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SYNTHESIS OF LINE SOURCE ANTENNAS

A Project ReportSubmitted in partial fulfillment of the requirements for the

Award of degree of

BACHELOR OF TECHNOLOGY

IN

ELECTRONICS AND COMMUNICATION ENGINEERING

By

K. S.N.L.SUDHA (05B01A0494) Y.VIJAYADURGA(05B01A04B5)

T.R.SRAVATHI (05B01A0475) K.PRATYUSHA (05B01A0463)

Under the guidance of

Prof. G.R.L.V.N.Srinivasa Raju

Department of Electronics and Communication Engineering

SHRI VISHNU ENGINEERING COLLEGE FOR WOMEN

(Approved by A.I.C.T.E., Affiliated to JNTU, Kakinada)

BHIMAVARAM 534 202

2008-2009

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SHRI VISHNU ENGINEERING COLLEGE FOR WOMEN(Approved by A.I.C.T.E., Affiliated to JNTU, Kakinada)

BHIMAVARAM 534 202

Department of

Electronics and Communication Engineering

CERTIFICATE

This is to certify that project work entitled SYNTHESIS OF LINE

SOURCE ANTENNAS USING ITERATIVE SAMPLING METHODisa bonafide work of K.S.N.L.Sudha, Y.Vijaya Durga, T.R.Sravanthi, K.Pratyusha bearing

Regd.No 05B01A0494, 05B01A04B5, 05B01A0465, 05B01A0463 of final year B.Tech

submitted in partial fulfillment of the requirements for the award of degree of

BACHELOR OF TECHNOLOGY IN ELECTRONICS AND

COMMUNICATION ENGINEERING during the academic year2008-2009

Internal Guide: Head of department:

G.R.L.V.N.Srinivasa Raju Dr.P.RAJESH KUMAR, Ph.DProfessor in E.C.E Dept. Electronics and communication engg.

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ACKNOWLEDGEMENT

Our most sincere and grateful acknowledgement is due to this sanctum, ShriVishnu Engineering College for Women, for giving us opportunity to fulfill our

aspirations and for successful completion of engineering.

We express our heartfelt thanks to our Director Prof.D.Raju, principal

Oblesh for providing us with the necessary facilities to carry out this project.

We express our deep sense of gratitude and sincere appreciation to our

guide Prof. G.R.L.V.N.Srinivasa Raju for his esteemed guidance and constant

encouragement throughout the project. We are indebted for his instruction guidelines that

proved to be very much helpful in completing our project successfully in time.

We also express our sincere thanks to Dr.P.Rajeshkumar, Head of

Electronics and Communication Department, for his valuable suggestions and

encouragement throughout the project.

We also express our sincere thanks to Prof. Mr.Siva Kumar, Mr.

S.Hanumantha Rao for their valuable suggestion and guidance in the completion of our

project.

We express our thanks to all other teaching and non-teaching staff and

associates of the department and also to our friends for their good wishes andconstructive criticism which led to the successful completion of our project.

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CONTENTS

ABSTRACT1. INTRODUCTION

1.1 ANTENNA SPECIFICATIONS1.2 LINE SOURCE ANTENNA1.3 ANTENNA SYNTHESIS1.4 BEAM SHAPING1.5 APPLICATIONS OF LINE SOURCE ANTENNAS

2. SYNTHESIS METHODS

2.1 WOODWARD-LAWSON METHOD2.2 ITERATIVE SAMPLING METHOD

3. DESIGN PARAMETERS AND FLOW CHARTS

3.1 DESIGN PARAMETERS3.2 FLOWCHARTS

4. SOURCE CODE

4.1 PROGRAM FOR WOODWARD-LAWSON METHOD4.2 PROGRAM FOR ITERATIVE SAMPLING METHOD

5. RESULTS

6. CONCLUSION

7. BIBLIOGRAPHY

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ABSTRACT

Aim of the project is to synthesizing a line source antenna with uniform progressive phase using Iterative sampling method with mat lab. In this Iterative

sampling method the standard design or experimental pattern is taken from Woodward-

Lawson method.

The Woodward-Lawson method is simple, elegant and provides an insight

into the process of pattern synthesis. Woodward-Lawson method is very useful for beam

shaping. This method is used to find the excitation function to produce the desired

radiation pattern.The main drawback in this method is that the pattern of each composing

function perturbs the entire pattern to be synthesized; it lacks local control over the side-

lobe level in the unshaped region of the entire pattern.

The method used in this project is Iterative Sampling method. Iterative

sampling method is introduced for the synthesis ofshaped-beam radiation patterns using

line sources. Given an original pattern which is some approximation to the desired

pattern, a series of correction patterns is added to it. Successive iterations are applied inthismanner untilthe desired performance is achieved. The current distribution is found

by a corresponding series of corrections. This method shows that patterns with low main-

beam ripple and/or low side-lobe level or sharp cut-off from the mainbeam can be

obtained. Unless there is significant ripple or side-lobe improvement, the complexity of

the required source current is usually lower thanthat ofthe original pattern. The iterative

sampling method is simple to apply and converges rapidly. The software package is

implemented using mat lab.

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1. INTRODUCTION

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An antenna (or aerial) is a transducer designed to transmit or receive

electromagnetic waves. It matches the transmitter or receiver to the free space. The

antenna is used for radiating energy in the desired direction and to suppress the radiation

in unwanted directions. A completely non directional or Omni directional radiator

radiates uniformly in all directions and is known as isotropic radiator. Such radiator is not

available in reality. For point to point communication antennas should be directive.

For wireless communication systems, the antenna is one of the most critical

components. A good design of the antenna can relax system requirements and improveoverall system performance. TV is example for which the overall broadcast reception can

be improved by utilizing a high-performance antenna. The antenna serves to a

communication system the same purpose that eyes and eyeglasses serve to human. The

field of antennas is vigorous and dynamic.

Very long array of discrete elements usually are more difficult to implement,

more costly, and have narrow bandwidths. For such applications, antennas with

continuous distributions would be convents to use. A very long wire and a large reflector

represent, respectively, antennas with continuous line and aperture distributions.

Continuous distribution antennas usually have larger side lobes, are more difficult to

scan. In general continuous distribution antennas are not as versatile as array of discrete

elements. The characteristics of continuously distributed sources can be approximated by

discrete-element arrays, and vice-versa, and their development follows and parallels that

of discrete-element arrays.

Continuous line source distributions are used to approximate linear array of

discrete elements. As the number of elements increases in a fixed length array the source

approaches continuous distribution.

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Antenna synthesis is the process of determining the excitation of a given

antenna type that either produces a radiation pattern which approximates a desired

radiation pattern or achieves a narrow main beam with low side lobes or a pattern withdecaying minor lobes or pattern which possesses null in certain directions.

There are various synthesis methods available for line sources antennas. Some

of the techniques are Fourier transform method, Woodward-Lawson method, Taylor line

sources method, Dolph-Tschebysheff polynomial method. Fourier transform method and

Woodward Lawson method are synthesis techniques which give the required source

distribution to produce a radiation pattern which closely approximate the desired

radiation pattern. These techniques are beam shaping techniques. Other techniques

include Tschebysheff array technique which produces pattern with narrow beams and low

side lobes.

Fourier transform method yields reconstructed pattern whose mean square

error from the desired pattern is minimum. Woodward method is flexible and can be used

to synthesize any radiation pattern. Tschebysheff technique is used for equal side lobe

levels and optimum beam width. In this tapering is not extreme. Taylor line sourcesyields a pattern that displays an optimum compromise between side lobe level and beam

width. Iterative sampling method is simple and converges rapidly. Iterative sampling

method is extension of Woodward -Lawson method.

Synthesizing the desired pattern of line source is done using mat lab software

and the plots and results are obtained.

1.1 ANTENNA SPECIFICATIONS:

Array factor:-

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The space factor (or) array factor is defined as the radiation pattern of similar arrayof non directive or isodirective elements. The degree of polynomial, which represents

an array, is always one less than the apparent number of elements. The actual number of

elements is almost equal to the apparent number. Array factor is a function of geometry

of array and excitation phase. It determines the beam shape and side lobe level of array

and excitation phase. The total field of an array is equal to the field of a single element

positioned at selected reference points multiplied by the array factor

E (total) = E (single element at reference point) * array factor

Directive gain:

The extent to which a particular antenna concentrates its radiated energy relative

to that of some standard antenna is termed as directive gain. The directive gain in a given

direction is defined as the ratio of the radiation intensity in that direction to the average

radiated power.

Directivity:

Directivity is the value of the directive gain in the direction of its maximum

value or directivity defined as the ratio of maximum radiation intensity of the subject

antenna to the radiation intensity of an isotropic antenna radiating the same total power.

Beam width:

Antenna beam width is a measure of directivity of an antenna. Beam width of the

major lobe of particular level is one of the ways to describe conveniently the radiation

Pattern of an antenna as a function of angular width. The angular width (in degrees) of

the major lobe between two directions at which the radiated or received power is one half

the maximum powers.

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Factors affecting beam width:-

a) The wave length

b) The shape of radiation pattern

c) Dimension (e.g.:-radius of aperture ..)

A narrow beam is desirable for direction finding applications and accuracy of

direction finding is inversely proportional to beam-width. The narrower the beam width,the gain or directivity is higher.

Bandwidth:

The bandwidth of an antenna is defined as the range of frequencies within which

the performance of the antenna with respect to some characteristics conforms to a

specified standard. The bandwidth can be considered to the range of frequencies on eitherside of the corner frequencies, where the antenna characteristics with in an acceptable

value of the center frequency.

Antenna gain:

The ability of an antenna array to concentrate the radiated power in a given

direction, or conversely to absorb effectively incident power from that direction, isspecified variously in terms of its gain, power gain, directive gain or directivity.

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Directive gain in particular direction is defined as the ratio of the power densely

radiated in that direction by the antenna to the power density that would be radiated by an

isotropic antenna.

The maximum directive gain is known as directivity. The gain directive of one of

the major lobes of the radiation pattern is known as directivity.

The power that must be radiated by an isotropic antenna to develop a certain

distance is divided by the optical power to yield a ratio. The only one difference between

power gain and directivity is:

In directivity the radiated power is considered where as in power gain the Power

fed to the antenna is considered.

Polarization:

Polarization refers to the direction in space of the electric vector of the electro

magnetic wave radiated from an antenna and is parallel to the antenna itself.

The polarization refers to the time varying behavior of the electric field strength

vector at some fixed point in space. Antennas are also referred to as vertically,

horizontally, elliptically and circularly polarized antennas.

Effective area:

The effective area or effective aperture of an antenna is defined in terms of thedirective gain of the antenna through the relation

G = (4 Ae) / 2

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The effective area is the ratio of power available at the antenna terminals to the

power per unit area of the appropriately polarized incident wave.

Radiation pattern:

The energy radiated in a particular direction by an antenna is measured in

terms of field strength at a point, which is at a particular distance from the antenna.

Radiation pattern of an antenna is a graph which shows the variation in actual field

strength at all points which are at equal distance from the antenna.

Obviously graph of a radiation pattern will be three-dimensional. Crosssections most frequently taken in radiation patterns are horizontal and vertical planes.

These are called the horizontal pattern and the vertical patterns respectively. The

graphical representation of radiation pattern of an antenna as a function of direction is

given by the name radiation pattern of the antenna. If the radiation from the antenna is

expressed in terms of field strength E is called field strength pattern. If radiation pattern is

expressed in power then it is called power pattern.

Antenna efficiency

The efficiency of an antenna is defined as the ratio of power radiated to the

total power supplied to the antenna and is denoted by .Thus

Antenna efficiency = Power Radiated/Total Input power

Thus antenna efficiency represents the fraction of total energy supplied to the antennawhich is converted into electromagnetic waves.

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Front to Back Ratio:

It is defined as the ratio of power radiated in desired direction to the power

radiated in the opposite direction.FBR=power radiated in desired direction/power radiated in opposite direction

The FBR changes if frequency of operation of antenna system shifts its value

tends to decrease if spacing between elements of antennas increases. In practice, for

receiving purposes adjustments are made to get maximum FBR rather than gain.

1.2 LINE SOURCE ANTENNA:

Continuous line-source distributions are functions of only one coordinate, and

they can be used to approximate linear arrays of discrete elements and vice-versa.

The number of elements increases in a fixed-length array, the source

approaches a continuous distribution. In the limit, the array factor summation reduces to

an integral. For a continuous distribution, the factor that corresponds to the array factor is

known as thespace factor. For a line-source distribution of length lplaced symmetrically

along thez-axis as shown in Figure the space factor (SF) is given by

L/2

SF()= ln(z)exp[j(vzcos+n(z)dz)]

-l/2

Where ln (z)and (z) represent, respectively, the amplitude and phase

distributions along the source. For a uniform phase distribution (z) = 0.

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Above equation is a finite one-dimensional Fourier transform relating the far-field pattern of the source to its excitation distribution? Two-dimensional Fourier

transforms are used to represent the space factors for two-dimensional source

distributions. These relations are results of the angular spectrum concept for plane waves,

introduced first by Booker and Clemmow and it relates the angular spectrum of a wave to

the excitation distribution of the source.

For a continuous source distribution, the total field is given by the product of

the elementand space factors. This is analogous to the pattern multiplication for arrays.

The type of current and its direction of flow on a source determine the element factor. For

a finite length linear dipole, for example, the total field is obtained by summing the

contributions of small infinitesimal elements which are used to represent the entire

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dipole. In the limit, as the infinitesimal lengths become very small, the summation

reduces to integration.

Discretization of Continuous Sources:

The radiation characteristics of continuous sources can be approximated by

discrete element arrays, and vice-versa. This is illustrated in Figure (b) whereby discrete

elements, with a spacing dbetween them, are placed along the length of the continuous

source. Smaller spacing between the elements yield better approximations, and they can

even capture the fine details of the continuous distribution radiation characteristics. For

example, the continuous line-source distribution In (z_) of can be approximated by adiscrete-element array whose element excitation coefficients, at the specified element

positions within l/2 z_ l/2, are determined by the sampling of In (z_) ejn (z_). The

radiation pattern of the digitized discrete-element array will approximate the pattern of

the continuous source.

The technique can be used for the discretization of any continuous

distribution. The accuracy increases as the element spacing decreases; in the limit, the

two patterns will be identical. For large element spacing, the patterns of the two antennas

will not match well. To avoid this, another method known as root-matching can be used.

Instead of sampling the continuous current distribution to determine the element

excitation coefficients, the root-matching method requires that the nulls of the continuous

distribution pattern also appear in the initial pattern of the discrete-element array. If the

synthesized pattern using this method still does not yield (within an acceptable accuracy)

the desired pattern, a perturbation technique can then be applied to the distribution of the

discrete-element array to improve its accuracy.

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1.3 ANTENNA SYNTHESIS:

Antenna synthesis is the process which determines the source distribution for

producing a given radiation pattern. Design is done to exhibit a desired distribution,

narrow beam width and low side lobe levels decaying minor lobes, nulls in far field

pattern... etc. The designed pattern should yield either exactly or approximately an

acceptable radiation pattern and it should satisfy other system constraints. In general

synthesis is to find not only the antenna configuration but also its geometric

dimensions and excitation distribution.

Antenna pattern synthesis usually requires that first an approximation analyticalmodel be chosen to represent either exactly or approximately the desired pattern .The

second step is to realize the analytical model by an antenna model. In general antenna

pattern synthesis can be classified into three categories.

1. Antenna patterns should posses nulls in the desired directions.

2. The patterns require exhibiting a desired distribution in the entire visible

region. This is referred as to beam shaping.3. The third category requires producing patterns with narrow beams and low

side lobes.

The Synthesis methods are used to design both line sources and linear arrays

whose space factors and array factors will yield desired far field radiation patterns. The

total pattern is formed by multiplying the space factor by the element factor. For very

narrow beam pattern, total pattern is nearly the same as the space or array factor. For very

narrow beam patterns, the total pattern is nearly the same as the space factor or array

factor.

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1.4 BEAM SHAPING:

The patterns that exhibit a desired distribution in the entire visible region. This

is referred to as beam shaping. Like wise in the case of electronic pulse and wave shaping

circuits the radiation pattern can also be shaped depending on the applications and user

requirements. However, the pattern synthesis is not adequately investigated to meet

modern demands. The highly directive beams attainable with microwave antennas have

been utilized to achieve large antenna gain, precision direction finding, and a high degree

of resolution of complex targets. The exploration of a wide angular region with such

sharp beams requires an involved scanning operation in which the scanning time becomes

a limiting factor. This problem is much simplified if the required scanning can be reducedto only one direction, the coverage of the angular region being completed by fanning the

beam broadly. For many applications, the characteristic shape of the fanned beam

obtained by simply reducing the corresponding dimension of the aperture is

unsatisfactory; it may be wasteful of the limited microwave power, or it may result in a

very unequal illumination of targets in different directions To overcome these limitations

it is necessary to impose on the beam by special design techniques some shape not

characteristic of the normal diffraction lobe. These beams are referred to as shapedbeams, and the antennas that produce them as shaped-beam antennas and this process is

called beam shaping.

Beam shaping applications and requirements:

There are a number of radar applications for microwave systems that impose

more or less severe beam shaping requirements upon the antenna.

a. Surface Antenna for Air Search : For use in search for aircraft, an antennaon the ground or on a ship is required to produce a beam sharp in azimuth

but shaped in elevation; the azimuth coverage is obtained by scanning. The

elevation shape of the beam must provide coverage on aircraft up to a

certain altitude and angle of elevation and out to the maximum range of the

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system. This is to be accomplished without wasteful use of availablepower.

The antenna beam need not meet the coverage requirement very accurately,

since conservation of power and a relatively constant signal on a plane at a

fixed altitude are the only objectives

b. Airborne Antenna for Surface Search: An airborne antenna is required toproduce a beam sharp in azimuth but, so shaped in elevation as to provide

uniform illumination on the ground; azimuthal coverage is achieved by

scanning.

When an airborne antenna is used primarily for surface search oversea against such point targets as ships and buoys, the purpose of beam

shaping is to conserve power, to maintain a relatively constant signal as the

target is approached, and to avoid overloading the indicator scope with sea

return. For successful surface search over land it is necessary to illuminate

the ground very uniformly in order to obtain solid painting on the indicator

scope and a fully intelligible picture.

c. Shipborne Antenna for Surface Search: Aship borne antenna for use insurface search must scan in azimuth with a sharp azimuth pattern. To

accommodate roll and pitch the beam of an unstabilized antenna must be

broad in elevation. This broadening will be more conservative of power

and will provide a more constant illumination of the target if it is

accomplished with a shaped beam rather than a simple fanned beam.

d. Surface Antenna for Height Finding: Aground or ship antenna designedfor height finding must have a sharp elevation beam for obtaining precise

elevation information and a rapid elevation scan. Provision must also be

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made for scanning the antenna slowly in azimuth or for turning the antenna

to an assigned azimuth. The beam must be relatively broad in azimuth in

order that the target will be held in the beam long enough to obtain height

information. If the beam is assumed to be stationary in azimuth, an airplane

flying across the beam will be illuminated for a period proportional to its

distance away. To increase the time of illumination on near-by crossing

targets, a low-intensity broadening of the azimuth beam is required. If a

fixed minimum of illumination is to be achieved at a given linear distance

on both sides of the centre line of the azimuth beam, the amplitude pattern

must have the so called beavertail shape.

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2. SYNTHESIS METHODS

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In general we have following synthesis methods

1. Schelkunoff Polynomial Method

2. Fourier Transform Method

3. Woodward-Lawson Method

4. Dolph-Tschebycheff Method

5. Taylor line source (Tschebycheff Error)

6. Taylor line source (One parameter)

Antenna pattern synthesis can be classified into three categories. One group

requires that the antenna patterns possess nulls in desired directions. The Schelkunoff

Polynomial Method introduced. By Schelkunoff can be used to accomplish it. Another

category requires that the patterns exhibit a desired distribution in the entire visible

region. This is referred to as beam shaping, and it can be accomplished using .The

Fourier transforms, the Woodward-Lawson and Iterative sampling methods. A third

group includes Techniques that produce patterns with narrow beams and low side lobes.

The methods used to accomplish this are namely the binomial method and the Dolph-

Tschebyscheff method (also spelled Tchebyscheff or Chebyshev). Other techniques that

belong to this family are the Taylor line-source (Tschebyscheff-error) and the Taylor

line-source (one parameter).

In this project we implementedIterative Sampling Method

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2.1 Woodward-Lawson Method:

The Woodward-Lawson method is simple, elegant, and provides insight into

the process of pattern synthesis. In Woodward-Lawson method the desired pattern can bespecified in either Piecewise form or Sampling form. A very popular antenna pattern

synthesis method used for beam shaping was introduced by Woodward and Lawson. The

synthesis is accomplished by sampling the desired pattern at various discrete locations.

Associated with each pattern sample is a harmonic current of uniform amplitude

distribution and uniform progressive phase, whose corresponding field is referred to as a

composing function. For a line-source, each composing function is of a bm*sin(m)/m

form. The excitation coefficient bm

of each harmonic current is such that its fieldstrength is equal to the amplitude of the desired pattern at its corresponding sampled

point. The total excitation of the source is comprised of a finite summation of space

harmonics. The corresponding synthesized pattern is represented by a finite summation of

composing functions with each term representing the field of a current harmonic with

uniform amplitude distribution and uniform progressive phase.

The formation of the overall pattern using the Woodward-Lawson method is

accomplished as follows. The first composing function produces a pattern whose main

beam placement is determined by the value of its uniform progressive phase while its

innermost side lobe level is about 13.5 dB; the level of the remaining side lobes

monotonically decreases. The second composing function has also a similar pattern

except that its uniform progressive phase is adjusted so that its main lobe maximum

coincides with the innermost null of the first composing function. This results in the

filling-in of the innermost null of the pattern of the first composing function; the amount

of filling-in is controlled by the amplitude excitation of the second composing function.Similarly, the uniform progressive phase of the third composing function is adjusted so

that the maximum of its main lobe occurs at the second innermost null of the first

composing function; it also results in filling-in of the second innermost null of the first

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composing function. This process continues with the remaining finite number of

composing functions.

The main drawback of this method is, the pattern of each composing function

perturbs the entire pattern to be synthesized, and it lacks local control over the side lobe

level in the unshaped region of the entire pattern. In 1988 and 1989 a spirited and

welcomed dialogue developed concerning the Woodward-Lawson method .The

Woodward-Lawson method deals with the synthesis of field patterns. The analytical

formulation of this method is similar to the Shannon sampling theorem used in

communications. In this method, the radiation pattern of an antenna can be synthesized

by sampling functions whose samples are separated by /lrad, where lis the length of thesource.

Line source

Let the distribution of a continuous source be represented with in -l/2zl/2 by afinite summation of normalized sources each of constant amplitude and line phase of theform

im (z) = (am/l) exp (-jkzcos m) -< z

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SF() = bm (Sin[kl(cos - cos m)/2])[kl(cos - cos m)/2]

Total pattern is

MSF () = bm Sin[kl(cos - cos m)/2]

m=-M [kl(cos - cos m)/2]

2.2 ITERATIVE SAMPLING METHOD:

The iterative sampling method is introduced for the synthesis of shaped-beam

radiation patterns using line-sources. Given an original pattern which is some

approximation to the desired pattern, a series of correction patterns is added to it.

Successive iterations are applied in thismanner untilthe desired performance is achieved

patterns with either low main-beam ripple and/or low side lobe level or sharp cut-off

from themainbeam can be obtained.

Let Fd (u)be the desired pattern where u=cosand is the angle from thezaxis

along which the current distribution of aperture length L is disposed. Since this is an

iterative procedure, it begins with any pattern which is some approximation to B(u)and

its corresponding source current. This original pattern F(0) (u)can be that of any standard

design or possibly eves an experimental pattern. A series of correction patterns is then

added to the original pattern. If the resulting pattern, called the first-iteration pattern, is

not satisfactory, further iterations may be applied. For the ith iteration, the total pattern

corrections the sum of the correction patterns weighted by correction coefficients as

follows,

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N

F (i) (u) = an (i) G (u un(i))n=-N

where an(i) is the correction coefficient and G(u-un(i)) is the correction pattern centred at

and having avalue of unity there. The number Nis chosen such thatthe largest number

of corrections (2N + 1 if odd and 2Nif even) of all the iterations is accommodated; for

other iterations many of the an(i) coefficients will be zero. Theresultant pattern afterK

iterations is the sum of theoriginal pattern and all corrections:

KF(K) (u) = F(0) (u) + F(i) (u) i=1

For a line source the correction pattern has a corresponding correction current term gn(i)

(s) related to it byL/2

Gap (u un(i)) = gn(i)(s) exp (j2us) ds-L/2

Where s is the normalized aperture coordinate z/X and Lis the normalized aperture

length L/h.

The ith iteration is for the line source

N

fap(i)

(s) = an(i)

gn(i)

(s)n =-N

The tota1 current is then the sum of the original and all correction currents and after K

iterations for the line source.

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K

fap(K) (s) = fap(0) + fap(i)(s)i =1

For line sources one of the simplest correction patterns is

Gap (u un(i)) =sin [L (u un(i)) ]/[(u un(i))L]

These functions satisfywith Corresponding to this we have

an(i) =Fd (un(i)) F(I = -1) (un(i))

A good choice of iterative sample points is the mean va.lue of the previous iterativesample points or

un(i) = [un(i-1)+ un-1(i-1)] / 2

With successive iterations the number of iterative sample points is reduced as the pattern

approaches the desired pattern to within acceptable limits, i.e., further corrections are

applied over regions where the pattern error is still unacceptable.

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3.1 DESIGN PARAMETERS

Woodward-Lawson method:-

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Input data to be given:-

a) The radiation pattern desired.

b) Number of elements (N).

c) Spacing between the elements (d).

d) Wavelength ().

e) Length of the source (l).

Objectives to be achieved:-

a) Determine the sampling points.

b) Calculate the excitation coefficients.

c) Determine the current distribution.

d) Determine the space factor.

e) Plot the normalized magnitude vs.

f) Plot the normalized current vs.

Iterative Sampling method:-

Input data to be given:

a) The radiation pattern desired.

b) Number of elements (N).

c) Spacing between the elements (d).d) Wavelength ().

e) Length of the source (l).

f) Number of iterations (K)

Objectives to be achieved:-

a) Determine the sampling points.

b) Calculate the excitation coefficients.

c) Calculate the correction coefficients.d) Calculate the correction patterns.

e) Determine the current distribution

f) Determine the space factor.

g) Plot the normalized magnitude vs.

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h) Plot the normalized current vs.

3.2 FLOW CHARTS:

Woodward-Lawson Method:

SPACE FACFOR FLOW CHART:

CURRENT DISTRIBUTION FLOW CHART:

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ITERATIVE SAMPLING METHOD:

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CURRENT DISTRIBUTION FLOW CHART:

SPACE FACTOR FLOW CHART:

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SOURCE CODE

4.1 Program for Woodward Lawson Method:

Current distribution:

clc

clear all;

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close all;

%----------- Parameters ------------

N = input('Enter the value of N --------> ');

N = round(N); % convert to integer

if(mod(N,2) == 0)

M = N/2;

Else

M = (N-1)/2;end

%M = 5;

lambda= 10;

samples = 'odd'; % possible values can be 'odd' or 'evn'

k = 2*pi/lambda;

if(samples == 'odd')

m = -M : M;

else

m = -M : M;

index = find(m == 0);

m(index) = [];

end

[row, col] = size(m);

bm= [zeros(1,2) ones(1,col-4) zeros(1,2)];

%--------------- Line Source Parameters & Code ----------------

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length = M*lambda;

kk = 1;

j=sqrt(-1);

for z=-length/2:1:length/2

sum = 0;

jj = 1;

[row, col] = size(m);

for ii = 1 : col

mm = m(ii);

yy = cos_theta_m(mm, lambda, length, samples);sum = sum + (bm(jj)*exp(-j*k*z*yy));

jj = jj + 1;

end

SF(kk) = sum/length;

kk = kk + 1;

end

constant=max(SF)

%---------------------------- Lets plot the results -----------

figure; grid; hold on;

z = -length/2 : 1 : length/2;

plot(z, SF/constant, 'r');

xlabel('source position');

ylabel('Normalized current');title('current distribution for line source');

%----------------------------------------------------------------

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SPACE FACTOR:

clc

clear all;

close all;

%----------- Parameters ------------

N = input('Enter the value of N --------> ');

N = round(N); % convert to integer

if(mod(N,2) == 0)

M = N/2;

else

M = (N-1)/2;

end%M = 5;

lambda = 1;

samples = 'odd'; % possible values can be 'odd' or 'evn'

k = 2*pi/lambda;

if(samples == 'odd')

m = -M : M;

else

m = -M : M;

index = find(m == 0);

m(index) = [];

end

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[row, col] = size(m);

bm = [zeros(1,2) ones(1,col-4) zeros(1,2)];

%--------------- Line Source Parameters & Code ----------------

length = M*lambda;

kk = 1;

for theta = 0 : pi/1000 : pi

sum = 0;jj = 1;

[row, col] = size(m);

for ii = 1 : col

mm = m(ii);

yy = cos_theta_m(mm, lambda, length, samples);

zeta = (k*length/2)*(cos(theta) - yy);

if(zeta == 0)

sum = sum + bm(jj);

else

sum = sum + bm(jj)*sin(zeta)/zeta;

end

jj = jj + 1;

end

SF(kk) = sum;

kk = kk + 1;end

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%---------------------------- Lets plot the results -----------

figure; grid; hold on;

theta = 0 : pi/1000 : pi;

plot(theta*180/pi, abs(SF), 'r');

xlabel('Observation angle theta (degrees)');

ylabel('Normalized magnitude');

title('Normalized amplitude patterns');

legend('Line-source |SF(theta)| (l=5*lambda));

%----------------------------------------------------------------

Function call program:

function y = cos_theta_m(m, lambda, length, samples) % samples can be 'odd' or 'evn'

if(samples == 'odd')

y = m*lambda/length;

elseif(m > 0)

y = (2*m-1)*lambda/(2*length);

else

y = (2*m+1)*lambda/(2*length);

end

end

4.2 Program for Iterative Sampling method:

Current distribution:

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5. RESULTS

Woodward-Lawson method:

Current distribution:

The total current with finite summation of all samples

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N=30, l=15

When N=20, l=10

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Space Factor

For Single composing function:

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N=30, l=10 , m=3

N=20, l=5 , m=-2

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Total pattern by summing all samples

When N=21,l=10

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when N=30, l=15

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Iterative sampling method:

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Current distribution:

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6. CONCLUSION

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The Woodward method reconstructs patterns whose values at the sample

points are identical to the ones of the desired pattern: it does not have any control of the

pattern between the sample points, and it does not yield a pattern with least mean square

deviation. Woodward method is more flexible, and it can be used to synthesize any

desired pattern in fact it can ever be used to reconstruct pattern which, because of their

complicated nature, cannot be expressed analytically. Measured pattern either analog or

digital can be synthesized using Woodward method.

The trade off of side lobe level and ripple with the transition width is

well known. The classical synthesis methods each provide some specific degree of tradeoff. However, the iterative sampling method allows the synthesis of a pattern whose

degree of trade off is close to that required by the particular design problem at hand.

Beginning with an origina1 pattern which is a rough approximation to the desired pattern,

one can apply corrections to the regions which require improvement while allowing the

closeness of fit to be relaxed in other regions. The pattern and its corresponding current

distribution are found by summing series of elementary functions.

7. BIBLIOGRAPHY

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1. WARAEN L.STUTZMAN, Synthesis of Shaped-Beam Radiation Pattern Using the

Iterative Sampling Method IEEE Trans. Antenna and Propagation, VOL.AP-19, pp.36-

41, January 1971.

2. Antenna Theory and design practice Constantine A.Balanis

3. Electromagnetic Waves and Radiation systems E.C.Jordan and K.G.Balmain

4. Microwave Antenna Theory and Design Samuel Silver

5. Antenna theory and design Stutzman warren.L.

6. Antennas John D.Kraus

7. Antenna design in computer applications David Pozar

8. Antennas and wave propagation G.S.N.Raju

9. Antennas and wave propagation K.D.Prasad

10. Getting started with MATLAB Rudra Pratap

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