behaviour if only horn interior

When no exterior geometry was defined, the previous version of CHAMP wouldcompute the results based on the mode-matching algorithm alone. This be-haviour has been changed, such that the BoR-MoM solver is used to analyzethe transition to the free-space region, even when no exterior geometry hasbeen defined. This approach provides more accurate results, in particular forthe return loss. The BoR-MoM algorithm may still be disabled by un-checking"Include exterior geometry in calculation" on the Analysis Tab.

Other major changes

A number of additional major changes have been included:

• In previous versions, it was not possible to include the exterior horn ge-ometry in a tolerance analysis. This restriction has now been removedand the tolerance analysis will automatically include all parts of the ge-ometry. However, the user-supplied manufacturing tolerances will onlybe applied inside the horn.

• The algorithm used to compute the phase center of a horn has beenimproved. In previous versions, the phase center curve could have smalljumps as a function of frequency. The new algorithm always provides asmooth curve as a function of frequency.

• It is now possible to plot a TICRA cut file generated outside CHAMP. Thisfeature is useful for comparing cuts obtained from other sources, such asGRASP or from measurements. The feature is available from the menu"Analysis->Plot Pattern Cut from File" on the Results Tab.

• In CHAMP2, each optimization goal typically produce several residues,which often lead to an excessive number of curves in the residual curvesplot. In CHAMP 3, only the worst-case residual is shown for each goal.

For a complete list of the enhancements as well as bug fixes, the user isreferred to the Release Note of CHAMP version 3.0.0.

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9. Technical Description

This chapter contains detailed information about the methods, models, calcu-lations and files used in CHAMP.

9.1 Analysis Methods

The analysis is in general divided into a horn-interior problem solved by modematching, and a horn-exterior problem solved by the method of moments.The analysis of the horn-exterior is only available for a horn excited withthe fundamental TE11-mode. Details about the analysis methods are furtherdescribed in this section.

9.1.1 Analysis of the Horn Interior

9.1.1.1 Overview

An accurate analysis of the inner structure of horns with circular cross-sectionis provided, based upon a decomposition of the structure into elementarymodules. The field analysis of the individual modules is accomplished byexpanding the field into cylindrical waveguide modes, and subsequent modematching.

This determines the scattering matrix for each module including the evanes-cent modes. By cascading the scattering matrix for the individual modules,the overall scattering matrix for the inner structure is obtained. For a givenexcitation of the horn in the feeding waveguide, the overall scattering ma-trix is in turn used to derive both the return loss at the horn throat and thefield incident on the horn aperture. The far field is then calculated from theKirchhoff-Huygens integral of the incident aperture field. This neglects modeconversion at the aperture, flange effects and the influence of the outer hornwalls.

The program assumes excitation by a single mode in the feeding waveguide.The mode is either the fundamental TE11-mode or one of the modes TM01,TE21, or TE01, used for tracking purposes.

9.1.1.2 Elementary Modules

The horn interior is decomposed into elementary modules. Each elementarymodule belongs to one of two generic types of modules, named a "regularmodule" or an "inverted module". The two module types are shown in Fig-ure 9-1.

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Figure 9-1 The ’regular’ (a1 < a2) and the ’inverted’ (a1 > a2)elementary modules.

Both types consist of a junction of two circular waveguides of different diame-ters, that (if d > 0) is reactively loaded by a short-circuited coaxial waveguide.Each of the circular waveguide sections and the short-circuited waveguidesection may be filled by a homogeneous dielectrics as shown in Figure 9-2.

Figure 9-2 Possibly dielectric filling of the elementary modules.

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9.1.1.3 Field Analysis

The field analysis of the elementary modules is achieved by the modal ex-pansion technique. The elementary module is subdivided into regions, 1, 2,and 3, in each of which the electromagnetic field can be expanded in termsof complete sets of known eigenfunctions.

The boundary conditions for the tangential electric and magnetic fields acrossthe common boundary plane between the subregions lead to an infinite sys-tem of coupled linear equations for the unknown expansion coefficients. Bymatrix multiplications, it is possible to express the amplitude of the reflectedmodes in terms of a scattering matrix times the amplitude of the incidentmodes.

The generalized scattering matrix valid for reference planes located at thethroat and at the aperture of the horn can be determined by cascading thescattering matrices for the the elementary modules. This leads to the follow-ing overall description of the field analysis:(

~b1~b2

)= S

(~a1~a2

)(9.1)

where ~a1 and ~b1 are the amplitudes of the incident and reflected modes at thethroat, and ~a2 and ~b2 are the amplitudes of the incident and reflected modesat the aperture.

In the analysis of the horn interior, it is assumed that there is no reaction fromthe horn throat or aperture, i.e. that no modes are reflected from outside intothe horn (as if the first elementary module at the throat and the last moduleat the aperture were connected to infinite waveguides with constant radius).In this way

~a1 = 0 and ~a2 = 0 (9.2)

except for the amplitude of the excitation mode, e.g.

a1(TE11) = 1 (9.3)

and similarly for one of the tracking modes. With ~a2 = 0 mode conversionat the aperture, flange effects and the influence of the outer horn walls areneglected.

However, as will be explained later, the analysis of the horn exterior (whichemploys the overall horn scattering matrix, (9.1), of the horn as input) leadsto an improved solution for ~a2, ~b1 and ~b2, and thus to an improved solution forthe radiated field and the return loss at the horn throat.

9.1.2 Analysis of the Exterior Geometry

CHAMP has been enhanced with a completely redesigned Method-of-Momentssolver for general bodies of revolution. The new solver employs an efficientdiscretization scheme using electrically large curved patches, which impliesthat the modeling speed is improved at least by a factor of 10 when compared

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to the previous version. In addition, the new solver allows greater modelingflexibility by allowing dielectric materials and infinitely thin conductors. It usesthe horn scattering matrix from the mode matching as input. The radiatedfield is calculated by integrating the induced surface currents.

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9.2 Input Definitions

9.2.1 Analysis Specifications

9.2.1.1 Frequency Specification

The frequency specification is given by a "Start frequency", fs, an "End fre-quency", fe, and the "Number of frequencies", Nf .

The frequencies used in the analysis are equally spaced between fs and fe,i.e.

fi = fs + (i− 1)fe − fsNf − 1

, i = 1, 2, .., Nf (9.4)

If Nf is set to unity, then fs is used in the analysis.

9.2.1.2 Excitation

The excitation is either the "Fundamental mode", TE11, or one of the "Trackingmodes", TM01, TE21, or TE01. The input specifications are different for the twotypes of modes and they are consequently described in separate sectionsbelow.

Because of the axisymmetric geometry, the azimuthal field distribution orig-inating the primary incident mode is retained throughout the horn structureand the radiated far fields may be represented by the same azimuthal fielddistribution.

As an example, if the polarisation of the primary excitation in the feedingwaveguide is assumed to be linear along the y-axis, the radiated far fieldsmay be represented as follows

Eθ(θ, φ) = Fθ(θ,m, n) sinmφ

Eφ(θ, φ) = Fφ(θ,m, n) cosmφ(9.5)

for TEmn-mode excitation, and

Eθ(θ, φ) = Gθ(θ,m, n) cosmφ

Eφ(θ, φ) = 0(9.6)

for TMmn-mode excitation. In these expressions, Fθ, Fφ and Gθ may be foundin e.g. Silver (1965). Their explicit forms are, however, not needed in thefollowing discussion.

9.2.1.2.1 Fundamental Mode Excitation

The fundamental mode excitation uses the TE11-mode at the horn throat asmode excitation. The excitation mode is completely described by a "polarisa-tion" and a "Complex polarisation ratio".

The "polarisation" may be set to either 1) "linear_x": linear polarisation alongthe x-axis, 2) "linear_y": linear polarisation along the y-axis, 3) "rhc": right-hand circular polarisation, or 4) "lhc": left-hand circular polarisation.

135

The "Complex polarisation ratio" is a complex number with amplitude lessthan or equal to unity. The definition of the polarisation ratio depends on theselected polarisation as described below:

Purely, linear polarisation along the y-axis:

If the polarisation is set to "linear_y" and the polarisation ratio equals zero,then the far field is calculated by an integration of all the TE1n- and TM1n-modes in the aperture, resulting in a far field of the form

Eθ(θ, φ) = fθ(θ) sinφ

Eφ(θ, φ) = fφ(θ) cosφ(9.7)

where fθ(θ) and fφ(θ) represent the E- and H-plane patterns, respectively.From continuity, we must have

fθ(θ = 0) = fφ(θ = 0) (9.8)

on the axis, θ = 0.

Purely, linear polarisation along the x-axis:

If the polarisation is set to "linear_x" and the polarisation ratio equals zero,then the far fields would similarly read

Eθ(θ, φ) = fθ(θ) cosφ

Eφ(θ, φ) = −fφ(θ) sinφ(9.9)

Purely, right-hand circular polarisation:

If the polarisation is set to "rhc" and the polarisation ratio equals zero, thenthe far fields would similarly read

Eθ(θ, φ) = fθ(θ)(cosφ− j sinφ) = fθ(θ)e−jφ

Eφ(θ, φ) = −fφ(θ)(sinφ+ j cosφ) = −jfφ(θ)e−jφ(9.10)

Purely, left-hand circular polarisation:

If the polarisation is set to "lhc" and the polarisation ratio equals zero, thenthe far fields would similarly read

Eθ(θ, φ) = fθ(θ)(cosφ+ j sinφ) = fθ(θ)ejφ

Eφ(θ, φ) = −fφ(θ)(sinφ− j cosφ) = jfφ(θ)ejφ(9.11)

General polarisation:

On the axis, the above equations (9.9), (9.7), (9.11), and (9.10) representpurely polarised fields. In order to construct a field with an arbitrary polari-sation on the axis we may proceed as follows, where a distinction betweenmainly linearly and mainly circularly polarised fields is appropriate.

Mainly linearly polarised along the y-axis:

136

If the polarisation is set to "linear_y" and the polarisation ratio is non-zero,then we define the liniear polarisation ratio, p = py, on the axis by

p = py = −Ex/Ey , |py| ≤ 1 (9.12)

(note the minus sign), and the above equations (9.9) and (9.7) may then becombined to yield

Eθ(θ, φ) = fθ(θ)(sinφ− py cosφ)

Eφ(θ, φ) = fφ(θ)(cosφ+ py sinφ)(9.13)

Mainly linearly polarised along the x-axis:

If the polarisation is set to "linear_x" and the polarisation ratio is non-zero,then we define the liniear polarisation ratio, p = px, on the axis by

p = px = Ey/Ex , |px| ≤ 1 (9.14)

and the above equations (9.9) and (9.7) may then be combined to yield

Eθ(θ, φ) = fθ(θ)(cosφ+ px sinφ)

Eφ(θ, φ) = −fφ(θ)(sinφ− px cosφ)(9.15)

Mainly rhc-polarised:

If the polarisation is set to "rhc" and the polarisation ratio is non-zero, thenwe define the circular polarisation ratio,

Q = QR = ELHC/ERHC , |QR| ≤ 1 (9.16)


Eθ(θ, φ) = fθ(θ)[e−jφ +QRe

jφ]

Eφ(θ, φ) = −jfφ(θ)[e−jφ −QRe

jφ] (9.17)

Mainly lhc-polarised:

If the polarisation is set to "lhc" and the polarisation ratio is non-zero, thenwe define the circular polarisation ratio,

Q = QL = ERHC/ELHC , |QL| ≤ 1 (9.18)


Eθ(θ, φ) = fθ(θ)[ejφ +QLe

−jφ]Eφ(θ, φ) = jfφ(θ)

[ejφ −QLe

−jφ] (9.19)

9.2.1.2.2 Tracking Mode Excitation

The tracking mode excitation uses either the TM01-, TE21-, or TE01-mode at thehorn throat as mode excitation. The excitation mode is completely describedby a "mode type" and a "rotation".

137

The "mode type" is simply a selection of one of the three possible trackingmodes. The "rotation" is a rotation of the mode in the xy-plane. This is onlyrelevant for the TE21-mode, and the far fields of the two other tracking modesare independent of φ.

For the TM01-mode the radiated far field may be written (cf. (9.5))

Eθ(θ, φ) = gθ(θ)

Eφ(θ, φ) = 0(9.20)

where on the axis

gθ(θ = 0) = gθ(θ = π) = 0 (9.21)

i.e. the far field contains no φ-directed electric field component in any direc-tion, and the field is independent of φ.

Similarly, for the TE01-mode, we have from (9.5)

Eθ(θ, φ) = 0

Eφ(θ, φ) = fφ(θ)(9.22)

where on the axis

fφ(θ = 0) = fφ(θ = π) = 0 (9.23)

i.e. the electric far field consists of only φ-directed field component, indepen-dent of φ.

When the primary excitation is the TE21-mode, the radiated far field may bewritten

Eθ(θ, φ) = fθ(θ) sin 2φ

Eφ(θ, φ) = fφ(θ) cos 2φ(9.24)

where, on the axis

fθ(θ = 0) = fθ(θ = π) = 0

fφ(θ = 0) = fφ(θ = π) = 0(9.25)

138

9.3 Output Definitions

This section presents the definitions of the output parameters calculated byCHAMP.

9.3.1 RF-Parameters

9.3.1.1 Return Loss

The Return Loss, RL, is in CHAMP defined as

RL = 10 log10

(1

|Γ|2

)(9.26)

where Γ is the reflection coefficient at the throat, i.e. the inverse ratio be-tween the amplitude of the excitation mode and the amplitude of the reflectedmode of the same type. The Return Loss is thus expressed in positive dB-values.

Expressed in terms of the mode amplitude, the Return Loss thus becomes

RL = −20 log10

(|b1(TXmn)||a1(TXmn)|

)(9.27)

where a1 and b1 are described in Section 9.1.1.3, and TXmn is one of theexcitation modes,

As an example, for the fundamental-mode excitation the Return Loss becomes

RL = −20 log10

(|b1(TE11)||a1(TE11)|

)(9.28)

9.3.1.2 On-axis Directivity

The On-Axis Directivity, DdBi, is in CHAMP defined as the directivity of theradiation pattern in the direction of the horn axis, θ = 0. The on-axis directivityis expressed in dBi.

9.3.1.3 Aperture Efficiency

The Aperture Efficiency, Aeff , is in CHAMP defined as

Aeff = 10(DdBi−DIdeal,dBi)/10 (9.29)

where DdBi is the calculated on-axis directivity in dBi, and DIdeal,dBi is the on-axis directivity in dBi of an aperture of the same size with uniform aperture-distribution. For at definition of the on-axis directivity, see Section 9.3.1.2.

The on-axis directivity from a circular aperture with radius rAp and with uni-form distribution is

DIdeal,dBi = 10 log10

(π(2rAp)

λ

)2

= 10 log10

((krAp)

2)) (9.30)

139

with λ and k = 2π/λ being the free-space wavelength and wavenumber, re-spectively.

Re-arranging (9.29) and (9.30) leads to an expression of the on-axis directivityin terms of the ideal directivity and the aperture efficiency:

DdBi = DIdeal,dBi + 10 log10(Aeff )

= 10 log10

(Aeff (krAp)

2) (9.31)

Note: The aperture size, rAp , is in CHAMP defined as the circular aper-ture of the last elementary module in the horn interior independent ofthe form and dimensions of the horn exterior. Hence, if the interfacebetween the mode matching region and the Method of Moment regionis not the actual horn aperture, then the calculation of the apertureefficiency becomes in error. In particular, when scattering structuresare present, an aperture efficiency above 100% may be calculated.

9.3.1.4 Maximum cx-Polar Level

The maximum cx-polar level is calculated for fundamental mode excitationonly. It is expressed in dB relative to the on-axis directivity.

The cx-polar pattern is calculated in the plane φ = 45◦ (except for purelycircular polarisation, where the plane φ = 0◦ is used as the far field patternis identical in all cuts) and a search for the maximum value performed. Thesearch is limited to the θ-interval from θmin to θmax.

The cx-polar level calculated in each analysis uses θmin = 0◦ and θmax = 90◦.When used by the optimisation goals, θmin and θmax are defined by the user.

9.3.1.5 Direction of Maximum cx-Polar Level

The direction of maximumm cx-polar level is calculated for fundamental modeexcitation only. Its expressed in degrees. It is defined as the θ-angle of thedirection in which the cx-polar maximum of Section 9.3.1.4 occurs.

9.3.1.6 Minimum XPD Level

The minimum XPD level is calculated for fundamental mode excitation only.

The XPD in. a given far-field direction, (θ, φ), is defined by:

XPD(θ, φ) =Eco(θ, φ)

Ecx(θ, φ)(9.32)

where Eco and Ecx are the co- and cx-polar field components, respectively. Ifall quantities is expressed in dB, (superscript "dB"), then the XPD is expressedas:

XPDdB(θ, φ) = EdBco (θ, φ)− EdB

cx (θ, φ) (9.33)

140

The cx-polar pattern is calculated in the plane φ = 45◦ (except for purelycircular polarisation, where the plane φ = 0◦ is used as the far field pattern isidentical in all cuts) and a search for the minimum XPD-value performed. Thesearch is limited to θ = 90◦.

9.3.1.7 Half Beam Width

When horns are used as feeds in reflector antenna applications, the co-polarbeamwidth corresponding to a certain dB-level below maximum is often oneof the design requirements.

For fundamental mode excitation, the co-polar half-beamwidths are calculatedin the planes φ = 0◦, 45◦ and 90◦ (except for purely circular polarisation,where the plane φ = 0◦ is used as the far field pattern is identical in all cuts).The co-polar pattern maximum is assumed to be on the axis (θ = 0◦) andbeamwidths corresponding to levels 3, 6, 10, 12, 15, 18 and 20 dB below theon-axis value are found. The beamwidth search is limited to θ = 90◦, meaningthat if a certain x-dB level beamwidth is larger than 90◦, the correspondingbeamwidth is set equal to 90◦.

For the tracking modes, the beamwidth has a slightly different meaning. Herethe θ-positions, corresponding to the same dB-levels as above, are foundrelative to the peaks of the Eθ- and/or Eφ-components. Again the search islimited to θ = 90◦ and starts from the position of the peak in the direction ofincreasing θ-values.

9.3.1.8 Best-Fit Phase Centres

The phase properties of a horn are important when used as a feed for a reflec-tor. In general, a horn does not possess a unique phase-centre, and hencea best-fit technique is employed to find a phase-centre, which, in a least-squares sense, will minimise the phase residual (Rusch and Potter (1970)).Due to the axisymmetric horn geometry, the phase-centre is restricted to lieon the z-axis. The location of the best-fit phase-centre will vary with theφ-angle, hence E- and H-plane phase centres are usually not coincident, al-though this is a highly desirable feature. Furthermore, the position will dependon the range of θ-values used in the best-fit calculations. Thus for examplea "10 dB phase-centre" is obtained by using phase-information out to the -10dB point of the radiation pattern in the fitting. The weight function in thebest-fit calculation is given as the amplitude of the E-field.

The phase-centre positions are given relative to the aperture plane, z = 0,which is the far-field phase reference. Hence a negative value indicates aphase-centre inside the horn, and a positive value in front of the aperture.

141

10. Reference Section

The reference section contains descriptions of the CHAMP classes and com-mand types, as well as the applicable units and file formats. Navigation inthis section is facilitated by means of an Alphabetical List of Classes andCommand Types.

Links

Alphabetical List of Classes and Command Types

Classes

Command Types

File Extensions

Applicable Units

File Formats

Contents

142

10.1 Alphabetical List of Classes and Command Types

Classes and command types are listed according to their display names asthey appear in the GUI. The associated name of the class or command typeis specified in parenthesis following the display name. The descriptions ofthe classes and command types are reached by clicking the names writtenin red.

Link to initial letter

A B C D E F G H IJ K L M N O P Q RS T U V W X Y Z

A Top of list

Add Field (add_field) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338Asymmetric Sine-Squared Profile (asymmetric_sine_squared_profile) . . . 181Axial Corrugations (simple_axial_corrugated_section) . . . . . . . . . . . . . . . . . . . . . 164

B Top of list

BOR Mesh (bor_mesh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220bor_mesh_exterior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . see BOR Mesh

C Top of list

circular_symmetric_horn_exterior . . . . . . . . . . . . . . . . . . . . . . . . . . see Horn ExteriorCombined Horn Section (combined_horn_section) . . . . . . . . . . . . . . . . . . . . . . . . . 149Coordinate System (coor_sys) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151coordinate_system .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . see Coordinate System

143

Corrugated Horn Mode Matching (corrugated_horn_mode_matching) . . . 237Corrugation List (corrugation_list) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

D Top of list

Dielectric Support Tube (dielectric_support_tube) . . . . . . . . . . . . . . . . . . . . . . . . . 213Dual Depth Corrugated Section (dual_depth_corrugated_section) . . . . . . . 157

E Top of list

Exponential Profile (exponential_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Export to 2D STEP File (export_step_2d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346Export to IGES File (export_iges) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348Export to STEP File (export_step) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344Exterior Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

F Top of list

Field Data (F2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364Field Data in Cuts (F2.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365Field Data in Rectangular Grid (F2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368Frequency Range (frequency_range) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

G Top of list

Get Field (get_field) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337Get Influence (get_influence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343Get Modes (get_modes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336Get Optimum (get_optimum) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342Get SWE (get_swe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340Goals to the Beam Pattern (optimisation_goals_radiation_pattern) . . . . . . 264

H Top of list

Horn Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .236

144

Horn Exterior (circular_symmetric_horn_exterior) . . . . . . . . . . . . . . . . . . . . . . . . 198Horn Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Horn Interior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153Horn Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Horn Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176Horn Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .292Horn Tolerance (horn_tolerance) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Hyperbolic Profile (hyperbolic_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

L Top of list

Linear Profile (linear_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

O Top of list

Optimisation Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260Optimisation Manager (optimisation_manager) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248Optimisation Variables (optimisation_variables) . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

P Top of list

Pattern Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285Piecewise Linear Pattern Template (piecewise_lin_pattern_template) . . . 286Piecewise Linear Reflector (piecewise_linear_reflector) . . . . . . . . . . . . . . . . . . . 209Piecewise Logarithmic Pattern Template (piecewise_log_pattern_template) 289piecewise_linear_exterior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . see Horn ExteriorPolynomial Profile (polynomial_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

R Top of list

Real Variable (real_variable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232Reflector Data (F1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361Reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .202Reshape Profile (reshape_spline_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Reshape Reflector (reshape_reflector) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

145

Return Loss Goals (goals_source_return_loss) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261Rotationally Symmetric Surface (F1.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

S Top of list

Simple Polynomial Profile (simple_polynomial_profile) . . . . . . . . . . . . . . . . . . . . 186Single Depth Corrugated Section (single_depth_corrugated_section) . . . 155Single Depth Section with Mode Converter (single_depth_mode_converter)

166Sinusoidal Profile (sinusoidal_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Smooth Walled Section (smooth_walled_section) . . . . . . . . . . . . . . . . . . . . . . . . . . 154Spherical Cut (spherical_cut) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Spherical Grid (spherical_grid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304Spherical Wave Expansion (SWE) (swe) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Spherical Wave Q-Coefficients (F3.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375spherical_field_grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . see Spherical GridSpline Profile (spline_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Spline Reflector (spline_circ_sym_reflector) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203Subtract Field (subtract_field) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339Support Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

T Top of list

Tabulated Feed Data (F3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374Tabulated Reflector (tabulated_circ_sym_reflector) . . . . . . . . . . . . . . . . . . . . . . . 206Tangential Profile (tangential_profile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Tracking Pattern Goals (optimisation_goals_tracking_pattern) . . . . . . . . . . . 280

V Top of list

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .231

W Top of list

Waveguide Section (circular_waveguide_section) . . . . . . . . . . . . . . . . . . . . . . . . . 162

146

Waveguide Step (section_step) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Links

Classes

Command Types

File Extensions

Applicable Units

File Formats

Reference Section

Contents

Classes 147

10.2 Classes

The CHAMP classes are divided into the following groups:

• Horn Geometry

• Horn Analysis

• Horn Optimisation

• Horn Results

Links


Command Types

File Extensions

Applicable Units

File Formats

Reference Section

Contents

148 Horn Geometry

HORN GEOMETRY

Purpose

This group contains classes which define the geometry of the hornanalysed or optimised in CHAMP:

Combined Horn Section

Coordinate System

Horn Interior

Horn Profile

Exterior Geometry

Summary:

All geometry included in the CHAMP-analysis must be rotationallysymmetric with respect to a common axis of symmetry. The userspecifies the geometry using the class Combined Horn Section. Thisclass has references to objects of other classes defining the geome-try.

First, it has a reference to a Coordinate System specification, whichimplicit defines the axis of symmetry (the horn axis) as well as theposition of the horn.

Second, it has a reference to a sequence of Horn Interior objectsdefining a section (a part) of the horn interior with a certain shapeand a certain corrugation layout. The horn shape may be easilyspecified using so-called Horn Profile objects.

Third, it may have references to objects defining the Exterior Geom-etry, either the outer geometry of the horn or other scatterers, suchas subreflectors and support structures.

Links

Classes→Horn Geometry

Combined Horn Section 149

COMBINED HORN SECTION (combined_horn_section)

Purpose

The class Combined Horn Section defines the interior as well as theexterior geometry of a circularly symmetric horn.

Links

Classes→Horn Geometry→Combined Horn Section

Syntax

<object name> combined_horn_section(

horn_sections : sequence(ref(<n>), . . .),scatterers : sequence(ref(<n>), . . .),obsolete_horn_exterior : ref(<n>),coor_sys : ref(<n>)

)

where

<n>= name of another object

Attributes

Horn Sections (horn_sections) [sequence of names of other objects],default: blank.

Reference to a sequence of Horn Interior objects defining acombined horn section. The referenced horn sections are com-bined in the same order as they are referenced, i.e. with thefirst referenced section closest to the horn throat, and the lastreferenced section closest to the horn aperture.

Scatterers (scatterers) [sequence of names of other objects], default:blank.

Reference to an object of one of the classes of Exterior Geom-etry.

Horn Exterior (Obsolete) (obsolete_horn_exterior) [name of anotherobject], default: blank.

150 Combined Horn Section

Obsolete, use the more general attribute Scatterers instead.The attribute is included for back-compatibility only and refersto a Horn Exterior object defining the geometry of the hornexterior except for a possible subreflector.

Coordinate System (coor_sys) [name of another object], default: blank.

Reference to a Coordinate System object defining the positionof the combined horn section. The combined horn section isplaced with the centre of the horn aperture at the origin of thecoordinate system, with the axis of symmetry along the z-axis,and with the positive z-axis pointing out of the horn.

Coordinate System 151

COORDINATE SYSTEM (coor_sys)

Purpose

The class Coordinate System specifies the position and orientation ofa coordinate system relative to the global coordinate system or toanother coordinate system.

Links

Classes→Horn Geometry→Coordinate System

Syntax

<object name> coor_sys(

origin : struct(x:<rl>, y:<rl>, z:<rl>),x_axis : struct(x:<r>, y:<r>, z:<r>),y_axis : struct(x:<r>, y:<r>, z:<r>),base : ref(<n>)

)

where


<r> = real number

<rl>= real number with unit of length

Attributes

Origin (origin) [struct].

Coordinates of the origin of the coordinate system.

x (x) [real number with unit of length], default: 0.

x-coordinate of origin.

y (y) [real number with unit of length], default: 0.

y-coordinate of origin.

z (z) [real number with unit of length], default: 0.

z-coordinate of origin.

x-Axis (x_axis) [struct].

152 Coordinate System

Coordinates of a point on the positive x-axis of the coordinatesystem.

x (x) [real number], default: 1.

x-coordinate of x-axis.

y (y) [real number], default: 0.

y-coordinate of x-axis.

z (z) [real number], default: 0.

z-coordinate of x-axis.

y-Axis (y_axis) [struct].

Coordinates of a point on the positive y-axis of the coordinatesystem.

x (x) [real number], default: 0.

x-coordinate of y-axis.

y (y) [real number], default: 1.

y-coordinate of y-axis.

z (z) [real number], default: 0.

z-coordinate of y-axis.

Base (base) [name of another object], default: blank.

Reference to another object of the class Coordinate System.If Base is specified, the coordinate system is defined relativeto that coordinate system. If Base is omitted, the coordinatesystem is defined relative to the global coordinate system.

Horn Interior 153

HORN INTERIOR

Purpose

This group contains classes which define various types of horn sec-tions used in the definition of the horn interior geometry. The follow-ing Horn Interior classes are available:

Smooth Walled Section

Single Depth Corrugated Section

Dual Depth Corrugated Section

Waveguide Step

Waveguide Section

Axial Corrugations

Single Depth Section with Mode Converter

Corrugation List

Links

Classes→Horn Geometry→Horn Interior

154 Smooth Walled Section

SMOOTH WALLED SECTION (smooth_walled_section)

Purpose

The class Smooth Walled Section defines a horn section without cor-rugations. The geometry of the section is defined by the referencedhorn section profile.

Links

Classes→Horn Geometry→Horn Interior→Smooth Walled Section

Syntax

<object name> smooth_walled_section(

profile : ref(<n>),conductivity : <rc>,dielectric_constant : <r>

)

where


<r> = real number

<rc>= real number with conductivity unit, S/m

Attributes

Profile (profile) [name of another object].

Reference to a Horn Profile object defining the profile of thesmooth-walled section, i.e. the smooth inner shape of the hornsection.

Conductivity (conductivity) [real number with conductivity unit, S/m].

The conductivity of the metal forming the sides of the hornsection. The conductivity is used to calculate the ohmic lossin the horn.

Dielectric Constant (dielectric_constant) [real number], default: 1.

The relative dielectric constant of a homogeneous, lossless di-electric material filling the entire horn section. The dielectricconstant must be larger than or equal to 1.

Single Depth Corrugated Section 155

SINGLE DEPTH CORRUGATED SECTION (single_depth_corrugated_section)

Purpose

The class Single Depth Corrugated Section defines a horn sectionwith a simple corrugation layout used for single-band horns. Thegeometry of the section is defined by the referenced horn sectionprofile.

Links

Classes→Horn Geometry→Horn Interior→Single Depth Corrugated Sec-tion

Syntax

<object name> single_depth_corrugated_section(

profile : ref(<n>),width_to_pitch_ratio : <r>,number_of_slots : ,start_depth : <rl>,end_depth : <rl>,conductivity : <rc>,dielectric_constant : <r>

)

where

 = integer


<r> = real number



Attributes


Reference to a Horn Profile object which defines the profile ofthe horn interior geometry.

Width-to-Pitch Ratio (width_to_pitch_ratio) [real number].

156 Single Depth Corrugated Section

The ratio of the slot width relative to the pitch. The ratio mustbe in the closed interval from 0 to 1. The pitch is the sum ofthe slot width and the tooth width.

Number of Slots (number_of_slots) [integer].

The total number of slots throughout the horn section. Thenumber must be positive. The number of corrugations equalsthe number of slots.

Start Depth (start_depth) [real number with unit of length].

The depth of the first slot. The depth must be larger than orequal to zero.

End Depth (end_depth) [real number with unit of length].

The depth of the last slot. The depth must be larger than orequal to zero.





Remarks

The corrugations have a fixed pitch as well as fixed width-to-pitch ra-tio. The corrugation depth varies linearly between the user-specifiedstart- and end-depth. If a more complicated corrugation layout is re-quired, the Single Depth Corrugated Section object can be convertedinto a Corrugation List by right-clicking on the section and selecting"Convert to corrugation list".

Dual Depth Corrugated Section 157

DUAL DEPTH CORRUGATED SECTION (dual_depth_corrugated_section)

Purpose

The class Dual Depth Corrugated Section defines a horn section witha simple corrugation layout used for dual-band horns. The geometryof the section is defined by the referenced horn section profile.

Links

Classes→Horn Geometry→Horn Interior→Dual Depth Corrugated Sec-tion

Syntax

<object name> dual_depth_corrugated_section(

profile : ref(<n>),width_to_pitch_ratio : <r>,number_of_slot_pairs : ,slot_sequence : <si>,deep_start_depth : <rl>,deep_end_depth : <rl>,shallow_start_depth : <rl>,shallow_end_depth : <rl>,conductivity : <rc>,dielectric_constant : <r>

)

where

 = integer


<r> = real number



<si>= item from a list of character strings

Attributes



158 Dual Depth Corrugated Section


The ratio of the slot width relative to the pitch. The ratio mustbe in the closed interval from 0 to 1. The pitch is the sum ofthe slot width and the tooth width. The ratio is for a singlecorrugation, and not for a corrugation pair (or slot pair).

Number of Slot Pairs (number_of_slot_pairs) [integer].

The total number of slot-pairs (deep and shallow) throughoutthe horn section. The number must be positive. The numberof corrugations equals twice the number of slot-pairs.

Slot Sequence (slot_sequence) [item from a list of character strings],default: shallow_deep.

Determines if the first slot is a shallow or a deep slot.

shallow_deep

The first slot is shallow.

deep_shallow

The first slot is deep.

Deep Start Depth (deep_start_depth) [real number with unit of length].

The depth of the first deep slot. The depth must be larger thanor equal to zero.

Deep End Depth (deep_end_depth) [real number with unit of length].

The depth of the last deep slot. The depth must be larger thanor equal to zero.

Shallow Start Depth (shallow_start_depth) [real number with unit oflength].

The depth of the first shallow slot. The depth must be largerthan or equal to zero.

Shallow End Depth (shallow_end_depth) [real number with unit oflength].

The depth of the last shallow slot. The depth must be largerthan or equal to zero.


Dual Depth Corrugated Section 159




Remarks

The corrugations have a fixed pitch as well as fixed width-to-pitchratio. The corrugations alternate between a deep and a shallow cor-rugation. The corrugation depth varies linearly between the user-specified start- and end-depth. Independent start- and end-valuesare given for the deep and the shallow corrugations. If a more com-plicated corrugation layout is required, the dual depth section canbe converted into a Corrugation List by right-clicking on the sectionand selecting "Convert to corrugation list".

160 Waveguide Step

WAVEGUIDE STEP (section_step)

Purpose

The class Waveguide Step defines a stepped, circularly symmetrichorn section, i.e. two joined waveguide sections with different radii.

Links

Classes→Horn Geometry→Horn Interior→Waveguide Step

Syntax

<object name> section_step(

input_radius : <rl>,output_radius : <rl>,l1 : <rl>,l2 : <rl>,conductivity : <rc>,dielectric_constant : <r>

)

where

<r> = real number



Attributes

Input Radius (input_radius) [real number with unit of length].

Radius of the circular input waveguide. The radius must be apositive value.

Output Radius (output_radius) [real number with unit of length].

Radius of the circular output waveguide. The radius must be apositive value.

L1 (l1) [real number with unit of length], default: 0.

Length of the circular input waveguide. The length must be apositive value.

Waveguide Step 161

L2 (l2) [real number with unit of length], default: 0.

Length of the circular output waveguide. The length must bea positive value.





162 Waveguide Section

WAVEGUIDE SECTION (circular_waveguide_section)

Purpose

The class Waveguide Section defines a circular waveguide.

Links

Classes→Horn Geometry→Horn Interior→Waveguide Section

Syntax

<object name> circular_waveguide_section(

radius : <rl>,length : <rl>,conductivity : <rc>,dielectric_constant : <r>

)

where

<r> = real number



Attributes

Radius (radius) [real number with unit of length].

The radius of the circular waveguide section. The radius mustbe a positive value.

Length (length) [real number with unit of length].

The length of the circular waveguide section. The length mustbe a positive value.




Waveguide Section 163


164 Axial Corrugations

AXIAL CORRUGATIONS (simple_axial_corrugated_section)

Purpose

The class Axial Corrugations defines a horn section with axial corru-gations.

Links

Classes→Horn Geometry→Horn Interior→Axial Corrugations

Syntax

<object name> simple_axial_corrugated_section(

input_radius : <rl>,slot_width : <rl>,slot_depth : <rl>,ridge_thickness : <rl>,axial_distance : <rl>,number_of_axial_slots : ,conductivity : <rc>,dielectric_constant : <r>

)

where

 = integer

<r> = real number



Attributes


The input radius of the tangential profile. The radius must bea positive value.

Slot Width (slot_width) [real number with unit of length].

The width of the slots forming the axial corrugations. The widthmust be a positive number.

Slot Depth (slot_depth) [real number with unit of length], default: 0.

Axial Corrugations 165

The depth of the slots forming the axial corrugations. Thedepth must be larger than or equal to zero.

Ridge Thickness (ridge_thickness) [real number with unit of length],default: 0.

The thickness of the ridges separating the axial corrugations.The ridge thickness must be a positive number.

Axial Distance (axial_distance) [real number with unit of length].

The distance measured along the horn axis between neigh-bouring corrugations. The distance must be a positive number.

Number of Axial Slots (number_of_axial_slots) [integer].

The number of axial corrugations (or slots). The number mustbe positive.





166 Single Depth Section with Mode Converter

SINGLE DEPTH SECTION WITH MODE CONVERTER(single_depth_mode_converter)

Purpose

The class Single Depth Section with Mode Converter defines a corru-gated horn section with a mode converter included. The Horn Wizardgenerates a horn of this class, as the horn section is completely de-fined in terms of a few input parameters only.

Links

Classes→Horn Geometry→Horn Interior→Single Depth Section withMode Converter

Syntax

<object name> single_depth_mode_converter(

profile : ref(<n>),width_to_pitch_ratio : <r>,number_of_slots : ,number_of_slots_mode_converter:

,

design_frequency : <rf>,output_frequency : <rf>,mode_converter_type : <si>,percentage_factor : <r>,min_ratio : <r>,max_ratio : <r>,conductivity : <rc>,dielectric_constant : <r>

)

where

 = integer


<r> = real number


<rf>= real number with unit of frequency


Single Depth Section with Mode Converter 167

Attributes




The ratio of the slot width relative to the pitch. The ratio mustbe in the closed interval from 0 to 1. The pitch is the sum ofthe slot width and the tooth width.

Number of Slots (number_of_slots) [integer].

The total number of slots throughout the horn section. Thenumber must be positive. The number of corrugations equalsthe number of slots.

Number of Slots in the Mode Converter (number_of_slots_mode_converter)[integer].

The total number of slots inside the mode converter part ofthe horn section. The number must be positive or zero. Thenumber of corrugations inside the mode converter equals thenumber of slots inside the mode converter.

Design Frequency (design_frequency) [real number with unit of fre-quency].

Determines the slot depth at the input of the horn section

Output Frequency (output_frequency) [real number with unit of fre-quency].

Determines the slot depth at the aperture of the horn

Mode Converter Type (mode_converter_type) [item from a list ofcharacter strings], default: variable_depth_slots.

Select the corrugation layout for the mode converter section.There are three types of mode converters to choose from. Seethe Remarks section for further details.


variable_depth_slots

The corrugations in the variable-depth-slot mode con-verter have fixed pitch as well as fixed width-to-pitchratio. The depth of the corrugations varies.

ring_loaded_slots

The corrugations in the ring-loaded-slot mode converterhave fixed pitch and a fixed width-to-pitch ratio, whenthe width is measured at the bottom of the corrugation.The opening width of the ring-loaded slot varies.

variable_width_to_pitch_slot

The corrugations in the variable-pitch-to-width modeconverter have fixed pitch and a varying width-to-pitchratio. The depth of the corrugations also varies.

Percentage Factor (percentage_factor) [real number], default: 45.

The ratio between the input and the output slot depth of themode converter section (matches the horn slot depth at thehorn input). Only values between 40 and 50% are valid. Theattribute is not used for ring-loaded-slots. See the Remarkssection for further details.

Min Ratio (min_ratio) [real number], default: 0.15.

The ratio between the input width-to-pitch and the nominalwidth-to-pitch. Only used for variable-width-to-pitch slots.

Max Ratio (max_ratio) [real number], default: 1.

The ratio between the output width-to-pitch and nominal width-to-pitch. Only used for variable-width-to-pitch slots.






Remarks

The Single Depth Mode Converter is a corrugated horn section witha mode converter included. The horn section geometry is defined bythe horn section profile and the corrugation layout.

The corrugation layout is based on the design formula’s presentedin the paper by Christophe Granet and Graeme L. James, "Design ofCorrugated Horns: A Primer", IEEE Antennas and Propagation Maga-zine, vol. 47, No. 2, April 2005, pp. 76-84, (with correction in vol.47,August 2005, p.98). The design formulas are summarised below. Ifa more complicated corrugation layout is required, the section withmode converter can be converted into a Corrugation List by right-clicking on the section and selecting "Convert to corrugation list".

The Single Depth Mode Converter is a corrugated section with N cor-rugations, where the NMC first corrugations form a mode converter.

According to Granet and James, there are basically three types ofmode converters to choose from. The choice of mode convertershould be made based on the required bandwidth:

• Variable-depth-slot mode converter: Used if fmax < 1.8fmin.

• Variable-pitch-to-width mode converter: Used if fmax < 2.05fmin.

• Ring-loaded-slot mode converter: Used if fmax < 2.4fmin.

The three mode converter types are described separately below. Thegeometry of the horn section outside the mode converter is indepen-dent of the choice of mode converter type, as also described below:

General

The horn section is defined by the horn section profile and the cor-rugation layout. The horn section input radius is denoted, ai, andthe output radius is denoted, ao. The design is based on two fre-quencies, namely the design frequency, fc (wavenumber kc), and theoutput frequency, fo (wavenumber ko).

In order to obtain a more compact notation, we introduce the func-tion, F , defined by:

F (k, a) =λ

4exp

[1

2.114(ka)1.134

], λ =

2π

k

Corrugation layout outside the mode converter


The corrugations in the horn section outside the mode converterhave fixed pitch as well as fixed width-to-pitch ratio. The corrugationdepth varies according to the following equation:

dj = F (kc, aj)−j −NMC − 1

N −NMC − 1[F (kc, ao)− F (ko, ao)]

In this expression, 1) the integer j is the corrugation number (runningfrom NMC + 1 to N), 2) aj is the radius of the selected horn profileat corrugation number j, 3) ao is the section output radius, and 4)kc and ko are the wavenumbers for the design and output frequency,respectively.

Variable-depth-slot mode converter

The corrugations in the variable-depth-slot mode converter have fixedpitch as well as fixed width-to-pitch ratio. The depth of the corruga-tions varies according to the following equations:

dj = σλc −j − 1

NMC

[σλc − F (kc, aj)]

In this expression, 1) the integer j is the corrugation number (run-ning from 1 to NMC), 2) aj is the radius of the selected horn profileat corrugation number j, 3) kc is the wavenumber for the design fre-quency, and 4) σ is the percentage factor for the first slot-depth ofthe mode-converter. According to the reference paper, σ should bechosen between 40% (0.4) and 50% (0.5).

Ring-loaded-slot mode converter

The corrugations in the ring-loaded-slot mode converter have fixedpitch and a fixed width-to-pitch ratio (with the width being the widthat the bottom of the corrugations). The opening width of the ring-loaded slot varies according to the following equation:

dj = F (kc, aj)

Here, j is the corrugation number (running from 1 to NMC), p is thepitch, and d is the width-to-pitch ratio. Thus, the opening width of thecorrugation varies from one tenth of the pitch to the nominal widthof the corrugations. The depth of the corrugations varies accordingto the following equations:

bj =

[0.1− j − 1

NMC

(0.1− δ)]p


and the height of the ring-load varies according to:

hj =2

3dj

Variable-pitch-to-width mode converter

The corrugations in the variable-pitch-to-width mode converter havefixed pitch and a varying width-to-pitch ratio. The depth of the cor-rugations varies according to the following equations:

dj =

[σλc

1.15− j − 1

NMC − 1

(σλc

1.15− λc

4

)]F (kc, aj)

As above, σ is the percentage factor for the first slot-depth of themode-converter. According the reference paper, σ should be chosenbetween 40% (0.4) and 50% (0.5). The width of the corrugationsvaries according to:

wj =

[∆min −

j − 1

NMC − 1(∆min −∆max)

]w

Here, ∆min (also denoted min-ratio) is the ratio between the mini-mum and nominal width-to-pitch ratio. Similarly, ∆max (also denotedmax-ratio) is the ratio between the maximum and nominal width-to-pitch ratio. The min-ratio should be between 0.125 and 1, and themax-ratio should be approximately 1.

172 Corrugation List

CORRUGATION LIST (corrugation_list)

Purpose

Objects of the class Corrugation List define a horn section in termsof a sequence of so-called elementary waveguide sections.

Links

Classes→Horn Geometry→Horn Interior→Corrugation List

Syntax

<object name> corrugation_list(

length_unit : <si>,corrugations : table(<r> <r> <r> <r> <r>

<r> <r> <r> <r> . . .),conductivity : <rc>

)

where

<r> = real number



Attributes

Length Unit (length_unit) [item from a list of character strings], de-fault: m.

The common length unit of all data specifying dimensions inthe corrugations attribute.

Corrugations (corrugations) [table (1,9)].

Data sets specifying the interior geometry of the horn section.Each set of data defines an elementary module in CHAMP andis given by 9 real numbers, 6 of which define the geometryand 3 of which define possible dielectric materials filling thehorn section.

a1 (a1) [real number].

The radius of the input waveguide region of the elemen-tary module. The radius must be a positive number.

Corrugation List 173

a1s (a1s) [real number].

The inner radius of the stub region of the elementary mod-ule. If the length, d, of the stub region is larger than zero,then the radius must be a positive number in the intervaldefined by a1 and a2.

a2 (a2) [real number].

The radius of the output waveguide region of the elemen-tary module. The radius must be a positive number.

d (d) [real number].

The length of the stub region of the elementary module.The length must be greater than or equal to zero.

del1 (del1) [real number].

The length of the input waveguide region of the elemen-tary module. The length must be greater than or equal tozero.

del2 (del2) [real number].

The length of the output waveguide region of the elemen-tary module. The length must be greater than or equal tozero.

eps1 (eps1) [real number].

The relative dielectric constant of a homogeneous, losslessdielectric material filling the input waveguide region of theelementary module. The dielectric constant must be largerthan or equal to 1.


The relative dielectric constant of a homogeneous, losslessdielectric material filling the output waveguide region ofthe elementary module. The dielectric constant must belarger than or equal to 1.


The relative dielectric constant of a homogeneous, losslessdielectric material filling the stub region of the elementarymodule. If the length, d, of the stub region is larger thanzero, then the dielectric constant must be larger than orequal to 1.


174 Corrugation List


Remarks

A Corrugation List is way to describe a very general set of corruga-tions or steps of a waveguide section.

The data needed for the table of the attribute Corrugations arevisualized in the following two figures. The 6 first table entries aregeometrical measures as illustrated in Figure 1. Note that two ele-mentary corrugations may be defined, the regular and the inverted,according to which of the radii a1 or a2 is the smallest.

Figure 1 The geometry of an elementary waveguide sectionwith the first 6 (geometrical) table entries forattribute Corrugations shown. Two types exist ofthe module: a regular for which a1 < a2 and aninverted with a1 > a2.

Corrugation List 175

The next 3 table entries specifies the relative dielectric constants forthe 3 regions indicated by the different colour codes in Figure 2.

Figure 2 Illustration of the regions which may have differentrelative dielectric constant (table entries ofCorrugations), eps1, eps2 and eps3.

An example of a Corrugation List may be generated by the GUI froma simple Single Depth Corrugated Section. This may be convertedto a Corrugation List by a right click on the Single Depth CorrugatedSection in the Geometry view of the GUI. It is noted that each corru-gation then becomes two entries in the Corrugation List.

176 Horn Profile

HORN PROFILE

Purpose

This group contains classes which define various horn profiles usedin the definition of the geometry of a horn section. The followingHorn Profile classes are available:

Linear Profile

Sinusoidal Profile

Asymmetric Sine-Squared Profile

Tangential Profile

Simple Polynomial Profile

Exponential Profile

Hyperbolic Profile

Polynomial Profile

Spline Profile

Links

Classes→Horn Geometry→Horn Profile

Linear Profile 177

LINEAR PROFILE (linear_profile)

Purpose

The class Linear Profile defines a horn profile which varies purelylinearly between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Linear Profile

Syntax

<object name> linear_profile(

input_radius : <rl>,output_radius : <rl>,length : <rl>

)

where


Attributes


The input radius of the linear profile. The radius must be apositive value.


The output radius of the linear profile. The radius must be apositive value.


The length of the linear profile and thus the length of the hornsection. The length must be a positive value.

Remarks

The horn profile has a purely linear variation between the input ra-dius, ai, and the output radius, ao, described by

a(z) = ai + (ao − ai)z

L

178 Linear Profile

where the parameter L is the length of the horn section, and wherez is a local coordinate along the horn axis, with z = 0 at the inputand z = L at the output.

Figure 1 Example of a smooth horn section with a linearprofile. The input parameters are ai = 15 mm, ao =40 mm, and L = 60 mm.

Sinusoidal Profile 179

SINUSOIDAL PROFILE (sinusoidal_profile)

Purpose

The class Sinusoidal Profile defines a horn profile which has a sinu-soidal variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Sinusoidal Profile

Syntax

<object name> sinusoidal_profile(

input_radius : <rl>,output_radius : <rl>,length : <rl>,exponent : <r>,weight : <r>

)

where

<r> = real number


Attributes


The input radius of the sinusoidal profile. The radius must bea positive value.


The output radius of the sinusoidal profile. The radius must bea positive value.


The length of the sinusoidal profile and thus the length of thehorn section. The length must be a positive value.

Exponent (exponent) [real number], default: 2.

A real-valued exponent in the range from 0.5 to 5.

180 Sinusoidal Profile

Weight (weight) [real number], default: 1.

The weighting between the linear, weight=0, and the sinu-soidal, weight=1, variation

Remarks

The horn profile has a sinusoidal variation between the input radius,ai, and the output radius, ao, described by

a(z) = ai + (ao − ai)[(1− A)

z

L+ A sinρ

(π2

z

L

)]where the parameter L is the length of the horn section, and wherez is a local coordinate along the horn axis, with z = 0 at the inputand z = L at the output. Further, the parameter A is the weightingbetween the linear, A = 0, and the sinusoidal, A = 1, variation, andthe parameter ρ is a real-valued exponent in the range from 0.5 to5.

Figure 1 Example of a smooth horn section with a sinusoidalprofile. The input parameters are ai = 15 mm, ao =40 mm, L = 60 mm, A = 1, and ρ = 2.

Asymmetric Sine-Squared Profile 181

ASYMMETRIC SINE-SQUARED PROFILE (asymmetric_sine_squared_profile)

Purpose

The class Asymmetric Sine-Squared Profile defines a horn profilewhich has a so-called "asymmetric sine-squared" variation betweenthe input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Asymmetric Sine-Squared Pro-file

Syntax

<object name> asymmetric_sine_squared_profile(

input_radius : <rl>,output_radius : <rl>,length : <rl>,length_ratio : <r>

)

where

<r> = real number


Attributes


The input radius of the asymmetric-sine-squared profile. Theradius must be a positive value.


The output radius of the asymmetric-sine-squared profile. Theradius must be a positive value.


The length of the asymmetric-sine-squared profile and thus thelength of the horn section. The length must be a positive value.

Length Ratio (length_ratio) [real number], default: 1.

182 Asymmetric Sine-Squared Profile

The ratio between the length of the second interval and thelength of the first interval.

Remarks

The horn profile has a variation between the input radius, ai, andthe output radius, ao, described with different expressions in twointervals.

The first interval is for z between zero and L1:

a(z) = ai + (ao − ai)2L1

Lsin2

(π

4

z

L1

)The second interval is for z between L1 and L:

a(z) = ai + (ao − ai)2L1

L

[L2

L1

sin2

(π

4

z + L2 − L1

L2

)+L1 − L2

2L1

]In these expressions, the parameter L is the length of the horn sec-tion, and z is a local coordinate along the horn axis, with z = 0 atthe input and z = L at the output. Further, the parameters L1 andL2 are the lengths of the two intervals (with L1 + L2 = L).

Asymmetric Sine-Squared Profile 183

Figure 1 Example of a smooth horn section with anAsymmetric Sine-Squared Profile profile. The inputparameters are ai = 15 mm, ao = 40 mm, L = 60mm, A = 1, and the Length Ratio = L2/L1 = 1.

184 Tangential Profile

TANGENTIAL PROFILE (tangential_profile)

Purpose

The class Tangential Profile defines a horn profile which has a tan-gential variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Tangential Profile

Syntax

<object name> tangential_profile(


)

where

<r> = real number


Attributes


The input radius of the tangential profile. The radius must bea positive value.


The output radius of the tangential profile. The radius must bea positive value.


The length of the tangential profile and thus the length of thehorn section. The length must be a positive value.



Tangential Profile 185


The weighting between the linear, weight=0, and the tangen-tial, weight=1, variation.

Remarks

The horn profile has a tangential variation between the input radius,ai, and the output radius, ao, described by

a(z) = ai + (ao − ai)[(1− A)

z

L+ A tanρ

(π4

z

L

)]where the parameter L is the length of the horn section, and wherez is a local coordinate along the horn axis, with z = 0 at the inputand z = L at the output. Further, the parameter A is the weightingbetween the linear, A = 0, and the tangential, A = 1, variation, andthe parameter ρ is a real-valued exponent in the range from 0.5 to5.

Figure 1 Example of a smooth horn section with a tangentialprofile. The input parameters are ai = 15 mm, ao =40 mm, L = 60 mm, A = 1, and ρ = 2.

186 Simple Polynomial Profile

SIMPLE POLYNOMIAL PROFILE (simple_polynomial_profile)

Purpose

The class Simple Polynomial Profile defines a horn profile which has apolynomial variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Simple Polynomial Profile

Syntax

<object name> simple_polynomial_profile(


)

where

<r> = real number


Attributes


The input radius of the simple-polynomial profile. The radiusmust be a positive value.


The output radius of the simple-polynomial profile. The radiusmust be a positive value.


The length of the simple-polynomial profile and thus the lengthof the horn section. The length must be a positive value.



Simple Polynomial Profile 187


The weighting between the linear, weight=0, and the polyno-mial, weight=1, variation.

Remarks

The horn profile has a polynomial variation between the input radius,ai, and the output radius, ao, described by

a(z) = ai + (ao − ai)[(1− A)

z

L+ A

( zL

)ρ]where the parameter L is the length of the horn section, and wherez is a local coordinate along the horn axis, with z = 0 at the inputand z = L at the output. Further, the parameter A is the weightingbetween the linear, A = 0, and the polynomial, A = 1, variation, andthe parameter ρ is a real-valued exponent in the range from 0.5 to5.

Figure 1 Example of a smooth horn section with asimple-polynomial profile. The input parameters areai = 15 mm, ao = 40 mm, L = 60 mm, A = 1, and ρ= 2.

188 Exponential Profile

EXPONENTIAL PROFILE (exponential_profile)

Purpose

The class Exponential Profile defines a horn profile which has anexponential variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Exponential Profile

Syntax

<object name> exponential_profile(


)

where


Attributes


The input radius of the exponential profile. The radius must bea positive value.


The output radius of the exponential profile. The radius mustbe a positive value.


The length of the exponential profile and thus the length of thehorn section. The length must be a positive value.

Remarks

The horn profile has an exponential variation between the input ra-dius, ai, and the output radius, ao, described by

a(z) = ai exp

[ln

(aoai

)z

L

]

Exponential Profile 189


Figure 1 Example of a smooth horn section with anexponential profile. The input parameters are ai = 15mm, ao = 40 mm, and L = 60 mm.

190 Hyperbolic Profile

HYPERBOLIC PROFILE (hyperbolic_profile)

Purpose

The class Hyperbolic Profile defines a horn profile which has a hyper-bolic variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Hyperbolic Profile

Syntax

<object name> hyperbolic_profile(


)

where


Attributes


The input radius of the hyberbolic profile. The radius must bea positive value.


The output radius of the hyberbolic profile. The radius mustbe a positive value.


The length of the hyperbolic profile and thus the length of thehorn section. The length must be a positive value.

Remarks

The horn profile has a hyperbolic variation between the input radius,ai, and the output radius, ao, described by

a(z) =

√a2i + (a2o − a2i )

z2

L2

Hyperbolic Profile 191


Figure 1 Example of a smooth horn section with a hyperbolicprofile. The input parameters are ai = 15 mm, ao =40 mm, and L = 60 mm.

192 Polynomial Profile

POLYNOMIAL PROFILE (polynomial_profile)

Purpose

The class Polynomial Profile defines a horn profile which has a poly-nomial variation between the input radius and the output radius.

Links

Classes→Horn Geometry→Horn Profile→Polynomial Profile

Syntax

<object name> polynomial_profile(

input_radius : <rl>,output_radius : <rl>,length : <rl>,exponent : <r>

)

where

<r> = real number


Attributes


The input radius of the polynomial profile. The radius must bea positive value.


The output radius of the polynomial profile. The radius mustbe a positive value.


The length of the polynomial profile and thus the length of thehorn section. The length must be a positive value.



Polynomial Profile 193

Remarks

The horn profile has a polynomial variation between the input radius,ai, and the output radius, ao, described by

a(z) = ai + (ao − ai)(ρ+ 1)

[1− ρz

(ρ+ 1)L

]( zL

)ρwhere the parameter L is the length of the horn section, and wherez is a local coordinate along the horn axis, with z = 0 at the inputand z = L at the output. Further, the parameter ρ is a real-valuedexponent in the range from 0.5 to 5.

Figure 1 Example of a smooth horn section with a polynomialprofile. The input parameters are ai = 15 mm, ao =40 mm, L = 60 mm, and ρ = 2.

194 Spline Profile

SPLINE PROFILE (spline_profile)

Purpose

The class Spline Profile defines a horn profile in terms of cubic splinefunctions passing through a number of data points.

Links

Classes→Horn Geometry→Horn Profile→Spline Profile

Syntax

<object name> spline_profile(

z_unit : <si>,rho_unit : <si>,data_points : table(<r> <r> . . .)

)

where

<r> = real number


Attributes

z-Unit (z_unit) [item from a list of character strings], default: m.

The length unit to be applied for the z-coordinates in the spec-ification of the Nodes.

Not available in the GUI where the default length unit is spec-ified under Preferences... in the File menu.

rho-Unit (rho_unit) [item from a list of character strings], default: m.

The length unit to be applied for the ρ-coordinates in the spec-ification of the Nodes.


Nodes (data_points) [table (*,2)].

A table of the z- and rho-coordinates for each of the splinecontrol points.

Spline Profile 195

Table specifying the coordinates of the points (the nodes) defin-ing the spline curve for the reflector, node by node for increas-ing ρ-values. The table must define at least two nodes. Theunit of the coordinates are specified under Preferences... inthe File menu.

z-Coordinate (z-Coordinate) [real number].

The z-coordinate of the data point.

rho-Coordinate (rho-Coordinate) [real number].

The ρ-coordinate of the data point.

Command Types

The re-calculation of the spline profile is activated by the command:

Reshape Profile

Remarks

The horn profile is given as a spline function, f = f(z) passing thougha number of user-defined data points.

Assume that the user has specified Np data points, (zi, ρi) , i =1, 2, ..., Np, with z1 < z2 < ... < zNp. The points define Np − 1 intervalsalong the z-axis. In each interval, the profile is a third-order polyno-mial. The polynomials are constrained such that the profile functionf(z) passes through the data points, and has continuous first andsecond order derivatives with respect to z at the data points. At thetwo end-points, z1 and zNp, there are no special restrictions on thefirst and second order derivatives. However, there are still too manyconstraints defined, and the same polynomial is therefore used inthe two first and in the two last intervals.

A minimum of 4 data-points must be defined.

By a right-click on the spline profile in the GUI it is possible to changethe number of points which define the profile. New points are theninserted upon the actual profile, see the command Reshape Profilefor more details. The more points, the more details may be modelled.

During an optimization procedure it is an advantage to increase thenumber of control points gradually in order to start with a smoothcurve and then add more and more details.

196 Spline Profile

Figure 1 Example of a smooth horn section with a splineprofile. The input parameters are the coordinates of10 data points, with the first and last points having ρ= 15 mm, and ρ = 40 mm, respectively.

Exterior Geometry 197

EXTERIOR GEOMETRY

Purpose

This group contains classes used in the definition of the exterior ge-ometry: The following Exterior Geometry classes are available:

Horn Exterior

Reflectors

Support Structures

BOR Mesh

Links

Classes→Horn Geometry→Exterior Geometry

198 Horn Exterior

HORN EXTERIOR (circular_symmetric_horn_exterior)

Purpose

By objects of the class Horn Exterior it is possible to describe whattypically is the exterior surface of a circular symmetric horn. A piece-wise linear curve, defined in a plane containing the axis of symmetry,is rotated around this axis whereby the exterior surface is generated.

A more general scatterer may be specified by an object of class BORMesh.

Links

Classes→Horn Geometry→Exterior Geometry→Horn Exterior

Syntax

<object name> circular_symmetric_horn_exterior(

snap_to_aperture : <si>,length_unit : <si>,coor_order : <si>,nodes : table(<r> <r> . . .),z_offset : <rl>

)

where

<r> = real number



Attributes

Snap to Aperture (snap_to_aperture) [item from a list of characterstrings], default: on.

Selects if the program should automatically connect the firstpoint of the exterior geometry to the last point of the horninterior defining the horn aperture.

on

The two points are automatically connected.

Horn Exterior 199

off

The program does not automatically connect the twopoints. In this case, the first point of the horn exteriormust equal the last point of the horn interior.


The length unit to be applied for the coordinates in the speci-fication of the Nodes.


Coordinate Order (coor_order) [item from a list of character strings],default: z_rho.

Specification of the order of the coordinates z and ρ in theattribute Nodes.

Not available in the GUI where the first coordinate in the at-tribute Nodes is z and the second is ρ.

z_rho

z is the first coordinate and ρ is the second coordinatein the specification of the Nodes.

rho_z

ρ is the first coordinate and z is the second coordinatein the specification of the Nodes.

Nodes (nodes) [table (*,2)].

Table with 2 columns specifying the coordinates of the points(the nodes) defining the piecewise linear geometry of the hornexterior, node by node. The unit of the coordinates are deter-mined by the attribute Length Unit.

c1 (c1) [real number].

First coordinate for the node, according to the attributeCoordinate Order.


Second coordinate for the node, according to the attributeCoordinate Order.

z-Offset (z_offset) [real number with unit of length], default: 0.

200 Horn Exterior

This specifies a constant value, which is added to the z-coordinatesof the defined Nodes whereby the exterior is displaced z-Offset along the z-axis (the axis of symmetry).

Remarks

Objects of the class Horn Exterior are used to define an exteriorsurface of a horn. The surface shall be described by a curve in aplane containing the axis of rotation. The surface is generated whenthis curve is rotated around the axis.

The curve is specified by a set of nodes which are connected bylinear segments in the order as the nodes are specified. The surfaceis not allowed to intersect itself unless at a node.

The scattering of the exterior is determined by Method of Moments,MoM.

In the GUI In the GUI the exterior shall be created through theCreate menu under the Geometry tab and the nodes can thenbe inserted by mouse left-clicks, node by node. When at least onenode is inserted, additional nodes may be inserted in the table inthe Property Editor by a right-click in the table for the Horn Exterior. The coordinates of the nodes may as well be edited in this tableby typing the desired values. Nodes may be deleted by right-clickingthe node in the table.

In the GUI it is possible to split an exterior at a node by a right-clickon this node. The node will then be the first node in the one part ofthe exterior and duplicated node will be the first node in the otherpart of the exterior.

One node of the exterior, marked by a left-click, may be linked toanother node by right-clicking on this. Hereby the latter point will beforced to coincide with the former.

Example

The following Figure 1 shows a smooth walled horn with an exterioradded.

Currents will be excited upon the exterior of the horn. These currentswill usually radiate far from the axis. To reduce these currents, achoke has here been added as part of the exterior.

Horn Exterior 201

Figure 1 A smooth conical horn (blue line) with a Horn Exterior(black line) added.

202 Reflectors

REFLECTORS

Purpose

This group is used to define circular symmetric reflectors. The fol-lowing Reflectors classes are available:

Spline Reflector

Tabulated Reflector

Piecewise Linear Reflector

Links

Classes→Horn Geometry→Exterior Geometry→Reflectors

Spline Reflector 203

SPLINE REFLECTOR (spline_circ_sym_reflector)

Purpose

The class Spline Reflector defines a rotational symmetric reflector bya reflector profile given as cubic spline functions passing through anumber of data points.

Links

Classes→Horn Geometry→Exterior Geometry→Reflectors→Spline Re-flector

Syntax

<object name> spline_circ_sym_reflector(

z_offset : <rl>,length_unit : <si>,coor_order : <si>,nodes : table(<r> <r> . . .)

)

where

<r> = real number



Attributes


This specifies a constant value, which is added to the z-coordinatesof the defined Nodes whereby the exterior is displaced z-Offset along the z-axis (the axis of symmetry).




204 Spline Reflector

Coordinate Order (coor_order) [item from a list of character strings],default: rho_z.


Not available in the GUI where the coordinates in the attributeNodes always is shown in the order (z, ρ).

z_rho


rho_z



Table with 2 columns specifying the coordinates of the points(the nodes) defining the spline curve for the reflector, node bynode for increasing ρ-values. The unit of the coordinates aredetermined by the attribute Length Unit.





Command Types

The re-calculation of the spline profile is activated by the command:

Reshape Reflector

Remarks

The reflector profile is given as a spline function, f = f(ρ) passingthough a number of user-defined data points.

Assume that the user has specified Np data points, (zi, ρi) , i =1, 2, ..., Np, with ρ1 < ρ2 < ... < ρNp. The points define Np − 1 in-tervals along the ρ-axis. In each interval, the profile is given by athird-order polynomial. The polynomials are constrained such that

Spline Reflector 205

the profile function f(ρ) passes through the data points, and hascontinuous first and second order derivatives with respect to ρ at thedata points. At the two end-points, ρ1 and ρNp, there are no spe-cial restrictions on the first and second order derivatives. However,there are still too many constraints defined, and the same polynomialis therefore used in the two first and in the two last intervals.

A minimum of 4 data-points must be defined.

An example on a Spline Reflector is given in Figure 1.

Figure 1 Example of a reflector given as a spline profiledefined by Np = 5 points from ρ = 0 to ρ = 113 mm.The reflector is illuminated by a simple smooth horn.

By a right-click on the spline profile in the GUI it is possible to changethe number of points which define the profile. New points are theninserted to fit the actual profile, see the command Reshape Reflectorfor more details. The more points, the more details may be modelled.

During an optimization procedure it is an advantage to increase thenumber of control points gradually in order to start with a smoothcurve and then add more and more details.

206 Tabulated Reflector

TABULATED REFLECTOR (tabulated_circ_sym_reflector)

Purpose

The class Tabulated Reflector defines a rotationally symmetric re-flector by means of tabulated data for a profile of the surface. Datapoints are given as z-values along a radial surface cut.

Links

Classes→Horn Geometry→Exterior Geometry→Reflectors→TabulatedReflector

Syntax

<object name> tabulated_circ_sym_reflector(

file_name : <f>,r_unit : <si>,z_unit : <si>,r_factor : <r>,z_factor : <r>,n_points : ,tip : <si>,list : <si>,z_offset : <rl>,obsolete_thickness : <rl>

)

where

 = integer

<r> = real number


<f> = file name


Attributes

File Name (file_name) [file name].

The name of the input file containing the data specifying thereflector front side. The format of this file is described in thesection Rotationally Symmetric Surface.

Tabulated Reflector 207

rho-Unit (r_unit) [item from a list of character strings], default: m.

The common unit assumed for file data in the radial direction(orthogonal to the axis of symmetry).

z-Unit (z_unit) [item from a list of character strings], default: m.

The common unit assumed for file data in the axial direction.

rho-Factor (r_factor) [real number], default: 1.

On input, the radial data in the file are scaled by this number.

z-Factor (z_factor) [real number], default: 1.

On input, the axial data in the file are scaled by this number.

Number of Points (n_points) [integer], default: 0.

The data points defining the reflector profile are interpolatedinto a set of equispaced points. If the attribute Number ofPoints is set to the default value of 0 the number of equis-paced points is the same as the number of data points in theoriginal data set. If the attribute is a positive number the dataare interpolated into Number of Points equispaced points.

Tip (tip) [item from a list of character strings], default: defined_in_file.

Specifies if the reflector has a tip at the centre or not, i.e.determines the local geometry on the axis of symmetry, ρ = 0.The setting may be defined in the file:

defined_in_file

The tip is controlled by the parameter KTIP in the datafile.

off

The reflector does not have a tip (independently of thesetting of KTIP in the data file).

on

The reflector has a tip (independently of the setting ofKTIP in the data file).

List (list) [item from a list of character strings], default: off.

Specifies if the subreflector data should be listed to the stan-dard output file.

208 Tabulated Reflector

off

The data should not be listed.

on

The data should be listed.


Defines a displacement of the subreflector along the z-axis, i.e.the axis of symmetry.

Thickness (Obsolete) (obsolete_thickness) [real number with unit oflength], default: 0.

This attribute is obsolete and will be ignored.

Remarks

The surface of the reflector is expressed as a function, z = z(ρ), ofthe radial distance, ρ, from the axis of symmetry.

The file contains n pairs of (z, ρ)-values that define z(ρ):

zi(ρi), i = 1, 2, ..., n, ρi ≥ 0 (1)

At intermediate points, the function is determined by cubic (3rd-order) interpolation in a set of equispaced points. In the end in-tervals,

0 ≤ ρ ≤ ρ2 and ρ > ρn−1, (2)

the interpolation is parabolic (2nd-order). This interpolation will usu-ally result in a tip at ρ = 0. If the attribute Tip is set to ’off’, thecubic interpolation will be continued across ρ = 0 applying an addi-tional definition point at ρ = −ρi with

z(−ρi) = z(ρi) (3)

where ρi is the smallest non-zero radial value read from the file.

The file may contain data not equispaced in ρ, in which case theprogram will pre-interpolate the data into a new, equispaced set.The number of points in the new set is determined by the attributeNumber of Points.

Piecewise Linear Reflector 209

PIECEWISE LINEAR REFLECTOR (piecewise_linear_reflector)

Purpose

The class Piecewise Linear Reflector defines a rotational symmetricreflector with a piecewise linear profile.

Links

Classes→Horn Geometry→Exterior Geometry→Reflectors→PiecewiseLinear Reflector

Syntax

<object name> piecewise_linear_reflector(

z_offset : <rl>,length_unit : <si>,coor_order : <si>,nodes : table(<r> <r> . . .),obsolete_grow_thickness : struct(status:<si>, thickness:<rl>)

)

where

<r> = real number



Attributes


Defines a displacement of the reflector along the z-axis, i.e.along the axis of symmetry. Each point on the reflector has az-coordinate defined as the sum of the z-coordinate specifiedin the attribute Nodes and the z-Offset displacement.


The common length-unit for all ρ- and z-values for all the pointsin the attribute Nodes defining the reflector geometry.

Order of Coordinates (coor_order) [item from a list of character strings],default: z_rho.

210 Piecewise Linear Reflector


Not available in the GUI where the coordinates in the attributeNodes always is shown in the order (z, ρ).

z_rho

The points are ordered as (z, ρ)-coordinate pairs, i.e. z1,ρ1, z2, ρ2, ...

rho_z

The points are ordered as (ρ, z)-coordinate pairs, i.e. ρ1,z1, ρ2, z2, ...


A table with the coordinates of the points defining the piece-wise linear geometry of the reflector. Each row in the tablecontains the two coordinates, ρ and z, of a point at the reflec-tor. The input order and the unit of the coordinates are deter-mined by the attributes Order of Coordinates and LengthUnit, respectively.

First Coordinate (First Coordinate) [real number].

The first coordinate of the point on the reflector, accordingto the attribute Order of Coordinates.

Second Coordinate (Second Coordinate) [real number].

The second coordinate of the point on the reflector, ac-cording to the attribute Order of Coordinates.

Grow Thickness (Obsolete) (obsolete_grow_thickness) [struct].

This attribute is obsolete and will be ignored.

Status (status) [item from a list of character strings], default:off.

Selects if the program should automatically add the rearsurface.

offNo rear surface is added.

onA rear surface is added.

Piecewise Linear Reflector 211

Thickness (thickness) [real number with unit of length], default:0.

The thickness of the reflector, i.e. the distance betweenthe identical front and rear surfaces of the reflector. Thethickness must be non-negative.

212 Support Structures

SUPPORT STRUCTURES

Purpose

This group contains classes used in the definition support structures.Only one class is presently available:

Dielectric Support Tube

Links

Classes→Horn Geometry→Exterior Geometry→Support Structures

Dielectric Support Tube 213

DIELECTRIC SUPPORT TUBE (dielectric_support_tube)

Purpose

An objects of class Dielectric Support Tube may specify a dielectrictube, cylindrical or conical, which connects two metallic surfaces,typically a horn and a small reflector which is then supported by thistube.

More complicated dielectric bodies may be modelled as a an objectof class BOR Mesh.

Links

Classes→Horn Geometry→Exterior Geometry→Support Structures→DielectricSupport Tube

Syntax

<object name> dielectric_support_tube(

input_point : struct(rho_i:<rl>, z_i:<rl>),output_point : struct(rho_o:<rl>, z_o:<rl>),wall_thickness : <rl>,conducting_length : struct(outer_length_at_input:<rl>,

outer_length_at_output:<rl>,inner_length_at_output:<rl>,inner_length_at_input:<rl>),

dielectric_constant : <r>,loss_tangent : <r>,z_offset : <rl>

)

where

<r> = real number


Attributes

Input Point (input_point) [struct].

214 Dielectric Support Tube

Specification of the input point of the dielectric support tube(the non-conducting end point with the lowest z-value).

Input Radius (rho_i) [real number with unit of length].

The outer radius of the dielectric tube at input.

Input z (z_i) [real number with unit of length].

The z-value for the input end of the dielectric tube.

Output Point (output_point) [struct].

Specification of the output point of the dielectric support tube(the non-conducting end point with the highest z-value).

Output Radius (rho_o) [real number with unit of length].

The outer radius of the dielectric tube at output.

Output z (z_o) [real number with unit of length].

The z-value for the output end of the dielectric tube.

Wall Thickness (wall_thickness) [real number with unit of length].

The thickness of the dielectric tube (the distance between theouter and the inner tube surfaces measured perpendicular tothe surfaces).

Conducting Length (conducting_length) [struct].

The ends of the tube (in a 2D drawing perpendicular to thecurved surfaces of the tube) are conducting surfaces. Theseconducting surfaces may continue along the inner and outersurfaces of the tube at both ends in agreement with the extentof the conducting structures at the ends of the tube. See theremarks section for details.

Outer Length at Input (outer_length_at_input) [real number withunit of length], default: 0.0.

Conducting length along the outer tube surface at input.

Outer Length at Output (outer_length_at_output) [real numberwith unit of length], default: 0.0.

Conducting length along the outer tube surface at output.

Inner Length at Output (inner_length_at_output) [real numberwith unit of length], default: 0.0.

Conducting length along the inner tube surface at output.


Inner Length at Input (inner_length_at_input) [real number withunit of length], default: 0.0.

Conducting length along the inner tube surface at input.

Dielectric Constant (dielectric_constant) [real number], default: 1.0.

The dielectric constant of the tube material.

Loss Tangent (loss_tangent) [real number], default: 0.0.

The loss tangent for the dielectric tube material.


This specifies a constant value which is added to the z-coordinates.Hereby the tube is displaced z-Offset along the z-axis (theaxis of symmetry).

Remarks

The Dielectric Support Tube may be cylindrical or conical. In bothcases the generatrix of the end surfaces of the tube are perpendicu-lar to the generatrix of the curved surfaces of the tube. The genera-trices are the lines seen in the 2D geometry window, the lines whichgenerate the surfaces of the tube when rotated around the axis ofthe tube (see figure Figure 3 below).

The tube is assumed to have contact with conducting (metallic) struc-tures at both ends. Thus the end surfaces of the tube are conduct-ing. The ends of the tube may further be inserted into the conductingstructures whereby parts of the outer and inner curved tube surfacesshall be considered conducting material. The conducting parts of thecurved surfaces are specified by the members of the attribute structConducting Length.

The tube has two ends denoted the input end and the output endcorresponding to the lowest and the highest, respectively, z-value ofthe free (i.e. non-conducting) part of the outer surface. The inputend is thus at (zi, ρi) given by

zi = Input Point->Input z andρi = Input Point->Input Radius,

and the output end is at (zo, ρo) given by

zo = Output Point->Output z andρo = Output Point->Output Radius.


Still on the outer surface, the conducting part of the tube at the inputend has the length loi,

loi = Conducting Length->Outer Length at Input

and at the output end the conducting part has the length loo

loo = Conducting Length->Outer Length at Output.

The total length of a dielectric cylindrical tube is then

loi + (zo - zi) + loo

as illustrated in Figure 1.

For the conical tube the expression is more complicated as zo and ziare measured along the z-axis while loi and loo are measured alongthe inclined surface of the conical tube.

The conical tube is illustrated in Figure 3.

Along the inner surface, the conducting part of the tube at the inputend has the length

lii = Conducting Length->Inner Length at Input

and at the output end the conducting part has the length

lio = Conducting Length->Inner Length at Output.

These lengths are measured from the end surfaces of the tube, cf.Figure 1.

The tube in the example of a Dielectric Support Tube shown in Figure1 is cylindrical, i.e. ρo = ρi. In the following Figure 2, the same tubeis shown, but here the parts are shown in an exploded view and it isseen how the conducting ends of the tube complete the conductingsurfaces for the horn (the Smooth Walled Section) and its exterior(the Horn Exterior) at the input end of the tube and complete thetwo parts of the reflector (two Piecewise Linear Reflectors) at theoutput end. These conducting parts must be modelled as parts ofthe Dielectric Support Tube (and only here) in order not to have adouble definition of the conducting surfaces.

Finally, Figure 3 shows a Dielectric Support Tube in its general formwhen the tube is conical. In the figure lii = loo = 0 in order to havea structure which can be assembled physically.


Figure 1 A cylindrical version of a Dielectric Support Tube withthe input parameters indicated (abbreviated, see thetext for the abbreviations). The input end is at theleft, output at the right with the z-axis pointing to theright.The supported reflector is modelled in two pieces(two objects of class Piecewise Linear Reflector, oneinside and another outside the tube, cf. Figure 2.)


Figure 2 The same cylindrical Dielectric Support Tube asshown in Figure 1 but here the parts are separated(by means of the attribute z-Offset) such that theconducting lengths at the inner and outer surfaces ofthe tube are visible.


Figure 3 A general version of a Dielectric Support Tube withthe input parameters indicated. There is no innerconducting length (lii = 0) at the input port and noouter conducting length (loo = 0) at the output port(see the text for the applied abbreviations).The supported reflector is modelled in two pieces(two objects of class Piecewise Linear Reflector, oneinside and another outside the tube).

220 BOR Mesh

BOR MESH (bor_mesh)

Purpose

By the class BOR Mesh it is possible to describe a scatterer which isa Body of Revolution, BOR. The scatterer may be metallic, dielectric,or composite metallic/dielectric.

As the scatterer is rotationally symmetric it may be described by acurve (the generatrix) in a plane containing the axis of rotation. Thefull geometry of the scatterer is then obtained by rotating this curvearound the axis. The curve is described by nodes (points) definingsegments of the curve, either linear or cubic segments.

It is possible to define homogeneous dielectric regions as closed re-gions enclosed by segments of the curve.

The BOR Mesh class may be used to describe general waveguide sec-tions or free scatterers (reflectors) as long as these have a rotationalsymmetry around the same axis.

Links

Classes→Horn Geometry→Exterior Geometry→BOR Mesh

Syntax

<object name> bor_mesh(

regions : table( <r> <r> <r> . . .),nodes : table( <r> <r> . . .),linear_segments : table( <r>

<r> . . .),cubic_segments : table( 

 <r> <r> . . .),length_unit : <si>,coor_order : <si>

)

where

 = integer

<r> = real number


Attributes

BOR Mesh 221

Regions (regions) [table (*,4)].

Table with 4 columns specifying the characteristics of the di-electric region(s).

Region Number (Region Number) [integer].

A unique, positive number for the region, apart from adefault region with the number 0 representing the freespace and closed regions with number -1 representing oneor more closed metallic region.

Permittivity (Permittivity) [real number].

The relative permittivity (dielectric constant) of the region.

Permeability (Permeability) [real number].

The relative permeability of the region.

Loss Tangent (Loss Tangent) [real number].

The loss tangent for the region.

Nodes (nodes) [table (2,3)].

Table with 3 columns specifying the nodes (the points) of thecurve (the generatrix) which describes the scatterer. The tablemust define at least two nodes. The unit of the coordinatesare determined by the attribute Length Unit.

Node Number (Node Number) [integer].

A unique, positive number of the node.





Linear Segments (linear_segments) [table (*,7)].

Specification of the linear segments in the specification of thegeneratrix. The table has 7 columns:

Segment Number (Segment Number) [integer].

A unique, positive number of the segment.

222 BOR Mesh

Node A (Node A) [integer].

The node at the first end of the segment. The segmentwill run linearly from node A to node B.

Node B (Node B) [integer].

The node at the last end of the segment.

Region 1 (Region 1) [integer].

The number of the region on the one side of the curvesegment.If Region 1 and Region 2 differ, the curve segment mayeither define a dielectric interface or a conducting surface,which is controlled by the real part of the entry Zs (seebelow). If Region 1 and Region 2 are identical, the curvesegment must define a conducting surface, implying thatZs(real) must be non-negative.


The number of the region on the second side of the curvesegment.

Zs (real) (Zs (real)) [real number].

The real part of Zs, in ohm/meter, Zs being the complexsurface impedance of the surface defined by the curvesegment. Zs(real) >= 0 specifies a conducting surface;Zs(real) = -1 specifies a dielectric interface and region 1and 2 must be different.The default value is Zs = 0 which specifies a perfect con-ductor.

Zs (imag) (Zs (imag)) [real number].

The imaginary part of Zs, in ohm/meter.

Cubic Segments (cubic_segments) [table (*,9)].

Specification of the third-order segments in the specification ofthe directrix. The table has 9 columns:

Segment Number (Segment Number) [integer].

A unique, positive number of the segment.

Node A (Node A) [integer].

The node at the first end of the segment. The segmentwill run from node A, through nodes B and C to node D.

BOR Mesh 223

Node B (Node B) [integer].

First intermediate node B of the segment.

Node C (Node C) [integer].

Second intermediate node C of the segment.

Node D (Node D) [integer].

The node at the last end of the segment.


The number of the region on the one side of the curvesegment.If Region 1 and Region 2 differ, the curve segment mayeither define a dielectric interface or a conducting surface,which is controlled by the real part of the entry Zs (seebelow). If Region 1 and Region 2 are identical, the curvesegment must define a conducting surface, implying thatZs(real) must be non-negative.


The number of the region on the second side of the curvesegment.

Zs (real) (Zs (real)) [real number].

The real part of Zs, in ohm/meter, Zs being the complexsurface impedance of the surface defined by the curvesegment. Zs(real) >= 0 specifies a conducting surface;Zs(real) = -1 specifies a dielectric interface and region 1and 2 must be different.The default value is Zs = 0 which specifies a perfect con-ductor.

Zs (imag) (Zs (imag)) [real number].

The imaginary part of Zs, in ohm/meter.




Coordinate Order (coor_order) [item from a list of character strings],default: z_rho.

224 BOR Mesh


Not available in the GUI where the first coordinate in the at-tribute Nodes is z and the second is ρ.

z_rho


rho_z


Remarks

Regions, nodes and segments are described in tables. The order ofthe regions, etc. in the tables is not important.

This section contains discussions on the following topics:

• Definitions

• Segments

• Mesh rules

• Mesh accuracy

and, finally, an example on specification of a mesh is given:

• Application example

Definitions

Objects of the class BOR Mesh defines a scatterer which is a Bodyof Revolution (BOR) i.e. the scatterer is rotational symmetry aroundan axis, the axis of rotation. The surface of the scatterer may bedescribed by a curve (or more curves), the generatrix, in a planecontaining the axis of rotation. The surface is generated when thiscurve is rotated around the axis.

It is thus sufficient to specify the curve in order to describe the scat-terer. The curve is specified by a set of nodes which are connectedeither by linear segments, linear from node to node, or by cubic seg-ments following a third order polynomial through a set of four con-secutive nodes. The segments shall be defined such that adjacentsegments have a node in common.

BOR Mesh 225

If the segments are arranged to form a closed volume (when rotated),this volume is referred to as a region. A region can be assigned ma-terial properties (the relative permittivity, the relative permeabilityand the loss tangent) modelling a volume filled with a homogeneousmaterial with these properties, e.g. a dielectric. Two closed volumeswith the same material properties must be considered as differentregions.

Segments

The segments of which the generatrix is constituted can be linearor curved. The linear segments are defined by two nodes and thecurved segments are defined by four nodes. The shape of a curvedsegment is modelled by a third order polynomial passing the speci-fied nodes.

The number of nodes and curve segments needed for describing asurface is determined by the curvature of the surface. Short seg-ments defined by many nodes will in general give the best descrip-tion of the geometry of a scatterer. On the other hand, the segmentsshould be as long as possible to minimise the number of unknownsin the computations and consequently the memory requirement andcomputation times. Internally, segments longer than 2 wavelengthswill be segmented as needed for the MoM computations. Hence, thenumber of segments used in the curve should be a trade-off betweenthe modelling accuracy and the resulting number of unknowns.

The curve segments are thus modelling the surfaces of the scattererand need not to depict the detailed mesh needed for the MoM cal-culations. This meshing is carried out internally.

The two types of curve segments are shown in Figure 1.

Figure 1 The two types of curve segments, the linear segmentdefined by two nodes, A and B, and the cubicsegment defined by four nodes, A, B, C and D.

Mesh rules

226 BOR Mesh

Some rules shall here be given for the segments of the generatrix.

The best connection between neighbour segments is obtained byhaving the same node defining the common end points of the seg-ments. This is, however, not mandatory. The neighbour segmentsmay start at nodes with different numbers as long as these nodeshave the same position. It is important to ensure connectivity be-tween the segments, cf. rule 2 below.

The following rules apply for a BOR Mesh:

1. Segments can only be connected at end points.

2. Two curve segments are considered connected if the position ofan end node of one segment is identical to the position of anend node of the other segment within a tolerance of 10−5λ, λbeing the wavelength.

If the rule is fulfilled the currents are allowed to flow from onesegment to the neighbour segment.

If the rule is not fulfilled, the segments will be regarded as in-dependent scatterers and the currents are not allowed to flowbetween the segments.

3. A node can be shared by no more than 4 segments. An error isissued during the computation if this condition is violated.

4. Dielectric regions must be closed. An error is issued during thecomputation if this condition is violated.

5. A closed metallic region should be assigned to be region number-1 if it is in contact with a dielectric region. If the region num-ber is not assigned to -1 a significant overhead is introducedin the computations since unnecessary basis functions are usedto model the zero currents on the internal side of the closedmetallic region.

If the closed metallic region is not in contact with a dielectricregion, there is no such overhead in the computations, and theregion number -1 needs not to be specified.

A Horn Exterior is considered a closed metallic region when itis starting at the aperture and is closed behind the aperture. Anexample is shown in Figure 2.

6. A dielectric region shall be given a positive region number. Thesegments bordering the region towards another dielectric regionand towards the free space must have Zs(real) = -1 in order to

BOR Mesh 227

flag that it is a dielectric boundary (Zs(imag) is not used). If thesegment is conducting then Zs(real) >= 0; this specifies thatthe neighbour region here is a conducting region or that thesegment is a conducting layer between two dielectric regions.

Mesh accuracy

The surface of the body of revolution is modelled by the curve seg-ments defined through the user-specified nodes. In the MoM compu-tations, points on this surface are used. It is up to the user to ensurethat the modelled curved segments follows the true surface shapewith a sufficient accuracy. That is, sufficiently fine segments mustbe provided as input to the BOR Mesh class.

Application example

In the following an example is given on how a mesh may be build,see the following Figure 2.

The figure shows an open-ended waveguide, defined as a SmoothWalled Section, with a radius of rwg. This is shown in blue in the fig-ure. This waveguide is used for excitation of a ring-shaped dielectricat the end of which a flat metallic plate is fastened. The result is aring-shaped aperture.

For the BOR Mesh sets of regions, sections and nodes shall be spec-ified. The sections connect the nodes and enclose one or more re-gions.

In the figure the Regions are specified by numbers in green. Regionnumber -1 indicates metallic structures and such regions shall beclosed regions, cf. the mesh rules above. Region number 0 indicatesthe free space and region number 1 is the dielectric region with adielectric constant (relative permittivity) of 3.0 and defined by:

regions : table(

1 3.00000E+00 1.00000E+00 0.00000E+00)

Next, the Nodes are defined. These are given by numbers in black inthe figure. Node 1 is defined at the end of the waveguide and nodes1 - 2 - 3 - 4 - 18 - 19 - 20 - 21 constitutes a horn exterior which hereis closed to the left with a waveguide flange. The nodes 1 through15 circumscribe the dielectric (region number 1) and nodes 13 - 14 -

228 BOR Mesh

Figure 2 An example of definition of a mesh. Numbers in blackare node numbers, numbers in red present linearsegments and numbers in green are segmentnumbers. See the text for details.

15 - 16 - 17 circumscribe the metallic splash plate at the end of thedielectric. The nodes are specified as follows:

nodes : table(

1 0.00000E+00 "ref(rwg)"2 0.00000E+00 "ref(rwg)+2"3 -8.00000E+00 "ref(rwg)+2"4 -8.00000E+00 "ref(rwg)+5"5 5.00000E+00 "ref(rwg)+5"

BOR Mesh 229

6 8.00000E+00 "ref(rwg)+10-5*cos(30*ref(dtr))"7 1.10000E+01 "ref(rwg)+10-5*cos(60*ref(dtr))"8 1.40000E+01 "ref(rwg)+10-5*cos(90*ref(dtr))"9 1.70000E+01 "ref(rwg)+10-5*cos(120*ref(dtr))"10 2.00000E+01 "ref(rwg)+10-5*cos(150*ref(dtr))"11 2.30000E+01 "ref(rwg)+10-5*cos(180*ref(dtr))"12 3.00000E+01 "ref(rwg)+10+5"13 3.00000E+01 "ref(rwg)+10"14 2.80000E+01 "ref(rwg)+10"15 2.80000E+01 "ref(rwg)"16 2.80000E+01 0.00000E+0017 3.00000E+01 0.00000E+0018 6.00000E+01 "ref(rwg)+5"19 -6.00000E+01 "ref(rwg)+12"20 -6.20000E+01 "ref(rwg)+12"21 -6.20000E+01 0.00000E+00

)

Note how the radial rho-values are specified by the Real Variablerwg and expressions in a way that if the waveguide radius, rwg,is changed then the dielectric will follow with a unchanged crosssection.

Finally, the segments are defined. These specifies how the nodesshall be connected resulting in the surfaces of the structure. Mostof the segments are Linear Segments connecting two nodes by astraight line. These segments are illustrated by red numbers in thefigure and are specified by the following table:

linear_segments : table(

1 1 2 1 0 0.00000E+00 0.00000E+002 2 3 1 0 0.00000E+00 0.00000E+003 3 4 1 0 0.00000E+00 0.00000E+004 4 5 1 0 0.00000E+00 0.00000E+005 11 12 1 0 0.00000E+00 0.00000E+006 12 13 1 0 0.00000E+00 0.00000E+007 13 14 1 0 0.00000E+00 0.00000E+008 14 15 1 0 0.00000E+00 0.00000E+009 15 1 1 0 0.00000E+00 0.00000E+0010 13 17 0 0 0.00000E+00 0.00000E+00

230 BOR Mesh

11 16 15 0 0 0.00000E+00 0.00000E+0012 4 18 0 0 0.00000E+00 0.00000E+0013 18 19 0 0 0.00000E+00 0.00000E+0014 19 20 0 0 0.00000E+00 0.00000E+0015 20 21 0 0 0.00000E+00 0.00000E+00

)

But two segments are Cubic Segments specifying the curved partsof the dielectric. The Cubic Segments are defined by four nodeseach, namely nodes 5 - 6 - 7 - 8 and nodes 8 - 9 - 10 - 11. TheCubic Segments are specified by the table:

cubic_segments : table(

1 5 6 7 8 1 0 0.00000E+00 0.00000E+002 8 9 10 11 1 0 0.00000E+00 0.00000E+00

)

Variables 231

VARIABLES

Purpose

This group contains classes used to define variable. Presently, onlyone class is available:

Real Variable

Links

Classes→Horn Geometry→Variables

232 Real Variable

REAL VARIABLE (real_variable)

Purpose

By the class Real Variable it is possible to define a real variable byname and value.

Links

Classes→Horn Geometry→Variables→Real Variable

Syntax

<object name> real_variable(

value : <r>)

where

<r> = real number

Attributes

Value (value) [real number].

The value of the real variable, given as a real number withouta unit (the unit appears from the context in which the variableis applied).

Remarks

An object of class Real Variable may be referred to from other ob-jects wherever a real number shall be specified. The value of thevariable will then be inserted and applied. This is very useful whengeometries which depends on other geometrical parameters shall beexpressed.

The value of a Real Variable is not a constant but may be changedduring optimizations.

The name of a Real Variable is case insensitive, i.e. ’R_out’ and’r_out’ refer to the same variable.

Available expressions

Variable may be applied in algebraic and trigonometric expressionswith the following (Fortran like) operators:

Real Variable 233

+ addition- subtraction* multiplication/ division** raising to power

functions (angles to be given in radians):

sqrt( ) square rootsin( ) sinecos( ) cosinetan( ) tangentexp( ) exponentiallog( ) logarithmic (base e)log10( ) logarithmic (base 10)abs( ) absolute valueaint( ) truncate (round towards zero)anint( ) round to nearest integerasin( ) inverse sineacos( ) inverse cosineatan( ) inverse tangentsinh( ) hyperbolic sinecosh( ) hyperbolic cosinetanh( ) hyperbolic tangent

and any level of parenthesis.

In the GUI

A Real Variable may be defined in the Geometry tab through theCreate menu. A name for the variable shall be specified whereafterthe variable appears with the value zero in the section Variables ofthe Property Editor.

Alternatively, a Real Variable may be defined when an existing valuein the Property Editor is replaced by a variable or an expression ofvariables. If the referred variables do not exist they will be createdand inserted with the value zero in the section Variables of theProperty Editor.

The value of the Real Variable may be changed by specifying a valuein the section Variables of the Property Editor.

234 Real Variable

Examples on expressions are

var1*(var2 + var3)and

2*cos(var1/50)

where var1, var2 and var3 are defined variables.

In the tor-file

When operating on the tor-file it is the name of the object (<objectname> in the syntax) which corresponds to the name of a variable inusual mathematical context. The attribute Value specifies the valueof the variable.

Let the name of the variable be x then the variable may be referredto by inserting "ref(x)" (including the double quotes) instead of thereal number. When an expression of variables is used it is the fullexpression which shall be enclosed in double quotes. Examples onexpressions are

"ref(var1)*(ref(var2) + ref(var3))"and

"2*cos(ref(var1)/50)"

where var1, var2 and var3 are defined as Real Variable.

Example with a tor-file

A smooth-walled horn may have an inner profile given by Linear Pro-file. This profile is specified by an Input Radius (input_radius),an Output Radius (output_radius) and a Length (length) whichall shall be specified as real numbers with unit of length. Thus theprofile may be specified as:

profile_example linear_profile(input_radius : 25.0 mm,output_radius : 35.0 mm,length : 50.0 mm

)

Real Variable 235

If the user defines a Real Variable with the name rad by

rad real_variable(value : 25.0

)

then this variable may be used in the specification of the profile.Thus when rad is defined as above it may be inserted instead ofthe number ’25.0’ in the specification of the input_radius, andif the user want to ensure that the output_radius is twice theinput_radius this may be applied in an expression for the out-put_radius:

profile_example linear_profile(input_radius : "ref(rad)" mm,output_radius : "2.*ref(rad)" mm,length : 50.0 mm

)

Note that the attribute input_radius, as requested, is given bya real number with unit of length, the real number is the value ofValue in the referred object rad and the unit is specified to mm(millimeter) after the value.

Another example on the application of expressions for a variable maybe found in the table defining the nodes in a BOR Mesh.

236 Horn Analysis

HORN ANALYSIS

Purpose

This group contains classes defining settings for the horn analysis inCHAMP:

Corrugated Horn Mode Matching

Frequency Range

Horn Tolerance

Summary:

The user is able to partly control the horn analysis by settings storedin the object Corrugated Horn Mode Matching. This class has refer-ences to an object defining the frequencies used in the analysis, butotherwise stores all settings in the object itself.

The frequencies used in the horn analysis are defined in terms ofthe start frequency, the end frequency, and the number of equidis-tantly spaced frequencies. The definition is stored in an object of theFrequency Range class referenced from the analysis object.

The program offers a statistical analysis of the influence of mechan-ical tolerances on the horn performance. A number of horn analysesare performed. In each analysis, random pertubations within the tol-erance limits are added to all dimensions, still maintaining the rota-tionally symmetric structure. Worst case performance and statisticalparameters are reported. The tolerance study is controlled by theHorn Tolerance class.

Links

Classes→Horn Analysis

Corrugated Horn Mode Matching 237

CORRUGATED HORN MODE MATCHING (corrugated_horn_mode_matching)

Purpose

The class Corrugated Horn Mode Matching defines the settings usedto control the analysis of a horn.

Links

Classes→Horn Analysis→Corrugated Horn Mode Matching

Syntax

<object name> corrugated_horn_mode_matching(

frequency : ref(<n>),horn : ref(<n>),excitation : <si>,fundamental_mode : struct(polarisation:<si>,

polarisation_ratio_real:<r>,polarisation_ratio_imag:<r>),

tracking_mode : struct(mode:<si>, rotation:<r>),additional_modes : ,exterior_analysis : <si>,segmentation_accuracy : <r>,expansion_accuracy : <si>,max_mesh_length : <r>,output_file_name : <f>,detailed_analysis_data : <si>,factor : struct(db:<r>, deg:<r>),coef_file_name : <f>,obsolete_exterior_segmentation:

<r>,

coor_sys : ref(<n>))

where

 = integer


<r> = real number

<f> = file name


238 Corrugated Horn Mode Matching

Attributes

Frequency (frequency) [name of another object].

A reference to a Frequency Range object defining the frequen-cies used in the analysis.

Horn (horn) [name of another object].

A reference to a Combined Horn Section defining the interiorand the exterior (optional) geometry of the horn to be analysed

Excitation (excitation) [item from a list of character strings], default:fundamental_mode.

Determines the single waveguide mode exciting the horn atthe horn throat.

fundamental_mode

The fundamental mode is used as excitation. The modeexcitation is further specified in the attribute "fundamen-tal_mode".

tracking_mode

One of the tracking modes, TE01, TM01, or TE21, is usedas excitation. The mode excitation is further specified inthe attribute "tracking_mode".

Fundamental Mode (fundamental_mode) [struct].

Specifies the mode excitation for the fundamental mode, TE11.Only used if the attribute "excitation" is set to "fundamen-tal_mode".

Polarisation (polarisation) [item from a list of character strings],default: linear_x.

The polarisation of the fundamental mode. There are fourchoises:

linear_xThe polarisation is mainly along the x-axis.

linear_yThe polarisation is mainly along the y-axis.

rhcThe polarisation is mainly right hand circular polari-sation.


lhcThe polarisation is mainly left hand circular polarisa-tion.

Polarisation Ratio Real Part (polarisation_ratio_real) [real num-ber], default: 0.

The real part of the possible polarisation ratio of the fun-damental mode.

Polarisation Ratio Imaginary Part (polarisation_ratio_imag) [realnumber], default: 0.

The imaginary part of the polarisation ratio of the funda-mental mode.

Tracking Mode (tracking_mode) [struct].

Specifies the mode excitation for one of the tracking modes.Only used if the attribute "excitation" is set to "tracking_mode".

Mode Type (mode) [item from a list of character strings], de-fault: TE01.

Selects which of the tracking modes are used as excitation.

TE01The TE01 mode.

TM01The TM01 mode.

TE21The TE21 mode.

Rotation (rotation) [real number], default: 0.

The rotation of the tracking mode.

Additional Modes (additional_modes) [integer], default: 0.

The program automatically determines the number of modesneccessary in the mode matching. In order to ensure that aconverged result has been obtained, the user may specify anumber of additional modes to be used. In ecah elementarywaveguide, the "additional_modes" are added to the numberof modes automatically determined.

Horn Exterior and Reflector Analysis (exterior_analysis) [item from alist of character strings], default: on.


Selects if the exterior geometry, e.g. reflectors, should beincluded in the analysis.

on

Includes reflectors and the horn exterior geometry in theanalysis.

off

No reflectors or exterior horn geometry will be includedin the analysis and only mode-matching will be per-formed.

exclude_sub_reflector

This option is obsolete and will result in the default be-havior.

Interior Segmentation Accuracy (segmentation_accuracy) [real num-ber], default: 30.

The accuracy of the segmentation of the horn interior geom-etry. If the horn contains a smooth section, the program au-tomatically segments the profile of this section as a staircasepattern whereby the horn may be modelled as a sequence ofelementary waveguides. The program segments the profilesuch that the maximum step size in the radial direction doesnot exceed the wavelength at the higest analysis frequencydivided by the "segmentation_accuracy". The attribute is notused for corrugated horn sections or waveguides.

Exterior Expansion Accuracy (expansion_accuracy) [item from a listof character strings], default: Normal.

Determines the accuracy of the polynomial expansion used torepresent the unknown currents on the horn exterior as wellas the scatterers. The polynomial expansion order is auto-matically adapted to the electrical size of each patch used inthe mesh (the internally generated mesh for the MoM calcu-lation). This default level of precision is sufficient for normalaccuracy. The expansion order can be increased which maylead to an improved accuracy of the solution but also lead tosignificantly longer computation time and higher memory re-quirements. The normal or the enhanced settings are sufficientfor most applications. If large variation of the unknown current


occurs on parts of the horn exterior or on the scatterers, thehigh or extreme accuracy setting may improve the solution.

Normal

The default level of precision sufficient for normal accu-racy.

Enhanced

Increased polynomial order for enhanced accuracy.

High

Further increased polynomial order for high accuracy.

Extreme

Highest polynomial order for extreme accuracy.

Maximum Mesh Length (max_mesh_length) [real number], default:2.

Determines the maximum allowed dimension of the patchesused in the mesh of the specified scatterers. It is recom-mended to use as large patches as possible, but not largerthan 2 wavelengths; a value of Maximum Mesh Length largerthan 3 (wavelengths) is not allowed. A value smaller than2 may be necessary if the geometry to be meshed is highlycurved. It is recommended to decrease the value to check theaccuracy of the geometrical approximation introduced by themeshing procedure.

Output File Name (output_file_name) [file name].

Name of file containing derived data from the mode matchinganalysis. The file is for CHAMP internal use only.

Detailed Analysis Data (detailed_analysis_data) [item from a list ofcharacter strings], default: on.

Determines if the program should calculate a number of de-tailed analysis data.

on

The detailed analysis data are calculated.

off

The detailed analysis data are not calculated.


Factor (factor) [struct].

The radiated field will be multiplied by a complex factor:

Amplitude in dB (db) [real number], default: 0.

Amplitude of the factor, in dB.

Phase in degrees (deg) [real number], default: 0.

Phase of the factor, in degrees.

Coefficient File Name (coef_file_name) [file name].

Name of a file containing coefficients obtained in the modematching analysis. The file is for CHAMP internal use only.

Exterior Segmentation Accuracy (Obsolete) (obsolete_exterior_segmentation)[real number], default: 15.

This attribute is obsolete and has no effect. Use MaximumMesh Length and Exterior Expansion Accuracy insteadto control the MoM accuracy.


A reference to a Coordinate System class, defining the originand orientation of the coordinate system used in a SphericalWave Expansion of the field radiated by the horn.

Remarks

The excitation is either the "Fundamental mode", TE11, or one of the"Tracking modes", TM01, TE21, or TE01. The input specifications aredifferent for the two types of modes as described in Section 9.2.1.2.

Because of the axisymmetric geometry, the azimuthal field distribu-tion originating the primary incident mode is retained throughout thehorn structure and the radiated far fields may be represented by thesame azimuthal field distribution.

Frequency Range 243

FREQUENCY RANGE (frequency_range)

Purpose

The class Frequency Range defines a set of equally spaced frequen-cies at which calculations are carried out.

Links

Classes→Horn Analysis→Frequency Range

Syntax

<object name> frequency_range(

frequency_range : struct(start_frequency:<rf>,end_frequency:<rf>,number_of_frequencies:)

)

where

 = integer

<rf>= real number with unit of frequency

Attributes

Frequency Range (frequency_range) [struct].

Definition of a list of equispaced frequencies.

Start Frequency (start_frequency) [real number with unit of fre-quency].

Start value in the list of frequencies with a valid frequencyunit (Hz, kHz, MHz, GHz, THz).

End Frequency (end_frequency) [real number with unit of fre-quency].

End value in the list of frequencies with a valid frequencyunit (Hz, kHz, MHz, GHz, THz).

Number of Frequencies (number_of_frequencies) [integer], de-fault: 0.

Number of frequency values in the list.

244 Horn Tolerance

HORN TOLERANCE (horn_tolerance)

Purpose

The class Horn Tolerance defines settings for a statistical analysis ofthe influence of mechanical tolerances on the horn performance.

Links

Classes→Horn Analysis→Horn Tolerance

Syntax

<object name> horn_tolerance(

source : ref(<n>),longitudinal_tolerance : <rl>,radial_tolerance : <rl>,no_of_samples : ,random_seed : ,statistics_file : <s>

)

where

 = integer



<s> = character string

Attributes

Source (source) [name of another object].

Reference to a Corrugated Horn Mode Matching object whichdirectly defines the analysis settings and indirectly defines thehorn and the frequencies to be used.

Longitudinal Tolerance (longitudinal_tolerance) [real number with unitof length], default: 0.

A common tolerance value for all longitudinal segments of thehorn mesh. The tolerance value is the upper limit of the per-turbations.

Horn Tolerance 245

Radial Tolerance (radial_tolerance) [real number with unit of length],default: 0.

A common tolerance value for all radial segments of the hornmesh. The tolerance value is the upper limit of the perturba-tions.

Number of Samples (no_of_samples) [integer], default: 10.

Number of perturbation cases to be performed, i.e. the numberof horn analyses to be performed in addition to the nominalanalysis.

Random Seed (random_seed) [integer], default: 0.

The seed for the random number generator. If this number isless than or equal to zero, a seed will be selected automaticallyusing the system time function. Otherwise, the specified seedwill be used thus enabling a re-run of the tolerance analysiswith exactly the same sequence of perturbed horns.

Statistics File (statistics_file) [character string], default: tolerance_stats.txt.

Name of the file where the results of the tolerance analysiswill be saved.

Command Types

The horn tolerance analysis is activated by the command:

Get Influence

Remarks

A corrugated horn can only be produced with a certain accuracy andmechanical tolerances must be specified for the manufacturing ofthe horn.

The program offers a statistical analysis of the influence of mechan-ical tolerances on the horn performance. A number of horn analy-ses are performed. In each analysis, random perturbations withinthe tolerance limits are added to all dimensions of the horn mesh.The horn is, however, still considered a purely rotationally symmetricstructure. From these analyses, worst case performance and statisti-cal parameters are reported. Only the mode matching is used in thetolerance analyses, and the exterior is thus not taken into account.

246 Horn Tolerance

The random perturbations are drawn from a uniform distribution.Hence, if a dimension of the nominal horn (i.e. the horn withoutany perturbations) is A and the specified tolerance t, the perturba-tions will be uniformly distributed on the range [A− t, A+ t]. The RMSvalue of the pertubations is then

RMS =

√1

12(A+ t− (A− t))2 =

t√3. (1)

The user may specify a longitudinal tolerance (along the horn axis)and a radial tolerance. Further, the user may specify the number ofmode-matching analyses to be used for the statistical analysis.

Given these data, the program will first analyse the nominal horn.Three specific performance measures will be calculated at the se-lected frequencies: The return loss, the on-axis directivity, and themaximum cross polarisation for θ ≤ 90o.

A sequence of analyses will subsequently be performed. In eachanalysis all horizontal and vertical lengths in the horn mesh are sub-ject to random perturbations, as described above. It is ensured thatthe horn is kept continuous despite the small perturbations. At theend of the sequence, mean values, standard deviations, and worstcase of the performance measures are written to a log-file.

In the GUI, the tolerance study is activated from the menu, Analysis→ Analyse Tolerances and the results are available in the ResultsManager.

In batch mode, the tolerance study is activated using the Get Influ-ence command, and the log-file is stored in the working directory orat the user-specified location.

Horn Optimisation 247

HORN OPTIMISATION

Purpose

This menu contains classes which define settings for the horn opti-misation in CHAMP:

Optimisation Manager

Optimisation Variables

Optimisation Goals

Summary:

The user is able to partly control the horn optimisation by settingsstored in the object Optimisation Manager. This class has referencesto an Optimisation Variables object defining the optimisation vari-ables used in the optimisation as well as a sequence of OptimisationGoals objects defining the goals (objectives) of the optimisation.

Links

Classes→Horn Optimisation

248 Optimisation Manager

OPTIMISATION MANAGER (optimisation_manager)

Purpose

The class Optimisation Manager collects the data controlling the op-timisation algorithms.

Links

Classes→Horn Optimisation→Optimisation Manager

Syntax

<object name> optimisation_manager(

variables : ref(<n>),goals : sequence(ref(<n>), . . .),accuracy : <r>,deriv_approx_delta : <r>,max_iterations : ,objective_measure : <si>,optimisation_algorithm : <si>,autoscaling : <si>,ga_population_size : ,ga_generations : ,ga_mutation_probability : <r>,ga_number_bits : ,ga_seed : ,summary : struct(status:<si>, summary_file:<s>),iteration_log : <si>

)

where

 = integer


<r> = real number



Attributes

Variables (variables) [name of another object], default: blank.

Optimisation Manager 249

A reference to the Optimisation Variables object defining theoptimisation variables to be used.

Goals (goals) [sequence of names of other objects].

A sequence of references to Optimisation Goals objects defin-ing the goals (objectives) used in the optimisation.

Accuracy (accuracy) [real number], default: 1.0E-006.

The required accuracy to be used by the optimisation algo-rithm. The usual stop criterion is that the relative differencebetween the two sets of optimisation parameters found in twosuccessive iterations is less than the "accuracy" value. Othercriteria are usually in effect such as the relative change of thenorm of the residuals being less than the "accuracy" value.The accuracy is not used by the Genetic Algorithm.

Derivative Approximation Delta (deriv_approx_delta) [real number],default: 1.0E-004.

The forward difference delta used to approximate partial deriva-tives. A relative step of delta is taken. Only used if the minmaxor the least squares optimisation algorithm is selected.

Maximum Iterations (max_iterations) [integer], default: 200.

The maximum number of iterations allowed in all optimisationalgorithms except in the Genetic Algorithm. The optimisationwill stop if the number of iterations exceeds this maximumnumber.

Objective Measure (objective_measure) [item from a list of characterstrings], default: minmax.

The problem type, i.e. the norm of the residual vector to beminimised. The objective measure may be:

minmax

The norm equals the maximum of all the residuals. Thisis also referred to as "worst case optimisation".

least_squares

The norm equals the sum of squares of all the residuals.


Optimisation Algorithm (optimisation_algorithm) [item from a list ofcharacter strings], default: minmax.

The optimisation algorithm to be used. The following algo-rithms are available:

minmax

The Hald-Madsen minmax solver.

least_squares

The Hanson and Krogh non-linear least-squares solver.

nm_simplex

The Nelder and Mead simplex solver

genetic_algorithm

The TICRA implementation of a standard Genetic Algo-rithm.

Autoscaling (autoscaling) [item from a list of character strings], de-fault: off.

Selects if all optimisation variables shall be scaled to be of thesame size.

off

The variables are not autoscaled.

on

The variables are autoscaled.

GA Population Size (ga_population_size) [integer], default: 50.

The number of individuals in a generation, which is the sameas the number of objective-function samples (also called thefitness function in GA literature). Only used by the GeneticAlgorithm.

GA Generations (ga_generations) [integer], default: 10.

The number of generations in the genetic algorithm. Only usedby the Genetic Algorithm.

GA Mutation Probability (ga_mutation_probability) [real number], de-fault: 0.05.

Optimisation Manager 251

The fraction of bits in all chromosomes that will be switchedwhenever a new generation is determined. A random selectionof bits is used. The fraction must be in the half open interval[0;1[. The default value equals 0.05 meaning that 5% of allbits in all chromosomes will be switched. Only used by theGenetic Algorithm.

GA Number of Bits (ga_number_bits) [integer], default: 24.

The number of bits used to represent each of the real valuedoptimisation parameters in their respective intervals. The in-terval is sampled by 2 to the power of "GA Number of Bits"equidistant values. Only used by the Genetic Algorithm.

GA Seed (ga_seed) [integer], default: 0.

The seed for the random generator which is used both in thecross-over selection during pairing and in the selection of bitsto be switched during mutation. If this number is less than orequal to zero, a seed will be selected automatically using thesystem time function. Otherwise, the specified seed will beused thus enabling a re-run of the optimisation with exactlythe same sequence of iterations. Only used by the GeneticAlgorithm.

Summary (summary) [struct].

A summary of the optimisaton may be saved in a so-calledsummary file.

Status (status) [item from a list of character strings], default:on.

Determines if the summary is saved.

onThe summary is saved in the summary file.

offThe summary is not saved.

Summary File (summary_file) [character string], default: op-tim_summary.osm.

The name of the summary file.

Iteration Log (iteration_log) [item from a list of character strings],default: off.


Determines if a log of the iterations shall be saved to a file.The name of the iteration log is set to the prefix of the tor-file-name amended with "_iteration.log". Hence, if the tor-fileis named "case1.tor", then the iteration log will be named"case1_iteration.log".

off

The log is not written.

on

The log is written.

Remarks

The value of the Derivative Approximation Delta may influence theperformance of the minmax and the least squares methods notice-ably. If very rapid termination is observed during initial optimisationruns, the user is asked to try with smaller or larger values.

Optimisation Variables 253

OPTIMISATION VARIABLES (optimisation_variables)

Purpose

The class Optimisation Variables defines the optimisation variablesas well as a number of so-called dependent parameters to be usedin an optimisation.

Links

Classes→Horn Optimisation→Optimisation Variables

Syntax

<object name> optimisation_variables(

real_variables : sequence(struct(

variable_object:ref(<n>),min:<r>,max:<r>),

. . .),explicit_variables : sequence(

struct(id:<s>,target_object:ref(<n>),parameter:<s>,min:<r>,max:<r>),

. . .),independent_variables : sequence(

struct(id:<s>,initial_value:<r>,min:<r>,max:<r>),

. . .),dependent_parameters : sequence(

struct(target_object:ref(<n>),parameter:<s>,transform:<s>),

. . .))

where

254 Optimisation Variables


<r> = real number


Attributes

Real Variables (real_variables) [sequence of structs].

A sequence of specifications of optimisation variables.

Target Object (variable_object) [name of another object].

Reference to an object of class Real Variable defining theoptimisation variable.

Min (min) [real number], default: -1.0E+099.

The lower bound on the optimisation variable during theoptimisation. The default value is -1.0E+099, equivalentto no bound specified.

Max (max) [real number], default: 1.0E+099.

The upper bound on the optimisation variable during theoptimisation. The default value is 1.0E+099 equivalent tono bound specified.

Explicit Variables (Obsolete) (explicit_variables) [sequence of structs].

Obsolete, use attribute Real Variables.

A sequence of specifications of optimisation variables. Eachspecification is given as a direct link to a real-valued parame-ter in another object. The parameter will then be used as anoptimisation variable.

ID (id) [character string].

A unique name of the explicit optimisation variable. Thename is given as a character string and must be uniquecompared to all other optimisation variables, explicit aswell as independent.

Target Object (target_object) [name of another object].

A reference to the object containing the parameter.

Parameter (parameter) [character string].

The target object in general contains several parameters,and the current input field specifies which of these shouldbe used as the optimisation variable. See the Remarkssection for further details.



The lower bound on the optimisation parameter during theoptimisation. The default value is -1.0E+099, equivalent tono bound specified.


The upper bound on the optimisation parameter during theoptimisation. The default value is 1.0E+099 equivalent tono bound specified.

Independent Variables (Obsolete) (independent_variables) [sequenceof structs].


A sequence of specifications of optimisation variables. Eachspecification defines an independent, real-valued optimisationvariable, i.e. this variable is not linked to a parameter in an-other object. Instead the tentative values of the independentoptimisation variable proposed in each iteration are mappedinto one or several dependent parameters (see below). Eachindependent optimisation variable must be used by one or sev-eral of the dependent parameters in order to have an influenceon the value of the objective function, and the optimisation willnot be allowed if this is not the case.

ID (id) [character string].

A unique name of the independent optimisation variable.The name is given as a character string and must beunique compared to all other optimisation variables, ex-plicit as well as independent.

Initial Value (initial_value) [real number].

The initial value of the independent optimisation variable,i.e. the value used as the start value in the optimisation.


The lower bound on the optimisation parameter during theoptimisation. The default value is -1.0E+099, equivalent tono bound specified.


The upper bound on the optimisation parameter during theoptimisation. The default value is 1.0E+099 equivalent tono bound specified.


Dependent Parameters (Obsolete) (dependent_parameters) [sequenceof structs].


A sequence of specifications of dependent parameters. Eachdependent parameter specifies a link from one or several ofthe optimisation variables (explicit or independent) to a real-valued parameter in another object. The specification includea functional transformation of the optimisation variables thatspecifies how the parameter depends on the optimisation vari-ables.

Target Object (target_object) [name of another object].

A reference to the object containing the parameter, whichmust be updated in each step of the optimisation.

Parameter (parameter) [character string].

The target object in general contains several parameters,and the current input field specifies which of these shouldbe updated in each step of the optimisation. See the Re-marks section for further details.

Transform (transform) [character string].

The functional expression relating the optimisation vari-ables to the parameter in the object. The expression mayconsist of the four arithmetic operators, the usual standardfunctions and any level of parenthesis.

Remarks

The Optimisation Variables class allows specification of the optimisa-tion variables, i.e the variables which are varied in each step of theoptimisation for reaching a given goal.

These variables are attributes used in other objects, most often at-tributes for geometrical quantities; an example is the output radiusof a horn segment. The optimisation variables shall be defined asReal Variables, see this class for how this may be done, an exam-ple is also found below. Variables representing an integer, such asthe number of slots in a corrugated horn, cannot be applied as anoptimisation variable.

The attribute Real Variables further allows the user for each op-timisation variable to specify upper and lower bounds during theoptimisation.


An unlimited number of optimisation variables may be specified inattribute Real Variables

The attribute Real Variables is general and replaces the use ofthe other attributes of this class which now are obsolete.

Example

Assume that a horn section given by a spline function is optimisedwith respect to its length. Let the spline function be given by fiveequidistant control points as we wish to keep equidistant during theoptimisation. In this case, we introduce a Real Variables repre-senting the length of the section and we give it the name L1. Thez-coordinates of the control points shall then be specified to

0.0, 0.25*L1, 0.5*L1, 0.75*L1 and L1

In the tor-file, the specification of the smooth-walled section looks asfollows. The Optimisation Variables object is found at the bottom ofthe list. Only the relevant objects of the tor-file are shown.

smooth_horn_section smooth_walled_section(profile : ref(smooth_horn_section_profile_0001),conductivity : 33000000.0 S/m

)

smooth_horn_section_profile_0001 spline_profile(z_unit : mm,rho_unit : mm,data_points : table(0.00000E+00 1.4314035478E+01"0.25*ref(L1)" 1.6957110426E+01"0.5*ref(L1)" 1.9017711222E+01"0.75*ref(L1)" 2.2893514200E+01"ref(L1)" 2.4886335269E+01

))

L1 real_variable(value : 60.0


)

optimiser optimisation_manager(variables : ref(optimiser_0001)

)

optimiser_0001 optimisation_variables(real_variables : sequence( struct(variable_object: ref(L1), min: 40.0,

max: 65.0))

)

In the GUI a Real Variable is specified through the Create menu ofthe Geometry tab. The table for the control points (Nodes) shallthen be specified as illustrated in Figure 1.


Figure 1 Specification in the GUI of the nodes equidistant in zfor a spline profile.

260 Optimisation Goals

OPTIMISATION GOALS

Purpose

This menu contains classes which define various types of optimisa-tion goals (objectives) used in the optimisation of the horn geometry.

The following classes of Optimisation Goals are available:

Return Loss Goals

Goals to the Beam Pattern

Tracking Pattern Goals

Links

Classes→Horn Optimisation→Optimisation Goals

Return Loss Goals 261

RETURN LOSS GOALS (goals_source_return_loss)

Purpose

The class Return Loss Goals defines optimisation goals (objectives)to the return loss of a horn.

Links

Classes→Horn Optimisation→Optimisation Goals→Return Loss Goals

Syntax

<object name> goals_source_return_loss(

source : ref(<n>),goal_spec : sequence(

struct(frequency_index:<r>,goal:<r>,weight:<r>,action:<si>),

. . .),super_weight : <r>

)

where


<r> = real number


Attributes


A reference to the source for which the return loss should beoptimised.

Return Loss Goal (goal_spec) [sequence of structs].

262 Return Loss Goals

A sequence of goal specifications for the return loss. For eachspecification, the following input must be given:

Frequency Index (frequency_index) [real number], default: -1.

Determines the frequency or frequencies for which thegoal is evaluated. The default value is "-1" meaning allthe frequencies used by the referenced source. The Fre-quency Index may be set to a positive integer, in whichcase the goal is evaluated at a single frequency, namelythe frequency with this index_number in the discrete setof frequency defined. The GUI only supports the defaultsetting of -1.

Goal (goal) [real number], default: 30.

The return-loss goal value for this specification.

Weight (weight) [real number].

The weight factor for this goal.

Action (action) [item from a list of character strings], default:maximise.

The optimiser should try to:

maximiseMaximise the return loss towards or above the goalvalue.

targetTarget the return loss towards the goal value.

minimiseMinimise the return loss towards or below the goalvalue.

Super Weight (super_weight) [real number], default: 1.

A common weight factor for all goal specifications in this ob-ject.

Remarks

The class has a reference to a Corrugated Horn Mode Matching ob-ject, which defines the mode matching analysis, and indirectly de-fines the horn geometry as well as the frequencies used in the modematching.

In each iteration of the optimisation, a mode matching is performed,and the return loss calculated. The Return Loss Goals calculates

Return Loss Goals 263

for each frequency, a residual defined as the weighted differencebetween the achieved return loss and the goal value for the returnloss. The class returns these residuals to the optimisation algorithm.

Return Loss Calculation

The Return Loss definition used in CHAMP is described in Section 9.3.1.1.

Following the mode matching at Nfreq frequencies, the Return Losshas been calculated at each frequency. The achieved Return Loss atfrequency No. j (j = 1, .., Nfreq) is denoted Achj.

A sequence of Ngoals Return-Loss-goals may be specified. The goalspecification No. i is given in terms of 1) a goal value, Goali, which isthe required value of the return loss expressed in positive dB-values,2) a weight factor, wi, for this goal, and 3) an action which tells theoptimiser either to maximise (default), target or minimise the returnloss.

Note that with the definition of the Return Loss as a loss, i.e. usingpositive dB-values, then a return loss of 40 dB is in most cases betterthan a return loss of 30 dB. Consequently, the typical action is tomaximise the return loss.

Residual Calculation

The total number of residuals equal the Ngoals goal specificationstimes the Nfreq frequencies. The residual with index (i, j) is cal-culated as:

Res(i, j) = W ∗ wi ∗ (Achj −Goali)

where W is a common weight factor for all residuals, specified in theattribute "super_weight".

The residual is thus proportional to the difference in the dB-values ofthe achieved and the required return loss.

264 Goals to the Beam Pattern

GOALS TO THE BEAM PATTERN (optimisation_goals_radiation_pattern)

Purpose

The class Goals to the Beam Pattern defines optimisation goals (ob-jectives) to the beam pattern radiated by a horn.

Links

Classes→Horn Optimisation→Optimisation Goals→Goals to the BeamPattern

Syntax

<object name> optimisation_goals_radiation_pattern(

source : ref(<n>),goals_on_axis_directivity : sequence(


. . .),goals_aperture_efficiency : sequence(


. . .),goals_directivity : sequence(

struct(frequency_index:<r>,theta:<r>,phi:<r>,component:<s>,goal:<r>,weight:<r>,action:<si>),

. . .),

Goals to the Beam Pattern 265

goals_cross_polar : sequence(struct(

frequency_index:<r>,theta_min:<r>,theta_max:<r>,goal:<r>,weight:<r>,action:<si>),

. . .),co_polar_template : sequence(

struct(frequency_index:<r>,template:ref(<n>),weight:<r>,action:<si>),

. . .),cx_polar_template : sequence(

struct(frequency_index:<r>,template:ref(<n>),weight:<r>,action:<si>),

. . .),goals_xpd : sequence(

struct(frequency_index:<r>,theta_min:<r>,theta_max:<r>,goal:<r>,weight:<r>,action:<si>),

. . .),goals_phase_centre : sequence(

struct(frequency_index:<r>,theta_max:<r>,goal:<r>,weight:<r>,action:<si>),

. . .),


goals_ripple : sequence(struct(

frequency_index:<r>,theta:<r>,goal:<r>,weight:<r>,action:<si>),


)

where


<r> = real number



Attributes


A reference to the source for which the beam-pattern param-eters should be optimised.

On-Axis Directivity (goals_on_axis_directivity) [sequence of structs].

A sequence of goal specifications for the on-axis directivity.


Determines the frequency or frequencies for which thegoal is evaluated. The default value is "-1" meaning allthe frequencies used by the referenced source. The Fre-quency Index may be set to a positive integer, in whichcase the goal is evaluated at a single frequency, namelythe frequency with this index_number in the discrete setof defined frequencies. The GUI only supports the defaultsetting of -1.


The goal value of the on-axis directivity in dBi.






maximiseMaximise the on-axis directivity towards or abovethe goal value.

targetTarget the on-axis directivity towards the goal value.

minimiseMinimise the on-axis directivity towards or below thegoal value.

Horn Aperture Efficiency (goals_aperture_efficiency) [sequence of structs].

A sequence of goal specifications for the aperture efficiency.




The goal value of the aperture efficiency in percent. Thegoal value must be larger than or equal to 50% and smallerthan or equal to 100%.





maximiseMaximise the aperture efficiency towards or abovethe goal value.

targetTarget the aperture efficiency towards the goalvalue.


minimiseMinimise the aperture efficiency towards or belowthe goal value.

Directivity in Specific Direction (goals_directivity) [sequence of structs].

A sequence of goal specifications for the directivity in specificfar-field directions.



theta (theta) [real number], default: 30.

The θ-value which together with the value of φ in the at-tribute phi defines the far-field direction in which the di-rectivity is evaluated.

phi (phi) [real number], default: 45.

The φ-value which together with the value of θ in the at-tribute theta defines the far-field direction in which thedirectivity is evaluated.

Component (component) [character string], default: co.

Selects if the goal is set up to the co- or the cx-polar field.

Goal (goal) [real number], default: -12.

The goal value of the directivity in dB. The directivity isgiven relatively to the on-axis value at the same frequency,and thus typically less than zero.



Action (action) [item from a list of character strings], default:target.


targetTarget the directivity towards the goal value.


maximiseMaximise the directivity towards or above the goalvalue.

minimiseMinimise the directivity towards or below the goalvalue.

Maximum cx-Polar to Peak (goals_cross_polar) [sequence of structs].

A sequence of goal specifications for the maximum cross-polarisationlevel.



theta-Min (theta_min) [real number], default: 0..

The maximum cross-polar level is searched inside an an-gular region of θ-values, where theta_min is the lowerlimit. The attribute is specified in degrees and must be inthe interval from 0 to 180 degrees.

theta-Max (theta_max) [real number], default: 90.

The maximum cross polar level is searched inside an an-gular region of θ-values, where theta_max is the upperlimit. The attribute is specified in degrees and must be inthe interval from 0 to 180 degrees.

Goal (goal) [real number], default: -30.

The goal value of the cross-polar level. The level is givenin dB relatively to the co-polar, on-axis directivity, and thusin general less than zero.



Action (action) [item from a list of character strings], default:minimise.



minimiseMinimise the cross polar level towards or below thegoal value.

targetTarget the cross polar level towards the goal value.

maximiseMaximise the cross polar level towards or above thegoal value.

co-Polar Template (co_polar_template) [sequence of structs].

A sequence of specifications by means of Pattern Templatesfor the co-polar pattern.



Template (template) [name of another object], default: blank.

Reference to one of the objects of the type Pattern Tem-plates presenting the goal to be reached. The values inthe Pattern Templates are given in dBi.




The optimiser should - within the range of the specifiedtemplate - try to:

minimiseMinimise the co-polar pattern towards or below thespecified template.

targetTarget the co-polar pattern towards the specifiedtemplate.


maximiseMaximise the co-polar pattern towards or above thespecified template. Note that if the pattern havenulls within the angular range of the template thenthe optimisation will primarily strive to maximisethese nulls in the pattern.

cx-Polar Template (cx_polar_template) [sequence of structs].

A sequence of specifications by means of Pattern Templatesfor the cross-polar pattern.



Template (template) [name of another object], default: blank.

Reference to one of the objects of the type Pattern Tem-plates presenting the goal to be reached. The values inthe Pattern Templates are given in dBi.




The optimiser should - within the range of the specifiedtemplate - try to:

minimiseMinimise the cross-polar pattern towards or belowthe specified template.

targetTarget the cross-polar pattern towards the specifiedtemplate.


maximiseMaximise the cross-polar pattern towards or abovethe specified template. Note that if the patternhave nulls within the angular range of the templatethen the optimisation will primarily strive to max-imise these nulls in the pattern.

Minimum XPD-Level (goals_xpd) [sequence of structs].

A sequence of goal specifications for the minimum cross-polarisationdiscrimination (XPD).



theta-Min (theta_min) [real number], default: 0..

The minimum cross polar level is searched inside an an-gular region of θ-values, where theta_min is the lowerlimit. The attribute is specified in degrees and must be inthe interval from 0 to 180 degrees.


The minimum cross polar level is searched inside an an-gular region of θ-values, where theta_max is the upperlimit. The attribute is specified in degrees and must be inthe interval from 0 to 180 degrees.


The goal value of the XPD. The XPD is given in dB andmeasures the difference between the co-polar and cross-polar level, and is thus typically a positive value.






maximiseMaximise the XPD towards or above the goal value.

targetTarget the XPD towards the goal value.

minimiseMinimise the XPD towards or below the goal value.

Phase Center Location (goals_phase_centre) [sequence of structs].

A sequence of goal specifications for the location of the best-fitphase centre.




The best-fit phase centre is determined for the part of theradiation pattern which is inside a cone of far field direc-tions from the boresight direction to θ equal to theta_max.The attribute is specified in degrees.


The goal value of the phase centre position.





targetTarget the achieved phase centre position towardsthe desired position.

minimiseMinimise the distance between the achieved and de-sired phase centre position.


maximiseMaximise the distance between the achieved and de-sired phase centre position.

Directivity Variation with Azimuthal Angle (goals_ripple) [sequence ofstructs].

A sequence of goal specifications for the maximum variationof the directivity on a conical arc in the far field.



theta (theta) [real number], default: 30.

The polar angle θ defining the conical cut in the far field,where the directivity variation is evaluated. The angle isspecified in degrees.


The goal value of the ripple of the directivity for a fixedvalue θ, i.e. on a conical circle.





targetTarget the directivity ripple towards the goal value.

minimiseMinimise the directivity ripple towards or below thegoal value.

maximiseMaximise the directivity ripple towards or above thegoal value.




Remarks


In each iteration of the optimisation, a mode matching is performed,and the beam parameters calculated. The Goals to the Beam Patterncalculates for each frequency, a number of residuals, each defined asthe weighted difference between an achieved value and a goal valuefor one of the beam parameters. The class returns these residualsto the optimisation algorithm.

On-Axis Directivity

Following the mode matching at Nfreq frequencies, the on-axis direc-tivity is calculated at each frequency according to the definition inSection 9.3.1.2. The achieved on-axis directivity in dBi at frequencyNo. j (j = 1, .., Nfreq) is denoted Achj.

A sequence of Ngoals goals for the on-axis directivity may be specified.The goal specification No. i is given in terms of 1) a goal value, Goali,which is the required value of the on-axis directivity expressed in dBi-values, 2) a weight factor, wi, for this goal, and 3) an action whichtells the optimiser either to maximise (default), target or minimisethe on-axis directivity.

The total number of "On-Axis Directivity" residuals equals the Ngoals

goal-specifications times the Nfreq frequencies. The residual with in-dex (i, j) is calculated as:

Res(i, j) = W ∗ wi ∗ (Achj − Goali)

where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the dBi-values of the achievedand the required on-axis directivity.

Aperture Efficiency

Following the mode matching at Nfreq frequencies, the aperture ef-ficiency is calculated at each frequency according to the definition


in Section 9.3.1.3. The achieved aperture efficiency in percent atfrequency No. j (j = 1, .., Nfreq) is denoted Achj.

A sequence of Ngoals goals for the aperture efficiency may be spec-ified. The goal specification No. i is given in terms of 1) a goalvalue, Goali, which is the required value of the aperture efficiencyexpressed in percent, 2) a weight factor, wi, for this goal, and 3) anaction which tells the optimiser either to maximise (default), targetor minimise the aperture efficiency.

The total number of "Aperture Efficiency" residuals equals the Ngoals



where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the percentage-values of theachieved and the required aperture efficiency.

Directivity in Specific Directions

Following the mode matching at Nfreq frequencies, the directivity in anumber of specific far-field directions is calculated at each frequency.The achieved directivity in dB relative to the co-polar, on-axis direc-tivity at frequency No. j (j = 1, .., Nfreq) is denoted Achj.

A sequence of Ngoals goals for the directivity may be specified. Thegoal specification No. i is given in terms of 1) a θ and a φ-angledefining the far-field direction in which the directivity is evaluated 2)a selection whether it is the co-polar or cross-polar directivity whichshould be evaluated, 3) a goal value, Goali, which is the requiredvalue of the directivity expressed in dB-values relatively to the co-polar, on-axis directivity, 4) a weight factor, wi, for this goal, and5) an action which tells the optimiser either to maximise (default),target or minimise the on-axis directivity.

The total number of "Directivity" residuals equals the Ngoals goal-specifications times the Nfreq frequencies. The residual with index(i, j) is calculated as:


where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the dB-values of the achievedand the required directivity.


Maximum cx-Polar Level

Following the mode matching at Nfreq frequencies, the maximum cx-polar level is calculated at each frequency according to the defini-tion in Section 9.3.1.4. By default the maximum cx-polar level isevaluated in the φ-cut with the maximum cx-polar level for the polarangle θ ranging from 0◦ to 90◦. The user may define a lower limit,"theta_min", and/or an upper limit, "theta_max", for the θ-interval.The achieved maximum cx-polar level in dB relatively to the on-axisco-polar directivity at frequency No. j (j = 1, .., Nfreq) is denotedAchj.

A sequence of Ngoals goals for the maximum cx-polar level may bespecified. The goal specification No. i is given in terms of 1) a goalvalue, Goali, which is the required value of the maximum cx-polarlevel expressed in dB relatively to the on-axis co-polar directivity,2) a weight factor, wi, for this goal, and 3) an action which tellsthe optimiser either to minimise (default), target or maximise themaximum cx-polar level.

The total number of "Maximum Cross-Polar Level" residuals equalsthe Ngoals goal-specifications times the Nfreq frequencies. The residualwith index (i, j) is calculated as:


where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the dB-values of the achievedand the required maximum cross-polar level.

Mimimum XPD Level

Following the mode matching at Nfreq frequencies, the minimum XPD-level is calculated at each frequency according to the definition inSection 9.3.1.6. By default the maximum cx-polar level is eval-uated in the φ-cut with the maximum cx-polar level for the po-lar angle θ ranging from 0◦ to 90◦. The user may define a lowerlimit, "theta_min", and/or an upper limit, "theta_max", for the θ-interval. The achieved minimum XPD-level in dB at frequency No.j (j = 1, .., Nfreq) is denoted Achj.

A sequence of Ngoals goals for the minimum XPD-level may be spec-ified. The goal specification No. i is given in terms of 1) a goalvalue, Goali, which is the required value of the minimum XPD-level


expressed in dB, 2) a weight factor, wi, for this goal, and 3) an ac-tion which tells the optimiser either to minimise (default), target ormaximise the minimum XPD-level.

The total number of "Maximum Cross-Polar Level" residuals equalsthe Ngoals goal-specifications times the Nfreq frequencies. The residualwith index (i, j) is calculated as:


where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the dB-values of the achievedand the required maximum cross-polar level.

Phace-Centre Position

Following the mode matching at Nfreq frequencies, the best-fit phasecentre is calculated at each frequency according to the definition inSection 9.3.1.8. By default the best-fit phase centre is evaluated inthe φ-cut with the maximum cx-polar level for the polar angle θ rang-ing from 0◦ to 90◦. The user may define an upper limit, "theta_max",for the θ-interval. The achieved position of the best-fit phase centreis denoted Achj, and is expressed in terms of the z-coordinate alongthe horn axis of the best-fit phase centre. Often, the best-fit phasecentre is located behind the horn aperture, z = 0, (i.e. inside thehorn) corresponding to a negative z-coordinate.

A sequence of Ngoals goals for the best-fit phase centre may be spec-ified. The goal specification No. i is given in terms of 1) a goal value,Goali, which is the required position on the horn axis of the phasecentre expressed in terms of the z-coordinate for this position, 2) aweight factor, wi, for this goal, and 3) an action which tells the op-timiser either to target (default), maximise or minimise the best fitphase-centre towards the goal position.

The total number of "Phase-Centre Position" residuals equals theNgoals goal-specifications times the Nfreq frequencies. The residualwith index (i, j) is calculated as:

Res(i, j) = W ∗ wi ∗(

Achj − Goaliλj

)where λj is the free-space wavelength at the frequency No. j, andW is the common weight factor, "super_weight". The residual is thusproportional to the difference (measured in free-space wavelengths)


between the z-coordinates of the achieved and the required phase-centre positions.

Directivity Ripple

Following the mode matching at Nfreq frequencies, the co-polar direc-tivity is calculated in a number of directions located on a cone in thefar field, and from these values the maximum ripple of the directivityvalues is calculated.

The cone of directions is defined by a fixed, user-defined value ofthe polar angle θ, and the azimuthal angle, φ, varying from 0 to 2π.The radiated field is first calculated in 16 sample directions on thiscone. Then the minimum and maximum directivity on the cone aredetermined by cubic interpolation of the directivity in between thesample points. The achieved ripple at frequency No. j (j = 1, .., Nfreq)is denoted Achj and is defined as the difference in dB between themaximum and the minimum directivity on the cone.

A sequence of Ngoals goals for the directivity may be specified. Thegoal specification No. i is given in terms of 1) a θ-angle defining thecone of far-field direction in which the directivity is evaluated 2) agoal value, Goali, which is the required value of the directivity ripplein dB 3) a weight factor, wi, for this goal, and 4) an action whichtells the optimiser either to target (default), maximise or minimisethe directivity ripple.

The total number of "Directivity Ripple" residuals equals the Ngoals



where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in the dB-values of the achievedand the required directivity ripple.

280 Tracking Pattern Goals

TRACKING PATTERN GOALS (optimisation_goals_tracking_pattern)

Purpose

The class Tracking Pattern Goals defines optimisation goals (objec-tives) to the tracking pattern radiated by a horn.

Links

Classes→Horn Optimisation→Optimisation Goals→Tracking Pattern Goals

Syntax

<object name> optimisation_goals_tracking_pattern(

source : ref(<n>),lobe_direction : sequence(


. . .),goals_phase_centre : sequence(



)

where


<r> = real number


Attributes


Tracking Pattern Goals 281

A reference to the source for which the tracking-pattern pa-rameters should be optimised.

Direction of Lobe Maximum (lobe_direction) [sequence of structs].

A sequence of goal specifications for the direction of the tracking-lobe.




The direction of the tracking lobe is search inside a cone offar field directions from the boresight direction to θ equalto theta_max. The attribute is specified in degrees.


The goal value of the direction of the tracking lobe. Thedirection is given in degrees relatively to the boresight di-rection.





targetTarget the direction of the tracking lobe towards thegoal value.

minimiseMinimise the direction of the tracking lobe towardsor below the goal value.

maximiseMaximise the direction of the tracking lobe towardsor above the goal value.


Phase Center Location (goals_phase_centre) [sequence of structs].

A sequence of goal specifications for the location of the best-fitphase centre.




The best-fit phase centre is determined for the part of theradiation pattern which is inside a cone of far field direc-tions from the boresight direction to θ equal to theta_max.The attribute is specified in degrees.


The goal value of the phase centre position.





targetTarget the achieved phase centre position towardsthe desired position.

minimiseMinimise the distance between the achieved and de-sired phase centre position.

maximiseMaximise the distance between the achieved and de-sired phase centre position.



Tracking Pattern Goals 283

Remarks


In each iteration of the optimisation, a mode matching is performed,and the tracking-pattern parameters calculated. The Tracking PatternGoals calculates for each frequency, a number of residuals, eachdefined as the weighted difference between an achieved value anda goal value for one of the beam parameters. The class returns theseresiduals to the optimisation algorithm.

Lobe Direction

Following the mode matching at Nfreq frequencies, the direction of thetracking lobe maximum is calculated at each frequency. By defaultthe lobe maximum is evaluated in the φ-cut where the tracking lobeis present for the polar angle θ ranging from 0◦ to 90◦. The user maydefine an upper limit, "theta_max", for the θ-interval. The achieveddirection (in degrees) of the lobe maximum at frequency No. j (j =1, .., Nfreq) is denoted Achj.

A sequence of Ngoals goals for the lobe direction may be specified.The goal specification No. i is given in terms of 1) the "theta_max"value described above, 2) a goal value, Goali, which is the requiredvalue of the lobe direction expressed in degrees relatively to theboresight direction, 3) a weight factor, wi, for this goal, and 4) anaction which tells the optimiser either to maximise (default), targetor minimise the on-axis directivity.

The total number of "Lobe Direction" residuals equals the Ngoals goal-specifications times the Nfreq frequencies. The residual with index(i, j) is calculated as:


where W is the common weight factor, "super_weight". The residualis thus proportional to the difference in degrees of the achieved andthe required directivity.

Phace-Centre Position

Following the mode matching at Nfreq frequencies, the best-fit phasecentre is calculated at each frequency according to the definition in


Section 9.3.1.8. By default the best-fit phase centre is evaluated inthe φ-cut with the maximum cx-polar level for the polar angle θ rang-ing from 0◦ to 90◦. The user may define an upper limit, "theta_max",for the θ-interval. The achieved position of the best-fit phase centreis denoted Achj, and is expressed in terms of the z-coordinate alongthe horn axis of the best-fit phase centre. Often, the best-fit phasecentre is located behind the horn aperture, z = 0, (i.e. inside thehorn) corresponding to a negative z-coordinate.

A sequence of Ngoals goals for the best-fit phase centre may be spec-ified. The goal specification No. i is given in terms of 1) a goal value,Goali, which is the required position on the horn axis of the phasecentre expressed in terms of the z-coordinate for this position, 2) aweight factor, wi, for this goal, and 3) an action which tells the op-timiser either to target (default), maximise or minimise the best fitphase-centre towards the goal position.

The total number of "Phase-Centre Position" residuals equals theNgoals goal-specifications times the Nfreq frequencies. The residualwith index (i, j) is calculated as:

Res(i, j) = W ∗ wi ∗(

Achj − Goaliλj

)where λj is the free-space wavelength at the frequency No. j, andW is the common weight factor, "super_weight". The residual is thusproportional to the difference (measured in free-space wavelengths)between the z-coordinates of the achieved and the required phase-centre positions.

Pattern Templates 285

PATTERN TEMPLATES

Purpose

This group contains classes used to define pattern templates for op-timization purposes. The following two templates are possible:

Piecewise Linear Pattern Template

Piecewise Logarithmic Pattern Template

Links

Classes→Horn Optimisation→Pattern Templates

286 Piecewise Linear Pattern Template

PIECEWISE LINEAR PATTERN TEMPLATE (piecewise_lin_pattern_template)

Purpose

Objects of the class Piecewise Linear Pattern Template are used todefine a pattern template by a set of linear sections. The templateis given as a table of directivity values for increasing angular values.

In the GUI, the pattern templates are defined from the menu inpattern-cut windows (under the Results Tab).

A logarithmic pattern template may be defined by an object of classPiecewise Logarithmic Pattern Template.

Links

Classes→Horn Optimisation→Pattern Templates→Piecewise Linear Pat-tern Template

Syntax

<object name> piecewise_lin_pattern_template(

template : table(<r> <r> . . .))

where

<r> = real number

Attributes

Template (template) [table (2,2)].

Table with 2 columns specifying the piecewise linear patterntemplate. The table must define at least two points.

Theta (Theta ) [real number].

The θ coordinate (in degrees) to a point of the piecewiselinear template definition.

Directivity (Directivity) [real number].

The directivity (in dBi) at this angle.

Remarks

An example applying Piecewise Linear Pattern Template s is shownin the following Figure 1. One template specifies that the gain in

Piecewise Linear Pattern Template 287

the interval 0◦ ≤ θ ≤ 7◦ shall be above 20 dBi, it is specified by thefollowing table:

Theta Directivity0.0 20.07.0 20.07.01 -99.0

The last line generates the (nearly) vertical line for θ = 0◦ (may beomitted).

The other template specifies that the gain in the interval 33◦ ≤ θ ≤180◦ shall be less then -10 dBi, and is specified by this table:

Theta Directivity32.9 99.933.0 -10.045.0 -10.090.0 -25.0180.0 -25.0

The first line in the table gives the (nearly) vertical line at θ = 33◦.

288 Piecewise Linear Pattern Template

Figure 1 A pattern with templates: one for the minimumdirectivity level within the main beam and anotherfor the maximum level in the side-lobe region.

Piecewise Logarithmic Pattern Template 289

PIECEWISE LOGARITHMIC PATTERN TEMPLATE(piecewise_log_pattern_template)

Purpose

Objects of the class Piecewise Logarithmic Pattern Template are usedto define a pattern template by a set of logarithmic sections andsections with a constant level. The template is given as a table ofdirectivity values for increasing angular values.

In the GUI, the pattern templates are defined from the menu inpattern-cut windows (under the Results Tab).

A pattern template consisting of linear sections may be defined byan object of class Piecewise Linear Pattern Template.

Links

Classes→Horn Optimisation→Pattern Templates→Piecewise Logarith-mic Pattern Template

Syntax

<object name> piecewise_log_pattern_template(

template : table(<r> <r> <r> <r> . . .))

where

<r> = real number

Attributes

Template (template) [table (1,4)].

Table with 4 columns specifying the piecewise logarithmic pat-tern template.

Theta Start (Theta Start) [real number].

The θ coordinate (in degrees) for the start of this logarith-mic section

Theta End (Theta End) [real number].

The θ coordinate (in degrees) where the logarithmic sec-tion ends

290 Piecewise Logarithmic Pattern Template

A (A) [real number].

The template is: A + Blog10 θ, A in dBi and B in dB

B (B) [real number].

The template is: A + Blog10 θ, A in dBi and B in dB

Remarks

An example applying a Piecewise Logarithmic Pattern Template isshown in the following Figure 1. The template specifies that the gainin the interval 12◦ ≤ θ ≤ 75◦ shall be below a logarithmic curvegiven by 12 − 75 log10 θ, then by a constant level, −20 dBi, anotherlogarithmic curve and finally a new constant level according to thefollowing table:

Theta Start Theta End A B12.0 75.0 70.0 -48.075.0 90.0 -20.0 0.090.0 135.0 73.8 -48.0135.0 180.0 -28.5 0.0

Piecewise Logarithmic Pattern Template 291

Figure 1 A pattern with a piecewise logarithmic template. Theconstant levels are obtained by specifying B = 0.

292 Horn Results

HORN RESULTS

Purpose

This menu contains classes which define settings for the field outputfrom CHAMP:

Spherical Cut

Spherical Grid

Spherical Wave Expansion (SWE)

Links

Classes→Horn Results

Spherical Cut 293

SPHERICAL CUT (spherical_cut)

Purpose

The class Spherical Cut defines points in cuts on a sphere at whichthe field is to be calculated. Polar as well as conical cuts can bespecified, both in the near-field and in the far-field region.

Links

Classes→Horn Results→Spherical Cut

Syntax

<object name> spherical_cut(

coor_sys : ref(<n>),cut_type : <si>,theta_range : struct(start:<r>, end:<r>, np:),phi_range : struct(start:<r>, end:<r>, np:),e_h : <si>,polarisation : <si>,polarisation_modification : struct(status:<si>, coor_sys:ref(<n>)),near_far : <si>,near_dist : <rl>,file_name : <f>,file_format : <si>,comment : <s>,frequency : ref(<n>)

)

where

 = integer


<r> = real number



<f> = file name


Attributes

294 Spherical Cut


Reference to an object of class Coordinate System defining thecoordinate system (the output coordinate system) in which thefield points will be calculated. Further, the origin serves as thephase reference for far-fields. The field polarisation compo-nents will also be expressed in this coordinate system unlessotherwise specified in the attribute polarisation_modification.

Cut Type (cut_type) [item from a list of character strings], default:polar.

Defines the direction of the cuts over the sphere. See also theremarks below.

polar

Polar cuts are cuts for which φ is constant and θ is vary-ing. Polar cuts will pass through the pole of the spherewhen θ = 0◦ is within the θ-range.

conical

Conical cuts are cuts for which θ is constant and φ isvarying.

theta-Range (theta_range) [struct].

Defines the range of the polar angle θ (see the remarks below).

Start (start) [real number].

Start value of the polar coordinate θ, in degrees.

End (end) [real number].

End value of the polar coordinate θ, in degrees.

Np (np) [integer].

Number of θ-values. When the cut_type is specified to ’po-lar’ np is the number of θ-values in each polar cut. Whenthe cut_type is specified to ‘conical’ np is the number ofconical cuts.

phi-Range (phi_range) [struct].

Defines the range of the azimuthal angle φ (see the remarksbelow).


Start value of the azimuthal coordinate φ, in degrees.

Spherical Cut 295


End value of the azimuthal coordinate φ, in degrees.

Np (np) [integer].

Number of φ-values. When the cut_type is specified to’polar’ np is the number of polar cuts. When the cut_typeis specified to ’conical’ np is the number of φ-values ineach conical cut.

E/H-Field (e_h) [item from a list of character strings], default: e_field.

Specifies whether the complex E-field or H-field shall be cal-culated.

e_field

The complex E-field is calculated.

h_field

The complex H-field is calculated.

Polarisation (polarisation) [item from a list of character strings], de-fault: linear.

Defines how the calculated field shall be decomposed. All com-ponents refer to the polarisation coordinate system as definedunder the attribute Polarisation Modification. In thenear field the r-component of the field is calculated as a thirdcomponent.

linear

Linear components are calculated according to Ludwig’s3rd definition, with the first component (Eco) along xand the second component (Ecx) along y (at θ = 0◦).The notation implies that for a field, which is mainly y-polarised then the second component (Ecx) representsthe co-polar field component.

circular

Circular components are calculated based on the linearcomponents defined above. The first component is theright hand circular (Erhc) and the second is left handcircular component (Elhc).

296 Spherical Cut

theta_phi

The field is decomposed along the θ- and φ-unit vectorswith the θ-component (Eθ) being the first component andthe φ-component being the second (Eφ).

major_minor

The field is de-composed along the major and minor axesof the polarisation ellipse. The first field component isparallel to the major axis (Emaj) and the second to theminor axis (Emin).

linear_xpd

The ratios Eco/Ecx and Ecx/Eco, where Eco and Ecx arethe first and second components as defined for the ’po-larisation: linear’ above. This is the linear cross-polardiscrimination ratio.

circular_xpd

The ratios Erhc/Elhc and Elhc/Erhc, where Erhc and Elhcare the first and second components as defined for the’polarisation: circular’ above. This is the circular cross-polar discrimination ratio.

theta_phi_xpd

The ratios Eθ/Eφ and Eφ/Eθ, where Eθ and Eφ are thefirst and second components as defined for the ’polari-sation: theta_phi’ above.

major_minor_xpd

The ratios Emaj/Emin and Emin/Emaj, where Emaj andEmin are the first and second components as defined forthe ’polarisation: major_minor’ above.

Spherical Cut 297

power

The first component is the amplitude of the field,∣∣∣ ~E∣∣∣,

(i.e. the square root of the power) and the secondcomponent is the complex square root

√Erhc/Elhc. The

phase of the latter component is the rotation angle ofthe polarisation ellipse.In the far field the square root of the power is deter-

mined from∣∣∣ ~E∣∣∣ =

√|Eco|2 + |Ecx|2

and in the near field it is determined from all three field

components:∣∣∣ ~E∣∣∣ =

√|Eco|2 + |Ecx|2 + |Er|2, Er being the

r-component of the field.

Polarisation Modification (polarisation_modification) [struct].

Defines a coordinate system in which the field polarisationcomponents are determined (if different from the output co-ordinate system defined).


Determines if the polarisation modification shall be per-formed:

offNo polarisation modification, the polarisation is de-fined in the above defined output coordinate systemand the polarisation coordinate system is identical tothe output coordinate system.

onThe polarisation is defined in the coordinate systemdefined next.

Coordinate System (coor_sys) [name of another object], de-fault: blank.

Reference to an object of class Coordinate System defin-ing the coordinate system (the polarisation coordinate sys-tem) in which the polarisation components of the calcu-lated field vectors will be expressed. Shall only be speci-fied for status: on.

Near Far (near_far) [item from a list of character strings], default:far.

298 Spherical Cut

The value specifies if a near or a far field is to be calculated.

far

A far field is calculated. In this case only two field com-ponents are calculated according to the specified polar-isation as described in the remarks below.

near

The three field components of a near field is calculated.These are the two components defined under the at-tribute polarisation below and the third component isthe radial component.

Near Dist (near_dist) [real number with unit of length], default: 0.

Defines the radius of a near-field sphere. For a far field thisattribute has no effect and needs not to be specified.


Name of a file, to which the calculated field values shall bewritten.

File Format (file_format) [item from a list of character strings], de-fault: EDX.

The file format used to store the field data:

EDX

The field is written in SI units in a format according tothe Electromagnetic Data Exchange (EDX) standard. Therecommended file extension is .cut.

TICRA

The field is written in GRASP units and stored as anASCII-file according to the TICRA-format described inField Data in Cuts. The recommended file extension is.cut.

EDI

Obsolete file format name. The same as EDX.

Comment (comment) [character string].

A line of text which will be written as a header in the filespecified by file_name above.

Spherical Cut 299

Frequency (frequency) [name of another object], default: blank.

Reference to a Frequency Range object, defining the frequen-cies for which the field is calculated. The reference must beto the same object as specified in the frequency attribute ofthe source generating the field. A frequency needs not to bespecified. In that case, the frequencies in the frequency objectof the source generating the field will be applied.

Command Types

The calculation of the specified field is activated by one of the com-mands:

Get Field

Add Field

Subtract Field

Remarks

The section introduces the position of the field points and the defini-tion of a polarisation coordinate system.

Field Points

Field points in a Spherical Cut are defined in usual spherical (θ, φ)-coordinates given in the output coordinate system. For far fields,(θ, φ) defines a direction

r = x sin θ cosφ+ y sin θ sinφ+ z cos θ

and for near fields, (θ, φ) defines a point

R = R(x sin θ cosφ+ y sin θ sinφ+ z cos θ)

where R =∣∣R∣∣ is the radius (given by Near Dist) of the near-field

sphere.

In a polar cut, φ is fixed and θ takes on the values

θi = θstart + ∆θ · (i− 1), i = 1, 2, ..., nθ (1)

with

∆θ = (θend − θstart)/(nθ − 1)

300 Spherical Cut

where θstart and θend are the members start and end, respectively,of the attribute theta_range, and nθ is the member np of the sameattribute.

The φ-angle is increased equidistantly from one cut to the next bythe values

φj = φstart + ∆φ · (j − 1), j = 1, 2, ..., nφ (2)

with

∆φ = (φend − φstart)/(nφ − 1)

where φstart and φend are the members start and end, respectively,of the attribute phi_range, and nφ is the member np of the sameattribute.

Figure 1 4 polar cuts for 0◦ ≤ θ ≤ 45◦, and φ = 0◦, 60◦, 120◦ and180◦.

In a conical cut θ is fixed and φ runs through the values given byEq. (2). From one conical cut to the next, the θ-angle is increasedaccording to Eq. (1).

Spherical Cut 301

Figure 2 3 conical cuts for θ = 0◦, 22.5◦ and 45◦, and0◦ ≤ φ ≤ 180◦.

The Polarisation Coordinate System

When the field polarisation is requested in another coordinate sys-tem than the output coordinate system then the attribute polarisa-tion_modification shall be applied with ‘status: on’ followed by a ref-erence to the polarisation coordinate system.

The attribute polarisation may be specified as ‘linear’ (Eco- and Ecx-components), ‘circular’ (Erhc- and Elhc-components) or ‘theta_phi’(Eθ- and Eφ-components). In the near field also an Er-componentwill be present. In case of ‘theta_phi’ polarisation the electric field isgiven by

E = Err + Eθθ + Eφφ

where r, θ and φ are the polarisation vectors in the polarisation co-ordinate system. The spherical cut in which the field is determinedis always given in the output coordinate system.

302 Spherical Cut

An example is shown in Figure 3, the cut is the polar cut shown inred and the field shall be determined at one of the output points, P .The output coordinate system is denoted x0y0z0 and the polarisationcoordinate system is xpypzp. In the figure the latter is a simple rota-tion of the former around the y-axis but any coordinate system maybe chosen as polarisation coordinate system.

Figure 3 In red is shown a single polar cut in the outputcoordinate system given by x0y0z0. A field point P atthe direction (θ0, φ0) is illustrated. The polarisation isexpressed in θφ-components (polarisation: theta_phi)along θp and φp in the polarisation coordinate systemxpypzp.

Internally in CHAMP the field is calculated in Cartesian componentsin the output coordinate system

E = Eoxx0 + Eoyy0 + Eoz z0

The field is then converted to the new components

E = Epxxp + Epyyp + Epz zp

before the Cartesian components are converted to (in this case) thepolar components in the usual way.

Spherical Cut 303

The resulting θp-component (shown in blue) is pointing away fromthe zp-axis in the same way as the standard θ0-component will pointaway from the z0-axis (along θ0).

304 Spherical Grid

SPHERICAL GRID (spherical_grid)

Purpose

The class Spherical Grid defines field points in a 2D grid on a spherewhere the field shall be calculated. Both near fields and far fieldsmay be calculated.

Links

Classes→Horn Results→Spherical Grid

Syntax

<object name> spherical_grid(

coor_sys : ref(<n>),grid_type : <si>,x_range : struct(start:<r>, end:<r>, np:),y_range : struct(start:<r>, end:<r>, np:),truncation : <si>,e_h : <si>,polarisation : <si>,polarisation_modification : struct(status:<si>, coor_sys:ref(<n>)),near_far : <si>,near_dist : <rl>,file_name : <f>,file_format : <si>,comment : <s>,frequency : ref(<n>)

)

where

 = integer


<r> = real number



<f> = file name


Attributes

Spherical Grid 305


Reference to an object of class Coordinate System defining thecoordinate system (the output coordinate system) in which thefield points will be calculated. Further, the origin serves as thephase reference for far fields. The field polarisation compo-nents will also be expressed in this coordinate system unlessotherwise specified in the attribute Polarisation Modifi-cation.

Grid Type (grid_type) [item from a list of character strings], default:uv.

The field points are positioned in a 2D grid over the sphericalsurface. The 2D grid is defined by the variables X and Y (seeX-Range and Y-Range) according to the following definitions(see also the figures in the remarks below).

uv

(X, Y ) = (u, v) where u and v are the two first coordi-nates of the unit vector to the field point. Hence,

r = (u, v,√

1− u2 − v2) (1)

u and v are related to the spherical angles by u =sin θ cosφ, v = sin θ sinφ. u and v have no units.

elevation_over_azimuth

(X, Y ) = (Az,El), where Az and El de-fines the direction to the field point by r =(− sinAz cosEl, sinEl, cosAz cosEl). Az and El are an-gles in degrees. Note that an antenna will be measuredin such a grid (with respect to the antenna) applying anazimuth-over-elevation set-up.

elevation_and_azimuth

(X, Y ) = (Az,El), where Az and El defines the di-rection to the field point through the relations Az =−θ cosφ,El = θ sinφ to the spherical angles θ and φ. Azand El are, as θ, angles in degrees.

306 Spherical Grid

azimuth_over_elevation

(X, Y ) = (Az,El), where Az and El de-fines the direction to the field point by r =(− sinAz, cosAz sinEl, cosAz cosEl). Az and Elare angles in degrees. Note that an antenna will bemeasured in such a grid (with respect to the antenna)applying an elevation-over-azimuth set-up.

theta_phi

(X, Y ) = (φ, θ), where θ and φ are the usual sphericalangles of the direction to the field point. θ and φ areangles in degrees.

elevation_over_azimuth_EDX

(X, Y ) = (Az,El), where Az and El de-fines the direction to the field point by r =(sinAz, cosAz sinEl, cosAz cosEl). Az and El areangles in degrees. Note that an antenna will be mea-sured in such a standard grid (with respect to theantenna) applying a real elevation-over-azimuth set-up.

azimuth_over_elevation_EDX

(X, Y ) = (Az,El), where Az and El de-fines the direction to the field point by r =(sinAz cosEl, sinEl, cosAz cosEl). Az and El areangles in degrees. Note that an antenna will be mea-sured in such a standard grid (with respect to theantenna) applying a real azimuth-over-elevation set-up.

X-Range (x_range) [struct].

Defines the range and number of points along the first gridcoordinate, X, as specified by the attribute Grid Type above.


Start value of the grid first coordinate X.


End value of the first grid coordinate X.

Np (np) [integer].

Number of field points along first grid coordinate X.

Y-Range (y_range) [struct].

Spherical Grid 307

Defines the range and number of points along the second gridcoordinate, Y , as specified by the attribute Grid Type.


Start value of the second grid coordinate Y .


End value of the second grid coordinate Y .

Np (np) [integer].

Number of field points along second grid coordinate Y .

Truncation (truncation) [item from a list of character strings], default:rectangular.

Specifies the area in which the field is calculated.

rectangular

The field is calculated in all of the grid points within therectangular area defined by X-Range and Y-Range.

elliptical

The field is only calculated at the grid points insidethe elliptical area with the axes of the ellipse definedby X-Range and Y-Range (in a plane rectangular XY -coordinate system).

E/H-Field (e_h) [item from a list of character strings], default: e_field.

Specifies the field type to be calculated.

e_field

The complex E-field is calculated.

h_field

The complex H-field is calculated.

Polarisation (polarisation) [item from a list of character strings], de-fault: linear.

Defines how the calculated field shall be decomposed. All com-ponents refer to the output coordinate system given in Coor-dinate System unless a polarisation coordinate system asdefined under the attribute Polarisation Modification.In the near field the r-component of the field is calculated asa third component.

308 Spherical Grid

linear

Linear components are calculated according to Ludwig’s3rd definition, with the first component (Eco) along xand the second component (Ecx) along y (at θ = 0◦).The notation implies that for a field, which is mainly y-polarised then the second component (Ecx) representsthe co-polar field component.

circular

Circular components are calculated based on the linearcomponents defined above. The first component is theright hand circular (Erhc) and the second is left handcircular component (Elhc).

theta_phi

The field is decomposed along the θ- and φ-unit vectorswith the θ-component (Eθ) being the first component andthe φ-component being the second (Eφ).

major_minor

The field is decomposed along the major and minor axesof the polarisation ellipse. The first field component isparallel to the major axis (Emaj) and the second to theminor axis (Emin).

linear_xpd

The ratios Eco/Ecx and Ecx/Eco, where Eco and Ecx arethe first and second components as defined for the ’po-larisation: linear’. This is the linear cross-polar discrimi-nation ratio.

circular_xpd

The ratios Erhc/Elhc and Elhc/Erhc, where Erhc and Elhcare the first and second components as defined for the’polarisation: circular’ above. This is the circular cross-polar discrimination ratio.

theta_phi_xpd

The ratios Eθ/Eφ and Eφ/Eθ, where Eθ and Eφ are thefirst and second components as defined for the ’polari-sation: theta_phi’ above.

Spherical Grid 309

major_minor_xpd

The ratios Emaj/Emin and Emin/Emaj, where Emaj andEmin are the first and second components as defined forthe ’polarisation: major_minor’ above.

power

The first component is the amplitude of the field,∣∣∣ ~E∣∣∣,

(i.e. the square root of the power) and the secondcomponent is the complex square root

√Erhc/Elhc. The

phase of the latter component is the rotation angle ofthe polarisation ellipse.In the far field the square root of the power is deter-

mined from∣∣∣ ~E∣∣∣ =

√|Eco|2 + |Ecx|2

and in the near field it is determined from all three field

components:∣∣∣ ~E∣∣∣ =

√|Eco|2 + |Ecx|2 + |Er|2, Er being the

r-component of the field.

Polarisation Modification (polarisation_modification) [struct].

Defines a coordinate system in which the field polarisationcomponents are determined (if different from the output coor-dinate system defined in attribute Coordinate System above).


Determines if the polarisation modification shall be per-formed:

offNo polarisation modification, the polarisation is de-fined in the above defined output coordinate systemand the polarisation coordinate system is identical tothe output coordinate system.

onThe polarisation is defined in the coordinate systemdefined next.

310 Spherical Grid

Coordinate System (coor_sys) [name of another object], de-fault: blank.

Reference to an object of class Coordinate System defin-ing the coordinate system (the polarisation coordinate sys-tem) in which the polarisation components of the calcu-lated field vectors will be expressed. Shall only be speci-fied for status: on.

Near/Far (near_far) [item from a list of character strings], default:far.

The value specifies if a near or a far field is to be calculated.

far

A far field is calculated. In this case only two field com-ponents are calculated according to the specified Po-larisation.

near

The three field components of a near field is calculated.These are the two components defined under the at-tribute Polarisation and the radial component.

Near-Field Distance (near_dist) [real number with unit of length], de-fault: 0.

Defines the radius of a near-field sphere. For a far field thisattribute has no effect and needs not to be specified.





EDX

The field is written in SI units in a format according tothe Electromagnetic Data Exchange (EDX) standard. Therecommended file extension is .grd.

Spherical Grid 311

TICRA

The field is written in GRASP units and stored as anASCII-file according to the TICRA-format described inField Data in Rectangular Grid. The recommended fileextension is .grd.

EDI


Comment (comment) [character string].

A line of text which will be written as a header in the filespecified by File Name above.

Frequency (frequency) [name of another object], default: blank.

Reference to a Frequency Range object, defining the frequen-cies for which the field is calculated. The reference must beto the same object as specified in the frequency attribute ofthe source generating the field. A frequency needs not to bespecified. In that case, the frequencies in the frequency objectof the source generating the field will be applied.

Command Types

The calculation of the specified field is activated by one of the com-mands:

Get Field

Add Field

Subtract Field

Remarks

The section introduces the grids specifying the positions of the fieldpoints and the definition of a polarisation coordinate system.

Field Points

The field points in a Spherical Grid are defined in usual spherical(θ, φ)-coordinates. For far fields, (θ, φ) defines a direction

r = x sin θ cosφ+ y sin θ sinφ+ z cos θ

312 Spherical Grid

and for near fields, (θ, φ) defines a point

R = R(x sin θ cosφ+ y sin θ sinφ+ z cos θ)

where R =∣∣R∣∣ is the radius of the near-field sphere (as given by the

attribute Near-Field Distance).

The unit vectors x, y and z are the unit vectors along the axes ofthe output coordinate system as defined by the attribute coor_sys.In the following figures the axes are denoted xo, yo and zo.

The field grid is defined by the ranges X-Range and Y-Range ina general XY -coordinate system where (X, Y ) may take one of thedefinitions given by the attribute Grid Type. The field grid thenconsists of the points

X = Xs + ∆X(i− 1) +X1

Y = Ys + ∆Y (j − 1) + Y1

where i and j takes on the values

i = 1, 2, . . . , Nx

j = 1, 2, . . . , Ny.

Moreover, Xs and Ys are the X-Range->Start values and Nx and Ny

are the number of values, X-Range->Np, of the attributes X-Rangeand Y-Range, respectively, and ∆X and ∆Y are the spacings in thegrid

∆X = (Xe −Xs)/(Nx − 1)

∆Y = (Ye − Ys)/(Ny − 1)

where Xe and Ye are the X-Range->End values of the attributesX-Range and Y-Range, respectively.

The Grids

The X and Y variables of the grid are related to the direction tothe field points according to the selected value of the attribute GridType. The different possibilities are illustrated in the following fig-ures. x0y0z0 is the output coordinate system as defined by the at-tribute Coordinate System. Some grids are related to a scanningprocedure, but for all grids the x0y0z0-coordinate system is fixed withrespect to the antenna and follows this during the scanning.

Spherical Grid 313

For all the grids, the central direction given by (X, Y ) = (0, 0) is alongthe z0-axis, θ = 0.

Note that many grid definitions involve the rotational angles azimuthand elevation. These grids are alike but have important differenceswhich are explained in the following sections.

Grid Type: uv

The uv-grid constitutes a regular grid when projected to the x0y0-plane. The far-field directions of this grid are obtained by projectingthe grid to a unit-sphere, see the following Figure 1. This grid is theonly grid not given in angles.

Figure 1 Grid Type: uv.The uv-grid is that drawn in the x0y0-plane, while thered grid upon the sphere (obtained by parallelprojection) shows the far-field directions of theirregular angles corresponding to the regular uv-grid.The grid is drawn for −0.5 ≤ u ≤ 0.5 and−0.5 ≤ v ≤ 0.5 with a spacing of 0.1 in both u and v.

Grid Type: elevation_over_azimuth

For the elevation-over-azimuth grid the direction to a field point canbe visualized by a telescope mounted in an elevation-over-azimuthset-up at the origin of the x0y0z0-coordinate system. When rotatedthe angles (Az,El), the telescope will point at the field point givenby the angles (Az,El). The grid has poles on the y0-axis, see Figure2.

314 Spherical Grid

Apart from the positive direction of the azimuth rotation, the grid isthe same as the azimuth_over_elevation_EDX-grid described below.

Figure 2 Grid Type: elevation_over_azimuth.The grid is drawn for −30◦ ≤ Az ≤ 30◦ and−30◦ ≤ El ≤ 30◦ with a spacing of 6◦ in both Az(azimuth) and El (elevation).

Grid Type: elevation_and_azimuth

This grid treats azimuth and elevation symmetrically but is not re-lated to physical rotations. The grid is shown in Figure 3.

Spherical Grid 315

Figure 3 Grid Type: elevation_and_azimuth.The grid is drawn for −30◦ ≤ Az ≤ 30◦ and0◦ ≤ El ≤ 30◦ with a spacing of 6◦ in both Az(azimuth) and El (elevation).

Grid Type: azimuth_over_elevation

Also for this grid the direction to a field point can be visualized by atelescope, now mounted in an azimuth-over-elevation set-up, placedat the origin of the x0y0z0-coordinate system. When rotated the an-gles (Az,El), the telescope will point at the field point given by theangles (Az,El). The grid has poles on the x0-axis, see Figure 4.

Apart from the positive direction of the azimuth rotation, the grid isthe same as the elevation_over_azimuth_EDX-grid described below.

316 Spherical Grid

Figure 4 Grid Type: azimuth_over_elevation.The grid is drawn for −30◦ ≤ Az ≤ 30◦ and−30◦ ≤ El ≤ 30◦ with a spacing of 6◦ in both Az(azimuth) and El (elevation).

Grid Type: theta_phi

This grid is a conventional grid in the spherical coordinates θ and φwith poles on the z0-axis (for θ = 0◦ and θ = 180◦), Figure 5.

Figure 5 Grid Type: theta_phi.The grid is drawn for 0◦ ≤ θ ≤ 30◦ and 0◦ ≤ φ ≤ 360◦

with a spacing of 6◦ in θ and 20◦ in φ.

Grid Type: elevation_over_azimuth_EDX

This grid is the grid in which an antenna will be sampled when it is

Spherical Grid 317

mounted in a traditional elevation-over-azimuth (El/Az) scanner whilethe direction to the field point is kept constant as in a far-field range.

In order to illustrate the elevation-over-azimuth scanning, a reflectorantenna is shown in the following figures. The scanner itself is notshown.

The grid type is one of the standard grid types in EDX1. The direc-tions in the grid are given by azimuth, Az, and elevation, El, alter-natively denoted α and ε, respectively, in order to distinguish fromthe azimuth and elevation angles in the azimuth-over-elevation grid(see following grid type). As for all other grids, the grid follows theantenna during rotations.

The grid has poles on the x0-axis and is shown in Figure 6.

Figure 6 Grid Type: elevation_over_azimuth_EDX (El/Az orε/α).To illustrate that this grid corresponds to rotation ofthe antenna in an elevation-over-azimuth positioner,this and the following figures shows the antennarotations, here before rotation, i.e. Az = α = 0◦ andEl = ε = 0◦. zrange indicates the direction to the fieldprobe (the far-field direction).The grid is drawn for −30◦ ≤ Az (α) ≤ 30◦ and−30◦ ≤ El (ε) ≤ 30◦ with a spacing of 6◦ in both Az(or α, azimuth) and El (or ε, elevation).

1EDX is a definition of how electromagnetic data may be exchanged between varioussoftware tools, see "Electromagnetic Data Exchange Field Data Dictionary definition", Euro-pean Space Agency and Satimo S.A., 2008

318 Spherical Grid

The rotation of an antenna mounted in an elevation-over-azimuth set-up is in the following figures illustrated step by step. The antenna isa front-fed reflector antenna which initially (i.e. for Az = 0◦ and El =0◦) is pointing in the far-field direction of the measurement rangewhich is along the z-axis of the range, zrange. The antenna is given inits output coordinate system (attribute Coordinate System) x0y0z0with the main beam along the z0-axis. This initial situation is shownin Figure 6.

When this antenna is rotated in azimuth we get Figure 7. The an-tenna beam is rotated to the left in the figure as given by the angleAz which - in the grid fixed to the antenna - is positive to the right.

Figure 7 The reflector antenna is first rotated in azimuth. Thegrid spacing is 6◦, thus Az = α = 12◦.

The antenna is then tilted in elevation (upon the rotated azimuthplatform), Figure 8. The antenna beam is hereby tilted down theangle El whereby the fixed far-field direction is moved the sameangle El up with respect to the antenna.

Spherical Grid 319

Figure 8 The reflector antenna is finally tilted in elevation. Thegrid spacing is 6◦ thus El = ε = 18◦ (andAz = α = 12◦, unchanged).

In all the above figures, the range coordinate system is kept fixed(zrange points in the same direction) while the antenna is rotating asin a (imagined) physical scanner. If we instead show the antenna andthe grid in a fixed antenna coordinate system, the x0y0z0-coordinatesystem, and move the field direction (represented by zrange) to thegrid point we obtain Figure 9. This figure is thus shown in the sameantenna perspective as Figure 6 but with a field direction correspond-ing to the grid point at (Az,El) = (18◦, 12◦).

320 Spherical Grid

Figure 9 The grid is here shown with the field direction movedto (Az,El) = (α, ε) = (18◦, 12◦) but the antenna keptfixed, while in Figure 8 the antenna was moved. Theantenna and the grid is therefore oriented in thesame way as in Figure 6. The field direction is givenby the z-axis of the range system, zrange, which herepoints near to directly out of the paper.

The elevation_over_azimuth-grid has poles on the x0-axis and is thusthe same as the azimuth_over_elevation-grid illustrated in Figure 4apart from the positive direction of the azimuth rotation (Az or α)which for the EDX grid increases to the right.

Grid Type: azimuth_over_elevation_EDX

This grid is the grid in which an antenna will be sampled when it ismounted in a traditional azimuth-over-elevation (Az/El) scanner whilethe direction to the field point (Az,El) is kept constant as in a far-field range.

In order to illustrate the azimuth-over-elevation scanning, a reflectorantenna is shown in the following figures. The scanner itself is notshown.

The grid type is one of the standard grid types in EDX2. As for allother grids, the grid follows the antenna when it is rotated. The gridhas poles on the y0-axis and is shown in Figure 10.

2EDX is a definition of how electromagnetic data may be exchanged between varioussoftware tools, see "Electromagnetic Data Exchange Field Data Dictionary definition", Euro-pean Space Agency and Satimo S.A., 2008

Spherical Grid 321

Figure 10 Grid Type: azimuth_over_elevation_EDX (Az/El).To illustrate that this grid corresponds to rotation ofthe antenna in an azimuth-over-elevation positioner,this and the following figures shows the antennarotations, here before rotation, i.e. Az = 0◦ andEl = 0◦. zrange indicates the direction to the fieldprobe.The grid is drawn for −30◦ ≤ Az ≤ 30◦ and−30◦ ≤ El ≤ 30◦ with a spacing of 6◦ in both Az(azimuth) and El (elevation).

The rotation of an antenna mounted in an azimuth-over-elevation set-up is in the following figures illustrated step by step. The antenna isa front-fed reflector antenna which initially (i.e. for Az = 0◦ and El =0◦) is pointing in the far-field direction of the measurement rangewhich is along the z-axis of the range, zrange. The antenna is given inits output coordinate system (attribute Coordinate System) x0y0z0with the main beam along the z0-axis. This initial situation is shownin Figure 10.

If this antenna is tilted in elevation we get Figure 11. The antennabeam is here tilted down the angle El whereby the fixed far-fielddirection is moved the same angle El up with respect to the antenna.

322 Spherical Grid

Figure 11 The reflector antenna is now tilted in elevation. Thegrid spacing is 6◦ thus El = 18◦ (and Az = 0◦).

Finally the antenna is rotated in azimuth upon the tilted elevationplatform, Figure 12. The antenna beam is now rotated to the leftas given by the angle Az which in the grid fixed to the antenna ispositive to the right.

Figure 12 The reflector antenna is finally rotated in azimuth.The grid spacing is 6◦ thus Az = 12◦ (and El = 18◦,unchanged).

In all these figures, the range coordinate system is kept fixed (zrangepoints in the same direction) while the antenna is rotating as in a(imagined) physical scanner. If we instead show the antenna andthe grid in a fixed antenna coordinate system, the x0y0z0-coordinate

Spherical Grid 323

system, and move the field direction (represented by zrange) to thegrid point we obtain Figure 13. This figure is thus shown in thesame antenna perspective as Figure 10 but with the grid point at(Az,El) = (18◦, 12◦).

Figure 13 The grid is here shown with the field direction movedto (Az,El) = (18◦, 12◦) and the antenna kept fixed,while in Figure 12 the antenna was moved. Theantenna and the grid is therefore oriented in thesame way as in Figure 10. The field direction is givenby the z-axis of the range system, zrange, which herepoints out of the paper.

The azimuth_over_elevation_EDX-grid has poles on the y0-axis and isthus the same as the elevation_over_azimuth-grid illustrated in Figure2 apart from the positive direction of the azimuth rotation (Az) whichfor the EDX-grid increases to the right.

The Polarisation Coordinate System

When the field polarisation is requested in another coordinate sys-tem than the output coordinate system then the attribute polarisa-tion_modification shall be applie d with ‘status: on’ followed by areference to the polarisation coordinate system.

The attribute polarisation may be specified as ‘linear’ (Eco- and Ecx-components), ‘circular’ (Erhc- and Elhc-components) or ‘theta_phi’(Eθ- and Eφ-components). In the near field also an Er-componentwill be present. In case of ‘theta_phi’ polarisation the electric field isgiven by

E = Err + Eθθ + Eφφ

324 Spherical Grid

where r, θ and φ are the polarisation vectors in the polarisation co-ordinate system. The spherical grid in which the field is determinedis always given in the output coordinate system.

An example is shown in Figure 14 in which only two perpendiculararcs of the grid are shown in red. The field is to be determined atthe observation point P . The output coordinate system is denoted byx0y0z0 and the polarisation coordinate system is xpypzp. In the figurethe latter is a simple rotation of the former around the y-axis but anycoordinate system may be chosen as polarisation coordinate system.

Figure 14 In red is shown two arcs of the spherical grid in theoutput coordinate system given by x0y0z0. Theobservation point P is specified by the direction(θ0, φ0). The polarisation is expressed in theta_phi

components along θp and φp in the polarisationcoordinate system xpypzp.

Internally in CHAMP the field is calculated in Cartesian componentsin the output coordinate system

E = Eoxx0 + Eoyy0 + Eoz z0.

Spherical Grid 325

The field is then converted to the new components

E = Epxxp + Epyyp + Epz zp

before the Cartesian components are converted to (in this case) thepolar components in the usual way.

The resulting θp-component (shown in blue) is pointing away fromthe zp-axis in the same way as the standard θ0-component will pointaway from the z0-axis (along θ0).

326 Spherical Wave Expansion (SWE)

SPHERICAL WAVE EXPANSION (SWE) (swe)

Purpose

In the class Spherical Wave Expansion (SWE) it is specified how thespherical wave coefficients of a field will be calculated. The specifi-cations include how the field shall be given in a regular grid on animaginary spherical surface (near or far field) and where to store thecoefficients.

The spherical wave coefficients constitute a unique way to define afield (e.g. of a measured feed) from which the near field as well asthe far field may be constructed.

Links

Classes→Horn Results→Spherical Wave Expansion (SWE)

Syntax

<object name> swe(

file_name : <f>,sphere_sample : struct(n_phi:, n_theta:),power_norm : <si>,list : <si>,file_format : <si>,comment : <s>,obsolete_file_coef : <si>,obsolete_frequency : ref(<n>)

)

where

 = integer



<f> = file name


Attributes


Spherical Wave Expansion (SWE) 327


Sphere Sample (sphere_sample) [struct].

Defines the number of field samples on the sphere (see theremarks below) along the φ- and θ-coordinates, respectively.

N phi (n_phi) [integer].

Number of field samples along a full azimuth circle, 0◦ <φ < 360◦; n_phi must be even and larger than or equal to4.

N theta (n_theta) [integer].

Number of field samples along a half polar circle, 0◦ ≤θ ≤ 180◦, both end points included; n_theta must be largerthan or equal to 3.

Power Norm (power_norm) [item from a list of character strings],default: off.

Power normalisation of the field expansion.

off

The field is not normalised.

on

The power contained in the spherical wave expansionis normalised to 4π. Hereby a field calculated from thecoefficients is given relative to isotropic level.

List (list) [item from a list of character strings], default: off.

Specifies whether a list of the spherical coefficients shall bereproduced in the standard output file.

off

No list is generated.

on

A list is generated.




EDX

The file is stored in a format according to the Electro-magnetic Data Exchange (EDX) standard.

TICRA

The file is stored as an ASCII-file and fulfills the TICRA-format described in Spherical Wave Q-Coefficients. Therecommended file extension is .sph.

EDI


Comment (comment) [character string], default: SWE.

A line of text which will be written as a header in the filespecified byfile_name above.

Coefficients in File (Obsolete) (obsolete_file_coef ) [item from a list ofcharacter strings], default: Q.

Specifies the type of spherical coefficients to be generated.The attribute is obsolete.

Q

The coefficients are the Q-coefficients (recommended)

ab

The coefficients are the ab-coefficients (obsolete, forcompatibility only).

Frequency (Obsolete) (obsolete_frequency) [name of another object],default: blank.

The attribute is obsolete and is maintained for backward com-patibility. The attribute is ignored.

Command Types

The calculation of the spherical coefficients is activated by the com-mand:

Get SWE

in which the source, for which the spherical coefficients are deter-mined, is specified.


Remarks

The spherical wave expansion is a very precise way to characterizethe field from a source, and this class, Spherical Wave Expansion(SWE), is used for generating the coefficients of the expansion.

When a field of a Corrugated Horn Mode Matching object is calcu-lated, this calculation is automatically determined on the basis ofa spherical expansion of the far field of the feed and objects ofclass Spherical Wave Expansion (SWE) need not to be set up by theuser See the remarks section below.

Objects of the present class should not be used in cases when thecoefficients of the spherical wave expansion are needed for export orwhen special attention is requested as for a (measured) pattern forwhich the most correct values of the number of modes are uncertain.

This section contains remarks on

• The reference centre for the SWE,

• The operation of the SWE class,

• The basic concepts of the SWE,

• The sample spacing.

Reference Centre

The SWE is calculated from the field on a sphere. The expansion de-pends on the position and the orientation of this sphere with respectto the source generating the field. The sphere is therefore definedin the coordinate system of this source with the polar axis of thesphere being the z-axis of the coordinate system and the centre ofthe sphere being at the origin of the system. The coordinate systemis specified by the relevant attribute of the actual Corrugated HornMode Matching.

The Corrugated Horn Mode Matching object is specified in the GetSWE command by which the coefficients are calculated.

Operation

Objects of the class Spherical Wave Expansion (SWE) are used fordefining a SWE of a radiating field. The field originate from a sourcewhich is specified in the command Get SWE. When this commandis issued the SWE is calculated in two steps. First, the field of thesource is calculated on a sphere related to this source (as specified in


the attribute Sphere Sample) and second, the requested expansioncoefficients are calculated from that field.

The coefficients are stored on the specified file. The Q-coefficientsare standard.

The field is completely described by the coefficients for all angulardirections and distances – including the far field – outside a minimumsphere.

The SWE

The SWE is a general expansion of a radiating field in sphericalmodes. The coefficients of these modes are the spherical coeffi-cients.

The modes are described by indices (m,n) related to the size of thesource, and a third index (s) for the Q-coefficients.

The integer m is referred to as the azimuthal index and describes thefield variations in φ by sinmφ and cosmφ terms. Similarly, the polarindex n describes the field variations in θ as sinnθ and cosnθ terms.

The polar index n has the range

1 ≤ n ≤ N (1)

For modes with polar index n, the azimuthal index m is within therange

−n ≤ m ≤ n. (2)

The number of modes are thus limited by N , and N is derived from

N = kr0 + max(10, 3.6 3√kr0) (3)

where k is the wavenumber, 2π/λ, and r0 is the radius of the smallestsphere completely enclosing all the sources of the field. The max-imum mode index N thus depends on the extend of the radiatingsources but also on the position of the centre of the sphere as theradii are measured from that centre.

The centre of the sphere is the origin of the coordinate system of thesource specified in the Get SWE command. A clever choice of thecoordinate system with respect to the extend of the source can thusreduce the number of modes which again reduces the computationtime.


Sampling on the Sphere

As mentioned above, the field is evaluated on a sphere in orderto calculate the coefficients. This sphere must be concentric withthe minimum sphere of radius r0 and it must surround the sourcecompletely. Thus, the radius of the sphere, A, must fulfill

A ≥ r0. (4)

The spacing of the field points on the sphere must be small enoughto represent all spherical modes. In the polar angle the fastest fieldvariation is given by sinnθ and cosnθ with n being equal to its max-imum value, n = N . The spacing between sample points must thenbe

∆θ = 180◦/N (or less) (5)

with N given by Eq. (3). Therefore the number of sample pointsalong a half circle are (both end points included):

n_theta =180◦

∆θ+ 1 = N + 1. (or larger) (6)

Similarly,

∆φ = 180◦/N (or less) (7)

for the general source and the number of sample points, n_phi, alonga full azimuthal circle is

n_phi =360◦

∆φ= 2N (or larger.) (8)

Very often the field variation in φ is limited to only a few azimuthalmodes and the maximum values for m is limited to M

|m| ≤M < N. (9)

In this case

n_phi = 2(M + 1). (10)

The sample increment in φ is then

∆φ = 180◦/(M + 1). (11)


The increment in φ may thus be much coarser than in θ when M �N .

For a pattern fully described by sinφ and cosφ, i.e.

M = 1

we have

n_phi = 4

which means that the pattern may be fully described by the principle-plane patterns

∆φ = 90◦.

It is the values of the specified n_phi and n_theta which determinesthe maximum mode indices M and N , given by

M = n_phi/2− 1 = 180◦/∆φ− 1, (12)

N = n_theta− 1 = 180◦/∆θ. (13)

Summations of the power contained in all modes up to the currentm and, respectively, up to the current n, n ≤ N are given in thestandard output file. These two tables shall be studied carefully.The power of excluded modes will spread out within the determinedmodes, and the power in the highest involved modes (in n as wellas in m) will increase. It is therefore a good check to assure that thecontribution to the total power from the highest involved modes iswithin the desired accuracy threshold.

It must be noted that a dense angular spacing will result in corre-sponding high values of M and N . It must be checked that

M ≤ N (14)

is not violated hereby, i.e. by Eqs. (10) and (6)

n_phi/2 ≤ n_theta (15)

shall be fulfilled. Furthermore, Eq. (4) must be fulfilled, i.e. by Eqs.(3) and (6) that

n_theta− 1 ≤ kA+ max(10, 3.6 3√kr0). (16)


There is, however, no reason to apply higher values of n_phi andn_theta than given by Eqs. (8), (6) and (3) as the space-limitedsource will not result in modes with higher indices.

Note that the chosen values of n_theta and n_phi influence the com-puting time for determination of the coefficients as this is based onthe Fast Fourier Transform algorithm (FFT). The FFT is fastest whenn_theta – 1 (=N) as well as n_phi can be written as a product ofmany small prime factors, e.g. N = 180 = 2 · 2 · 3 · 3 · 5. Factors above5 should be avoided.

Finally, the correct number of expansion coefficients for a sourcedoes neither depend on the radius, A, nor on n_phi nor n_theta.

334 Command Types

10.3 Command Types

Purpose

Commands are used in CHAMP to activate calculations. A commandmust be of one of the available ”command types” listed below.

The command types described here follow the syntax:

COMMAND OBJECT <target> command (attributes)

where <target> is the object which is the target for the command(i.e. the object upon which the command operates), command isthe actual command type and attributes is a list of attributes whichspecifies the input to the command type.

Command type(s) for mode-matching analysis:

Get Modes (get_modes)

Command type(s) for field and pattern computations:

Get Field (get_field)

Add Field (add_field)

Subtract Field (subtract_field)

Command type(s) for optimisation of geometry:

Get Optimum (get_optimum)

Command type(s) for the analysis of geometrical tolerances:

Get Influence (get_influence)

Command type(s) for exporting the reflector geometry to CADfiles:

Export to STEP File (export_step)

Export to IGES File (export_iges)

Export to 2D STEP File (export_step_2d)

Command type(s) for field expansion in spherical waves:

Get SWE (get_swe)

Command type(s) for modifying geometry:

Reshape Profile (reshape_spline_profile)

Command Types 335

Reshape Reflector (reshape_reflector)

Links


Classes

File Extensions

Applicable Units

File Formats

Reference Section

Contents

336 Get Modes

GET MODES (get_modes)

Purpose

A command of the type Get Modes activates the mode matching ofa horn.

The mode matching is controlled by a number of user-defined set-tings in the Corrugated Horn Mode Matching object which is the tar-get of the command. This object also defines a name of a file, wherethe calculated overall scattering matrix for the horn is stored, andthus allows the object to be used as a source for subsequent fieldcomputations.

Links

Command Types

Syntax

COMMAND OBJECT <target> get_modes()

where

<target>= name of an object of type Corrugated Horn ModeMatching

Target

<target> [name of another object].

Reference to an object of class Corrugated Horn Mode Match-ing specifying the geometry and further necessary parametersfor which the scattering matrix is determined. The name ofthe file to which the scattering matrix is written is also definedhere.

Remarks

The Get Modes command has no arguments.

Get Field 337

GET FIELD (get_field)

Purpose

A command of the type Get Field activates the computation of thefield from a given Corrugated Horn Mode Matching object at thepoints specified in a Spherical Cut or Spherical Grid object.

Links

Command Types

Syntax

COMMAND OBJECT <target> get_field(

source : sequence(ref(<n>), . . .)

)

where

<target>= name of an object of type Spherical Cut; Spherical Grid

<n> = name of another object

Target


Reference to a Field Storage object. This object defines thefield points and the field to be calculated. Any field alreadycontained in the object will be overwritten as will existing files.

Attributes

Source (source) [sequence of names of other objects].

Reference to an object of the class Corrugated Horn ModeMatching from which the field shall be calculated and stored.

338 Add Field

ADD FIELD (add_field)

Purpose

A command of the type Add Field activates the computation of thefield from a given Corrugated Horn Mode Matching object at thepoints specified in a Spherical Cut or Spherical Grid object. The com-puted field is added to the field already contained in the specifiedobject.

Links

Command Types

Syntax

COMMAND OBJECT <target> add_field(


)

where



Target


Reference to a Field Storage object. This object defines thefield points and the field components to be calculated. Thecalculated field will be added to the field already contained inthe object, and it is the resulting field which will be stored. TheField Storage object must exist and it must have been referredto in an earlier Get Field command such that it is not empty.

Attributes


Reference to an object of the class Corrugated Horn ModeMatching from which the field shall be calculated. The cal-culated field is added to the field already stored in the targetobject.

Subtract Field 339

SUBTRACT FIELD (subtract_field)

Purpose

A command of the type Subtract Field activates the computationof the field from a given Corrugated Horn Mode Matching object atthe points specified in a Spherical Cut or Spherical Grid object. Thecomputed field is subtracted from the field already contained in thespecified object.

Links

Command Types

Syntax

COMMAND OBJECT <target> subtract_field(


)

where



Target


Reference to a Field Storage object. This object defines thefield points and the field components to be calculated. The cal-culated field will be subtracted from the field already containedin the object. It is the resulting field which will be stored. TheField Storage object must exist and it must have been referredto in an earlier Get Field command such that it is not empty.

Attributes


Reference to an object of the class Corrugated Horn ModeMatching from which the field shall be calculated. The cal-culated field is subtracted from the field already stored in thetarget object.

340 Get SWE

GET SWE (get_swe)

Purpose

A command of the type Get SWE activates the computation of thespherical wave coefficients from a given Corrugated Horn Mode Match-ing object, as specified in a Spherical Wave Expansion (SWE) object.

Links

Command Types

Syntax

COMMAND OBJECT <target> get_swe(

source : ref(<n>))

where

<target>= name of an object of type Spherical Wave Expansion(SWE)


Target


Reference to an object of the class Spherical Wave Expansion(SWE). This object defines how the spherical wave coefficientsshall be calculated as well as a possible file for storage of thecoefficients. If an output file is specified and it already exists,it will be overwritten.

Attributes

Source (source) [name of another object], default: blank.

A reference to a Corrugated Horn Mode Matching object radi-ating the field to be expanded in spherical modes.

Remarks

The field of the specified source is calculated in the grid defined inthe Spherical Wave Expansion (SWE) object. The spherical wave ex-

Get SWE 341

pansion is next carried out on basis of these field values and thecoefficients are stored in the file defined in the Spherical Wave Ex-pansion (SWE) object.

342 Get Optimum

GET OPTIMUM (get_optimum)

Purpose

A command of the type Get Optimum activates the optimisation ofthe horn geometry as specified in a Optimisation Manager object.

Links

Command Types

Syntax

COMMAND OBJECT <target> get_optimum()

where

<target>= name of an object of type Optimisation Manager

Target


Name of the Optimisation Manager object that controls theoptimisation.

Remarks

The Get Optimum command has no arguments.

Get Influence 343

GET INFLUENCE (get_influence)

Purpose

A command of the type Get Influence activates the horn-toleranceanalysis as specified in the Horn Tolerance object, which is the targetof the function.

Links

Command Types

Syntax

COMMAND OBJECT <target> get_influence()

where

<target>= name of an object of type Horn Tolerance

Target


An object of class Horn Tolerance according to which the toler-ance analysis is carried out.

Remarks

The output data from the horn-tolerance analysis is stored in a datafile as specified in the target-object.

344 Export to STEP File

EXPORT TO STEP FILE (export_step)

Purpose

A command of the type Export to STEP File exports the geometry ofa horn to a CAD file. The produced CAD file will be in the STEP formatand the recommended extension is .stp (or .step). The surface of theexported scatterer will have zero thickness.

Links

Command Types

Syntax

COMMAND OBJECT <target> export_step(

output_file_name : <f>,tolerance : <rl>

)

where

<target>= name of an object of type Waveguide Section; CombinedHorn Section; Corrugation List; Dual Depth Corrugated Section;Waveguide Step; Axial Corrugations; Single Depth CorrugatedSection; Single Depth Section with Mode Converter; Smooth WalledSection

<rl> = real number with unit of length

<f> = file name

Target


Name of an object (of one of the classes listed in the sectionSyntax). It is the geometry of this object which is exported.

Attributes


The name of the file to which the STEP-3D representation ofthe geometry is written. The default file extension is .stp.

Tolerance (tolerance) [real number with unit of length].

Export to STEP File 345

The maximum allowed difference between the approximateSTEP-3D representation and the actual geometry.

Remarks

The export to the CAD file works for all parts of the geometry, i.e.for the horn interior as well as the horn exterior. The horn exteriorshall be specified by an object of class Combined Horn Section.

The horn will be represented as a single surface shell in the CAD file.The surface shell will consist of a number of connected sub-surfaces.The thickness of the horn is zero.

The output CAD file is written with the length unit ’mm’.

346 Export to 2D STEP File

EXPORT TO 2D STEP FILE (export_step_2d)

Purpose

A command of the type Export to 2D STEP File exports a 2D-representationof the horn geometry to a CAD file. The produced CAD file will be inthe STEP format and the recommended extension is .stp (or .step).The lines of the exported horn will have zero thickness.

Links

Command Types

Syntax

COMMAND OBJECT <target> export_step_2d(


)

where



<f> = file name

Target



Attributes


The name of the file to which the STEP-2D representation ofthe geometry is written. The default file extension is .stp.


Export to 2D STEP File 347

The maximum allowed difference between the approximateSTEP-2D representation and the actual geometry.

Remarks


The rotational symmetric 3D geometry may be represented by a setof curves in a plane containing the axis of symmetry. A rotationof these curves around the axis of symmetry generates the full 3Dgeometry. It is the 2D geometry of these curves which are exported.For exporting the full 3D geometry apply the command Export toSTEP File.

The thickness of the lines is zero.


348 Export to IGES File

EXPORT TO IGES FILE (export_iges)

Purpose

A command of the type Export to IGES File exports the geometry ofa horn to a CAD file. The produced CAD file will be in the IGES formatand the recommended extension is .igs (or .iges). The surface of theexported scatterer will have zero thickness.

Links

Command Types

Syntax

COMMAND OBJECT <target> export_iges(


)

where



<f> = file name

Target



Attributes


The name of the file to which the IGES representation of thegeometry is written. The default file extension is .igs.


Export to IGES File 349

The maximum allowed difference between the approximateIGES representation and the actual geometry.

Remarks


The horn will be represented as a single surface shell in the CAD file.The surface shell will consist of a number of connected sub-surfaces.The thickness of the horn is zero.


350 Reshape Profile

RESHAPE PROFILE (reshape_spline_profile)

Purpose

A command of the type Reshape Profile (re)defines a spline profileby fitting to the existing profile with more (or less) control points.

Links

Command Types

Syntax

COMMAND OBJECT <target> reshape_spline_profile(

fit_to_profile : ref(<n>),number_of_points : 

)

where

<target>= name of an object of type Spline Profile

 = integer


Target


Reference to a Spline Profile object into which the fitted profileis to be stored.

Attributes

Fit to Profile (fit_to_profile) [name of another object].

Reference to an existing profile of class Horn Profile to whichthe new profile shall fit.

Number of Points (number_of_points) [integer].

The number of control points, including the end points, for theshaped profile.

Remarks

Reshape Profile 351

This command may be used in connection with optimization of a pro-file given by a spline function. If the optimization shall work upon aprofile given by many control points there is a risk for the optimiza-tion to be ineffective. It is therefore recommended to start with asimple profile given by a few control points. When an optimum hasbeen found for this simple profile then the profile may be refined byfitting it to a new profile with a higher number of control points forwhich the details are then optimized.

If <target> is specified to the same Spline Profile as that specifiedin attribute Fit to Profile then the latter will be overwritten, theprofile is reshaped.

Method

An existing Spline Profile is used as base for a new Spline Profilewith a specified number of control points. The existing profile isdetermined at a number of function points, ten times as many asthe by Number of Points specified number of control points. Thenew control points are then determined such that the resulting splinefunction fits the function points best possible (by a least squares fit).

352 Reshape Reflector

RESHAPE REFLECTOR (reshape_reflector)

Purpose

A command of the type Reshape Reflector (re)defines a reflectorspline profile by fitting to the existing profile with more (or less)control points.

Links

Command Types

Syntax

COMMAND OBJECT <target> reshape_reflector(

fit_to_reflector : ref(<n>),number_of_points : 

)

where

<target>= name of an object of type Spline Reflector

 = integer


Target


Reference to a Spline Reflector object into which the fittedprofile is to be stored.

Attributes

Fit to Reflector (fit_to_reflector) [name of another object].

Reference to an existing profile of one of the classes Reflectorsto which the new profile shall fit.

Number of Points (number_of_points) [integer].

The number of control points, including the end points, for theshaped profile.

Remarks

Reshape Reflector 353

This command may be used in connection with optimization of areflector profile. If the optimization shall work upon a profile givenby many control points there is a risk for the optimization to beineffective. It is therefore recommended to start with a simple profilegiven by a few control points. When an optimum has been found forthis simple profile then the profile may be refined by fitting it toa new profile with a higher number of control points for which thedetails are then optimized.

If <target> is specified to the same Spline Reflector as that specifiedin attribute Fit to Reflector then the latter will be overwritten,the profile is reshaped.

Method

An existing reflector profile given by a spline function may be used asbase for a new spline profile with a changed number of control points.The existing profile is determined at a number of function points, tentimes as many as the by Number of Points specified number ofcontrol points. The new control points are then determined such thatthe resulting spline function fits the function points best possible (bya least squares fit).

354 Applicable Units

10.4 Applicable Units and the dB-Scale

Units

CHAMP offers the following units for the attributes, where appropriate:

Valid units of length are

mm for millimetre(s)cm for centimetre(s)m for metre(s)km for kilometre(s)in for inch(es)ft for foot (feet)

Valid units of frequency are

Hz for hertzkHz for kilohertzMHz for megahertzGHz for gigahertzTHz for terahertz

The unit for conductivity is

S/m for Siemens per metre

dB-scale and field units

In CHAMP the Pattern Cuts may be plotted in the Results Manager. Theprogram shows the amplitude and of the directivity pattern. The amplitude,A is proportional to the power contents of the field and thus proportional tothe amplitude of the field squared,

AdB ∼ 10 log10(∣∣∣ ~E∣∣∣2) = 20 log10(

∣∣∣ ~E∣∣∣) (1)

It is also possible to plot the phase of pattern cuts, which is the phase ofthe E-field, calculated in CHAMP.

In CHAMP the aperture fields may be plotted in the Results Manager. Theprogram shows an amplitude in dB, AdB defined by

AdB = 10 log10(∣∣∣ ~E∣∣∣2) = 20 log10(

∣∣∣ ~E∣∣∣) (2)

Applicable Units 355

where ~E is the field in SI-units, i.e. V/m. The excitation mode has a powerof 1 Watt. The phase of the pattern cuts may also be plotted. This is thephase of the E-field calculated in CHAMP.

Links


Classes

Command Types

File Extensions

File Formats

Reference Section

Contents

356 File Extensions

10.5 File Extensions

Purpose

For the files used for input and output in CHAMP it is recommendedto use different file extensions depending on the content of the files.The recommended file extensions are listed below together with ashort description.

Project Control:.tor Object repository (input of the objects describing the

case to be calculated).tci Command input (calculation commands).champ CHAMP project file (input).out General output file from a CHAMP calculation.log General log file from a CHAMP calculationReflector Descriptions:.rsf Numerical, rotationally symmetric surface, input to

class Tabulated Reflector. The content is described inRotationally Symmetric Surface.

Source (Feed) Positions and Excitations:.sph Spherical modes for a feed, output from class Spher-

ical Wave Expansion (SWE). The content of the file isdescribed in Spherical Wave Q-Coefficients.

Patterns and Fields:.cut Field pattern in cuts, output from class Spherical Cut.

The content is described in Field Data in Cuts..grd Field pattern in grid, output from class Spherical Grid.

The content is described in Field Data in RectangularGrid.

Links


Classes

Command Types

Applicable Units

File Formats

Reference Section

File Extensions 357

Contents

358 File Formats

10.6 File Formats

This section contains a description of the data files used by CHAMP. The Listof File Formats is given below.

CHAMP reads and generates a number of data files which serve as links toother programs. The format of the files is compatible with previous versionsof CHAMP. Numbers and character strings are read record by record in freeformat (apart from two file types which shall be written in fixed format)meaning that the format is arbitrary except that there must be at leastone space between each data value (numbers and character strings) in therecord. Alternatively, a comma is allowed as separator, possibly surroundedby blanks. Because the blanks may be used as separators blanks cannot beaccepted within a character string. Character strings are denoted stringin the following (under the column heading Format). However, in headingand text records blanks are accepted. These are specified as charactersin the following.

The format of the input records is described in the following, record byrecord. A record number is given (under the column heading Record) butthis is only used for reference here. Thus, there may be several records inthe input file with the same record number.

The contents of the input records are given (under the column headingContents) in one of two ways:

1. The record must contain the specific stated content. This is then givenin brackets (which must be included). Such records are used as head-ers. Example:

[title]

and the seven characters ”[title]” must be inserted in the input record.

2. A list of variables is given. The types of the variables are given in thecolumn Format. Commonly used types are characters, string,integer and real number. Example:

NP, KSPACE, KTIP (3 integers)

and three integers must be specified in this input record.

The values to be given for the variables are explained in the text below eachinput record.

File Formats 359

The input of an array of numbers (e.g. coordinates to points in a plane) isindicated in the following way:

((X(I), Y(I), I=1,NP) (real numbers)

which means that the vectors X and Y must be given in the sequence:

X(1), Y(1), X(2), Y(2),..., X(NP), Y(NP).

It is insignificant how many numbers are given in each record as long asthey are stored in the correct order and separated by blanks or by commas.

The sequence in which a two-dimensional array is stored is indicated byconstructions like

(Z(I,J), J = 1, NY), I = 1, NX) (real numbers)

meaning that the second index J is running faster than the first index, i.e.the sequence becomes:

Z(1,1), Z(1,2),. . ., Z(1,NY), Z(2,1),. . ., Z(2,NY),. . ., Z(NX,1),. . .,Z(NX,NY).

The following types of data files are defined together with the applied FileExtensions:

F1 Reflector DataF1.1 Rotationally Symmetric Surface .rsfF2 Field DataF2.1 Field Data in Cuts .cutF2.2 Field Data in Rectangular Grid .grdF3 Tabulated Feed DataF3.1 Spherical Wave Q-Coefficients .sph

Links


Classes

Command Types

360 File Formats

File Extensions

Applicable Units

Reference Section

Contents

File Formats 361

F1 Reflector Data

The following reflector data file types are available:

• Rotationally Symmetric Surface

Links

List of File Formats

Reference Section

362 File Formats

F1.1 Rotationally Symmetric Surface

Format

The format is used in the definition of surfaces of class TabulatedReflector and the file extension is .rsf. The surface is rotationallysymmetric around the z-axis and specified by a number of points ona radial arc where the distance is defined by

ρ =√x2 + y2 (3)

The format is:

Record Contents Format

1 TEXT (characters)

TEXT - Record with identification text

2 NP, KSPACE, KTIP (3 integers)

NP - Number of points, at least 3.KSPACE = 0 - Equispaced points in ρ.

= 1 - Unequally spaced points in ρ.KTIP = 0 - Surface will have tangent parallel to

the xy-plane at ρ =0.= 1 - Reflector will have tip at ρ =0.

If KSPACE = 1, go to record No. 3.1 else go to record No.3.2.

3.1 (RHO(I), Z(I), I=1,NP) (real numbers)

RHO - Radial distance from z-axis to I’thpoint. Must be given in increasing or-der.

Z - z-coordinate at the I’th point.

---end of file for KSPACE=1---

3.2 RS, RE (2 real numbers)

File Formats 363

RS - Start value andRE - End value of radial distance from z-

axis to surface point.

3.3 (Z(I), I=1,NP) (real numbers)

Z(I) z-coordinate at the distance ρ from thez-axis where ρ = RS + ∆ρ · (I-1) and ∆ρ =(RE-RS)/(NP-1)

---end of file for KSPACE=0---

Links

Reflector Data


Reference Section

364 File Formats

F2 Field Data

The file formats for field values in cuts and grids are described in the fol-lowing sections.

• Field Data in Cuts

• Field Data in Rectangular Grid

Links


Reference Section

File Formats 365

F2.1 Field Data in Cuts

Format

The file is generated by objects of the class Spherical Cutfor storingfield data in cuts. The file extension is .cut.

A cut consists of records of types 1, 2 and 3 as described below. Ifmore than one cut is contained in a file all records must be repeatedfor each cut.


1 TEXT (characters)

TEXT - Record with identification text

2 V_INI, V_INC, V_NUM, C, ICOMP, ICUT, NCOMP (2 realnumbers, one integer, 1 real number, 3 integers)

The V_ and C values are angles in degrees and theirdefinition is controlled by the parameter ICUT:

V_INI - Initial value.V_INC - Increment.V_NUM - Number of values in cut.C - Constant.ICOMP - Polarisation control parameter.ICUT - Control parameter of cut.NCOMP - Number of field components.

For spherical cut:

The V_ and C values are angles in degrees and theirdefinition is controlled by the parameter ICUT:

ICUT =1 A standard polar cut where φ is fixed(C) and θ is varying (V_)

ICUT =2 A conical cut where θ is fixed (C) and φis varying (V_).

The field components F1, F2 are specified by the pa-rameter ICOMP. For near fields the third componentF3 always contains the radial Eρ-component. F1 andF2 are for

366 File Formats

ICOMP

=1 Linear Eθ and Eφ.=2 Right hand and left hand circular (Erhc

and Elhc).=3 Linear Eco and Ecx (Ludwig’s third defi-

nition).=4 Linear along major and minor axes of the

polarisation ellipse, Emaj and Emin.=5 XPD fields: Eθ/Eφ and Eφ/Eθ.=6 XPD fields: Erhc/Elhc and Elhc/Erhc.=7 XPD fields: Eco/Ecx and Ecx/Eco.=8 XPD fields: Emaj/Emin and Emin/Emaj.=9 Total power

∣∣E∣∣ and √Erhc/Elhc.

NCOMP - Number of field components.=2 The file contains two field components

for each point as specified above.=3 When the field is a near field the file

also contains the third radial compo-nent, Eρ.

NCOMP - Number of field components.=3 The file contains three field com-

ponents for each point as specifiedabove.

Record No. 3 and the following records contain the fieldvalues

If NCOMP=2

3 (F1(I),F2(I), I = 1, V_NUM) (4 real numbers on eachrecord)

F1,F2 - Complex arrays containing the two com-ponents of the field for the I’th datapoint.V = V_INI + V_INC*(I-1)

If NCOMP=3

3 (F1(I),F2(I),F3(I), I = 1, V_NUM)(6 real numbers oneach record)

File Formats 367

F1,F2,F3 - Complex arrays containing the threecomponents of the field for the I’thdata point.V = V_INI + V_INC*(I-1)

---end of data file---

For ICOMP=1, 2, 3, 5, 6 or 7 F1, F2 (and optionally F3) contain thereal and imaginary parts of the field in linear scale.

For ICOMP=4:

Real part of F1 is the major axis of the polarisa-tion ellipse (linear scale).Real part of F2 is the minor axis of the polarisa-tion ellipse (linear scale).Imaginary parts of F1 and F2 are zero.

For ICOMP=8

Real part of F1 is the major axis divided bythe minor axis of the polarisation ellipse (linearscale).Real part of F2 is the minor axis divided bythe major axis of the polarisation ellipse (linearscale).Imaginary parts of F1 and F2 are zero.

For ICOMP=9

Real part of F1 is the total power∣∣E∣∣ of the field

(linear scale)Imaginary part of F1 is zero.F2 is the complex square root of the ratiorhc/lhc. The phase of this value is the rotationangle of the polarisation ellipse.

Links

Field Data


Reference Section

368 File Formats

F2.2 Field Data in Rectangular Grid

Format

This format is used for storing field values in a rectangular grid. Filesof this type are generated by objects of the class Spherical Grid, andthe file extension is .grd. Data points are located either on a sphere.

If the field points are located on a sphere the direction to a fieldpoint r is related to the polar angles θ and φ by

r = x sin θ cosφ+ y sin θ sinφ+ z cos θ (4)

If the field points are located on a plane it is assumed that the planeis parallel to the xy-plane of the output coordinate system so that apoint can be defined by its x- and y-coordinates.

If the field points are located on a cylinder the vector to a field point~r is defined by

r = xρ cosφ+ yρ sinφ+ zz (5)

where ρ is the constant radius of the cylinder and φ and z are thetwo variables that specifies a point on the cylinder.

The field points are in all cases parameterised by two variables whichare generally denoted X and Y and which run from XMIN to XMAX andfrom YMIN to YMAX, respectively. The file is organised so that X isvarying faster than Y. The variables X and Y should be considered asgeneral names for the actual variables which may e.g. be φ and θfor points on a sphere or any of the other options as specified byIGRID below.

The file format is:


1 TEXT (characters)

TEXT - Record with identification text. This recordis repeated until a record containing ++++ as thefirst 4 characters is reached.

2 KTYPE (integer)

File Formats 369

Specifies type of file format

KTYPE = 1 - standard format for 2D grid. For filesused in CHAMP this variable is always 1.

3 NSET, ICOMP, NCOMP, IGRID (4 integers)

NSET - Number of field sets or beams.ICOMP - Control parameter of field components.NCOMP - Number of components.IGRID - Control parameter of field grid type.

For spherical grid:

The field components F1, F2 are controlled by theparameter ICOMP. For near fields the third compo-nent F3 always contains the radial Er component.

ICOMP

=1 linear Eθ and Eφ.=2 Right and left hand circular components

(rhc,lhc).=3 Linear co and cx components (Ludwig’s

third definition).=4 Major and minor axes of polarisation

ellipse.=5 XPD fields: Eθ/Eφ and Eφ/Eθ.=6 XPD fields: rhc/lhc and lhc/rhc.=7 XPD fields: co/cx and cx/co.=8 XPD fields: major/minor and mi-

nor/major.=9 total power

∣∣E∣∣ and √rhc/lhc.

If ICOMP is negative the above polarisation defi-nitions apply according to ICOMP’s absolute value,but the negative sign indicates that the polarisa-tion is not defined the grid coordinate system (at-tribute polarisation_modification has been set to‘on’ in the grid-defining object, see class Spher-ical Grid).

370 File Formats

NCOMP - Number of field components.=2 The file contains two field components

for each point as specified above.=3 If the field is a near field the file

also contains the third radial compo-nent.

IGRID - Type of field grid.=1 uv-grid:

(X, Y ) = (u, v) where u and v are the twofirst coordinates of the unit vector tothe field point. Hence,r =

(u, v,√

1− u2 − v2)

u and v are related to the spherical an-gles by u = sin θ cosφ, v = sin θ sinφ.

=4 Elevation over azimuth:(X, Y )=(Az,El), where Az and El definethe direction to the field point byr = − sinAz cosEl, sinEl, cosAz cosEl.

=5 Elevation and azimuth:(X, Y )=(Az,El), where Az and El de-fine the direction to the field pointthrough the relationsAz = -θ cosφ, El = θ sinφto the spherical angles θ and φ.

=6 Azimuth over elevation:(X, Y )= (Az, El), where Az and El definethe direction to the field point byr = − sinAz, cosAz sinEl, cosAz cosEl.

=7 θφ-grid:(X, Y ) = (φ, θ), where θ and φ are thespherical angles of the direction tothe field point.

4 (IX(I), IY(I), I=1, NSET) (2 integers on eachrecord)

IX,IY - Centre of set or beam No. I. See thefollowing record for explanation.

All the following records are repeated NSET times

File Formats 371

5 XS, YS, XE, YE (4 real numbers)

Limits of 2D grid. The grid points (X,Y) run throughthe values

X = XCEN + XS +DX*(I-1)Y = YCEN + YS +DY*(J-1)

where

DX = (XE-XS)/(NX-1), DY = (YE-YS)/(NY-1)

and

XCEN = DX*IX, YCEN = DY*IY

The number of grid values NX and NY and the rangeof the index I and J are defined in the followingrecords.

6 NX, NY, KLIMIT (3 integers)

NX - Number of columnsNY - Number of rowsKLIMIT - Specification of limits in a 2D grid

=0 Each row contains data for all NXcolumns.

=1 The number of data points for each rowis defined in the following records.

The following records 7 and 8 are repeated NY times (J=1,NY)for each beam

If KLIMIT = 0 skip to records No. 8 with IS = 1 and IE =NX

If KLIMIT = 1 record 7 is read

7 IS, IN (2 integers)

IS - Column number of first data point in rowJ

IN - Number of data points in row J

If KLIMIT = 0, IS and IN are always assumed to be 1 andNX, respectively.

372 File Formats

If IN = 0 skip records No. 8. and repeat from record No.7.If IN > 0 continue at record No. 8.2 or 8.3 with IE =IS+IN-1.

If NCOMP = 2

8.2 (F1(I), F2(I)), I = IS, IE (4 real numbers on eachrecord)

F1,F2 - Complex field with two components.

If NCOMP = 3

8.3 (F1(I), F2(I), F3(I)), I = IS, IE (6 real numberson each record)

F1,F2,F3 - Complex field with three components.

---end of data file---

For ICOMP=1, 2, 3, 5, 6 or 7 F1, F2 (and optionally F3) contain thereal and imaginary parts of the field in linear scale.

For ICOMP=4 F1 and F2 contain

Real part of F1 is major axes of polarisation el-lipse (linear scale)Real part of F2 is minor axes of polarisation el-lipse (linear scale)Imaginary part of F1 and F2 is zero

For ICOMP=8

Real part of F1 is the major axis divided bythe minor axis of the polarisation ellipse (linearscale).Real part of F2 is the minor axis divided bythe major axis of the polarisation ellipse (linearscale).Imaginary parts of F1 and F2 are zero.

For ICOMP=9 F1 and F2 contain

File Formats 373

Real part of F1 is total power∣∣E∣∣ of field (linear

scale)Imaginary part of F1 is zeroF2 is the complex square root of the ratiorhc/lhc. The phase of this value is the rotationangle of the polarisation ellipse.

Links

Field Data


Reference Section

374 File Formats

F3 Tabulated Feed Data

The following tabulated feed data file types are available:

• Spherical Wave Q-Coefficients

Links


Reference Section

File Formats 375

F3.1 Spherical Wave Q-Coefficients

Format

This file with extension .sph contains the spherical wave Q-coefficients

The first 8 records contain various header information. Althoughsome of these are not used here, they must nevertheless be presentin the file.

The Spherical Wave Expansion coefficients may be specified at sev-eral frequencies, sequentially defined in the Frequency Range objectreferred in the object writing or reading the coefficients file. For eachfrequency in the sequence, the data structure described below mustbe concatenated into one file, one set of data for each frequency,and the data must be concatenated according to the frequency se-quence. The data structure contains for each frequency a headersection followed by the Spherical Wave Expansion coefficients.

The file is read in the following free formatted fashion:


1 PRGTAG (characters)

PRGTAG - Program tag and time stamp, text plantedby the program that created the file.

2 IDSTRG (characters)

IDSTRG - Record with identification text.

3 NTHE, NPHI, NMAX, MMAX (4 integers)

Control data for the Spherical Wave Expansion

376 File Formats

NTHE Number of θ-samples over 360◦, NTHE mustbe even and NTHE ≥ 4 ∗) .

NPHI Number of φ-samples over 360◦, NPHI ≥ 3∗) .

NMAX Maximum value for polar index n in theexpansion,1 ≤ NMAX ≤ NTHE/2.

MMAX Maximum value for azimuthal index |m| inthe expansion,0 ≤ MMAX ≤ min([(NPHI-1)/2],NMAX) with min(I1,I2) being thesmaller of I1 and I2 and [X] being theinteger part of X.

∗) See ’Note on definition of sample spacing’ be-low.

The following 5 records contain dummy data items of thetype specified.

4 TEXT STRING (characters)

5 FIVE REAL DATA ITEMS (5 real numbers)

6 FIVE REAL DATA ITEMS (5 real numbers)



-- end of header records --

The following records contain the Spherical Wave Expan-sion coefficients in the order of the azimuthal modes.For each azimuthal mode of indices m and −m, the se-quence of the Q-coefficients, Q′smn, are preceded by arecord containing the modal index |m| for that mode, as

File Formats 377

well as the power contained in the mode. The scheme isas follows :

m.1 M, POWERM (1 integer, 1 real number)

M Azimuthal mode index, |m|POWERM Power in all coefficients of index ±m

m.2 Q1MN, Q2MN (4 real numbers on each record)

Q1MN, Q2MN - Wave coefficients Q′smn for s =1,2 and ((m=-m and m=+m), n =max (1, |m|) , ..., Nmax)

The above scheme is repeated for all azimuthal modes, |m| = 0, ...,MMAX.

Explicitly, for m = 0 the sequence is{Q′101, Q

′201, Q

′102, Q

′202, . . . , Q

′1,0,Nmax

, Q′2,0,Nmax

}(6)

while for |m| = 1 we have the sequence

{Q′1,−1,1, Q′2,−1,1, Q′111, Q′211, Q′1,−1,2, Q′2,−1,2, Q′112, Q′212, ...,Q′1,−1,Nmax

, Q′2,−1,Nmax, Q′1,1,Nmax

, Q′2,1,Nmax} (7)

and - in general - for |m| = µ

{Q′1,−µ,µ, Q′2,−µ,µ, Q′1µµ, Q′2µµ, Q′1,−µ,µ+1, Q′2,−µ,µ+1, Q

′1,µ,µ+1, Q

′2µ,µ+1, ...,

Q′1,−µ,Nmax, Q′2,−µ,Nmax

, Q′1,µ,Nmax, Q′2,µ,Nmax

}. (8)

The number of coefficients for each |m| is 4(Nmax -(|m|-1)), except form = 0, where only 2Nmax coefficients are present.

The electric field, ~ESI in SI-units, is given by the following expansionin spherical waves

~ESI(r, θ, φ) = k√ζ∑smn

Qsmn~Fsmn(r, θ, φ). (9)

For this field, the total radiated power, P , is given by

P =1

2

∑smn

|Qsmn|2 (Watts). (10)

378 File Formats

When the total radiated power is 4π Watts then the far-field patternis normalised to dBi.

The coefficients in the file, Q′smn, are related to the coefficients, Qsmn,in the spherical expansion, Eq. (9), by

Q′smn =1√8πQ∗smn (11)

where the asterisk means complex conjugation (see the note below).This normalisation of the coefficients in the file implies that a fieldnormalised to dBi, i.e. a field radiating a power of 4π watts, will have(cf. Eq. (10))

P =1

2

∑smn

|Qsmn|2 = 4π(Watts) (12)

and hence (cf. Eq. (3))∑smn

|Q′smn|2

= 1. (13)

The Q′smn-coefficients in the file thus reflect the power of the fieldand the parameter POWERM is given by

POWERM =1

2

∑sn

|Q′smn|2

(|m| is fixed, |m| = M) (14)

and the total power P is expressed as

P =∑|m|

POWERM =1

2

∑smn

|Q′smn|2. (15)

This applies whether the pattern is power normalised or not. Forpower normalised patterns radiating 4π Watts we find

P =1

2. (16)

If POWERM and P of Eqs. (14) and (15) are multiplied by 8π the poweris expressed in Watts.

Note on Normalisation:

For historical reasons - and in order to stay compatible with othersoftware - the definition of the coefficients in the file has been re-tained as the one originally introduced by Larsen in 1980. He used

File Formats 379

the time dependence e−iωt, whereas CHAMP employs ejωt in Eq. (9).Hence the complex conjugation in Eq. (11).

He introduced the excitation, v, of the antenna and the transmissioncoefficients, Tsmn, by

Q′smn = vTsmn. (17)

The transmission coefficients are characteristic for the antenna andindependent of the antenna excitation. If the antenna is matchedand lossless then we have∑

smn

|Tsmn|2 = 1. (18)

Accordingly, for the radiated power, P,

P =1

2

∑smn

|Q′smn|2

=1

2|v|2

∑smn

|Tsmn|2 =1

2|v|2 (19)

and a normalisation corresponding to v = 1 was a natural choiceleading to Eq. (16).

Note on definition of sample spacing:

It shall be noted that NTHE (record No. 3) is different from theattribute n_theta in the object of class Spherical Wave Expansion(SWE) generating the file. The two quantities are related throughNTHE = (n_theta − 1) × 2. Further, NPHI may be odd which is notallowed for the attribute n_phi.

Links

Tabulated Feed Data


Reference Section

380 References

References

[1] C. Granet and G. James.Design of Corrugated Horns: A Primer.Antennas and Propagation Magazine, Vol. 47, Issue 2, pp. 76-84, 2005.Note correction in Issue 4, same year., 2005.

[2] R.C. Johnson and H. Jasik.Antenna Engineering Handbook.McGraw-Hill Book Company, 1984.

[3] J. Leech, B.K. Tan, G. Yassin, P. Kittara, A. Jiralucksanawong, and S. Wang-suya.Measured performance of a 230 GHz prototype focal-plane feedhorn ar-ray made by direct drilling of smooth-walled horns.21st International Symposium on Space Terahertz Technology, 2010.

[4] F.J.S. Moreira and A. Prata.Generalized Classical Axially Symmetric Dual-Reflector Antennas.IEEE Transaction on Antennas and Propagation, Vol. 49 No. 4, April 2001,2001.

[5] P. D. Potter.A New Horn Antenna with Suppressed Sidelobes and Equal Beamwidths.Technical Report No. 32-354, 1963.

[6] O. Sørensen.Application of the geometrical theory of diffraction to Cassegrain subre-flectors with laterally defocused feeds.Electromagnetics Institute, Technical University of Denmark, Lyngby,1974.

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