DESIGN, REALIZATION AND ANALYSIS OF A 836 – 964 MHZ LUMPED ELEMENT BAND PASS FILTER WITH CAPACITIVELY COUPLED PI
RESONATORS
Eric Lundquist B.S., California State University, Sacramento 2006
PROJECT
Submitted in partial satisfaction of the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL 2010
ii
DESIGN, REALIZATION AND ANALYSIS OF A 836 – 964 MHZ LUMPED ELEMENT BAND PASS FILTER WITH CAPACITIVELY COUPLED PI
RESONATORS
A Project
by
Eric Lundquist Approved by: __________________________________, Committee Chair B. Preetham Kumar, Ph.D __________________________________, Second Reader Paul Kovacich, Senior Design Engineer ____________________________ Date
iii
Student:
Eric Lundquist
I certify that this student has met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to
be awarded for the Project.
__________________________, Graduate Coordinator ________________ B. Preetham Kumar, Ph.D Date Department of Electrical and Electronic Engineering
iv
Abstract
of
DESIGN, REALIZATION AND ANALYSIS OF A 836 – 964 MHZ LUMPED ELEMENT BAND PASS FILTER WITH CAPACITIVELY COUPLED PI
RESONATORS
by
Eric Lundquist
With the amount of wireless impact in today’s society, filter design is a very
important and integral aspect of modern communication systems. The main purpose of
filtering is to improve the signal to noise ratio, SNR, noise
signal
PP
NS= , which describes how
much noise has contaminated the original signal. By filtering the noise, the signal to
noise ratio is increased, and the signal becomes easier to receive and comprehend.
This particular filter, designed and fabricated in this project, is targeted for space
communication applications. It will demonstrate optimal performance at temperature
extremes and zero pressure environments. The design will also exhibit the highest form
of reliability due to its application. The design must be so reliable that it will operate for
a minimum of 17 years with the smallest probability of failure; less than 1%.
The particular kind of filter is a band pass filter, which will be designed using
lumped elements using a capacitively coupled pi resonator filter structure. Once the filter
is realized and fabricated, the performance of the filter will be evaluated against the
specifications it was designed to meet.
v
_______________________, Committee Chair Preetham Kumar, Ph.D _______________________ Date
vi
Acknowledgements
I would like to thank Commercial Microwave Technology for providing me with
an environment to learn and grow as an engineer. Thank you to Paul Kovacich and Nam
Han for their time and patience while filling my head with their engineering experiences.
I also wish to thank my advisor, Dr. Preetham Kumar, for his support and
guidance throughout my undergraduate and graduate studies at California State
University, Sacramento. Thank you to Junaid Hossain for enduring all of those years in
the library studying with me.
Special thanks should be given to my parents, David and Patty, who have loved
and supported me throughout my entire life. Thank you to my sister, Jessica, for setting
the bar so high. Finally, words alone cannot express the thanks I owe to Kimberly
Pasma, for her encouragement, support and love.
vii
TABLE OF CONTENTS
Page
Acknowledgments....................................................................................................... vi
List of Figures ............................................................................................................ ix
List of Tables ............................................................................................................... x
Chapter
1. INTRODUCTION ................................................................................................ 1
1.1 Overview .................................................................................................... 1
1.2 Goals of the Project .................................................................................... 2
1.3 Organization of Project Report ................................................................... 3
2. CUSTOMER SPECIFICATIONS ........................................................................ 4
2.1 Filter Specifications .................................................................................... 4
2.2 Physical Requirements ................................................................................ 7
3. BAND PASS FILTER AND ATTENUATOR - EQUALIZER DESIGN ........... 9
3.1 Band Pass Filter Design ............................................................................. 9
3.2 Attenuator – Equalizer Design ................................................................. 19
4. BAND PASS FILTER AND ATTENUATOR - EQUALIZER SIMLUATION 21
4.1 Touchstone Simulation ............................................................................ 21
4.2 Simulation vs. Specifications ................................................................... 24
5. BAND PASS FILTER AND ATTENUATOR - EQUALIZER REALIZATION ..........................................................................................................................27
5.1 Filter Components .................................................................................... 27
5.2 Filter Layout ............................................................................................. 30
5.2.1 Band Pass Filter Layout ............................................................ 30
5.2.2 Attenuator - Equalizer Layout .................................................. 33
5.2.3 Housing Arrangement ............................................................... 35
5.3 Tuning ...................................................................................................... 37
viii
6. FINAL PERFORMANCE OF THE 836 – 964 MHZ BAND PASS FILTER AND ATTENUATOR – EQUALIZER ........................................................................41
6.1 Analysis & Conclusion of Measured Data ............................................... 41
Appendix .................................................................................................................... 48
References ................................................................................................................... 53
ix
LIST OF FIGURES
Page
1. Figure 1. Customer Specification, Electrical Performance ...............................4
2. Figure 2. Diagram of Filter Parameters ............................................................6
3. Figure 3. Customer Specification, Physical Characteristics .............................8
4. Figure 4. Block Diagram of the Filter ...............................................................9
5. Figure 5. ComSyn Main Menu Screen ...........................................................11
6. Figure 6. Capacitively Coupled “Pi” Resonators ............................................18
7. Figure 7. T Pad Attenuator..............................................................................19
8. Figure 8. Block Diagram of Band Pass Filter and Attenuator Equalizer ........21
9. Figure 9. Simulated Filter Response, S21 & S11 Parameters ...........................23
10. Figure 10. Simulated Responses .....................................................................23
11. Figure 11. Inductor Designed by CoilCalc .....................................................30
12. Figure 12. Capacitors Soldered onto Steel Carrier .........................................31
13. Figure 13. Capacitors Soldered onto Steel Carrier, Alternate Angle ..............32
14. Figure 14. A Few Sections of the Completed Filter .......................................33
15. Figure 15. Attenuator - Equalizer ...................................................................34
16. Figure 16. Feed Through and Shroud Design .................................................36
17. Figure 17. Filter Covers with Recessed Cavities ............................................37
18. Figure 18. Fixturing used for Tuning Process ................................................38
19. Figure 19. Air Capacitor used for Tuning Process .........................................39
20. Figure 20. Measured Data from the Completed Filter, S11 Parameter Only ...41
21. Figure 21. Measured Data from the Completed Filter, 1.5 dBc Bandwidth, S21 Parameter Only ................................................................................................42
22. Figure 22. Measured Data from the Completed Filter, Pass Band Variation, S21 Parameter Only ................................................................................................43
23. Figure 23. Measured Data from the Completed Filter, Rejection Performance, S21 Parameter Only ................................................................................................44
x
LIST OF TABLES
Page
1. Table 1. Rejection Characteristics entered into ComSyn ...............................13
2. Table 2. Filter Characteristics Versus Number of Filter Sections ..................15
3. Table 3. List of G Values for Each Filter Element .........................................16
4. Table 4. Element Values Calculated by ComSyn ...........................................17
5. Table 5. Resistor Values Needed for Desired Attenuation Level ...................20
6. Table 6. Filter Specifications Versus Simulated Capability ...........................25
7. Table 7. Specification Versus Measured Filter Performance .........................44
1
Chapter 1
INTRODUCTION
The aim of this project is to design and fabricate a capacitively coupled pi
resonator filter for space flight applications. The specifications of this design are very
stringent; hence a considerable amount of effort has been devoted to meeting the
customer specifications.
1.1 Overview
The design of this filter will take into account a lot of the research that has been
completed in this field. Some of this research is current; however, older research
articles, that have become building blocks for the industry, are also used. The program
used to design the filter, ComSyn, is based on an article written in 1971 by Robert J.
Wenzel [22]. The program was refined using an article written in 1958 by Saal and
Ulbrich [20]. These two articles contain many of the standards used in all passive filter
designs.
The capacitively coupled pi resonator filter structure was selected from a few
different articles, Orchard and Temes’ article [16] and Hajek’s article [9]. The
attenuator – equalizer’s range of capability is analyzed in depth using an article written
by Abromowitz [1]. The overall design, fabrication and performance of passive
networks will be scrutinized [5]. By minimizing parasitic capacitances and modeling
2
them in Touchstone, their effects are minimized using techniques found in Neugebauer’s
article [14].
During the design process, many different aspects of current research were
accounted for. Different filter topologies for passive filters were considered [13] and
passive enhancements to resonator Q [11] were also examined. In the simulation and
realization process of the filter design, optimization of the filter [6] was a very important
factor.
A list of filter specifications including: center frequency, bandwidth, minimum
and maximum pass band insertion loss, maximum pass band variation, maximum pass
band VSWR, minimum rejection requirements, and maximum input power handling
capability were supplied by a customer. The designed filter was constructed within a
housing of a particular size, with connectors at locations specified by the customer. The
type of input/output connectors was also designated in the filter specification.
These specifications were met using a series combination of a band pass filter
and attenuator - equalizer. The band pass filter that was designed is a passive device,
and does not need an external power source to operate, as opposed to an active device
which requires an external power source. This allows much more versatility when
designing a transmission system requiring a filter. [17].”
1.2 Goals of the Project
This project involved the engineering process of designing and fabricating a
band pass filter to meet a list of specifications. The filter was designed within a
3
confined area designated by the specification and consisted of a band pass filter in series
with an attenuator – equalizer. The specification also called out an MSSS (expand the
terms MSSS) connector as its interface, so the filter was designed to use this type of
connector as its input and output. The filter must operate hot and cold temperature
extremes as well as ambient temperature. Every aspect of the dynamic specification was
met by this project; however some details of the design process were omitted due to
proprietary information belonging to Commercial Microwave Technology (CMT).
1.3 Organization of Project Report
The project report is organized as follows: Chapter 2 provides the goals of the
project; what specifications, electrical and physical, will need to be met. Chapter 3 lays
out how these goals will be met and which of the specifications will be the most difficult
to meet. The filter and attenuator – equalizer will be designed as well. Chapter 4 will
summarize the analysis of the by modeling the filter in Touchstone. This simulation will
approximate the filters electrical characteristics. Chapter 5 will discuss how the
theoretical values of the filter components will be realized. The layout of the filter and
attenuator will also be discussed in depth. Chapter 6 includes the analysis of the filter
and the conclusion of the project. The circuit files used in this project can be found in
the Appendix.
4
Chapter 2
CUSTOMER SPECIFICATIONS
2.1 Filter Specifications
The following chart shows the electrical characteristics the customer desires the
filter to have.
Parameter Specification Center Frequency, fo 900 MHz Minimum -1.5 dB Bandwidth 155 MHz Maximum Low Side -1.5 dB Frequency 829 MHz Minimum High Side -1.5 dB Frequency 970 MHz Pass band for Insertion Loss and VSWR 836 to 964 MHz Maximum Pass band Insertion Loss at Center Frequency
8.0 dB
Minimum Pass band Insertion Loss at Center Frequency
7.0 dB
Maximum Pass band Variation 0.9 dB Maximum Pass band VSWR 1.5:1 (≥ 14.0 dB Return Loss) Minimum Rejection Requirements
46 dBc ≤ 676 MHz 46 dBc ≤ 700 MHz 40 dBc ≤ 740 MHz 28 dBc ≤ 780 MHz 7 dBc ≤ 796 MHz 7 dBc ≥ 1004 MHz 28 dBc ≥ 1020 MHz 40 dBc ≥ 1060 MHz 46 dBc ≥ 1100 MHz 46 dBc ≥ 1124 MHz 46 dBc ≥ 2000 MHz, ≤ 5000 MHz
Figure 1 – Customer Specification, Electrical Performance
5
To get a better understanding of these parameters, the following diagram, figure
2, has been created to help illustrate them individually. “The S11 plot shows the input
port voltage reflection coefficient and the S21 plot shows the forward voltage gain.”
These two parameters are defined by the following equations [21]:
and
.
The center frequency of filter, fo, is the point at which the filter is designed
around. It is also used to define other parameters. For example, the -1.5 dB bandwidth
is taken from the S21 plot, 1.5 dB below the loss at center frequency, fo. The horizontal
line beneath the S21 plot defines the -1.5 dB bandwidth for clarity. The minimum and
maximum -1.5 dB frequency refers to the start and stop points of the -1.5 dB bandwidth.
This is illustrated in the figure by the intersection of the horizontal -1.5 dB bandwidth
and the S21 plot. The pass band for insertion loss and VSWR defines the frequencies
where the filter must meet the specifications for those two parameters. The insertion
loss at center frequency is defined by the loss at fo; it must be within the 7.0 dB to 8.0
dB range. Pass band variation refers to the amount of change of insertion loss within the
pass band that is tolerable. In this case, the variation of the insertion loss across the pass
band should not exceed 0.9 dB. The VSWR, or voltage standing wave ratio, refers to
the loss of the S11 plot across the pass band; it must exceed 1.5:1. The minimum
6
rejection requirements refer to the loss of the S21 plot at specific frequencies and are
referenced to the insertion loss at fo, or dBc. dBc (decibels relative to the carrier) is
defined as “the power ratio of a signal to a carrier signal, expressed in decibels [8].” For
example, if the loss a center frequency was measured at 8.0 dB, 7.0 dBc could also be
expressed as 15 dB.
Figure 2 – Diagram of Filter Parameters
7
2.2 Physical Requirements
Not only must the filter design be able to meet the all of the electrical
specifications, it must be built within the physical constraints provided by the customer.
Figure 3 shows the physical size and shape of the filter. The location and type of
connectors is also defined. The eight dark circles on the bottom side of the filter
housing represent the connectors. The housing will hold four individual filters,
completely independent of the others. This is the reason behind eight connectors being
defined and not just two. The type of connector requested is an MSSS type connector
manufactured by Micromode. This connector is not frequently used but they will be
addressed in the design as well. The dark circles in the top view represent screws in the
covers used to secure them to the housing.
8
Figure 3 – Customer Specification, Physical Characteristics
9
Chapter 3
BAND PASS FILTER AND ATTENUATOR – EQUALIZER DESIGN
3.1 Band Pass Filter Design
The overall filter design will be a series combination of a band pass filter (BPF)
and an attenuator - equalizer. A block diagram of the filter and attenuator – equalizer
can be seen in figure 4 below. The attenuator will allow the filter we design to meet the
7.0 – 8.0 dB insertion loss requirement. The equalizer will allow us to control the
flatness of the pass band and be crucial for meeting the pass band variation requirement.
This approach will allow ample margin to the electrical performance for these
parameters.
Figure 4 – Block Diagram of the Filter
The first step is to determine what kind of a filter should be designed to meet the
specifications. A combline filter has a high “Q” value and has low insertion loss. To
determine if this typology can be used, the length of the resonator must be determined.
10
A value of theta equal to approximately 40° (electrical degrees) will yield manageable
gaps for spacing and capacitances. To find the length of a resonator used for the center
frequency, 900 MHz, the following equation is used [12].
λ=of
c
Where c is the speed of light in inches and fo is the center frequency in GHz.
This calculation yields a λ = 13.1142 inches. This value represents 360°
(electrical degrees). To find the 40° length, λ is divided by 9, leading to a resonator that
is 1.457 inches long. This will not fit within the housing restrictions provided by the
customer; the maximum height for the filter housing is 0.400 inches. Therefore, a
combline filter can not be used. In general, a lumped element filter does not have as low
insertion loss as a combline filter, but since this specification has a unique insertion loss
requirement, a window between 7 and 8 dB, it can be used.
Design and synthesis of the lumped element filter shall be completed using
ComSyn, an interactive filter design, analysis and synthesis program, proprietary to
CMT. ComSyn uses trade-offs to perform analyses. The filter generated by this trade-
off analysis is synthesized and the physical parameters of the filter elements are
computed by ComSyn. This program will be used to determine the number of sections
used in the filter design. Figure 5 below shows the menu of options in ComSyn.
11
***************************************** COMSYN - NH101004fb ***************************************** Computer Aided Filter Synthesis and Design
OPTIONS: 1) C: Comsyn - Optimum Combline Filter Design by Z-plane Synthesis. 2) L: Lef - Lumped Element Filter Design. 3) U: Utility - Branches to DOS Shell. - type 'EXIT' to return to program. 4) E: Editor - Provides text editor with Notepad. 5) R: Read data - Reads filter data from a file. 6) S: Save data - Saves filter data to a file. 7) D: cktDir - Opens Circuit File folder with Explorer. 0) X: eXit - Exit this program. > COMSYN -- Press a capitalized letter to make the selection. Press 'ENTER' to select default value shown in <>. Press 'Q' and 'C' to configure default settings.
COMMAND > Comsyn, Lef, eXit. (<C>/L/X):
Figure 5 – ComSyn Main Menu Screen
First the combline section of the program will be used to estimate the number of
sections required for the design. This number will then be used by the lumped element
section of the program. The following numbers were entered into the program. Pass
band edges, F1 = 836.0 MHz, F2= 964.0 MHz, Pass band Ripple = 0.02 dB and Theta =
40 degrees. A Chebyshev filter will be designed. It offers steeper roll off on the skirts
of the filter but has more pass band ripples than a Butterworth filter. This ripple will be
designed to be very small, 0.02 db, which will result in a return loss of approximately
21.5 dB or 1.18:1 VSWR. The rejection points were also entered into the program with
12
one variation. The 28 dBc point on the low side was increased by 15 dB. This is due to
the nature of the filters pass band to skew on the low side. In a combline filter, which is
canonically a low pass filter, there is one shunt inductor which causes one of the poles
fall at zero, or DC, and the rest of the poles, (2N-1), fall at infinity. “N” is equal to the
number of sections in the filter. This is what causes the skewing, or flaring, of the low
side of the pass band.
Table 1 shows the design parameters as they were entered into ComSyn. The
rejection values have all been increased by 8 dB, the maximum allowable insertion loss
at fo, to convert the levels from dBc to dB.
13
-- COMSYN Design --
>> F1= 836.00 MHz, F2= 964.00 MHz, Ripple=0.020 dB, Theta=40.00 deg
Frequency (MHz) Rejection (dB)
700.0 54.0
740.0 48.0
780.0 42.5
796.0 15.0
1004.0 15.0
1020.0 36.0
1060.0 48.0
1100.0 54.0
Table 1 – Rejection Characteristics entered into ComSyn
The results from ComSyn can be seen in table 2 below. The “0” column restates
the initial design values entered into ComSyn. The results show that the specification
can not be met without a minimum of 8 sections in the filter. The PBER column
represents the total equal ripple band divided by the filter passband. This calculation is
important when considering the drift of the filter at temperature extremes. For the 8
section filter, PBER = 1.11, or can allow for 11% total drift which should be ample margin.
14
As the number of sections was increased, the rejection at the 780 MHz, 28 dBc point did
not vary. This shows that this will be the most difficult rejection point to meet with the
filter design.
15
Filter Results Generated By ComSyn
Number of Sections 0 8 9 10 11
Equal Ripple Band Edge (Low, MHz) 836.0 829.0 822.1 816.4 811.7
Equal Ripple Band Edge (High, MHz) 964.0 971.0 977.9 983.6 988.3
ER/PB 1.0 1.110 1.217 1.306 1.38
Rejection Frequency Rejection (dB)
700.0 MHz 54.0 77.9 83.4 89.1 95.2
740.0 MHz 48.0 63.3 66.8 70.4 74.3
780.0 MHz 42.5 42.5 42.5 42.5 42.5
796.0 MHz 15.0 30.8 28.4 25.4 22.2
1004.0 MHz 15.0 40.0 37.9 35.1 31.7
1020.0 MHz 36.0 54.2 55.2 56.0 56.7
1060.0 MHz 48.0 80.7 91.8 91.8 97.7
1100.0 MHz 54.0 100.6 109.1 117.8 126.7
Table 2 – Filter Characteristics Versus Number of Filter Sections
The ComSyn lumped element filter section is now used to give the g values,
which are the roots of the Chebyshev polynomial. The design impedance of the filter is
100 ohms, this will yield element values that are easier to realize. The following tables
16
show the output of ComSyn. The G-values, in Table 3, can be used to calculate the
element values for the shunt capacitors and series inductors. Table 4 shows the
calculated values for the capacitors and inductors that will make up our circuit. Figure 6
shows the configuration of the elements.
** Lumped Element Filter with Chebyshev prototype. **
I G-values 1 0.89564135427883 2 1.43966446206494 3 1.86067258354695 4 1.68029266936584 5 1.92466098796153 6 1.62442867693562 7 1.64903773991752 8 0.78192451106392
Table 3 – List of G Values for Each Filter Element
17
COMSYN design values output:
N Cap A (pF) Ind (nH) Cap B (pF) Coupling (reference)
2.652111 pF (Input coupling)
1 1.861003 17.849743 2.568579 1.001370 pF (Node 1 to 2)
2 2.568579 17.849743 2.875202 0.694747 pF (Node 2 to 3)
3 2.875202 17.849743 2.926869 0.643080 pF (Node 3 to 4)
4 2.926869 17.849743 2.937649 0.632299 pF (Node 4 to 5)
5 2.937649 17.849743 2.926869 0.643080 pF (Node 5 to 6)
6 2.926869 17.849743 2.875202 0.694747 pF (Node 6 to 7)
7 2.875202 17.849743 2.568579 1.001370 pF (Node 7 to 8)
8 2.568579 17.849743 1.861003 2.652111 pF (Output coupling)
Table 4 – Element Values Calculated by ComSyn
18
Figure 6 – Capacitively Coupled “Pi” Resonators
Figure 6 shows the “pi” type resonator constructed by Cap A and Cap B, with a
series inductor in the middle. The coupling element is a capacitor, creating capacitive
inter stage coupling. This is how the phrase capacitively coupled pi resonator is coined.
The output circuit file generated by ComSyn can be seen in the Appendix.
19
3.2 Attenuator – Equalizer Design
In order to meet the insertion loss specification, an attenuator will be placed in
series with the band pass filter. The attenuator will allow the insertion loss to meet the 7
to 8 dB window the specification requests at the center frequency, fo. The equalizer will
allow the insertion loss to be optimized for flatness to meet the insertion loss variation
specification as well. A balanced T pad was designed as the attenuator for this filter. An
example of this T pad circuit can be seen in Figure 7 below [3].
Figure 7 – T Pad Attenuator
The values for the resistors in the attenuator were calculated using the following
equations [2]:
+
−=
110(
110(,)
20(
)20
(
21 dB
dB
oZRSRS and
−=
110(
10(2)
10(
)20
(
dB
dB
oP ZR
20
Where RS1, RS2 and Rp are the calculated resistor values, Zo is the desired impedance of
the network and dB is the desired amount of attenuation. The attenuator is designed to
have 50 Ω input and output impedance.
Using the equation above, the resistor values needed are listed below in Table 5.
Attenuation Desired (dB) RS1, RS2 (Ω) Rp (Ω)
6.0 16.5 66.5
6.5 17.8 60.4
7.0 19.1 55.8
Table 5 – Resistor Values Needed for Desired Attenuation Level
The actual amount of attenuation caused by the attenuator will be determined
when the filter is physically constructed and tested. By calculating a range of resistor
values for various amounts of attenuation, we will be prepared to attenuate the final result
of the filter properly.
The equalizer is also designed using ComSyn, in the same manner as the band
pass filter. It is designed as a low Q, two section filter. It is optimized in Touchstone as
well. The series inductors and capacitors allow the two poles of the equalizer to be
controlled, minimizing the amount of pass band variation that can be achieved.
The circuit file for the attenuator – equalizer can be seen in the Appendix in
combination with the optimized filter circuit.
21
Chapter 4
BAND PASS FILTER AND ATTENUATOR – EQUALIZER SIMULATION
4.1 Touchstone Simulation
The final optimization and electrical performance analysis will be performed by
the “Touchstone” program. Touchstone is a commercially available circuit analysis and
optimization program. It does an excellent job of predicting how the calculated circuit
values will perform. Touchstone was introduced to the microwave industry in 1984 by
EEsof, Inc. (which was later acquired by Agilent Technologies). Touchstone was used to
initially simulate the response of the frequency filter. “A touchstone file is an ASCII text
file used for documenting the n-port network parameter data and noise data of linear
active devices, passive filters, passive devices, or interconnect networks [10].” It
simulates capacitors and inductors as finite values within the circuit. A block diagram of
the circuit, band pass filter and attenuator –equalizer, can be seen below.
Figure 8 – Block Diagram of Band Pass Filter and Attenuator Equalizer
22
The output of ComSyn is a Touchstone file format; therefore the filter designed
by ComSyn can immediately begin the optimization process. The attenuator – equalizer
designed in section 3.2 is placed in series with the filter. The following two figures,
figures 9 and 10, show the simulated output from the Touchstone circuit file. Each figure
shows the same x axis scale, 32 MHz per division, in which four divisions about the
center represent the pass band. The figure 9 shows the response of the band pass filter
and equalizer - attenuator; the rejection and return loss have been plotted. The Figure 10
demonstrates the effect of the attenuator equalizer on the filter. There are three plots
included in this figure. The plot closest to 0 dB at fo shows the band pass filter’s pass
band performance. The second plot shows the output of the two section attenuator –
equalizer filter. The plot that is the furthest below 0 dB at fo is the series combination of
the band pass filter and the attenuator - equalizer. The pass band loss of the two filters is
added together to create this third plot. Using this type of design, the insertion loss of the
band pass filter can almost be completely neglected during the filter design process. As
long as it is within the 0 to 7.0 dB range and designed to have a small ripple, the
attenuator – equalizer will allow us to attenuate the response to the desired level within
the 7.0 to 8.0 dB window.
23
Figure 9 – Simulated Filter Response, S21 & S11 Parameters
Figure 10 – Simulated Responses. The three plots are the band pass filter, attenuator – equalizer and series combination. Only the S21 parameters are plotted.
24
4.2 Simulation vs. Specifications
The following table shows the approximate capabilities of the filter simulated by
Touchstone. Actual measurements of the filter will be examined in the conclusion of this
report. The actual measurements will be compared to these simulated values to judge
their accuracy.
25
Parameter Specification Simulation Capability
Center Frequency, fo 900 MHz 900 MHz Minimum -1.5 dB Bandwidth 155 MHz > 155 MHz Maximum Low Side -1.5 dB Frequency
829 MHz 818 MHz
Minimum High Side -1.5 dB Frequency
970 MHz 984 MHz
Pass band for Insertion Loss, and VSWR
836 to 964 MHz 836 to 964 MHz
Maximum Pass band Insertion Loss at Center Frequency
8.0 dB 7.8 dB
Minimum Pass band Insertion Loss at Center Frequency
7.0 dB 7.2 dB
Maximum Pass band Variation
0.9 dB 0.4 dB
Maximum Pass band VSWR 1.5:1 (≥ 14.0 dB Return Loss)
≥ 17.0 dB
Minimum Rejection Requirements
46 dBc ≤ 676 MHz > 60 dBc 46 dBc ≤ 700 MHz > 60 dBc 40 dBc ≤ 740 MHz 50 dBc 28 dBc ≤ 780 MHz 31 dBc 7 dBc ≤ 796 MHz 15 dBc 7 dBc ≥ 1004 MHz 15 dBc 28 dBc ≥ 1020 MHz 31 dBc 40 dBc ≥ 1060 MHz 50 dBc 46 dBc ≥ 1100 MHz > 60 dBc 46 dBc ≥ 1124 MHz > 60 dBc 46 dBc ≥ 2000 MHz, ≤ 5000 MHz > 60 dBc
Table 6 – Filter Specifications Versus Simulated Capability
26
As expected, the 28 dBc points are the most difficult parameter to meet.
Although 3 dB should be ample margin to meet the customer’s specification, it is by far
the closest parameter to the specification value. When tuning the filter, these two points
will require the most attention out of all the rejection points. The other parameters are
well within the customer’s specification.
27
Chapter 5
BAND PASS FILTER AND ATTENUATOR – EQUALIZER REALIZATION
5.1 Filter Components
The two main components of the band pass filter that must be realized are
inductors and capacitors. When realizing these components, a very important factor to
take into account is the Q factor. The Q of an element in a filter means a “Higher Q
indicates a lower rate of energy loss relative to the stored energy.” “A high Q tuned
circuit in a radio receiver would be more difficult to tune, but would have more
selectivity; it would do a better job of filtering out signals from other stations that lie
nearby on the spectrum [19].” The physical realization process of the inductors and
capacitors will be discussed at a later point in this chapter.
The band pass filters will be built on steel carriers. The steel carriers will be
mounted to the aluminum housing using 9x 0-80 stainless steel screws. Steel will be used
for the carriers because it’s coefficient of thermal expansion is closer to that of alumina
than the coefficient of aluminum. Aluminum has a thermal expansion coefficient of
approximately 23.0. Steel has a coefficient of approximately 13.0 and Alumina’s
coefficient is approximately 5.4 [7]. Soldering the alumina capacitors to the steel carriers
will not be an issue as long as the overall dimensions of the capacitors are kept below
.200 x .150 inches. If the capacitors were soldered directly onto the aluminum housing,
the dimensional limit of the capacitors would be much smaller. If the capacitor
28
dimensions are too large, the expansion and contraction of the two different types of
materials will cause hair line fractures in the capacitors that would cause the filter to fail.
For this reason, two different types of NTK material [15] are utilized to keep the overall
dimensions of each capacitor within the desired range. A capacitor that is too small
becomes extremely difficult to work with, for this reason the over all dimensions of the
capacitor should be kept above the range of .040 x .030 inches. For capacitance values
that are so low that they fall outside of the desired dimensional range using the lower
dielectric ceramic material (εr = 12.6), double sided copper clad Duroid (εr = 2.2) is used
instead. Duroid is a Teflon based, soft board type material.
The capacitance is calculated using the following equation [11]:
where: C is the capacitance; A is the area of the two plates; εr is the dielectric constant of the material between the plates; ε0 is a constant (ε0 ≈ 8.854×10−12 F m–1); d is the distance between the two plates.
The capacitors in the band pass filter circuit and attenuator are realized using
NTK type A material, a ceramic substrate very similar to alumina, which has a dielectric
constant (εr) of approximately 12.6 and NTK type F material, a ceramic substrate similar
to barium titanate, which has a dielectric constant (εr) of approximately 36.7. This higher
dielectric material is utilized to realize higher capacitance values. The thickness of the
dielectric material used is .010 inches. The material is metalized on both sides using a
29
process known as sputtering. This allows a capacitor to be realized; two metal plates
separated by a dielectric material. The metallization also allows the capacitors to be
soldered on both sides. This high “Q” material allows the filter to be realized closer to
the simulated output and it allows the capacitors to give us an optimal performance for
the housing area allowed.
The inductors for the band pass filter and the attenuator are calculated using a
proprietary in house program known as Coil Calc. By inputting an inductance value and
varying the wire size, the program calculates the number of turns required to achieve the
desired inductance value. It also gives a total wire length, including coil feet for
soldering. An example of the program’s output can be seen in figure 11 below. The
inductors are wound using pure silver wire, this helps keep the “Q” of the inductor as
high as possible. The inductors will be soldered onto the capacitors, microwave printed
circuit boards or onto posts depending on the situation.
30
╔════════════════════════════╗ Desc: CH2 L1 ║ SINGLE LAYER AIR CORE COIL ║ C M T Inc. 05-15-2009 -- 18:27:26 ╚════════════════════════════╝ version 080112 ┌──────────────────────────────────────┬───────────────────────────────────────┐ │ INDUCTANCE @ DC ..... 12.05 nH │ INPUT LEG/FOOT .... .025 / .030 inch │ │ │ │ │ No. of TURNS .......... 3.00 turns │ OUTPUT LEG/FOOT ... .025 / .030 inch │ │ │ │ │ INNER DIAMETER ........ .0650 inch │ TOTAL WIRE LENGTH ...... 0.823 inch │ │ │ │ │ WIRE DIAMETER ..# 30... .0100 inch │ COIL BODY LENGTH ........ 0.090 inch │ │ │ TOTAL COIL LENGTH ....... 0.140 inch │ │ SPACING btw'n turns ... .0200 inch │ CAPACITANCE (Cp) ........ 0.071 pF │ │ │ SELF RESONANT FREQ ..... 5454.6 MHz │ │ SHIELD DIA. (.03) .... .272 inch │ INDUCTANCE of LEG ....... 0.51 nH │ ├──────────────────────────────────────┴───────────────────────────────────────┤ │ INDUCTANCE at 900.0 MHz is 12.36 nH, 12.36 nH. Qu = 293 │ ├──────────────────────────────────────────────────────────────────────────────┤ │ For a 3.00 turn coil, the Outer Diameter of the coil is 0.085 inch. │ │ │ │ Use a 0.065 inch diameter Mandrel. Total Wire Length = 0.823 inch. │ │ │ │ INPUT Foot+Leg= 0.055 inch. BODY= 0.090 inch. OUTPUT Foot+Leg= 0.055 inch. │ └──────────────────────────────────────────────────────────────────────────────┘ The Unloaded Q may be inaccurate. (range: .4 < Coil D./Shield D. < .7)
Figure 11 – Inductor Designed by CoilCalc
5.2 Filter Layout
5.2.1 Band Pass Filter Layout
As previously discussed, the filters will be constructed on steel carriers. The
bottom layer of capacitors, or shunt capacitors, will be soldered to the carrier first using
Sn96 solder. The series capacitors, inductors and air capacitors will be soldered to the
shunt capacitors using Sn62. The shunt capacitors have a minimum gap of .020 inches
between one another; this will reduce unwanted parasitic, or stray, capacitances in the
filter. Figures 12 and 13 below show the steel carrier with just the capacitors soldered on.
Figure 13 shows the same carrier in figure 12 but from a different angle. This was
included for clarity and to help the reader visualize the layering of the capacitors. The
31
“+” marks in the first figure are scribed onto the carrier during the fabrication of the part.
They provide the assembler a reference location for each capacitor and will ensure the
.020 inch gap is maintained.
Figure 12 –Capacitors Soldered onto Steel Carrier
32
Figure 13 – Capacitors Soldered onto Steel Carrier, Alternate Angle
Figure 14 shows the completed filter, with the inductors and straps soldered to the
shunt capacitors. This picture was taken from this angle to help the reader understand the
physical layers of the design.
33
Figure 14 – A Few Sections of the Completed Filter
5.2.2 Attenuator - Equalizer Layout
The attenuator section of the filter is realized using a Duroid microwave printed
circuit (MPC) board that is copper clad on one side. The copper is etched off in such a
way to create two 50 ohm lines; one between the end of the filter section and the input of
the attenuator and the other between the output of the attenuator and the output of the
filter housing. A few silver shims have been soldered on top of the 50 ohm lines during
34
the tuning process to improve the filters performance. An additional shim has been
soldered at the junction of the three resistors as well. The MPC board is epoxied to the
steel carrier using a nonconductive structural epoxy. The inductors and capacitors of the
equalizer can be seen in the lower portion of figure 15. The three resistors making the T-
pad attenuator can be easily distinguished as well.
Figure 15 – Attenuator - Equalizer
35
The input to the band pass filter section is also realized using a Duroid MPC
board that is copper clad on one side. It is also etched in the same manner as the
attenuator MPC board to create a 50 ohm line between the input feed through and the
input of the filter section.
5.2.3 Housing Arrangement
Feed throughs will be utilized to create coaxial input and output ports at the
customer specified locations. The feed through consists of a center conductor encased in
glass and a Kovar ring which is fired. The center conductor is realized by a Kovar pin
that is plated with a thin layer of electroplate nickel and a more conductive gold layer.
The outer Kovar feral ring is also plated with nickel and gold. In order to connect the
inside feed through pin to the input and output MPC boards, a small brass feed through
bushing is soldered on to the feed through pin. This allows a .003 silver ribbon to be
soldered to connect the two together.
The customer specification requires the use of MSSS connectors at both
interfaces. An MSSS shroud will be held in the housing with a press fit. The interface of
the MSSS shroud and feed through will be inspected for concentricity; it must be
concentric for it to properly accept an MSSS cable or bullet. Figure 16 shows the
arrangement of the MSSS shroud, feed through and feed through bushing. It also helps
demonstrate how the components are arranged in the housing.
36
Figure 16 – Feed Through and Shroud Design
In order to achieve the largest volume for the filter, the cover was recessed. This
design allowed the screw heads to lay below maximum envelope of the housing while not
sacrificing volume for the filter cavity. This can be seen in the figure above. If the cavity
is too small, the “Q” of the filter components will degrade, which is not desirable. Figure
17 shows the recessed covers.
37
Figure 17 – Filter Covers with Recessed Cavities
5.3 Tuning
Tuning is the process of changing the capacitor and inductor values to optimize
the filters response. The tuning of the filter will be completed with the assembled filter in
the housing. The housing will be placed in a fixture allowing the MSSS output interface
to be connected to an MSSS to SMA adapters. The network analyzers used for the tuning
process use an SMA interface. The unit is attached to a set of stilt like fixtures that
allows room for the MSSS to SMA fixturing on the bottom of the unit and grants the
technician access to the top of the filter for tuning. It also provides stability to the unit.
The fixturing used can be seen in figure 18 below.
38
Figure 18 – Fixturing used for Tuning Process
The inductor values will be tuned by adjusting the spacing between the turns. The
spacing between the inductor and the ground plane is important to setting its inductance
value. In extreme cases, the inductors can be rewound with a smaller or larger inner
diameter to adjust the inductance.
The capacitors will be tuned by trimming the metallization on the top surface with
a diamond scribe or by soldering a .003 inch thick silver shim on top of the capacitor.
When a shim is added, the amount of metal hanging over the edge of the capacitor creates
39
an air capacitor to add capacitance to the component. Most of the series capacitors in the
circuit are designed to have a tunable air capacitor next to the fixed series capacitor.
Figure 19 is a diagram of the air capacitor and it can be seen below. The air capacitor is
made by soldering a .003 inch thick silver shim on one end and leaving the other end
hanging above the next shunt capacitor. By increasing and decreasing the distance
between this air capacitor and the shunt capacitor, the capacitance is changed, allowing
the series capacitance to be tuned. The dimensions in the figure below are in inches.
Figure 19 – Air Capacitor used for Tuning Process
By trimming the metal on the top surface of the capacitor with a diamond scribe,
the surface area of the parallel plate capacitor is lowered, therefore decreasing its
capacitive value.
The filter will be tuned well within the customer’s specifications. The two
specification points that will be the toughest to meet are the two 28 dBc points. As a
goal, the filter will be tuned to at least 31 dBc at those two frequencies. The initial tuning
40
process will focus on the 28 dBc points in the specification and the pass band VSWR.
The series resistors in the attenuator will be replaced with silver shims to simulate a 50
ohm line. After the filter tuning is complete, the silver shims are removed and the
resistors are soldered in. Minimal tuning will be needed in the filter at this point, and
most of the tuning will be done in the attenuator/equalizer section. It is very difficult to
tune the filter with the equalizer/attenuator properly installed. The resistors mask the
filter’s response and it becomes difficult to decipher what exactly is happening while
tuning.
41
Chapter 6
FINAL PERFORMANCE OF THE 836 – 964 MHz BAND PASS FILTER AND ATTENUATOR - EQUALIZER
6.1 Analysis & Conclusion of Measured Data
The following figures are plots are data from a network analyzer characterizing
the realized filter’s performance.
Figure 20 – Measured Data from the Completed Filter, S11 Parameter Only. The 8 poles of the filter can be easily distinguished in the return loss of this plot.
42
Figure 21 - Measured Data from the Completed Filter, 1.5 dBc Bandwidth, S21 Parameter Only.
43
Figure 22 - Measured Data from the Completed Filter, Pass Band Variation, S21 Parameter Only.
44
Figure 23 - Measured Data from the Completed Filter, Rejection Performance, S21 Parameter Only. Markers are referenced to the center frequency marker.
Table 7 compares the capability of the simulation to the actual measured numbers
of the realized filter. This will allow the quality of the simulation to be assessed and
where we can expect to have issues with future designs. Ideally, the measured values
would exceed the simulation’s expected values. This would allow for greater confidence
in how the realized filter will perform if the simulation meets the given specifications.
45
Table 7 – Specification Versus Measured Filter Performance.
Parameter Specification Simulation Capability
Measured
Center Frequency 900 MHz 900 MHz 900 MHz Minimum -1.5 dB Bandwidth
155 MHz > 155 MHz 171.9 MHz
Maximum Low Side -1.5 dB Frequency
829 MHz 818 MHz 814.6 MHz
Minimum High Side -1.5 dB Frequency
970 MHz 984 MHz 986.5 MHz
Pass band for Insertion Loss and VSWR
836 to 964 MHz 836 to 964 MHz <836 to >964 MHz
Maximum Pass band Insertion Loss at Center Frequency
8.0 dB 7.8 dB 7.6 dB
Minimum Pass band Insertion Loss at Center Frequency
7.0 dB 7.2 dB 7.6 dB
Maximum Pass band Variation
0.9 dB 0.4 dB 0.1 dB
Maximum Pass band VSWR
1.5:1 (≥ 14.0 dB Return Loss)
1.35:1 (≥ 17.0 dB Return Loss)
1.166:1 (22.3 dB Return Loss)
Minimum Rejection Requirements
46 dBc ≤ 676 MHz > 60 dBc 78.2 dBc 46 dBc ≤ 700 MHz > 60 dBc 70.5 dBc 40 dBc ≤ 740 MHz 50 dBc 55.3 dBc 28 dBc ≤ 780 MHz 31 dBc 32.7 dBc 7 dBc ≤ 796 MHz 15 dBc 19.3 dBc 7 dBc ≥ 1004 MHz 15 dBc 17.9 dBc 28 dBc ≥ 1020 MHz 31 dBc 31.4 dBc 40 dBc ≥ 1060 MHz 50 dBc 59.9 dBc 46 dBc ≥ 1100 MHz > 60 dBc 80.8 dBc 46 dBc ≥ 1124 MHz > 60 dBc 90.6 dBc 46 dBc ≥ 2000 MHz, ≤
5000 MHz > 60 dBc > 80 dBc
46
The performance of the filter is well within the customer’s specifications. The
simulation created by Touchstone turned out to be very accurate when predicting the
filters performance. By designing such a large margin at the 28 dBc points, we were able
to have the realized filter performance with an excess of the 3 dB margin that was
desired. A trade off relationship exists between rejection and VSWR, by improving the
rejection of the filter, the VSWR becomes worse and vise versa. The other rejection
points were not as critical as the 28 dBc points, this was anticipated. The measured
return loss of the filter was over 8 dB within the specification, 22.3 dB (VSWR: 1.166:1)
when only 14.0 dB (VSWR: 1.5:1) was required.
The attenuator – equalizer allowed the overall insertion loss and insertion loss
variation to be controlled precisely. The insertion loss at center frequency was 7.6 dB,
which is almost exactly in the middle of the 7 to 8 dB window allowed by the
specification. The pass band variation was 0.1 dB, well within the 0.9 dB window. The
attenuator - equalizer allowed these two parameters to be adjusted very easily.
The combination of ComSyn and Touchstone allowed the assembly to be
designed, optimized and realized very close to the calculated response. ComSyn
calculated the initial element values and Touchstone optimized the element values for
realization. ComSyn was used for almost all of the initial design calculations for the
filter and virtually eliminated almost all hand analysis. It determined the number of
47
required sections and rejection levels very accurately. It also revealed the 28 dBc points
to be the most difficult to achieve, which was very helpful during the tuning process.
The optimizing algorithms in Touchstone made a significant difference in the
difficulty of this project. The program’s option to fix some element values while
optimizing other values was extremely useful. Having the ability to add or remove
elements from the circuit file and analyze the results was very helpful.
By looking at the results of this project, it is easy to conclude that computer
analysis is an extremely useful tool in filter design. ComSyn and Touchstone were
created over 20 years ago and are still very efficient and useful. Numerous design
programs used for applications other than filter design, become outdated and obsolete.
For example a program used for IC design would be outdated within a few years as
transistor technology advances and IC’s become smaller and smaller. The equations that
ComSyn and Touchstone are based on have not changed with time.
48
APPENDIX
Output for ComSyn
!============================================================================ ! Capacitively Coupled Pi-Resonstors ! Lumped Bandpass Filter: Chebyshev prototype. Zo= 50 ohms. ! N= 8, F1= 829.00 MHz, F2= 971.00 MHz, Ripple= 0.020 dB VAR Qc = 800.0 ! capacitor Q Ql = 200.0 ! inductor Q Fq = 0.90000 ! frequency of Q CKT CAPQ 1 2 C= 2.65211 Q^Qc F^Fq MOD=3 CAPQ 2 0 C= 1.86100 Q^Qc F^Fq MOD=3 INDQ 2 102 L= 17.84974 Q^Ql F^Fq MOD=3 CAPQ 102 0 C= 2.56858 Q^Qc F^Fq MOD=3 CAPQ 102 3 C= 1.00137 Q^Qc F^Fq MOD=3 CAPQ 3 0 C= 2.56858 Q^Qc F^Fq MOD=3 INDQ 3 103 L= 17.84974 Q^Ql F^Fq MOD=3 CAPQ 103 0 C= 2.87520 Q^Qc F^Fq MOD=3 CAPQ 103 4 C= 0.69475 Q^Qc F^Fq MOD=3 CAPQ 4 0 C= 2.87520 Q^Qc F^Fq MOD=3 INDQ 4 104 L= 17.84974 Q^Ql F^Fq MOD=3 CAPQ 104 0 C= 2.92687 Q^Qc F^Fq MOD=3 CAPQ 104 5 C= 0.64308 Q^Qc F^Fq MOD=3 CAPQ 5 0 C= 2.92687 Q^Qc F^Fq MOD=3 INDQ 5 105 L= 17.84974 Q^Ql F^Fq MOD=3 CAPQ 105 0 C= 2.93765 Q^Qc F^Fq MOD=3 DEF2P 1 105 HALF HALF 1 2 CAPQ 2 3 C= 0.63230 Q^Qc F^Fq MOD=3 HALF 4 3 DEF2P 1 4 FIL OUT FIL DB[S21] GR1 FIL DB[S11] GR1A FIL Td[S21] GR2 FIL S11 FREQ SWEEP 0.700000 1.110000 0.001000 GRID RANGE 0.7000 1.1100 0.0400
49
GR1 0 -100 10 GR1A 0 -50 GR2 0 50 5 OPT RANGE 0.8290 0.9710 FIL DB[S11] < -23.4 !===================================================================== !-- COMSYN -- Synthesis -- ! Lumped Element Filter: Overall Degree = 16. ( 8 0 0 8 design) ! F1= 829.00 MHz, F2= 971.00 MHz, Ripple=0.020 dB, Theta= 0.000 deg ! Fo= 900.00 MHz, %BW= 11.0 %, Length of Resonator= 0.0000 inch ! Doubly terminated: Zsource = Zload = 1 Ohms -- TRANSFER FUNCTION ANALYSIS OF LUMPED ELEMENT FILTER -- Q(ind)= 220.00, Q(cap)= 820.00 (Q of resonator = 173.46) Connector pair Loss = 0.050 x SQR(F GHz) dB included Freq(MHz) Loss(dB) Rej.(dBc) Td(nS) Td-Td@Fo delta Td 676.000 107.019 105.084 0.573 -12.628 0.000 700.000 97.250 95.315 0.738 -12.463 0.165 720.000 88.226 86.291 0.943 -12.258 0.205 740.000 78.123 76.189 1.257 -11.944 0.314 760.000 66.528 64.593 1.785 -11.416 0.528 780.000 52.714 50.779 2.816 -10.385 1.031 796.000 39.109 37.175 4.701 -8.501 1.884 800.000 35.177 33.242 5.554 -7.648 0.853 820.000 11.134 9.200 27.007 13.806 21.453 829.000 4.159 2.225 31.392 18.191 4.385 836.000 2.991 1.057 22.292 9.090 -7.677 840.000 2.728 0.793 20.295 7.093 -1.997 860.000 2.151 0.217 15.554 2.352 -4.741 880.000 1.967 0.033 13.851 0.649 -1.703 900.000 1.935 0.000 13.201 0.000 -0.649 920.000 2.002 0.068 13.404 0.203 0.203 940.000 2.214 0.280 14.633 1.432 1.229 960.000 2.818 0.884 18.321 5.120 3.688 964.000 3.078 1.143 19.854 6.652 1.533 970.400 3.992 2.057 25.787 12.585 5.933 971.000 4.163 2.229 26.801 13.600 1.014 980.000 9.612 7.678 27.017 13.815 0.215 1000.000 29.907 27.972 5.706 -7.495 -21.310 1004.000 33.373 31.438 4.808 -8.394 -0.899 1011.200 39.074 37.139 3.707 -9.495 -1.101
50
1014.800 41.704 39.769 3.310 -9.891 -0.396 1020.000 45.283 43.348 2.854 -10.348 -0.457 1040.000 57.164 55.230 1.800 -11.401 -1.053 1060.000 66.914 64.979 1.264 -11.937 -0.536 1080.000 75.209 73.274 0.946 -12.256 -0.318 1085.200 77.179 75.244 0.884 -12.318 -0.062 1088.800 78.504 76.569 0.845 -12.357 -0.039 1100.000 82.437 80.502 0.739 -12.463 -0.106 1124.000 90.045 88.111 0.572 -12.630 -0.167 ***** SUMMARY of ANALYSIS ***** * Pass band edges: 836.000 MHz, 964.000 MHz. * Insertion Loss: 2.991 dB, Min= 1.935 dB, 3.078 dB. * Bandedge Loss Var: 1.057 dB, 1.143 dB. * Group Delay: 22.292 nS, Min= 13.201 nS, 19.854 nS. * Group Delay Var: 9.090 nS, 6.652 nS. * Crit. Freq (MHz): 780.000 1020.000 * Ins. Loss (dB): 52.714 45.283 * Rejection (dBc): 49.636 42.205
Circuit File of Equalizer and Optimized Band Pass Filter Touchstone Circuit File of Complete Band pass Filter !============================================================================ ! Capacitively Coupled Pi-Resonators ! Lumped Band pass Filter: Chebyshev prototype. Zo= 50 ohms. ! N= 8, F1= 829.00 MHz, F2= 971.00 MHz, Ripple= 0.020 dB ! 100 OHM RESONATOR IMPEDANCE DIM FREQ GHZ LNG MIL TIME NS VAR Qc = 820.0 ! capacitor Q Ql = 220.0 ! inductor Q Fq = 0.90000 ! frequency of Q C2 = 3.2 C1 = 2.6
51
CKT CAPQ 1 2 C\ 3.73354 Q^Qc F^Fq MOD=3 CAPQ 2 0 C^c1 Q^Qc F^Fq MOD=3 INDQ 2 102 L\ 13.2734 Q^Ql F^Fq MOD=3 CAPQ 102 0 C^c2 Q^Qc F^Fq MOD=3 CAPQ 102 3 C\ 1.37028 Q^Qc F^Fq MOD=3 CAPQ 3 0 C^c2 Q^Qc F^Fq MOD=3 INDQ 3 103 L\ 15.2631 Q^Ql F^Fq MOD=3 CAPQ 103 0 C^c2 Q^Qc F^Fq MOD=3 CAPQ 103 4 C\ 0.863908 Q^Qc F^Fq MOD=3 CAPQ 4 0 C^c2 Q^Qc F^Fq MOD=3 INDQ 4 104 L\ 15.9851 Q^Ql F^Fq MOD=3 CAPQ 104 0 C^c2 Q^Qc F^Fq MOD=3 CAPQ 104 5 C\ 0.794378 Q^Qc F^Fq MOD=3 CAPQ 5 0 C^c2 Q^Qc F^Fq MOD=3 INDQ 5 105 L\ 16.1002 Q^Ql F^Fq MOD=3 CAPQ 105 0 C^c2 Q^Qc F^Fq MOD=3 DEF2P 1 105 HALF HALF 1 2 CAPQ 2 3 C \ 0.77732 Q^Qc F^Fq MOD=3 HALF 4 3 DEF2P 1 4 FIL !ATTENUATOR-EQUALIZER RES 1 2 R = 16.5 RES 2 12 R = 66.5 RES 2 3 R = 16.5 INDQ 12 7 L = 0.5 Q^Ql F^Fq MOD=3 INDQ 7 0 L = 15.7617 Q^Ql F^Fq MOD=3 INDQ 7 13 L = 13.0741 Q^Ql F^Fq MOD=3 CAPQ 13 0 C = 1.29062 Q^Qc F^Fq MOD=3 CAPQ 13 14 C = 0.4102 Q^Qc F^Fq MOD=3 INDQ 14 0 L = 18.3368 Q^Ql F^Fq MOD=3 CAPQ 14 0 C = 1.06391 Q^Qc F^Fq MOD=3 DEF2P 1 3 EQ !ASSEMBLY FIL 1 2 EQU 2 3 DEF2P 1 3 FILEQ OUT FILEQ DB[S21] GR1 FILEQ DB[S11] GR1A FILEQ TD[S21] GR1A
52
FILEQ Td[S21] GR2 FILEQ DB[S21] GR2A EQU db[s21] GR3 FILEQ db[s21] GR3 FIL DB[S21] GR3 FREQ SWEEP 0.700 1.1000 0.0100 SWEEP 0.8224 0.97760 0.1552 SWEEP 0.8296 0.9704 0.1408 SWEEP 0.836 0.964 0.1408 SWEEP 0.796000 1.004000 0.208000 SWEEP 0.780000 1.020000 0.240000 SWEEP 0.740000 1.060000 0.320000 SWEEP 0.676000 1.124000 0.320000 GRID RANGE 0.7080 1.0920 0.03200 GR1 0 -100 10 GR1A 0 -50 10 GR2 0 30 5 GR2A -6 -9 -.5 GR3 -1 -9 -.5 GR3A -1 -9 -.5
53
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