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Design methodology for multilayer microwave filters and Balun circuits

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DESIGN METHODOLOGY FOR MULTILAYER
MICROWAVE FILTERS AND BALUN CIRCUITS
by
CHOONSIK CHO
B.S., Seoul National University, Seoul, 1987
M.S., University of South Carolina, 1995
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Electrical and Computer Engineering
1998
i
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This thesis for the Doctor of Philosophy degree by
Choonsik Cho
has been approved for the
Department of
Electrical and Computer Engineering
by
K.C. Gupta
Richard C. Booton, Jr.
tw
We
The final copy of this thesis has been examined by the
signators, and we find that both the content and the form
meet acceptable presentation standards of scholarly work in
the above mentioned discipline.
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Choonsik Cho, (Ph.D., Electrical Engineering)
Design Methodology for Multilayer Microwave Filters and Baiun Circuits
Thesis directed by Professor K.C. Gupta
A systematic and efficient approach to the design for a broad class of
passive microwave circuits in multilayer configurations is presented. Multilayer
configurations are becoming popular at microwave frequencies due to their sev­
eral advantages over single layer configurations. However, systematic design
procedures for multilayer circuits have not been yet available. Design proce­
dures for several types of microwave circuits in multilayer configurations have
been developed. Parallel coupled-line band-pass filters, end-coupled band­
pass filters and three-line baluns have been designed with the systematic de­
sign procedures developed. Procedures developed have been verified by com­
paring the results with full-wave electromagnetic simulations. These circuits
have also been fabricated and measured to verify the design procedures. Wide
bandwidth, size/volume compaction, flexible design and physically realizable
dimensions are the factors th at multilayer structures provide compared to sin­
gle layer configurations.
A network modeling is employed to characterize multilayer m ulticonductor transmission line systems. Since the microwave circuits developed
utilize multiple coupled lines in multilayer configurations, the characterization
of these coupled lines plays a significant role in derivation of design equations
and generation of design procedures. Using this modeling approach, a multiple
coupled line system can be transformed to a multiple uncoupled line system.
These equivalent uncoupled lines are used to derive network parameters ([S],
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iv
[Y] or [Z] matrix) for coupled lines. The normal mode parameters (NMPs) for
coupled lines derived in terms of system specifications are utilized to obtain the
physical geometries. An optimization process is employed to find the geome­
tries which yield the desired NMPs calculated from circuit specifications. For
optimizing the geometry, a quasi-static field analysis program, Segmentation
and Boundary Element Method (SBEM), is employed to calculate inductance
and capacitance matrices for specific dimensions of the multilayer configura­
tions. A general optimization algorithm, Simplex method, is used in conjunc­
tion with SBEM to obtain the physical geometry for various coupled lines.
Sometimes, this optimization process generates local minima and takes consid­
erable time in computer simulation. Therefore, an Artificial Neural Network
Modeling (ANN) is used to save the optimization time. Because end-coupled
band-pass filters employ gap coupled sections, the 2-dimensional SBEM is not
applicable for optimizing the gap dimensions. In this case, an ANN model has
been developed and used to design this kind of filters based on the procedure
developed here.
Two case studies of parallel coupled-line band-pass filters are pre­
sented following the design procedure developed. A quasi-static analysis by
SBEM and simulation result from a full-wave electromagnetic simulator are
presented along with measurements for verification. Two designs of paral­
lel coupled filter carried out in coplanar waveguide (CPW) are also reported.
Three-line baluns have been designed in two layer structures, simulated and
verified by measurement results.
Two examples of multilayer end-coupled
band-pass filters have been designed using the procedure developed. One ex­
ample of these filters is also designed with an ANN model for comparison. A
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discussion of results from these circuits and suggestions for future work
presented.
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vi
ACKNOWLEDGMENTS
I would like to thank many people who helped continuously to make
this dissertation come true without any difficulty. I am preferably thankful
for Dr. K. C. Gupta, the dissertation advisor, for his endless encouragement
directing the correct way to aim, patient guidance and invaluable advice. Also,
I appreciate Jaeheung Kim, Zhiping Feng and Dr. Wenge Zhang who always
assisted me with difficult fabrication of many circuits. I thank Dr. Roop
L. Mahajan and Martin Hausler for installing and running a software of the
artificial neural network model. I wish to thank Dr. Zoya B. Popovic and her
many students for assisting experiments. Besides, I am grateful for Dr. Melinda
Picket-May and Dr. Richard C. Booton, Jr. for serving on my committee.
I am also grateful for my parents, brother and sister for encouraging
me from a distance. Finally I want to express my gratitude from the bottom
of heart to my wife, Misoo Kwon, for her endless devotion and speechless
encouragement. This dissertation would not have been possible without her
love and endurance. Also, I thank my child, Yeonjoo, for being always patient
of not having enough time to play with me.
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CONTENTS
CHAPTER
1
IN TR O D U C TIO N ............................................................................
1
1.1 Advantages of Multilayer C i r c u i t s .......................................
1
1.2 The Need for Developing Design Procedures.......................
3
....................................................
5
1.3 Organization of the Thesis
2
A REVIEW OF MULTILAYER
2.1 Two Types of Multilayer C ircuits..........................................
8
2.2 Multilayer Integration of MicrowaveC i r c u i t s .....................
9
2.2.1
MMICs (Monolithic Microwave Integrated Circuits)
9
2.2.2
MCM (Multi-Chip M o d u les)...................................
9
2.3 Multilayer Circuits Using Multilayer Transmission Lines .
12
2.3.1
3
MICROWAVE CIRCUITS . .8
Circuit Functions Realized with Multilayer Trans­
mission L in es................................................................
12
2.3.2
Coupled-Line C o u p le rs .............................................
14
2.3.3
Parallel Coupled-Line Band-Pass F i l t e r s
16
2.3.4
End-Coupled Band-Pass F i l t e r s .............................
18
2.3.5
Planar B a l u n s .............................................................
19
2.3.6
Other Multilayer C o m p o n e n ts ................................
20
DESIGN M E T H O D O L O G Y .........................................................
21
3.1 Network M o d eling....................................................................
22
3.2 Analysis Approach for Multilayer C irc u its ..........................
31
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viii
3.3
Circuit S ynthesis......................................................................
33
4 DESIGN OF PARALLEL COUPLED-LINE BAND-PASS FIL­
TERS IN MULTILAYER CONFIGURATIONS..........................
37
4.1
Derivation of Design P ro ced u re............................................
37
4.1.1
Z-M atrix for 2-Port Coupled Line Sections . . . .
39
4.1.2
Evaluation of the Normal Mode Parameters for
Homogeneous C onfigurations...................................
4.1.3
Evaluation of the Normal Mode Parameters for Inhomogeneous C o n fig u ratio n s...................................
4.1.4
4.2
4.3
4.4
44
45
An Alternative Approach to the Evaluation of NMPs
in Inhomogeneous Configurations.............................
47
Description of Design Procedures.........................................
48
4.2.1
Homogeneous C onfigurations...................................
48
4.2.2
Inhomogeneous C onfigurations................................
50
Design E xam ples......................................................................
53
4.3.1
Homogeneous Filters
................................................
53
4.3.2
Inhomogeneous F ilte rs ................................................
59
4.3.3
CPW F i l t e r s ................................................................
66
Discussion
................................................................................
70
5 DESIGN OF END-COUPLED BAND-PASS FILTERS IN MUL­
TILAYER C O N FIG U R A TIO N S...................................................
73
5.1
Derivation of Design P ro ced u re.............................................
73
5.2
Description of Design P r o c e d u re ..........................................
77
5.3
Design E xam ples......................................................................
79
5.4
Design of End-Coupled Filters with ANN M odels
85
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ix
5.4.1
ANN M odeling............................................................
85
5.4.2 ANN Modeling Methodology for Multilayer EndCoupled Filters
.........................................................
88
5.4.3 The Design of Multilayer End-Coupled Filters Us­
ing ANN M odels.........................................................
5.5
Discussion
..............................................................................
90
94
6 MODELING FOR THREE-LINE BALUNS IN MULTILAYER
C O N FIG U R A TIO N S......................................................................
96
6.1
In tro d u c tio n ...........................................................................
96
6.2
Description of Design P r o c e d u re ........................................
97
6.2.1 Representation of a Baiun by Two Coupled-Line
C o u p le rs ......................................................................
97
6.2.2 Design of 3-Line B alu n s.............................................
102
6.2.3 Physical Geometry for the 3-Line B a iu n .................
104
Design Exam ples......................................................................
106
6.3.1 Single-Layer 3-Line B a lu n s.......................................
106
6.3.2 Two-Layer B a lu n s.......................................................
107
D is c u ss io n ..............................................................................
117
7 SUMMARY AND FUTURE W O R K ............................................
118
6.3
6.4
7.1
Multilayer Microwave Circuit DesignMethodology . . . .
118
7.2
Multilayer Microwave Circuit E x a m p le s ...........................
120
7.3
7.2.1 Parallel Coupled-Line Band-Pass F i l t e r s
120
7.2.2 End-Coupled Band-Pass F i l t e r s ..............................
121
7.2.3 Three-Line B aluns.......................................................
122
Future W o r k ............................................................................
123
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X
7.3.1
Compaction of F ilt e r s ................................................
7.3.2
Bandwidth Considerations in Designing Three-Line
123
B a l u n s .........................................................................
125
7.3.3
Other Multilayer C irc u its .........................................
125
BIBLIOGRAPHY
.........................................................................................
126
APPENDIX
A AN OPTIMIZATION OF PHYSICAL GEOMETRY USING
“SIMPLEX” ALGORITHM ............................................................
138
A .l
Main f u n c t io n ........................................................................
138
A.2
Link to S B E M ........................................................................
141
A.3
“Simplex” function..................................................................
143
B DATA FLOW FROM EM-ANN MODELS TO HP-MDS . . . .
145
B.l
User-defined linear m o d e l.....................................................
145
B.1.1
Creating and preparing a directory ..........................
145
B .l.2 Run the “makemod” ...................................................
145
B.1.3 Editing the C-code template f i l e .............................
145
B.2
The feed-forward ANN function
........................................
150
B.3
An EM-ANN weight f ile ........................................................
151
B.4
Compiling and linking the m o d e l........................................
152
B.5
Read design icons file into M D S ........................................
152
B.6
Notes on model u s a g e ...........................................................
153
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xi
TABLES
TABLE
1.1
A sensitivity analysis of the S-parameters for coupled lines
on same layer (left side in Figure 1.1) and coupled lines on
different layer (right side in Figure 1.1) with respect to the
spacing (5 )........................................................................................
4.1
The specifications for homogeneous parallel coupled-line band­
pass f i l t e r s ..........................................................................................
4.2
.............................
58
The filter specifications used for inhomogeneous parallel coupledline band-pass filters
4.6
56
Center frequency, bandwidth and ripple level for homoge­
neous parallel coupled-line band-pass filters
4.5
56
Physical dimensions for a homogeneous 4-layer parallel coupledline band-pass filter (units in m m ) ................................................
4.4
54
Physical dimensions for a homogeneous 3-layer parallel coupledline band-pass filter (units in m m ) ................................................
4.3
3
.......................................................................
59
Physical dimensions for the inhomogeneous (a) 3-layer par­
allel coupled-line band-pass filter and (b) 5-layer parallel
coupled-line band-pass f i l t e r ..........................................................
4.7
62
Center frequency, bandwidth and ripple for inhomogeneous
parallel coupled-line band-pass f i lte r s ..........................................
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65
x ii
4.8 The specifications used for multilayer CPW parallel coupledline band-pass filters
...................................................................
66
4.9 Physical dimensions for 3-layer CPW parallel coupled-line
band-pass filters, (a) Topology A (b) Topology B ...................
68
4.10 Center frequency, bandwidth and ripple for 3-layer CPW par­
allel coupled-line band-pass filter d e s ig n s ................................
71
5.1 Specifications for multilayer end-coupled band-pass filters . .
80
5.2 Physical dimensions of a two-layer end-coupled band-pass
filter (units in mm) for Design A. Dimensions W \, W2,g and
I are shown in Figure 5 . 1 ............................................................
80
5.3 Physical dimensions of a two-layer end-coupled band-pass
filter (units in mm) for Design B. Dimensions W \, W2,g and
I are shown in Figure 5 . 1 .............................................................
82
5.4 Center frequency, bandwidth and ripple level for multilayer
end-coupled band-pass filte rs ......................................................
84
5.5 Physical dimensions of a two-layer end-coupled band-pass
filter (units in mm) with ANNs (Design A ) .............................
93
5.6 Center frequency, bandwidth and ripple for a two-layer endcoupled band-pass filter with A N N s ..........................................
94
5.7 Design times and required iterations for end-coupled filters
with ANN modeling and without A N N s ...................................
95
6.1 Some choices of Zoi,Zq 2 for balun input/output impedances
Zin =
= 50ft
..........................................................................
101
6.2 Parameters for the design example of a single-layer 3-line balun
106
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6.3
Parameters for the design example of a two-layer 3-line balun
(Topology A ) ..................................................................................
6.4
Parameters for the design example of a two-layer 3-line balun
(Topology B ) ..................................................................................
6.5
108
Summary of a two-layer 3-line balun performance (Topology
A ) .....................................................................................................
6.6
107
115
Summary of a two-layer 3-line balun performance (Topology
B ) .....................................................................................................
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116
x iv
FIGURES
FIGURE
1.1
Coupled-line couplers used for determining the sensitivities
of the S-parameters with respect to the spacing dimension
(left : hi = 20 mil, /i2 = 10 mil, er i = er2 = 9.6, rig h t: hi =
20 mil, h2 = 5 mil, /i3 = 5 mil, erl = er2 = er3 = 9 .6 ) .............
2.1
The layout of a 3-D multilayer MMIC (from Ref. [1])
2.2
The cross-sectional view of an MCM used for multilayer inter­
connects
3.1
....
.........................................................................................
2
10
11
Cross sectional view of various examples of multilayer coupled
lin es...................................................................................................
22
3.2
A
system of n-conductor transmission li n e s .................
22
3.3
A
network model of n-conductor transmission line system . .30
3.4
Anetwork model of two-coupled l i n e .......................................
31
3.5
A
32
3.6
A flow diagram for analysis of multilayer circuits consisting
network model of three-coupled lin e ...........................
of sections of multi-conductor lines
3.7
.........................................
A flow diagram for synthesis of a single coupled-line section
of a multilayer c ir c u it ...................................................................
3.8
33
34
Synthesis of multilayer circuits consisting of several coupled
line s e c t io n s ...................................................................................
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35
XV
4.1
The layout of a parallel coupled-line band-pass filter using 4
coupled line sections (top view )...................................................
4.2
A typical filter section consisting of a coupled line with two
ports o p e n ......................................................................................
4.3
38
An admittance inverter model used for modeling a 2-port
coupled section shown in Figure 4 . 2 ..........................................
4.4
38
38
An equivalent circuit using admittance inverter models for a
coupled-line band-pass filter similar to one shown in Figure 4.1
39
4.5 An equivalent circuit for the transmission line of the length 29
39
4.6
An equivalent circuit for the admittance inverters at both
ends of Figure 4 . 4 ..........................................................................
4.7
An equivalent network corresponding to the parallel coupledline band-pass filter circuits shown in Figure 4 . 1 ...................
4.8
40
40
A lumped element equivalent circuit for the band-pass filter
configuration...................................................................................
4.9 The cross-sectional view of a typical homogeneous configuration
40
43
4.10 The cross-sectional view of a typical inhomogeneous config­
uration .............................................................................................
45
4.11 The procedure for the design of multilayer parallel coupledline band-pass filters in homogeneous configurations.............
49
4.12 The procedure for the design of multilayer parallel coupledline band-pass filters in inhomogeneous configurations . . . .
52
4.13 The cross-sectional view of a 4-layer homogeneous parallel
coupled-line band-pass f i l t e r .......................................................
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53
xvi
4.14 The layout used for simulation of a homogeneous 3-layer par­
allel coupled-line band-pass f i l t e r ...........................................
55
4.15 The layout used for simulation of a homogeneous 4-layer par­
allel coupled-line band-pass f i l t e r ...........................................
55
4.16 The performance of a 3-layer parallel coupled-line band-pass
filter embedded in a homogeneous dielectric...........................
57
4.17 The performance of a 4-layer parallel coupled-line band-pass
filter embedded in a homogeneous dielectric...........................
58
4.18 (a) The cross sectional view and (b) the layout of an inho­
mogeneous 3-layer parallel coupled-line band-pass filter. . .
60
4.19 (a) The cross sectional view and (b) the layout of an inho­
mogeneous 5-layer parallel coupled-line band-pass filter. . .
61
4.20 The photograph of multilayer parallel coupled-line band-pass
filters fabricated on RT/Duroid 5880 (right: 3-layer filter left:
5-layer filte r).................................................................................
63
4.21 The performance of an inhomogeneous 3-layer parallel coupledline band-pass f i l t e r ......................................................................
64
4.22 The performance of an inhomogeneous 5-layer parallel coupledline band-pass filters
...................................................................
65
4.23 The layout of 3-layer CPW parallel coupled-line band-pass
filter configuration for (a) Topology A, (b) Topology B . . . .
67
4.24 The performance of a 3-layer CPW parallel coupled-line band­
pass filter for topology A .............................................................
69
4.25 The performance of a 3-layer CPW parallel coupled-line band­
pass filter for topology B .............................................................
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70
xv ii
5.1 The layout of a multilayer end-coupled band-pass filter . . .
74
5.2 An equivalent transmission line circuit for end-coupled band­
pass f i l t e r s .....................................................................................
74
5.3 A modified transmission line model for end-coupled band­
pass f i l t e r s .....................................................................................
75
5.4 An equivalent circuit using admittance inverters and A/2 res­
onators (<t> = 180°).........................................................................
75
5.5 The relation between an admittance inverter and a gap ex­
pressed by susceptances and transmission l i n e s ......................
5.6 A design procedure for multilayer end-coupled band-pass filters
76
78
5.7 The physical layout for a two-layer end-coupled band-pass
filter (Design A ) ............................................................................
81
5.8 The performance of a two-layer end-coupled band-pass filter
(Design A ) .....................................................................................
81
5.9 The photograph of two-layer end-coupled band-pass filters
fabricated on RT/duroid 5880 (bottom: Design A, top: De­
sign B ) ............................................................................................
82
5.10 The physical layout for a two-layer end-coupled band-pass
filter (Design B ) ............................................................................
82
5.11 The performance of a two-layer end-coupled band-pass filter
(Design B ) .....................................................................................
83
5.12 The architecture of typical single hidden layer artificial neural
netw ork............................................................................................
87
5.13 Analysis ANN model for gap coupled sections..........................
89
5.14 Synthesis ANN model for gap coupled s e c tio n s .......................
89
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x v iii
5.15 Flow of data for linking EM-ANN models to commercial mi­
crowave circuit sim ulators............................................................
91
5.16 A synthesis procedure for gap coupled sections using ANN
m o d e ls ............................................................................................
92
5.17 Performance of a two-layer end-coupled filter using ANNs . .
93
6.1 The general configuration of a 3-line b a l u n .............................
97
6.2 The block diagram of b a l u n s ......................................................
98
6.3 The bifurcated block diagram of b a lu n s ...................................
99
6.4 A 3-line balun composed of two 2-line couplers.......................
99
6.5 Equivalence between (a) a section of 3-coupled lines and (b)
a 6-port network combination of two couplers..........................
103
6.6
A design procedure for 3-line b a lu n s .........................................
105
6.7
The physical
layout of a
single-layer 3-line b a lu n .........
106
6.8
The physical
layout of a
two-layer 3-line balun
(Topology A)107
6.9
The physical
layout of a
two-layer 3-line balun
(Topology B)108
6.10 The performance of two-layer 3-line balun (Topology A) de­
signed by the procedure developed and comparison with an
‘ideal’ b a l u n ...................................................................................
109
6.11 The performance of two-layer 3-line balun (Topology B) de­
signed by the procedure developed and comparison with an
‘ideal’ b a l u n ...................................................................................
110
6.12 The phase imbalances of two-layer 3-line baluns designed by
the procedure developed................................................................
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Ill
x ix
6.13 (a) The layout of a two-layer 3-line balun fabricated on
Duroid RT5880, (b) the photograph of a two-layer 3-line
balun fabricated on Duroid RT5880 .........................................
112
6.14 The measured performance of a two-layer 3-line balun (Topol­
ogy B) designed by the procedure developed and comparison
with a full-wave sim u latio n .........................................................
113
6.15 The measured phase imbalance of a two-layer 3-line balun
designed by the procedure developed.........................................
7.1
A possible layout of a more compact parallel coupled-line
band-pass f i l t e r ............................................................................
7.2
124
A possible layout of a more compact end-coupled band-pass
filter
7.3
114
................................................................................................
124
A possible layout of a cascaded three-line b a l u n ...................
125
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CHAPTER 1
INTRODUCTION
1.1
Advantages of Multilayer Circuits
Most of the microwave circuits have been developed in single layer
configurations since microstrip lines were introduced to replace striplines. Mi­
crowave integrated circuits (MICs) and monolithic microwave integrated cir­
cuits (MMICs) have mainly been realized on the top of a single-layer substrate
material on which active circuits and passive circuits are placed. This single­
layer substrate environment provides a simple and convenient method to design
and fabricate microwave components. However, as the need to reduce the size
of area and volume has increased, substantial efforts have been made to im­
plement MICs and MMICs in multilayer substrate environments. As a result,
passive and/or active microwave components are now being integrated in a
single multilayer module [1, 2]. Furthermore, some circuits are of themselves
becoming more compact using multilayer configurations [3-5].
There are two strong motivations for implementing the designs of
MICs and MMICs in multilayer configurations. One of these is the need to inte­
grate microwave components (as many as possible) within a given size/volume
constraint. In this case, circuits developed in the single layer configuration may
be utilized and the effect of multiple substrates that is not considered before is
now taken into account. Many low frequency and digital systems are adapting
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2
this methodology to reduce the overall size and volume.
The other motivation that is mainly considered in this thesis is to
develop designs for novel components and circuits using multilayer configu­
rations. Using this, an enhanced performance is expected when the multiple
layers are used. The use of multilayer multiple coupled-lines is an example
for this purpose. They create a tight coupling when used for directional cou­
plers, and a wide bandwidth when used for coupled line filters, baluns, etc.
These performances are usually not obtained from single-layer coupled-lines.
Multilayer configurations also provide more topological freedom in circuit lay­
outs because the components can be placed more flexibly than the single layer
structures. In addition, because single-layer designs can frequently cause a
difficulty in obtaining physical geometry with reasonable fabrication tolerance,
multiple layers can be used to overcome this problem.
1^2 )^r2
h i >£ri
Figure 1.1. Coupled-line couplers used for determining the sensitivities of the
S-parameters with respect to the spacing dimension (le ft: h\ = 20 mil, hi = 10
mil, eri = er2 = 9.6, right : hi = 20 mil, /i2 = 5 mil, /i3 = 5 mil, eri = er2 = er3
= 9.6)
Another advantage is a lower sensitivity as compared to single-layer
topology. The sensitivity analysis [6] can be performed for a coupler consisting
of 2 conducting strips placed at different layers. This circuit is compared to
a coupler consisting of 2 conducting strips placed at the same layer as shown
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3
Table 1.1. A sensitivity analysis of the S-parameters for coupled lines on same
layer (left side in Figure 1.1) and coupled lines on different layer (right side in
Figure 1.1) with respect to the spacing (S ).
Sensitivity
ISnl
l-Snl
to il
\S a i \
Coupled lines on same layer
0.5999
0.0753
0.0811
0.2230
Coupled lines on different layer
0.0204
0.0062
0.0103
0.0186
in Figure 1.1. Table 1.1 shows a comparison of sensitivities 1 of S-parameters
between these two different structures. We alter the spacing dimensions (ex­
pressed as S) for two cases with holding constant widths for two conducting
strips (expressed as W\ and W->). As shown in Table 1.1, the sensitivities of Sparameters for the coupler on same layer are larger than those for the coupler
on different layer. In other words, the coupler on different layer is less sensitive
to a change of the spacing dimension than the coupler on same layer, therefore,
the multilayer configurations using conducting strips placed at different layer
are more tolerable to the spacing dimension.
1.2
The N eed for Developing Design Procedures
Continuous efforts have been going on for development of multilayer
microwave components and circuits to overcome the difficulties associated with
single layer configurations and even to compact their size and volume. Direc­
tional couplers designed in a single layer have created difficulties in providing
tight couplings. Therefore, two-layer circuits have been utilized for obtaining
1The sensitivity (F) of P with respect to 5 is calculated as F £ = ^
coupling or the isolation, and S is the spacing dimension in this example
where P is the
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4
tight couplings (around 3 dB) and wide bandwidth. Research on two-layer
directional couplers has resulted in design procedures for implementing these
directional couplers. Parallel coupled-line band-pass filters have also been ex­
plored recently using multiple layers to achieve wide bandwidths th at are not
attainable in single-layer structures. However, the design procedures for de­
signing these filters to desired specifications have not been available until now.
In the research reported in this thesis, design procedures have been developed
for multilayer parallel coupled-line band-pass filters. Multilayer end-coupled
band-pass filters have also been reported in the literature [7] earlier. How­
ever, this work had been limited to only striplines and coplanar waveguide
(CPW) configurations. In this thesis, microstrip version of end-coupled multi­
layer filters have been investigated and design procedure is developed for their
implementation. Baiuns have attracted much attention for several application
areas at microwave frequencies. Two-layer planar Marchand baluns [8] have
been in use for almost a decade for obtaining a wide bandwidth and a good
balance performance. More compact version for baluns is a three-line balun.
The two-layer version of this class of baluns provides compactness, flexibility
and physically realizable dimensions compared to the single-layer version. A
design procedure for these baluns has been developed in this thesis.
In this thesis, more efficient and systematic procedures for the design
of multilayer microwave circuits and components (such as filters and baluns) are
presented and verified. For illustrating these methods, several design examples
are included. A quasi-static analysis and a full-wave electromagnetic simula­
tion program have been used for enhancing the circuit performance. Design
procedures have also been verified by fabricating several designs and measuring
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5
their performance.
1.3
Organization of the Thesis
This thesis begins with an investigation of the multilayer configura­
tions suitable for microwave circuits. In Chapter 2, a review of multilayer
structures at microwave frequencies is described. The current status in the de­
sign of multilayer circuits is reviewed for various applications such as couplers,
filters, baluns, antennas and so on. Chapter 3 presents the design methodol­
ogy used throughout this thesis. Since multilayer multi-conductor transmission
lines are employed to model parallel coupled line filters and three-line baluns,
the network modeling of these lines plays a crucial role in deriving design pro­
cedures for various multilayer circuits. This network model is used to derive
network parameters such as [Z], [Y], and [S] matrices needed for setting up the
design equations. The network parameters used can be obtained from the nor­
mal mode parameters (NMPs) which include voltage ratios, impedances and
phase velocities for various modes existing in multi-conductor line sections. A
quasi-static field analysis method, SBEM [9, 10], is used to determine these
NMPs for various cases. An analysis using SBEM used to analyze multilayer
multi-conductor lines is presented. Using the analysis process, a synthesis ap­
proach to the design of circuits is discussed later. This synthesis approach
makes the circuit design possible because a procedure to find out the physical
geometry appropriate for desired circuit specifications can be based on this
synthesis process. An optimization process has been employed to optimize
the physical geometry for designing parallel coupled line filters and three-line
baluns. Commonly used optimization processes can often converge to local
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6
minima and therefore require considerable computer time resource. Therefore,
an alternative modeling based on the use of ANNs has been used in the design
of end-coupled band-pass filters. This ANN modeling reduces the CPU time
requirement dramatically.
The remaining chapters of this thesis constitute various examples of
multilayer microwave circuits th at have been developed. In Chapter 4, paral­
lel coupled-line band-pass filters are modeled using network modeling method
discussed in Chapter 3. Because the traditional method had been developed for
only symmetrical coupled lines in single layer configurations, non-symmetrical
coupled lines in multiple layers are employed and a design procedure for this
kind of filters is derived. A wide bandwidth can be obtained in this multilayer
configurations, and more freedom is possible in the choice of physical geome­
try. Filter examples in homogeneous, inhomogeneous and CPW configurations
have been used to verify the design procedure developed. Simulated and mea­
sured results are presented and compared with calculated performance using
SBEM. In Chapter 5, end-coupled band-pass filters are designed in multilayer
configurations. Since this filter configuration utilizes gap coupled sections, twodimensional SBEM is not appropriate for this design. Instead, the capacitances
associated with the gap geometry have been determined using a full-wave sim­
ulator (HP-Momentum [11])- These capacitances have been calculated repeat­
edly to optimize gap geometry needed for desired parameters. The desired
parameters for each gap-coupled section have been derived for non-symmetric
and multilayer configurations. To speed up the optimization process, an ANN
modeling has been employed successfully. In Chapter 6, three-line baluns in
two layers are presented along with the design procedure developed. These
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7
baluns are more compact than the planar Marchand balun [8]. The design
procedure begins with bifurcation of the 3-line configuration into two identical
2-line couplers. Design procedure for 2-line couplers using two layers is an
intermediate step for the balun design. Once the couplers are designed from
balun specifications, desired normal mode parameters (NMPs) for 3-coupled
lines are derived, then these NMPs are evaluated using SBEM and an optimiza­
tion process. Detailed design equations are presented. Two designs have been
performed and presented together with simulation and measurement results to
verify the design procedure developed. The thesis concludes with a discussion
of results and some suggestions for future research in Chapter 7.
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CHAPTER 2
A REVIEW OF MULTILAYER MICROWAVE CIRCUITS
This Chapter reviews various kinds of multilayer circuits reported in
the literature.
2.1
Two Types of Multilayer Circuits
From the point of view of design methodology, multilayer circuits
can be divided into two groups. In the first group of these, one integrates
various single-layer circuits into a single multilayer module, whereas the second
group represents planar components employing multilayer transmission line
structures.
For the multilayer circuits in the first group, passive components
and/or active devices are integrated into a single module for miniaturization
and cost-effective production [1]. When these circuits are integrated, verti­
cal vias between different layers and apertures in the ground plane are placed
appropriately considering miniaturization, crosstalk and productivity.
Multilayer couplers, filters, baluns, inductors, etc. belong to the sec­
ond group because these employ multilayer transmission structures to overcome
difficulties associated with single-layer designs. The research reported in this
thesis relates to multilayer circuits in this group.
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9
2.2
M u ltilay er In te g ra tio n of M icrow ave C irc u its
2.2.1
M M IC s (M onolithic M icrow ave In te g ra te d C ircu its)
Multilayer MMICs [1,12] are constructed using a semiconductor substrate and
multilayer passive circuits integrated with active devices on the semiconductor
substrate. Active devices, resistors and MIM (M etal-insulator-metal) capaci­
tors are formed on the surface of a semiconductor wafer. Dielectric films and
conductors are stacked on the wafer, and transmission lines and the ground lay­
ers are connected through via-holes. This structure allows transmission lines
with reduced line widths, vertical interconnections with short signal delays and
miniaturized connections in a small area. In addition, this provides miniature
but low-loss transmission lines, and high design flexibility.
As examples of this multilayer topology, several miniature passive
circuits such as directional couplers, Wilkinson dividers, transmission lines,
and planar baluns have been designed and fabricated. Active circuits such as
mixers, amplifiers, phase shifters and up-converters are integrated with passive
circuits in planar forms. Figure 2.1 [1] shows the typical configuration of a
multilayer MMIC. In Figure 2.1, a 3-D multilayer MMIC fabricated on a GaAs
substrate integrates active devices, resistors, and MIM capacitors on the surface
of a semiconductor wafer. A thin film microstrip line offers a compact meanderline configurations while thin polyimide films and conductors are stacked on
the wafer and a ground metal is inserted between layers.
2.2.2
M C M (M u lti-C h ip M odules)
An MCM [13-15] as
shown in Figure 2.2 is defined as multilayer sandwiches of dielectric and con­
ducting layers, on which integrated circuits and passive components (if any)
are mounted directly on (or inside of) the sandwich structure, without separate
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10
Vertical ground plane
Ground metal
between layers
Vertical via
Active device
Semiconductor Substrate
Figure 2.1: The layout of a 3-D multilayer MMIC (from Ref. [1])
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11
Inductor
Substrate
Figure 2.2. The cross-sectional view of an MCM used for multilayer inter­
connects
packaging for each of the active components. That is, the chips are mounted
bare onto the MCM’s, which then provide the required power and ground, as
well as all the signal interconnect and the electrical interface to the external
environment. The entire MCM, including chips and passive components, may
be placed in a hermetic package much like a large single-chip carrier, or may be
directly covered with a sealant material (such as epoxy or a glass passivation
coating) to protect the components from physical damage.
Three general categories of MCM’s are MCM-C (for MCM-Ceramic),
MCM-L (for MCM-Laminates) and MCM-D (MCM-Deposited). MCM-C’s
are manufactured by stacking unfired layers of ceramic dielectric, onto which
liquid metal lines are “silk screened” using a metal ink process. The individual
inked layers are then aligned, pressed together, and cofired into a solid pla­
nar structure, onto which integrated circuits can be installed. MCM-L’s are
manufactured through the lamination of sheet layers of organic dielectrics, and
are very similar to traditional printed circuit board technology. MCM-D’s are
manufactured through the deposition of organic or inorganic dielectrics onto a
silicon or alumina support substrate. After each dielectric layer is deposited,
one of several techniques is used to pattern metal lines as well as metal vias.
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12
The chips are then installed on the upper surface.
MCM-D technology can provide a versatile platform for the integra­
tion of GaAs MMICs and silicon devices for microwave circuits where perfor­
mance, size and weight are critical factors. Multilayer circuits such as spi­
ral inductors, baluns, coupled-line couplers, Lange couplers, transmission line
transformers, filters, amplifiers, and voltage controlled oscillators have been
integrated using this technology [13, 14].
2.3
M u ltila y e r C irc u its U sing M u ltila y e r T ran sm issio n Lines
2.3.1
sio n Lines
C irc u it F u n ctio n s R ealized w ith M u ltila y e r T ran sm is­
Couplers [16-31], filters [4, 5, 32-39], baluns [8, 40-43], hybrid
circuits [44-47], and microstrip antennas [48-52] are several examples of multi­
layer microwave components developed so far. Multilayer configurations have
recently received increasing attention because they make design more com­
pact, increase design flexibility, and often lead to better performance. In the
design of coupled-line directional couplers, single-layer coupled-line couplers
are well suited for weak coupling only [7]. Consequently, multilayer structures
have been widely explored [16-31] in the design of high directivity coupledline couplers and re-entrant type couplers. Since a tight coupling is possible
in multilayer coupled lines, a high coupling like 3 dB is easily obtained. Be­
sides, multilayer configurations are inherently non-symmetrical with reference
to the two-coupled lines at different layers, thus they provide much flexibility in
design. Coupled-line couplers and re-entrant type couplers developed in mul­
tilayer configurations also show compact design and often better performance
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13
compared to single layer configurations. For microwave filter circuits, paral­
lel coupled-line band-pass filters and end-coupled band-pass filters have been
extensively explored in multilayer configurations. In designing coupled-line
filters, single-layer configuration, based on the traditional design procedure, is
adequate when the bandwidth is less than 15 % [7]. This bandwidth limitation
can be easily overcome by using multilayer coupled-lines because they can be
designed for a tight coupling in each coupled section. Non-symmetry also adds
more flexibility to the design of these filters. Designs for these multilayer filters
are discussed in Chapter 4. In the designs for end-coupled band-pass filters,
the bandwidth has been restricted to about 15 % due to the limit of gap be­
tween microstrip lines [7]. As in the case of parallel coupled-line band-pass fil­
ters, multilayer end-coupled filter configurations can also be designed for wide
bandwidth by using the tight coupling caused by overlapping gap between two
conductors at different levels. Designs of these filters are discussed in Chap­
ter 5. In the design of balun circuits, multilayer geometry has been utilized
to obtain more compact and flexible designs for planar Marchand baluns and
three-line baluns. Since coupled lines are used for these classes of baluns, wide
bandwidth and flexibility are very important advantages achievable compared
to single-layer baluns. These circuits are presented in Chapter 6. In addition
to couplers, filters and baluns; hybrid circuits like magic-T and branch-line
couplers and microstrip patch antennas have also been developed in multilayer
configurations. Microstrip patch antennas fed from a lower layer provide wider
bandwidth than those implemented in a single layer [48-52]. Branch-line cou­
plers and m agic-T’s designed in multilayers show some advantages [44-47].
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14
However, for the various microwave circuits reported in multilayer configura­
tions, we do not have systematic procedures available for engineers to arrive at
specific designs starting from circuit performance specifications. In this thesis,
we discuss a systematic design methodology for a broad class of multilayer mi­
crowave circuits (like filters and baluns) th at make use of coupled transmission
line sections as basic circuit elements. This design approach is discussed in
Chapter 3.
2.3.2
C o u p le d -L in e C o u p lers
For coupled-line directional
couplers to function ideally, they should have perfect matching at all the four
ports, perfect isolation and quadrature phase outputs over all frequency range
of interest. Matching at the four ports is closely related to perfect isolation
and directivity. Also, a tight coupling is frequently required in the design of
coupled-line directional couplers for several applications. Single layer config­
urations show a considerable difficulty in achieving the tight coupling because
of narrow spacing between adjacent lines and correspondingly increased sen­
sitivity to dimensional tolerances. As an alternative, various efforts to obtain
ideal performance for coupled-line directional couplers have been made by us­
ing multilayer configurations and by modifying geometries topologically. Since
multilayer configurations allow a tight coupling for coupled lines, they are in­
creasingly utilized for obtaining better performance for coupled-line couplers.
Horno and Medina [25] used broadside couplers in multilayers to obtain a high
directivity. They designed several coupled-line couplers with 3 dB to 20 dB
coupling based on the graphs drawn based on a number of calculations. They
also implemented high directivity couplers with directivity values ranging from
53 dB to 61 dB by equalizing the two phase velocities. However, these designs
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15
were restricted to symmetrical geometries. In addition, a systematic proce­
dure for designing these couplers is not available. Masot et al. [26] designed a
coupled-line coupler using suspended multilayer coupled lines and showed how
to optimize the physical geometry. This design is restricted to suspended sym­
metrical coupled lines. Schwab and Menzel [53] proposed various multilayer
topologies to be used in couplers and filters, and have reported a coupler using
slots and coupled lines in a multilayer configuration. This coupler has a very
narrow bandwidth and poor directivity as seen by theoretical and measured
results. Prouty and Schwarz [27] developed a two-level coupler showing 3 dB
coupling around 300 MHz, but this design has a poor directivity. Mernyei et
al. [18] presented a coupled-line coupler in CPW using two layers. This coupler
shows the control of the coupling in -3 to -30 dB range with a 100 % bandwidth
at 30 GHz, but has poor directivity and matching at all ports. However, it
has been pointed out [18] th at CPW structure in multilayers leads to a good
possibility for obtaining better performance of coupled-line couplers. Fan and
Pennock [28] presented two examples of broad side couplers using inset dielec­
tric guide (IDG). Again no design procedure is available for design and broad
bandwidth is not obtained even in multilayer structure. Person et al.
[17]
developed a 3 dB coupler in multilayer thick-film technology showing a wide
bandwidth, but not good matching and directivity. Banba and Ogawa [19]
reported multilayer MMIC couplers using thin dielectric layers. They used
symmetrical coupled lines along with an extra conductor located in a different
layer. Engels and Jansen [16] designed quasi-ideal couplers in multilayer con­
figurations. They have presented design equations for coupled-line couplers
and obtained wideband, high directivity and matched performance by use of
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16
a full-wave simulation. In this design, a slot in ground plane is used which
makes fabrication more complicated. Also equal port impedances are used
leading to limited freedom for choosing those impedances. In the literature
[20], a systematic design procedure for multilayer coupled-line couplers having
no additional conductors and/or slots has been proposed. Using this proce­
dure, a 3 dB coupler can be designed to yield broad bandwidth performance
and good directivity and matching.
R e - E n tr a n t T y p e C o u p lers:
When a directional coupler
with high coupling is required, multilayer re-entrant type coupler is an attrac­
tive alternative. This configuration for tight coupling is a planar version of the
re-entrant type couplers made up of two coupled lines on one layer and another
wide microstrip line on the adjacent layer. This coupler makes a tight coupling
possible without tight fabrication tolerance requirement of a narrow gap. After
Cohn [29] proposed coaxial re-entrant type couplers, several planar versions
of re-entrant couplers have been explored [27, 30, 31]. Pavio and Sutton [30]
adapted multilayer structures for re-entrant type couplers based on the design
procedure for re-entrant coaxial couplers. Prouty and Schwarz [27] have re­
ported multilayer re-entrant type coupler design connecting two coupled-line
couplers, and obtained a tight coupling and a good directivity over a wide
band. But they have not reported any detailed procedure for design. Hayes
et al. [31] proposed a stripline coupler in cofired ceramic multilayer circuits
showing 3-dB coupling and acceptable return loss.
2.3.3
P ara lle l C o u p le d -L in e B a n d -P a s s F ilte rs
symmetrical coupled-line band-pass filters in single-layer configurations have
been utilized for a long time and their design procedure is well documented
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Parallel
17
in [7]. Traditional single-layer coupled-line filters have an inherently narrow
bandwidth due to weak coupling, caused by single-layer parallel coupled lines.
Therefore multilayer configurations have been explored to obtain broad band­
width. Since the design procedure in [7] was developed for symmetrical coupled
lines in single-layer configurations, a modified design method has been devel­
oped [33] in this thesis (Chapter 4) for using asymmetrical coupled lines in
multilayer structures. Tran and Nguyen [35] reported the development of par­
allel coupled-line band-pass filters in a two-layer configuration. They used
the topological freedom in choosing geometry to achieve a wide bandwidth,
and verified their designs by experimental measurements. However, the design
procedure for how to calculate the desired parameters and to obtain physical
geometry was not presented. Lutz et al. [4] presented a multilayer coupledline band-pass filter showing an example. Also, design equations for desired
J-param eters to be optimized were reported. But, further procedure leading
to filter layouts is not available. In Chapter 4, designs for these filters are
discussed.
P a ra lle l C o u p led—L ine B a n d -P a s s C P W F ilte rs:
Mul­
tilayer coupled-line band-pass filters can also be implemented in Coplanar
Waveguide (CPW ). CPW circuits have drawn much attention due to their sev­
eral advantages over microstrip circuits. CPW circuits are easily fabricated,
are relatively insensitive to the substrate thickness and can have low disper­
sion effect because their structure is uni-planar (with all conductors in a single
plane). Menzel et al. [36] developed multilayer coupled-line filters in CPW
circuits showing what kind of CPW-microstrip transitions can provide better
performance. But they restricted their design to around 10 % bandwidth, and
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18
this narrow bandwidth needs to be extended for several applications. These
CPW filters can be designed using the same procedure for parallel coupled line
filters as discussed in Chapter 4.
2.3.4
E n d -C o u p le d B a n d —P a ss F ilte rs
Single-layer end-
coupled band-pass filters are well documented in [7, 54], where a design pro­
cedure has been described for finding the desired admittances for each gapcoupled section and for obtaining the physical geometry based on the graphs
showing the relation between the gap dimension and corresponding capacitance
in single-layer symmetry. Since single-layer circuits are suitable for narrow
bandwidth only, multilayer circuits have been investigated for achieving a wide
bandwidth in the design of end-coupled band-pass filters. Schwab and Menzel [53] proposed a two-layer end-coupled band-pass filter using striplines,
but this work is only applicable to narrow bandwidth and restricted to a
stripline structure. Nguyen [37] presented a wideband end-coupled filter using
CPW structure; but, any systematic design procedure is not given. Tzuang et
al. [5, 38] proposed a considerably attractive physical layout for this class of
filters. They designed it in stripline structure for obtaining a wideband. The
design is limited to the stripline structure only and a design procedure is not
available. Schwab et al. [34] and Williams et al. [39] have also presented this
kind of narrow band filters in CPW configurations. They also implemented a
wide band end-coupled filter in a two-layer stripline configuration, but wide
band filters using microstrip lines have not been reported. A design procedure
for wide band end-coupled filters using microstrip lines in multilayer configu­
rations is presented in Chapter 5.
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19
2.3.5
P la n a r B alu n s
Baluns transform a balanced signal to an
unbalanced signal and vice versa. A large number of balun configurations have
been reported in literature. For use in microwave integrated circuits (MIC)
and microwave monolithic integrated circuits (MMIC), wide bandwidth and
compactness are of prime interest.
M a rc h a n d B alu n :
A planar version of Marchand balun has
been adapted in multilayer structure for this purpose. Pavio and Kikel [8]
presented planar Marchand baluns in two dielectric layers using an equivalent
transmission line model. Because coupled sections in two-layer configuration
can provide an extremely tight coupling, these baluns showed a wide band
performance in 6 to 18 GHz frequency range. In this paper [8], the return loss at
the input port (Sn ) has not been reported. Also, the design procedure leading
to the physical dimensions has not been reported. Schwindt and Nguyen [40]
have described a computer-aided analysis of a planar Marchand balun based
on [S] parameter description.
Although they analyzed this kind of baluns
quantitatively, it was not discussed how their configuration worked as a balun.
Engels and Jansen [41] proposed a design of this class of baluns where they
have used [S] and [Y] parameters to derive the design equations. T utt et al. [42]
have described a low loss monolithic planar Marchand balun using two thick
layers. They implemented a wide bandwidth of 5.5 to 20 GHz and 0.7 dB loss
over 6 to 21 GHz, but no synthesis techniques was provided.
T h re e -L in e B a lu n s:
Three-line baluns have been proposed
in [43], however, this balun is discussed in single layer configurations only fo­
cusing on theoretical analysis and not the synthesis procedure. Furthermore,
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20
design procedure is not available and no method to obtain the physical geom­
etry has been reported. Since this class of balun is more compact and can be
realized in double layers, design procedure and examples are presented in more
detail in Chapter 6.
2.3.6
O th e r M u ltila y e r C o m p o n en ts
Other components such
as hybrids and patch antennas have also been developed in multilayer config­
urations.
H y b rid s:
Branch-line couplers [44] and magic-T’s [45-47] have
been developed using multilayer configurations to produce better performance
than what is realized in single layer structures. More flexible designs can be
obtained when multilayer branch line couplers are utilized. More compaction
and flexibility is obtained when a multilayer configuration is used for magicT ’s.
P a tc h A n ten n as:
Microstrip patch antennas have been developed
in multilayer structures since this configuration can offer wider bandwidth than
that obtained with single-layer patch antennas.
Generally the feed line is
placed at the lower layer and the patch is placed at the top surface. A large
number of applications have been reported [48-52].
In this Chapter, the previous work on multilayer microwave circuits
has been reviewed. The following chapters describe the design procedure de­
velopment and its applications to multilayer circuits including: (i) parallel
coupled-line band-pass filters in microstrip lines and CPW, (ii) end-coupled
band-pass filters, and (iii) three-line baluns.
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CHAPTER 3
DESIGN METHODOLOGY
The approach for developing design procedures, for the class of mul­
tilayer circuits discussed in this thesis, has been arrived by recognizing that
sections of coupled transmission lines constitute the basic building blocks for
this class of circuits. Examples of these coupled-line configurations used as ba­
sic circuit elements for multilayer circuits are shown in Figure 3.1. The ports of
a section of coupled lines, whose cross-sectional views are shown in Figure 3.1,
could be terminated in many different ways. These different terminations lead
to different characteristics of the sections. These appropriately terminated
coupled line sections axe used in the design of different kinds of multilayer mi­
crowave circuits. In this Chapter, we have developed a general analysis and
synthesis procedure of multilayer microwave circuits using the network mod­
els for multilayered coupled line sections. For the design examples performed
throughout this work, we have utilized a quasi-static field analysis program,
Segmentation and Boundary Element Method (SBEM) described in [9, 10], to
calculate capacitance and inductance matrices for multilayer multi-conductor
transmission lines. Computations based on other analysis methods could as
well be used for implementing the multilayer circuit design methodology pre­
sented later.
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22
ground plane
Figure 3.1. Cross sectional view of various examples of multilayer coupled lines
3.1
Network M odeling
Since the circuits we discuss are made up of various coupled line sec­
tions with terminations, a generalized network modeling for multilayer multi­
conductor transmission lines is a key step in the analysis and synthesis of these
circuits. This modeling has been discussed in the literature [9, 10, 20, 55] on
multi-conductor lines, and we use it in developing the design methodology for
multilayer circuits.
V, (x),
i,(x)
V jx ) , irjlx)
Figure 3.2: A system of n-conductor transmission lines
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23
Although multi-conductor transmission lines in an inhomogeneous
medium do not support a pure TEM mode, voltages and currents can be ap­
proximated by a quasi-TEM mode. The system of multi-conductor transmis­
sion lines shown in Figure 3.2 is characterized using these voltages and currents.
Assuming the time dependence is e?ut and the wave flows along the x direction,
dv
-z i
(3.1)
= -y v
(3.2)
=
dx
m
dx
where
v =
Vx V2 ... vn
1 =
Zl %2 ... In
z =
Zn
Z\2 • • * Zin
221
322 ' ' ' Z2n
3 il
3 ,2
2/11
2/12 • • •
2 /ln
2/21
2/22 ' ' •
2/2n
2/nl
Vn2
2inn
‘‘ *
Z nn
and
y=
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24
za and ya {i= 1, 2,
n) are the self-impedance and admittance per
unit length of line i in the presence of all the other lines. zi} and yij (i ^ j)
are the mutual impedance and admittance per unit length between line i and
j. It is noted th at both z and y matrices are symmetrical.
The equations (3.1) and (3.2) can be transformed to the following two
wave equations:
92v
a * = zyv
<3-3>
d2i
a ? = yzv
. .
<3-4>
By assuming x dependence of the voltage vector
as e71, Eq. (3.3)
becomes a typicalcharacteristic equation for n conductorlines.This equation
has n eigenvalues:
2
2
2
2
7 = 7 i >72) • • • > m
and a matrix E consisting of eigenvalues along the diagonal can be defined as
E =
7l
72
•••
(3.5)
7n
diag
These n eigenvalues are related to the phase velocities of n orthogonal
modes and the corresponding eigenvector for each eigenvalue represents the
voltage ratios for n conductors in each mode. The n eigenvectors form the
voltage eigenvector matrix R as:
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25
1
1
1
i?21 R-22 ' *‘ R2n
R =
Rnl
Rn2 ' ' '
(3-6)
Rnn
From linear algebra about eigenvector and eigenvalues [56], it is known
that
R " 1(zy)R = E
(3.7)
Taking the transpose of Eq. (3.7),
R T(y z )(R -1)T = E T = E
(3.8)
This equation implies that, if Eq. (3.4) is solved instead of Eq.(3.3),
the same eigenvalues are obtained and the corresponding current eigenvector
matrix becomes (R T)_1. This eigenvector matrix can be normalized as all the
elements in the first row are 1. Therefore, the current eigenvector matrix S
can be defined as
S= (R ^ P
(3.9)
where
P=
151 151
fu
fn
'
151
fn l
(3.10)
J diag
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26
and fij is the cofactor of Rij. The characteristic impedance Z ^j (for the mode
i, at the conductor j ) can now be solved using Eq. (3.1) or Eq. (3.2). How­
ever, only n out of these impedances are independent because the character­
istic impedances for the same modes at the different conductors are related
by voltage and current ratios which are represented by voltage and current
eigenvector matrices. Here, the characteristic impedances of conductor 1 in n
different modes are selected to be calculated as
Zm
(3 1 1 )
where k is any integer between 1 and n. All other characteristic impedances
can then be determined by the following equation.
R21
521
Zc =
■'ell
Jc21
•^2 n
■<Cl
_
where Zcl =
Rln
R22
522
Rft1
Rn2 . . .
5nl
5n2
(3.12)
Rnn
5nn -
Jcn 1
diag
It should be pointed out that only n (n + l) parameters (called “normal
mode parameters”) are necessary to characterize the n-conductor transmission
lines and these parameters are determined by solving the Maxwell’s equations
with appropriate boundary conditions. In the above derivation, normal mode
parameters are composed of n eigenvalues, n (n -l) variables in the voltage eigen­
vector matrix and n characteristic impedances. All the other parameters can
also be determined by using these normal mode parameters. Now, consider
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27
the system of n-conductor transmission lines of each line length I as shown in
Figure 3.2 again.
The voltage vector for 2n ports is assumed as:
0
0
R
1
1
(3.13)
1
M
R D ”1
R
1__
RD
A =
O
R
G
R
l
V =
where
V
=
Vi V2
A
=
Ai A2
vn vn+1
. . .
• • •
An
j4n+1
•••
v2n
• • •
A2n
and
D =
3-7i i p-~ni
o-yni
diag
The vector A is a voltage amplitude vector that solely depends on the
external excitation and is used as a dummy variable. The matrix D represents
the propagation delay of this multi-conductor transmission line system. It can
be shown th at the corresponding current vector is expressed as
I =
h
h
-
In In+1
-
hn
0
0
szc-‘
-D
1
sz^1
rH
SZJi D "
A =
rH
-S Z ^ D
-S Z ^ 1
1----
i
SZ^1
D '1
(3.14)
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28
Using Eq. (3.13) and Eq. (3.14), the impedance matrix Z of this 2n
port network is given by
Z = V I1
R
0
1
1
1
-1
ZciS- 1
0
R
D
D "1
-D
D "1
0
R
0
1
1
1
-1
ZclP" 1
0
R
D
D "1
-D
D 1
0
i -i
0
zcls0
ZclP-
R
0
0
R
(3.15)
= XMXt
where the matrix M is the product of the three inner matrices in Eq. (3.15).
Since the m atrix M consists of the two matrices (the second and the third)
for the propagation delay and the forth matrix involving the characteristic
impedances, the operations performed by the matrix M can be represented by
n uncoupled transmission lines with different electrical lengths and impedances
corresponding to n different modes. This can be seen by writing the matrix M
for 2 line case as:
R =
1
1
Rc R*
D =
e- * 1
0
0
e~n*1
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29
hx
o
0
u
1*1
1*1
P -1=
0
1- R c / R r
1
0
1—R r / Rc
^c\
1 —R c / R r
-&JL
0
0
1
0
1
0
-1
o
0
1
0
1
0
1
0
-1
e-7J
0
end
0
1
0)
1
£
0
f/Tcl
0
0
e - i,i
o
D7iri
O
~e~ ^ 1
0
e1rl
Z'l
l-R c/R r
0
0
I-R r/R c
0
0
0
0
------ 1
1
1
M =
1 -R r/R c
0
0
0
0
Jzx.
1 -R r/R c
ZclCOth'Tcl
ZelCSCh'ld
1- R c / R *
l-R c /R r
J
0
ZrXCOthlrl
ZrlCsdl'Trl
1- R r / R c
1- R r / R c
Z c\csch-fel
ZclCOth'Tcl
I-R e /fir
l-R c /R r
0
ZrlCsdl'Trl
l-R r/R c
0
-1
0
l-R c /R r
0
____ 1
Z dP "1 =
(3.16)
0
ZrlCOth'Trl
I-R r /R c J
The corresponding network is shown in Figure 3.4.
Furthermore, a transformation of M by X (X M X T) is equivalent
to a connection of these n uncoupled transmission lines (expressed by M )
with transformer banks (expressed by X ) at both ends.
Since the matrix
R represents the voltage ratios between conductors as shown in Eq. (3.6), the
matrix X is expressed by transformers which correspond to these voltage ratios.
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30
Figure 3.3 represents this network modeling for a multi-conductor transmission
line system.
n+1
n+2
RntjRn.1,1
fel :&>
Rn2
R32
1:R-»i
R21 *31
R22IR32
Rn-u ;Rn;
Figure 3.3: A network model of n-conductor transmission line system
The network parameters such as [S], [Y] and [Z] parameters can now
be calculated easily for any type of coupled line sections when this modeling
approach is used. Two- and three-conductor lines are of important interest for
different kinds of multilayer circuits investigated in this thesis. Generic models
for two- and three-conductor coupled lines (special cases of the model in Fig­
ure 3.3 with n = 2 and 3) are shown in Figure 3.4 and Figure 3.5 respectively.
It may be noted that these models represent coupled line sections in terms
of characteristic impedances, voltage ratios and phase velocities of n-different
normal modes of the n-conductor lines.
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31
4
♦
♦
3
1 -R./R
Figure 3.4: A network model of two-coupled line
In Figure 3.4, R c and R* are the voltage ratios at c- and 7r-modes,
Zci and Z ni are the characteristic impedances for the two modes, and 0C and
9n are the electrical lengths for the two modes. In Figure 3.5, Rij (i = m,n,p;
j = 1,2,3) is the voltage ratio for the i mode at the conductor j , Zn 1 is the
characteristic impedance at i mode, (0* is the electrical length at i mode, R is
the voltage eigenvector matrix, and fa is the cofactor of Rij.
3.2
A nalysis A p p ro ac h for M u ltila y e r C irc u its
Multilayer circuits consisting of multilayer coupled line sections can
be analyzed step by step as shown in Figure 3.6. This analysis procedure is
JThe subscript ‘c’ from Z cn representing the characteristic impedances for the i mode at
the conductor 1 was removed for simplicity
I
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32
• 4
• 5
• 6
1
Rtnj2:Rm3<
1 J7~6
ml‘ml
*Ni3 ;Rn2
Rn2 :Rn3
Figure 3.5: A network model of three-coupled line
later used for developing design procedures for various multilayer circuits. As
shown in Figure 3.6, the analysis of each of the coupled section in the circuit
starts from the calculations of inductance and capacitance matrices for the
coupled line section. Several different methods such as quasi-static analysis,
spectral domain analysis, etc. can be used. For the research performed here,
we utilized a quasi-static field analysis method, SBEM [9, 10], to calculate [L]
and [C] matrices for a specific multilayer multi-conductor geometry. After the
calculation of [L] and [C], the normal mode parameters (NMPs) are determined
based on the equations derived in Section 3.1. The network parameters like [S],
[Y] or [Z] are determined using these NMPs with appropriate port terminations.
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33
For simple circuits using only a single coupled line section, circuit performance
is obtained from these [S], [Y] or [Z] parameters and any further calculation is
not needed. For circuits consisting of several coupled line sections, the network
parameters for all individual single sections need to be combined to yield the
final network parameters of the overall circuit.
Physical geometry
[L] and [C]
Normal mode parameters
Port terminations
[S], [Y] or [Z]
Useful for circuits
using single coupled sections
Combined with
other sections
[S] for the overall circuit
Figure 3.6. A flow diagram for analysis of multilayer circuits consisting of
sections of multi-conductor lines
3.3
Circuit Synthesis
The synthesis methodology for multilayer microwave circuits can be
developed by rearranging the various steps in the circuit analysis procedure dis­
cussed in Section 3.2. The synthesis method aims at finding a set of physical
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34
layout dimensions from the given circuit performance specifications. By revers­
ing the steps shown in Figure 3.6, synthesis procedure for a single section of
multilayer coupled circuit may be expressed as shown in Figure 3.7. As seen in
Figure 3.7, one starts with expressing the circuit specifications in terms of the
network parameters, [S], [Y] or [Z]. For example, multilayer parallel coupledline filters can be designed for realizing the performance specifications such
as the bandwidth, the center frequency, the ripple level, and etc. These fil­
ter specifications are used to represent desired [Z] parameters for each coupled
section as discussed later.
Specifications for a
single coupled line section
[S], [Y] or [Z]
Normal mode parameters
Optimization
Physical geometry
Figure 3.7. A flow diagram for synthesis of a single coupled-line section of a
multilayer circuit
In the next step of the multilayer circuit synthesis procedure, [Z]
parameters for each coupled section can be expressed using the NMPs [9, 10,
20,57]. These NMPs are presented to an optimization process to find a physical
geometry for the coupled section. This optimization process incorporates a field
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35
Circuit specifications
Evaluation of number of coupled line sections needed
and specifications for each section
Synthesis of each section
as in Figure 3.7
Physical layout of the complete circuit
Figure 3.8. Synthesis of multilayer circuits consisting of several coupled line
sections
analysis method of multilayer transmission lines.
For the circuits consisting of several coupled sections, there is an addi­
tional initial step of obtaining characterizations for various coupled line sections
from the circuit specifications. This is depicted in Figure 3.8. The synthesis
procedure of Figure 3.7 is then repeated for different coupled line sections. For
multilayer microwave circuits, coupled sections with conductors placed at dif­
ferent layers are mostly non-symmetrical. Thus, there is an additional design
flexibility in the choices of terminal impedances for each coupled line section.
This leads to an additional choice in the selection of the appropriate network
parameters ([S], [Y] or [Z]) than th at available for the single-layer symmetrical
coupled lines. This non-symmetry provides more freedom in the optimization
process used for obtaining the physical geometry.
This design methodology is used for the design of filters and baluns
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discussed in Chapter 4,5, and 6.
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CHAPTER 4
DESIGN OF PARALLEL COUPLED-LINE BAND-PASS FILTERS IN
MULTILAYER CONFIGURATIONS
The design procedure of single-layer filters using symmetric coupled
microstrip lines is well documented in the literature [7, 54, 58] and most of
the filter designs make use of this procedure. These filters have been made
possible by cascading quarter-wavelength coupled line sections which are openended at two of the ports. Often, very tightly coupled lines are needed, and
these are difficult to be fabricated in single-layer configurations. Multilayer
configurations overcome this difficulty because of the flexibility in overlapping
coupled lines on different layers. Also, multilayer circuits can be implemented
in both homogeneous (as embedded circuit components) and inhomogeneous
(as microstrip-like circuits) layered dielectric media.
In this Chapter, design procedures for homogeneous (stripline), inho­
mogeneous (microstrip) and coplanar waveguide (CPW) filters are investigated.
4.1
Derivation of Design Procedure
A general configuration for parallel coupled-line band-pass filters
made up of four coupled line sections (A/4 each at the design frequency)
is shown in Figure 4.1.
For multilayer circuit design, various conductors
( 1 ,2 ,3,4,etc.) may be located asymmetrically at different layers.
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38
Top view
Figure 4.1. The layout of a parallel coupled-line band-pass filter using 4 cou­
pled line sections (top view)
PORT 1 »
O P E N C IR C U IT
O P E N C IR C U IT
«
PO RT2
Figure 4.2. A typical filter section consisting of a coupled line with two ports
open
^ 0 (N -1 )
0
e
Figure 4.3. An admittance inverter model used for modeling a 2-port coupled
section shown in Figure 4.2
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39
4.1.1
Z -M a trix for 2 - P o r t C oupled L ine S ections
metrical coupled line sections with open ends at two of the ports have been
widely utilized for the implementation of band-pass filters. For multilayer con­
figurations, asymmetrical coupled line sections as shown in Figure 4.2 allow
more flexibility. The wave propagation and electrical behavior of asymmetrical
coupled line sections are characterized by different voltage ratios (Rc and R^),
mode impedances (Zcl, Z„i, Z c2 and Z v2) and phase velocities for the two nor­
mal modes (known as c- and 7r-modes) as discussed in Chapter 3. Following
the conventional coupled line filter design procedure, the admittance inverter
representation (shown in Figure 4.3) is utilized to derive the corresponding
lumped element filter as explained in [7, 54, 58]. The general coupled line filter
in Figure 4.1 may be redrawn as shown in Figure 4.4 by using the equivalent
admittance inverter models.
------ , ■a »
A
A
- a >----__ _
^N+l r#
J.
-90°
. _ ^]N_
-90°
-90°
M ^ •m
m-----
^
Figure 4.4. An equivalent circuit using admittance inverter models for a
coupled-line band-pass filter similar to one shown in Figure 4.1
-jZpjjCOte
ZoN
_* _
-jZnjjCOte
i;_i
T
X
sin29
Ljjij -p Cfj
T
Figure 4.5: An equivalent circuit for the transmission line of the length 26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sym­
40
l:JZ r
X/4-
<=!>
Figure 4.6. An equivalent circuit for the admittance inverters at both ends of
Figure 4.4
Zo
l
J T
F
7LN2 -J 7^
Zo
Figure 4.7. An equivalent network corresponding to the parallel coupled-line
band-pass filter circuits shown in Figure 4.1
u
c;
-j'm r —11—
Ln’ Cn’
Figure 4.8. A lumped element equivalent circuit for the band-pass filter con­
figuration
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41
The equivalent circuit shown in Figure 4.4 consists of cascaded trans­
mission lines of the length 2d and admittance inverters. The transmission line
sections can be replaced by lumped element equivalent circuits shown in Fig­
ure 4.5 where L n = ^ ^ - , C n = 2zfN'uo•
E dition, the admittance inverters
at both ends (J\ and J n +i ) can be replaced by circuits containing transformers
shown in Figure 4.6.
Finally the filter circuit in Figure 4.1 is transformed to an equivalent
network in Figure 4.7. The input admittance of this equivalent network for N
= 2 is represented as :
1
y
{ . /Ci / UJ
t M—
U uo
V
^ 0\ ,
-
— ) + — 7=
U
*^2
—
L*2 't J o
-------------- }
- ffi) + Z0JI
(4.1)
W
Since the lumped element filter circuit as shown in Figure 4.8 can be
equated to the equivalent circuit as shown in Figure 4.7, the input admittance
for N = 2 is calculated where the frequency transformation and the impedance
scaling have been used [54] (L\ =
= ^ ,L '2 =
^
where A = Ui~“l , the fractional bandwidth, and gi,g2 are the prototype lowpass filter elements expressing L’s and C’s.).
•—
v i > <*
“
V
t (s
(4-2)
- “ ) + z »
Equating the input admittances of Eq. (4.1) and Eq. (4.2), ./-parameters
for N = 2 case may be written as:
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42
2Z oZ o\Q\
2y/ Z q\Z q29i 92
(4.3)
2Z qZ o292
Generalizing the number of coupled sections, J-param eters can be
determined as:
/ =
1
JN =
/
V2ZoZoi9i
.... 7r. ^ - . =
2 \ / Z o{n - i )Z on9n - i 9n
,
J n +i =
(4.4)
A
2ZoZo^g^g^+i
7T
where N > 2, A is the fractional bandwidth, Zo is the impedance of the input
and the output lines, J n is the admittance of an equivalent admittance inverter
model for the N th coupled section, Z 0i, Z02 , • • • , Zqn are the line impedances
at the two ports of coupled sections, and lg’ parameters are determined from
the table for lumped element low-pass filter coefficients [7, 54, 58].
Once the admittance inverter model (value of J n ) corresponding to
an asymmetrical coupled line section is derived by using Eq. (4.4), the normal
mode parameters for each coupled section can be determined using the ABCD
matrix or impedance matrix for the 2 -port asymmetrical coupled lines with
open-ended ports as shown in Figure 4.2. The impedance matrix [Z] for a
2-port coupled line section is represented as [57, 59, 60]:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[Z] =
Zyy Zy2
Z cy
h -R c /R ,
Z2y Z 22
O
O
ct«?*
1
43
R ccsc 9C
(4.5)
R c esc 9C R 2 cot 9C
cot 9„
Rn CSC9,r
1
1
R ttCSC9n R l cot 0,
where R C, R ,r represent voltage ratios, Zci, Z^y represent mode impedances,
and 9e, 9Wrepresent electrical lengths for the two modes of the coupled section.
On the other hand, the impedance matrix for the admittance inverter
model shown in Figure 4.3 can be expressed as:
-j(JNZo(N-i)Zo* + zo(N-i)) sinScos9
Z\\ Z\2
Z21 Z22
-jJNZ0(N-l)ZoN
x
—jJ^ZoyN-iyZoN
-j{J%z 0(N-i)ZlN + Zqn) sin0cos6
(4.6)
where X = sin 2 6—J ^ Z 0^ - i )Z qn cos2 9 and 9 may be taken as 90° at the design
frequency for the filter design. Until now, we have not made any assumption
of homogeneity.
Figure 4.9: The cross-sectional view of a typical homogeneous configuration
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44
4.1.2
E v a lu a tio n of th e N o rm a l M o d e P a ra m e te rs for H o­
m ogeneous C o n fig u ra tio n s
The cross-sectional view of a typical homo­
geneous configuration is shown in Figure 4.9. For homogeneous configura­
tions, phase velocities of 2 modes (9C and 9V) are equal (say 6). Equating the
impedance matrices in Eq. (4.5) and Eq. (4.6) yields the normal mode param­
eters for the N th coupled section for a homogeneous configuration explicitly in
terms of ^o(tv-i)j-^on' «md Jyv us:
These normal mode parameters are used for obtaining physical dimen­
sions of the filter configurations since a set of physical dimensions corresponds
to specific values of NMPs uniquely through the calculation of [L] and [C] ma­
trices [57, 59]. The designs are then analyzed by SBEM and/or a full-wave
electromagnetic simulator.
If the symmetric coupled sections are used in single-layer structures,
the voltage ratio is 1 or -1 for the two modes. Therefore, the normal mode
parameters for a symmetrical section can be written as:
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45
Rc = -Rx = 1
Zq = Zoi = Zq2 — • • ■= Zqn
Z c\ = 1 + JNZo + J ^ Z q
(4.8)
Z ni = 1 —JNZ 0 + J%2%
These two impedances (Zci and Z nX) are exactly same as those derived
for a single-layer symmetrical case in [54] using a different approach.
air
£n
Figure 4.10. The cross-sectional view of a typical inhomogeneous configuration
4.1.3
E v a lu a tio n o f th e N o rm al M o d e P a ra m e te rs for In h o ­
m ogeneous C o n fig u ratio n s
The cross-sectional view of a typical “inho­
mogeneous” configuration is shown in Figure 4.10. For inhomogeneous dielec­
tric configurations, phase velocities for c- and 7r-modes are not equal, therefore,
we cannot use the NMPs derived in Eq. (4.7) used for the homogeneous case.
For the evaluation of desired normal mode parameters in an inhomogeneous
case, we consider that for each A/4 section, tandc and tanO* are so large that
.Z,riiCi tan 0,r,c
Zo(v-i) and ^o(tv-i) tan0^iC >• Zxl)Cl. This approximation is
justified because both 9C and 9W are close to 90°, and provides a reasonable
method to proceed with the filter design. As mentioned in [9, 10, 20] earlier,
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46
one additional intermediate design parameter (say ‘a’) is introduced to derive
normal mode parameters for inhomogeneous configurations. For this parameter
to be introduced, the coupling factor (5 (for the N th coupled section) between
the port 1 and the adjacent open port of the four-port coupled line section in
Sn
S21
to
1
h—
*
1
Figure 4.2 is used to find [S] matrix for the N th coupled section as:
S12
- j 2/ V l - / ? 2
(4.9)
2(32 — 1
S22
The [S] matrix for the N th coupled section for the equivalent admit­
tance model can also be obtained from the [Z] matrix in Eq. (4.6) as:
Sn
Sn
S21
S22
_
2 \ / Z o(n - i )Z on
1
“ D
2y/Zo(N-i)ZoN
j(JrfZ 0(N-.i)ZoN —1 JJ n )
(4.10)
where D = (J n Z o(n - i )Z qn + l/«7iv)(j2sin20 —j + 2sin0cos0).
Equating the [S] matrix in Eq. (4.9) to the [S] matrix in Eq. (4.10)
for 9 = 90°,
is found to be:
/? =
J n Z o(n - i )Z qn
1 + JtfZ0(N-l)ZoN
(4.11)
Once the coupling factor (3 is determined by Eq. (4.11) using J#,
Zo(jv-i) and Z 0/v, one additional intermediate parameter ‘a’ is chosen for the
N th coupled section, and lV is calculated [9, 10, 20] using:
/? =
(Vab—l )2
(1 + g )(1 + b)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4.12)
47
From ‘a ’ and ‘6’ obtained in Eq. (4.12), normal mode parameters for
the N th coupled section for an inhomogeneous configuration can be expressed
as [9, 10, 20]:
ry _ ry
/a ( l + 6)
^ i- ^ - D V T T T
•7^ j r l- — 7 ^ 0 ( A / - 1 ) 1
'
1+ b
6(1 + a)
This relation is used to find NMPs for each section and to find the
physical dimensions to yield this set of NMPs.
4.1.4
A n A lte rn a tiv e A p p ro a c h to th e E v a lu a tio n o f N M P s
in In h o m o g e n eo u s C o n fig u ra tio n s
If the two electrical lengths are nearly
90°, NMPs are determined more easily equating ABCD-matrices of the 2-port
coupled section in Figure 4.2 and the admittance inverter model in Figure 4.3.
Assuming 6C~ 9* ~ 6 = 90°, the ABCD-matrix of the 2-port coupled section
is
[ABCD] =
(^ ir^ c l
[w jQCOS9
cO S^
RcRn(.Zcl Z^l)
_*
s in 9
R c R r { iZ c \ ' —Z -jr \)
9{RlfZel'~RcZxl)(RcZcl RieZirl) Rir Rc(Zci Zn\ P
^• COS^
COS2 B{^FCk Z c \ — R c Z i e \ } { R c Z c \ — R w Z l t \') —
— R i r R c { LZ c \ —
{RiF~‘&c)(.Zcl~Zxi')siTlQ
(4.14)
(ftc Z c i~ ftr^ ]ri)c o s 0
Z c 1—Z x l
The ABCD-matrix of the admittance inverter model is also expressed
as:
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48
[ABCD] =
(JivZo(Jv-i) + 7^
7 ) sin 0 cos 0
i t j . v v o , sin2 6 ~
3 {Jn Z 0(N- i )Z0N sin 2 0 - ^ cos2 0 )
cos2 *)
sin 0 c o s 0
(4.15)
Equating these two ABCD-matrices around 0 = 90°, the following
relations are achieved.
RnZci —R cZy\ _
R cR , ( Z c l - Z , x) ~
1
N 0{n~1) + J n Z on
R * ~ Rc
_ _____ 1______
R cR tt{ZcI — Z 7ri)
J n Z o(h - i )Z on
RcZcl ~ RnZ.„\ _ j ry ,
1
— - — - — = j n ^ qn +
------Ac\ — 6 -k\
J n ^Q(N-I)
^
The three equations in Eq. (4.16) consisting of 4 NMPs are now ex­
pressed using Jn,Zq(n-i) and Zqn- These new three parameters in the left
hand sides in Eq. (4.16) can be used as the desired target parameters instead
of 4 NMPs as derived in Eq. (4.13). Note th at only three parameters need to be
optimized for determining the physical geometry. This provides a design flexi­
bility similar to the choice of the intermediate parameter ‘a’ in the procedure
of Section 4.1.3.
4.2
Description of Design Procedures
4.2.1
Homogeneous Configurations
Based on the discussion
in Section 4.1, a design procedure for filters in a homogeneous multilayer config­
uration (Figure 4.9) may be summarized as shown in Figure 4.11. We start the
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49
design from the filter specifications (bandwidth, number of coupled sections,
ripple level, attenuation etc.) and then find ‘<7’ parameters (the prototype low
pass filter elements) from the classical filter design tables available in the liter­
ature [7, 54]. From the given filter specifications, ‘<7’ parameters, and selected
line impedances (Z0(at-i), Z on), we determine equivalent admittance parame­
ters as derived in Eq. 4.4 for each asymmetric coupled section. Desired target
NMPs are then calculated explicitly using these admittance parameters. Once
NMPs are determined from the filter specifications, these parameters are then
used for obtaining an appropriate physical geometry.
Part J
Filter specifications
Initial guess for w,
and s
Calculate [L]&[C] by SBEM
Choose
5xn-d
^
Change wj ,w, ,s
5>n
Bad
Normal mode parameters
for each coupled section
Calculate
Compare
normal mode parameters
Good
Physical dimensions
Part 3
Part 2
EM simulation
Comparison
Final Design
Figure 4.11. The procedure for the design of multilayer parallel coupled-line
band-pass filters in homogeneous configurations
The overall design procedure can be broken up into following three
parts:
(1) Evaluation of desired NMPs as discussed in Section 4.1.2,
(2) Determination of physical dimensions (width, spacing, etc.) to obtain
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50
the desired mode parameters as computed in Part (1), and
(3) Electromagnetic/network simulation and/ or experimental measurement
of physical layouts obtained in P art (2) to verify the design.
For Part (2), desired NMPs for each coupled section obtained from
Part (1) are utilized to come up with physical dimensions for each coupled sec­
tion. In order to obtain physical dimensions for each coupled section, we have
used an optimization method called ‘Simples? algorithm [61]. This optimiza­
tion process compares the desired NMPs obtained from the filter specifications
mentioned in Part (1) with those calculated from capacitance and inductance
matrices [57, 59, 60] for a geometry. The capacitance and inductance matrices
can be determined using SBEM analysis [9, 10] of a specific physical structure.
For Part (3) of the design procedure, S-parameters are determined
for each coupled section starting from the physical dimensions finally arrived
at, and then these S-parameters for various sections are combined for evalu­
ating the filter performance. The complete circuit combining all coupled sec­
tions is analyzed for determining the insertion loss and the return loss. Also,
an electromagnetic simulation is carried out using the physical dimensions on
Momentum ™ (an HP-EEsof product), a simulation package using the method
of moments. The filter design is finally verified by comparing the performance
obtained from EM simulations.
4.2.2
In h o m o g en eo u s C o n fig u ratio n s
The design procedure
for inhomogeneous configurations (Figure 4.10) is slightly different and may
be summarized as shown in Figure 4.12. As in the case of homogeneous con­
figurations, we start the design from the filter specifications and then find
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51
‘g’ parameters from the classical filter design tables available in the litera­
ture [7, 54]. From the given filter specifications, ‘p’ parameters, and selected
line impedances {Z q^ - \ ) i Z on), we determine equivalent admittance param­
eters for each asymmetric coupled section. For an inhomogeneous dielectric
medium, one additional parameter (‘a’) needs to be introduced for specifying
the coupling factor (5 (Eq. 4.12). Alternatively, 3 new desired target parame­
ters defined in Eq. (4.16) can also be used for synthesis process as discussed
in Section 4.1.4. Therefore, the desired NMPs (c- and 7r-mode voltage ratios
and impedances) are obtained from Eq. (4.13) or Eq. (4.16).
Once NMPs are determined from the filter specifications, these pa­
rameters are then used for obtaining an appropriate physical geometry. Since
we have one additional parameter (‘o’) or 3 desired target parameters for in­
homogeneous media, this configuration provides more flexibility in finding the
physical dimensions of the filter.
The overall design procedure can also be broken up into following
three parts:
(1) Evaluation of desired NMPs as discussed in Section 4.1.3 or Section 4.1.4.
(2 ) Determination of physical dimensions (width, spacing, etc.) to obtain
the desired mode parameters as computed in P art (1), and
(3) Electromagnetic/ network simulation and/ or experimental measurement
of physical layouts obtained in Part (2) to verify the design.
For P art (2), desired NMPs for each coupled section obtained from
P art (1) are utilized to come up with physical dimensions for each coupled
section. In order to obtain physical dimensions for each coupled section, we
have also used an optimization method called ‘Simplex1 algorithm [61]. The
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52
Part 1
Filter specifications
Wj ,w> and s for various sections
from the homogeneous solution
Choose Z
W N -l)
and Z
Change w,
ON
,s
Bad
Normal mode parameters
for each coupled section
Calculate
Compare
normal mode parameters
Good
Physical dimensions
Part 2
EM simulation
Comparison
Final Design
Part 3
Figure 4.12. The procedure for the design of multilayer parallel coupled-line
band-pass filters in inhomogeneous configurations
physical dimensions obtained from the design of homogeneous multilayer filters
are used for an initial guess for the iterative evaluation of physical dimensions
for an inhomogeneous medium. The line impedances, ZQi through Z qn at the
interfaces between different coupled line sections, can be altered within the
range of 10 Ct to 80 Q for obtaining more reasonable physical dimensions. For
an inhomogeneous dielectric medium, the additional parameter (‘a ’) may also
be selected iteratively for finding an appropriate physical layout. Alternatively,
only 3 target parameters can be used as derived in Section 4.1.4 for the target
parameters for synthesis.
For Part (3) of the design procedure, S-parameters are determined for
each coupled section starting from the physical dimensions finally arrived at,
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53
and then these S-parameters for all sections are all combined together for eval­
uating the expected performance. The complete circuit combining all coupled
sections is analyzed for determining the insertion loss and the return loss. Also,
an electromagnetic simulation is carried out using the physical dimensions on
Momentum ™ (an HP-EEsof product), a simulation package using the method
of moments. The filter design is finally verified by comparing the performance
obtained from EM simulations and experimental measurements.
4.3
D esign E x a m p les
4.3.1
H om ogeneous F ilte rs
We illustrate this procedure by
performing two examples of multilayer filters embedded in a homogeneous di­
electric as shown in Figure 4.9 and Figure 4.13. The filter specifications are
selected as shown in Table 4.1 where Z on’s are line impedances at two ports
of the n th coupled line section. These impedances are selected so as to avoid
too narrow or too wide line widths and spacings.
Figure 4.13. The cross-sectional view of a 4-layer homogeneous parallel
coupled-line band-pass filter
Following the design procedure developed and discussed earlier, and
performing iterations with SBEM leads to the physical dimensions for the two
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54
Table 4.1. The specifications for homogeneous parallel coupled-line band-pass
filters
Center frequency
Bandwidth
Ripple
Number of resonators
eT
/14
h3
h2
h1
^0
Z qi
Zq2
Z 03
3-layer filter
10 GHz
40%
0.5 dB
3
4-layer filter
10 GHz
40 %
0.5 dB
3
2.2
2.2
120 mil
20 mil
20 mil
20 mil
—
80 mil
20 mil
20 mil
50 Q
40 n
60 Q
40 Q
50
40
60
40
Q
Q
Q
n
filter examples as shown in Table 4.2 and Table 4.3, respectively. W i, W2,
W0
and S are layout dimensions obtained as shown in Figure 4.1. The length of
each line of all coupled sections is made shorter than the physical dimensions
shown in Table 4.2 and Table 4.3 to take into account open-end discontinu­
ity reactances [62, 63]. The physical layouts of these two filters are shown in
Figure 4.14 and Figure 4.15.
Using the physical dimensions optimized for two examples, filter cir­
cuits are simulated on a full-wave EM simulator. Performances for two different
multilayer filters in homogeneous dielectrics, as obtained by EM simulations
and an ideal response from the Chebyshev filter, are shown in Figure 4.16
and Figure 4.17. Center frequency, bandwidth and ripple level for these two
filters as obtained from SBEM analysis and EM simulations are compared in
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55
Figure 4.14. The layout used for simulation of a homogeneous 3-layer parallel
coupled-line band-pass filter
Figure 4.15. The layout used for simulation of a homogeneous 4-layer parallel
coupled-line band-pass filter
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56
Table 4.2. Physical dimensions for a homogeneous 3-layer parallel coupled-line
band-pass filter (units in mm)
Section #
Wi
w2
S
m ,w 0
1
2
4
3
1.304 1.368 1.136 1.119
1.119 1.136 1.368 1.304
-0.836 -0.525 -0.525 -0.836
2.3 22
Table 4.4. A good agreement with the desired values verifies the design proce­
dure proposed here.
Note that SBEM is a program for quasi-static evaluation of [L] and
[C] matrices for multilayer multi-conductor coupled lines. Results of SBEM axe
used in a network simulator (HP-MDS) to obtain filter performance (marked as
SBEM) in Table 4.4. These results do not incorporate discontinuity reactances
and spurious mutual coupling among various sections. A full-wave simulation
takes all these effects into account. We note that results from SBEM analysis
and EM simulation are in close agreement. However, S2i at frequency above
the pass-band as obtained from the EM simulation decays more rapidly than
Table 4.3. Physical dimensions for a homogeneous 4-layer parallel coupled-line
band-pass filter (units in mm)
Section #
Wi
w
2
S
W i,W 0
1
1.787
2.026
-0.572
3
2.638 0.642
0.642 2.638
-0.958 -0.958
3.4187
2
4
2.026
1.787
-0.572
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57
0.0 dB
—
—
-—
-10.0 dB
IS111 (Momentum)
IS211 (Momentum)
IS111 (Ideal)
IS21I (Ideal)
-20.0 dB
-30.0 dB
-40.0 dB
2.0
4.0
6.0
8.0
10.0 12.0
frequency (GHz)
14.0
16.0
18.0
Figure 4.16. The performance of a 3-layer parallel coupled-line band-pass
filter embedded in a homogeneous dielectric
th at obtained by connecting all S-parameters for coupled sections based on
calculated NMPs. This may be caused by discontinuity reactances which were
not taken into account in design process. Although the open end compensation
was carried out in an approximate manner, the center frequency shift is also
likely caused by other discontinuity reactances. An unwanted coupling between
two different coupled sections affects the filter performance in that this can
cause another pole at the stop band. Also, the optimization process used in
determining physical dimension from [L] and [C] matrices is not perfect.
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58
0.0 dB
—
—
-—
-10.0 dB
IS111 (Momentum)
IS211 (Momentum)
IS11I (Ideal)
IS21I (Ideal)
-20.0 dB
-30.0 dB
-40.0 dB
2.0
4.0
6.0
8.0
10.0 12.0
frequency (GHz)
14.0
16.0
18.0
Figure 4.17. The performance of a 4-layer parallel coupled-line band-pass
filter embedded in a homogeneous dielectric
Table 4.4. Center frequency, bandwidth and ripple level for homogeneous par­
allel coupled-line band-pass filters
Center
Frequency
(GHz)
Spec.
SBEM
3-layer filter
4-layer filter
Momentum
3-layer filter
4-layer filter
10
3 dB
Bandwidth
(%)
40
Ripple
Level
(dB)
0.5
10
10
42
42
< 0.378
< 0.378
10.13
9.85
40.97
42.33
< 0.546
< 0.935
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59
Table 4.5. The filter specifications used for inhomogeneous parallel coupledline band-pass filters
Center frequency
Bandwidth
Ripple
Number of resonators
£>5
£r4
Sr3
Sr2
Erl
h$
3-layer filter
6 GHz
50%
0.5 dB
3
—
—
2.2
2.2
2.2
/14
—
—
h3
h2
hi
20 mil
20 mil
20 mil
4.3.2
In h o m o g en eo u s F ilte rs
5-layer filter
6 GHz
50 %
0.5 dB
3
2.2
2.2
2.2
2.2
2.2
20
20
20
20
20
mil
mil
mil
mil
mil
The design procedure is demon­
strated by performing two inhomogeneous multilayer parallel coupled-line band­
pass filters, selected specifications of which are shown in Table 4.5. An opti­
mization process for evaluating physical dimensions, in this case also, has been
carried out using the 'Simplex1 algorithm [61] (as performed in a homoge­
neous dielectric case [33]), and the line impedances and three desired target
parameters as explained in Section 4.1.4 are optimized together with physical
dimensions. Making iterations with SBEM leads to the physical dimensions
appropriate for two filter examples as shown in Table 4.6. W\, W2 and S are
layout dimensions as shown in Figure 4.1.
The layouts of these filters using these physical dimensions are shown
in Figure 4.18 and Figure 4.19. The length of each coupled section is taken
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60
(a)
(b)
Figure 4.18. (a) The cross sectional view and (b) the layout of an inhomoge­
neous 3-layer parallel coupled-line band-pass filter.
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61
(a)
(b)
Figure 4.19. (a) The cross sectional view and (b) the layout of an inhomoge­
neous 5-layer parallel coupled-line band-pass filter.
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62
Table 4.6. Physical dimensions for the inhomogeneous (a) 3-layer parallel
coupled-line band-pass filter and (b) 5-layer parallel coupled-line band-pass
filter
Section #
Wi (mm)
W2(mm)
S(m m)
Z on(Q)
input
4.796
—
—
50
1
2.445
0.557
-0.469
70
2
0.905
0.611
-0.568
60
3
0.611
0.905
-0.568
70
4
0.557
2.445
-0.469
output
—
4.796
—
50
3
1.571
3.001
-0.176
55
4
2.013
3.908
-0.283
output
—
7.993
—
50
(a)
Section #
W \(mm)
W iim m )
S(m m)
Z oh(Q)
input
1.506
—
—
50
1
0.755
1.206
-0.980
55
2
1.338
1.827
-0.274
60
(b)
as the quarter-wavelength (at the center frequency) based on the arithmetic
mean of the two phase velocities for the coupled section. The length of each line
in all coupled sections is made shorter to take into account open end fringing
capacitance [62, 63]. The physical layouts of these two filters (which were used
by full-wave electromagnetic simulations) are shown in Figure 4.18 (b) and
Figure 4.19 (b).
Using the physical layouts, filter circuits are simulated on a full-wave
EM simulator. Experimental measurements have been performed using the
fabricated filters as shown in Figure 4.20. In Figure 4.20, the 3-layer filter is
shown in the right side, and the 5-layer filter is shown in the left side.
Performances for two different filters in an inhomogeneous dielectric,
as obtained by EM simulations and an ideal Chebyshev filter response, are
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63
\
■
\
*
Figure 4.20. The photograph of multilayer parallel coupled-line band-pass
filters fabricated on RT/Duroid 5880 (right: 3-layer filter left: 5-layer filter)
shown in Figure 4.21 and Figure 4.22. Center frequency, bandwidth and ripple
level for these filters as obtained from EM simulations and measurements are
shown in Table 4.7. A good agreement with the desired values verifies the
design procedure proposed here. We note th at results from the design calcu­
lation (SBEM) and the EM simulation are in close agreement. However, S21
values at frequency above the pass-band as obtained from the EM simulation
show a slight deviation. The main reason for this behavior is the discontinuity
reactances between the two different coupled sections (other than open-ends)
which were not taken into account in the design process. Approximations used
in the equations concerning the two different phase velocities in inhomogeneous
dielectrics as described in Section 4.1 can cause the deviation from the desired
filter specifications as shown in Figure 4.21 and Figure 4.22. Center frequency
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64
0.0 dB
tow
-10.0 dB
-20.0 dB
-30.0 dB
IS111(Momentum)
IS211 (Momentum)
IS111 (Ideal)
IS21I (Ideal)
IS111(Measured)
IS211 (Measured)
-40.0 dB
-50.0 dB •
1.0
Li
2.0
i
i
3.0
i
i
4.0
i lL
LI
i
dJ .
5.0 6.0 7.0
frequency (GHz)
i
8.0
i
i
9.0
i
l!
10.0 11.0
Figure 4.21. The performance of an inhomogeneous 3-layer parallel coupledline band-pass filter
shift is also perhaps caused by other discontinuity reactances. Also, the op­
timization process used in determining physical dimensions from [L] and [C]
matrices is not perfect.
Experimental results are also included for comparison. It is noted
that the measured results are slightly more deviated to higher frequency side
than the EM simulation results. It is mainly because of an alignment problem
for several layers, finite ground planes and possible air gaps between substrates.
These imperfections in the fabrication process can cause such deviation. These
measurements were carried out by a full 2-port calibration (S-O -L-T cali­
bration [64]). W ith a TRL calibration [64], better measured results could be
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65
O.OdB
Ooooo
------ IS11
------ IS21
------IS11
------ IS21
° IS11
• IS21
-10.0dB
-20.0dB
,
(Momentum)
(Momentum)
(Ideal)
(Ideal)
(Measured)
(Measured)
-30.0dB
-40.0dB
-50.0dB
1.0
2.0
3.0
4.0
5.0 6.0 7.0
frequency (GHz)
8.0
9.0
10.0 11.0
Figure 4.22. The performance of an inhomogeneous 5-layer parallel coupledline band-pass filters
Table 4.7. Center frequency, bandwidth and ripple for inhomogeneous parallel
coupled-line band-pass filters
Ideal response
SBEM
3-layer filter
5-layer filter
M om entum
3-layer filter
5-layer filter
Measured
3-layer filter
5-layer filter
Center
Frequency
(GHz)
6
3 dB
Bandwidth
(%)
50
Ripple
Level
(dB)
0.5
5.79
5.96
49.7
49.1
< 0.42
< 0.39
5.86
6.00
48.5
43.7
< 1.25
< 0.85
6.00
6.15
41.3
43.1
< 2.68
< 2.88
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66
Table 4.8. The specifications used for multilayer CPW parallel coupled-line
band-pass filters
Topology A
Center frequency
Bandwidth
Ripple
Number of resonators
£t3
Zr2
£rl
h3
h2
hi
4 GHz
30 %
0.5 dB
2
10.2
10.2
10.2
25 mil
10 mil
25 mil
Topology B
4 GHz
30 %
0.5 dB
2
10.2
10.2
10.2
25 mil
10 mil
25 mil
obtained.
4.3.3
C P W F ilte rs
Very few designs of multilayer CPW filters
have been reported so far [32, 34, 36, 39]. In this thesis, the methodology
developed has been used for designing CPW filters in multilayer configura­
tions. In this design, coplanar lines are combined with asymmetric microstrip
lines, thereby combining the advantage of CPW with the design flexibility of
multilayer configurations.
Two examples of multilayer CPW filters are shown in Figure 4.23. In
these layouts, air bridges are not needed at the end of CPW coupled sections
where the ground planes are connected on CPW layer. This is an advantage of
using multiple substrates. EM simulations with air-bridges incorporated at the
input and output ports showed th at performance changes are not significant.
Filter specifications selected for CPW configurations are shown in Table 4.8.
An optimization process for evaluating physical dimensions has also
been carried out using the ‘Simple^ algorithm [61] as in multilayer microstrip
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67
(a)
(b)
Figure 4.23. The layout of 3-layer CPW parallel coupled-line band-pass filter
configuration for (a) Topology A, (b) Topology B
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68
Table 4.9. Physical dimensions for 3-layer CPW parallel coupled-line band­
pass filters, (a) Topology A (b) Topology B
Section #
W\ (mm)
W2(mm)
S(m m )
g(mm)
Z qh(SI)
input
1.104
—
—
0.674
50
1
0.504
2.027
-1.161
0.974
18
2
1.26
1.241
-0.39
—
18
3
2.1
0.502
-1.285
0.944
output
—
1.084
—
0.653
50
2
0.287
0.277
-0.058
—
40
3
0.674
0.521
-0.377
0.604
output
—
0.948
—
0.39
50
(a)
Section #
W\ (mm)
W2(mm)
S(m m )
g(mm)
Z qn(Q)
input
0.951
—
—
0.391
50
1
0.521
0.674
-0.374
0.606
40
(b)
filters, and the line impedances and three target parameters as explained in
Section 4.1.4 are also optimized together with the physical dimensions. Mak­
ing iterations with SBEM leads to the physical dimensions for the two filter
examples as shown in Table 4.9. Wi, W2, S and additional physical dimension
g (the distance between the conducing strip and the ground layer as shown in
Figure 4.23) are layout dimensions. The length of each coupled section is again
taken as the quarter-wavelength (at the center frequency) based on the arith­
metic mean of the phase velocities for the two modes in the coupled section.
Also, the length of each line in all coupled sections is made shorter to take into
account open end fringing capacitances.
Using the physical layouts, filter circuits are simulated on a full-wave
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69
0.0 dB
—
—
-—
-10.0 dB
IS111 (Momentum)
IS211 (Momentum)
IS111 (Ideal)
IS21I (Ideal)
-20.0 dB
-30.0 dB
-40.0 dB
-50.0 dB
1.0
2.0
3.0
4.0
5.0
frequency (GHz)
6.0
7.0
Figure 4.24. The performance of a 3-layer CPW parallel coupled-line band­
pass filter for topology A
EM simulator. The performances of two different CPW filters in multilayer
configurations are shown in Figure 4.24 and Figure 4.25. Center frequency,
bandwidth and ripple level for these filters as obtained from the design cal­
culation (based on SBEM and MDS) and EM simulations are shown in Ta­
ble 4.10. Here we have compared these simulation results. A good agreement
to the desired values verifies the design procedure proposed here. However,
deviations at the higher frequencies may be related to the loss of accuracy of
quasi-TEM approximation. The results from the EM simulation show a fairly
good agreement to our design based on SBEM analysis. As in the cases of in­
homogeneous microstrip filters, the shift of center frequency and the deviation
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70
0.0 dB
—
—
-—
-10.0 dB
IS111(Momentum)
IS211 (Momentum)
IS111 (Ideal)
IS211 (Ideal)
-20.0 dB
-30.0 dB
-40.0 dB
-50.0 dB
1.0
2.0
3.0
4.0
5.0
frequency (GHz)
6.0
7.0
Figure 4.25. The performance of a 3-layer CPW parallel coupled-line band­
pass filter for topology B
from the desired filter response are attributed to the effect of other disconti­
nuity reactances. Taking the arithmetic mean of two different phase velocities
for the calculation of the length of the coupled lines may also be a reason for
the deviation from the desired specifications.
4.4
Discussion
Systematic design procedures for asymmetric parallel coupled-line mi­
crostrip filters in a homogeneous and an inhomogeneous multilayer substrate
environment and for CPW filters have been presented. The necessary design
equations have been formulated and lead to the implementation of various
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71
Table 4.10. Center frequency, bandwidth and ripple for 3-layer CPW parallel
coupled-line band-pass filter designs
Ideal response
SBEM
Topology A
Topology B
M omentum
Topology A
Topology B
Center
Frequency
(GHz)
4
3 dB
Bandwidth
(%)
30
Ripple
Level
(dB)
0.5
3.69
3.69
38.21
38.48
< 0.66
< 0.65
3.73
3.72
38.61
34.41
< 1.41
< 1.55
parts in the design procedure. The design procedure of homogeneous multi­
layer filters is used as the starting point for the development of the design
for inhomogeneous coupled line microstrip filters. An optimization procedure
combined with SBEM analysis is used to arrive at the physical dimensions of
the filter starting from filter specifications. The critical part of the design is
the optimization process used in finding the physical dimensions. Other meth­
ods such as Artificial Neural Network modeling discussed in Chapter 5 may be
used to accelerate the optimization process substantially.
S-parameters for each coupled section are calculated separately and
then combined to provide the performance of the whole circuit. Since the
calculation using NMPs from SBEM is based on a quasi-static analysis, it
does not take into account the existing fringing field around the open-end
lines. However, it provides an approximate but a fast way to verify the design.
A full-wave EM simulation using the method of moments has been used to
verify the design procedure. Finally experimental measurements have been
performed to verify these designs.
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72
The determination of line impedances affects the width of each cou­
pled section. In some cases, these impedances can play a significant role in
deciding the corresponding physical geometry. For the procedure described
here, we used values between 10 Q and 80 f2 for the line impedances.
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CHAPTER 5
DESIGN OF END-COUPLED BAND-PASS FILTERS IN MULTILAYER
CONFIGURATIONS
Another kind of filter configuration studied in this project is endcoupled band-pass filters. This configuration results in a simple physical struc­
ture containing gap coupled sections between half-wavelength resonators. No
discontinuities, other than capacitively coupled gaps, occur in this circuit. Con­
ventionally, these filters have been utilized in single layer configurations and
designed based on the method available in the literature [7, 54]. This method,
however, is suitable for a single-layer filter structure only. The single layer
restricts the bandwidth less than 15 % [7].
In this Chapter, multilayer end-coupled band-pass filters are dis­
cussed. The key motivation has been overcoming the narrow band restriction
existing in single-layer configurations. A design procedure has been developed
using a full-wave simulation program (HP-Momentum). Besides, an ANN
model has been developed successfully for reducing the design time.
5.1
Derivation of Design Procedure
The general configuration of an end-coupled band-pass filter realized
in two-layer structure is shown in Figure 5.1. Each resonator is half-wavelength
long at the design frequency, and can be placed at different layers depending
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74
on the design topology.
Cross-section at xx’
Figure 5.1: The layout of a multilayer end-coupled band-pass filter
Single-layer end-coupled band-pass filters using the equal widths of
resonators have been designed following the design procedure available in the
literature [7, 54]. Because the tight coupling between the resonators is needed
for wideband filters, multilayer configurations are employed in this thesis. To
derive design equations, the general end-coupled band-pass filter in Figure 5.1
is redrawn as a transmission line circuit shown in Figure 5.2. The gaps between
the resonators are modeled by 7r-network of capacitances [7,65]. For these endcoupled band-pass filters, the characteristic impedances for each resonator can
be different and the resonators can be placed at different layers.
i.
M)N
Figure 5.2. An equivalent transmission line circuit for end-coupled band-pass
filters
This transmission line circuit in Figure 5.2 can be rewritten as shown
in Figure 5.3 when dN = 4>+—-+^*+‘ . An equivalent circuit shown in Figure 5.4
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75
using admittance inverters and half-wavelength resonators is then employed to
eventually rewrite transmission line circuit shown in Figure 5.2 using the net­
work equivalence shown in Figure 5.5. Figure 5.4 shows that this equivalent
circuit is now identical in form with the parallel coupled-line filter equivalent
circuit shown in Figure 4.4. In Figure 5.4, J-param eters are determined from
the characteristic impedances (Z0, Z 0j , . . . , Z on), low pass filter prototype el­
ements and the bandwidth as derived in Eq. (4.4). <j>is 180° at the design
frequency. For the circuits in Figure 5.2 and Figure 5.4 to be equivalent, the
admittance inverters must be equivalent to the capacitors and the transmission
lines combination as shown in Figure 5.5.
fti.i
3 L = = » H l-iC ± 3 C
------ -------
Figure 5.3. A modified transmission line model for end-coupled band-pass
filters
-90
-90
-90
Figure 5.4. An equivalent circuit using admittance inverters and A/2 resonators
{<f>= 180°)
Equating ABCD matrices of the two circuits in Figure 5.5, the fol­
lowing relations are derived.
B pon + B.S N
B p \n + B sn
_
Z q (N -I)
Z qn
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(5.1)
76
J®SN
• --------
• --------
A
-------- •
JN
- 90 °
j^ P lN ,^
jfi>2N
ZpN
--------•
Figure 5.5. The relation between an admittance inverter and a gap expressed
by susceptances and transmission lines
BpiN + Bp2N +
B
p i n B p 2n
+ 1 / ( Z q(n - i ) Z q n )
Bsn
J n Z o(n - \ ) Z qn
— JN = K 2
(5.2)
Then, <f>N and On are then determined as:
(j>N ~ tan_1[____________________ 2(Bsn + Bp 2n)_____________________j
Z o(n - i ){B p \ n B p 2n + B p2n B s n + BSNB P1N — 1 /(Z o(n - i )Z qn)
(5.3)
On — 180° +
<t>N + <t>N+ 1
(5.4)
For a simple case of single layer filters using the same characteristic
impedances (Z q) and ignoring shunt susceptances (B p i n etc.), we get
B sn =
Jn
1 - ( J n Z q )2
0jv = —tan 1(2Z qB s n )These relations are exactly same as those available in the literature [7,
54]
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77
The two equations (5.1) and (5.2) are used for finding the values of
the shunt and series susceptances needed for the filter design. Once the values
of these susceptances are determined, the electrical lengths to be used are
calculated through the values of <j>^ s in Eq. (5.3). Since the gap between the
two resonators determines the susceptances (Bpin, Bp 2 n and B Sn) in Eq. (5.1)
and Eq. (5.2), the design of the gap geometry plays a crucial role in the design
of end-coupled band-pass filters. A full-wave simulation program has been
used for calculating these susceptances and optimizing the geometries for the
gap to yield the desired parameters (K i and K 2)- In most cases, it takes a long
time to optimize this gap geometry using a full-wave simulator. Therefore,
an ANN model has been developed as an alternative method (discussed in
Section 5.4) to reduce the optimization and design time.
5.2
Description of Design Procedure
The overall design procedure developed for multilayer end-coupled
band-pass filters is summarized in Figure 5.6. This procedure can be divided
into three parts:
(1) Evaluation of two design parameters (K \ and K 2) as derived in Eq. (5.1)
and Eq. (5.2),
(2) Determination of physical dimensions (widths and gap spacings) that
yield the design parameters (K \ and K 2) as evaluated in Part (1), and
(3) EM simulation and experimental measurement based on the physical
geometry obtained in Part (2) to validate the design.
For P art (1), desired design parameters (K i and K 2) for each gap
are evaluated using filter specifications (bandwidth, the number of resonators,
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78
.Ran.I
Filter specifications
Initial guess for w j'w2 and g
for each gap
C h a n g e ^ ’s
Change wj ,v^ ,g
Momentum
Bad
2 design parameters
(K, , K , )
for each gap
Calculate
Compare
(Kj . K j )
Good
Part 2
Calculate
Calculate
Length of sections
Part 3
EM simulation/
Measurement
Comparison
Final design
Figure 5.6: A design procedure for multilayer end-coupled band-pass filters
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79
ripple level and characteristic impedances of transmission lines) as derived in
Eq. (5.1) and Eq. (5.2). Since the widths of half-wavelength transmission line
resonators can be selected by the design, the characteristic impedances (Z0/v’s)
can be chosen independently. The values of impedances (Z0N’s) affect the
values of design parameters ( K\ and K 2).
For Part (2), design parameters (Ki and K 2), determined in Part
(1) for each gap, are used to find the physical geometry for each gap coupled
section. In order to find physical dimensions for each gap, HP-Momentum
was used to calculate the series and shunt capacitances. These capacitances
determine the values of the left hand sides of Eq. (5.1) and Eq. (5.2) (i.e.
K \ and K 2). EM simulations are carried out iteratively for each gap until
correct values of the desired design parameters (K\ and K 2) are obtained. The
characteristic impedances (Zo/v’s) are also optimized for appropriate physical
geometry of each gap coupled section leading to the desired K\ and K 2.
For P art (3) of the design procedure, the susceptances for each gap de­
termine the electrical lengths of transmission line resonators given by Eq. (5.4).
Using the physical dimensions (widths, gap spacings and lengths), the com­
plete circuit is simulated on HP-Momentum. For better performance, some
adjustment may be performed for the gap spacing after EM simulations of the
complete circuit. Eventually, the results of this simulation are compared to the
experimental measurements to verify the design.
5.3
Design Examples
Two design examples of two-layer end-coupled band-pass filters (A
and B) correspond to the filter specifications shown in Table 5.1. Because these
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80
Table 5.1: Specifications for multilayer end-coupled band-pass filters
Design frequency
Bandwidth
Ripple
Number of resonators
Sr2
£rl
h2
h .L
Design A
3 GHz
30 %
0.5 dB
5
2.2
2.2
10 mil
10 mil
Design B
4 GHz
35 %
0.5 dB
5
2.2
2.2
10 mil
10 mil
filters are implemented in two layer structures, adjacent transmission line res­
onators are placed at different levels. A gap geometry consists of two different
widths at the two sides and an overlapping section as shown in Figure 5.1.
All the 3 dimensions {W\, W2 and g) for each of the gaps are optimized using
HP-Momentum by adjusting the spacing and the characteristic impedances
of transmission lines. The optimized values of gaps’ dimensions are listed in
Table 5.2 and Table 5.3.
Electromagnetic simulations were carried out for the physical geome­
tries of the two filters shown in Figure 5.7 and Figure 5.10. Figure 5.8 and
Table 5.2. Physical dimensions of a two-layer end-coupled band-pass filter
(units in mm) for Design A. Dimensions Wi, W 2, g and I are shown in Figure 5.1
Section #
W!
w2
9
I
1
1.6004
1.991
4.7
28.7251
2
1.991
1.6004
3.12
32.2453
3
1.6004
1.991
2.5
30.8652
4
1.991
1.6004
2.5
32.2373
5
1.6004
1.991
3.12
28.7837
6
1.991
1.6004
4.7
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-
81
Figure 5.7. The physical layout for a two-layer end-coupled band-pass filter
(Design A)
O.OdB
IS111(Momentum)
IS211 (Momentum)
o IS111(Measured)
• IS211 (Measured)
-1 O.OdB
-20.0dB
-30.0dB
-40.0dB
-50.0dB
1.5
2.0
2.5
3.0
3.5
frequency (GHz)
4.0
4.5
Figure 5.8. The performance of a two-layer end-coupled band-pass filter (De­
sign A)
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82
Table 5.3. Physical dimensions of a two-layer end-coupled band-pass filter
(units in mm) for Design B. Dimensions W\,
g and I are shown in Figure 5.1
Section #
Wx
W2
9
I
1
1.6004
1.991
3.73
21.172
2
1.991
1.8054
2.58
23.5294
3
1.8054
1.895
2.16
22.588
4
1.895
1.8054
2.16
23.5237
5
1.8054
1.991
2.58
21.1621
6
1.991
1.6004
3.73
-
Figure 5.9. The photograph of two-layer end-coupled band-pass filters fabri­
cated on RT/duroid 5880 (bottom: Design A, top: Design B)
Figure 5.10. The physical layout for a two-layer end-coupled band-pass filter
(Design B)
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83
O.OdB OOOOOOO^OOOOOOOf OOOOfrOOfT
^rooooooo^oooooo
o<>
Oo I
-1 O.OdB
-20.0dB
-30.0dB
____ 2>l____
IS111(Momentum)
IS211 (Momentum)
IS111(Measured)
IS211 (Measured)
-40.0dB
-50.0dB
2.0
2.5
3.0
3.5
4.0
4.5
frequency (GHz)
5.0
5.5
6.0
Figure 5.11. The performance of a two-layer end-coupled band-pass filter
(Design B)
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84
Table 5.4. Center frequency, bandwidth and ripple level for multilayer endcoupled band-pass filters
Specification
Design A
Design A
Momentum simulation
Design A
Design B
Measured
Design A
Design B
Center
Frequency
(GHz)
3 dB
Bandwidth
(%)
Ripple
Level
(dB)
3
4
30
35
0.5
0.5
3.071
4.071
27.65
33.65
<1.017
<1.317
3.2
4.2
20.31
25.95
<1.75
<1.71
Figure 5.11 show the performances obtained from full-wave simulations and
experimental measurements. Two filters have been fabricated on RT/duroid
5880 for experiment as shown in Figure 5.9. Gap spacings can be adjustable
for better performance. A good agreement between the filter specifications and
the simulated performance is shown in Table 5.4 in terms of three important
parameters. The center frequency shifted slightly higher and the 3-dB band­
width is smaller than what was expected. Furthermore, the pass-band ripple
level is greater than the desired 0.5 dB. This may have been caused by ignoring
the real part in the determination of capacitances of gap coupled sections as
only the imaginary parts of Y-parameters have been used for calculating [C]
matrix. Dielectric loss and conductor loss also affect the pass-band ripple. Less
accurate calculation of the lengths of gaps and transmission lines may yield a
frequency shift.
Measured results show a slight deviation from the specifications and
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85
simulation results. This may be caused by imperfect alignment of two substrate
layers, finite ground plane and possible air gaps between two layers. Since an
air gap makes the height of the bottom substrate higher and the effective
dielectric constant lower than the nominal values, the center frequency shifted
to higher and the insertion loss was worsened. This air gap will cause the
simulation results to change by including this effect into the simulation process.
Specially, the decrease of 3-dB bandwidth arises from the dielectric, conductor
and radiation losses that worsen the magnitude response of the insertion loss.
5.4
D esign o f E n d -C o u p le d F ilte rs w ith A N N M odels
A long computer time is required to optimize various gap dimensions
because repeated full-wave simulations need to be carried out. This kind of
time consuming optimization process does not lead to a fast and convenient
design for end-coupled band-pass filters. The use of ANN models can reduce
considerably the required CPU time to optimize gap dimensions. The method­
ology used for developing accurate and efficient ANN models has been well
discussed and demonstrated in [66]. Some basic concepts of ANN modeling
are reviewed here. The use of ANN models for design of end-coupled filters is
demonstrated.
5.4.1
A N N M odeling
The ANN architecture used in model­
ing end-coupled filters is shown in Figure 5.12 and consists of an input layer,
an output layer, and one hidden layer. It is a multilayer, feed-forward ANN,
utilizing the error-backpropagation learning algorithm [67]. The hidden layer,
which incorporates nonlinear activation functions, allows modeling of complex
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86
input/ output relationships between multiple inputs and multiple outputs. In­
puts are connected to the hidden layer by a set of weights.
The input Uj of the j - th neuron in the hidden layer is obtained by
the summation of the weighted input variables and an additional bias term.
Thus the input Uj can be represented as:
% = E
w* x ‘
<5-5)
x=0
where X 0 = 1 and WjP is the corresponding connection weight between the
input layer and the hidden layer. The output of the neuron in the hidden layer
is obtained as:
Zj = g{uj)
(5.6)
where g(u) is the activation function of the neuron. The activation function of
the input layer is the identity
the hidden layer.
function since the inputs are directly passed to
Betweenthe hidden layer and the output layer, a sigmoidal
function is used for the activation function as:
=
<5-7>
The hidden layer is connected to the output layer by another set of
weights. The outputs of the output layer are obtained in a manner similar to
the ones of the hidden layer. By combining all these steps one can obtain the
input/output relation of the ANN as:
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87
u
«>>
es
00
3
B*
O
3
o
o
o
N
2e
■
•oo
X
00
oo
3Q.
C
Figure 5.12. The architecture of typical single hidden layer artificial neural
network
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88
Yk = g{vk)
= « ( £ < ’» ( £ " # ’*))
j= 0
(5-8)
i= 0
Training of the ANN model is accomplished by adjusting these weights
to give the desired response. The ANN learns relationships among sets of in­
pu t/output d ata which are characteristic of the component under considera­
tion. First, the input vectors of the training dataset are presented to the input
neurons and output vectors are computed. ANN outputs are then compared
to the known outputs (of the training dataset) and errors are computed. Error
derivatives are then calculated and summed up for each weight until all the
training examples have been presented to the network. These error derivatives
are then used to update the weights for neurons in the model. Training pro­
ceeds until errors become lower than prescribed values. Details of the training
algorithm are given in [68, 69].
5.4.2
C o u p led F ilte rs
A N N M o d elin g M eth o d o lo g y for M u ltila y e r E n d In order to shorten the optimization time, ANN models
may be employed. In this thesis, CU-ANN® has been used for this purpose.
ANN models can be used to effectively determine physical values for gap cou­
pled sections from given desired parameters (synthesis). ANN models have
also been developed providing the correct Y - or S-parameters based upon the
physical geometry (analysis) to be used in commercial microwave circuit sim­
ulators. Simulations using HP-Momentum are used to provide a training data
for both the synthesis and analysis ANN models. Training data is obtained by
specifying the design frequency, the physical dimensions and their ranges for
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89
the gap coupled sections under consideration. Y - or S-parameters obtained
from EM simulations are used for training the ANN models.
/
Analysis model
W1
for a coupling gap
g
Figure 5.13: Analysis ANN model for gap coupled sections
/
Synthesis model
K 1
for a coupling gap
K„
Figure 5.14: Synthesis ANN model for gap coupled sections
For analysis model, the design frequency and physical dimensions
such as widths and gap spacing are used as inputs to ANN models as shown
in Figure 5.13. The outputs are the elements of the Y-parameters. Once
the Y-parameters of a given gap coupled section have been obtained, they
can be used to determine 2 design parameters (K i and K 2) in Eq. (5.1) and
Eq. (5.2), and then <f>s s in Eq. (5.3). Transmission lines in the multilayer
structure are also modeled using ANNs to yield the characteristic impedances
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90
and propagation constants as outputs. Since these two parameters determine
S-parameters consequently, analysis models of the gap and the transmission
line models are linked to commercial microwave circuit simulators as shown in
Figure 5.15 for circuit analysis and optimization. This simulator passes the
input variables to the user defined linear model subroutine, which is used to
integrate the model into the circuit simulator [70].
For synthesis model, two design parameters ( K i , K 2) and the design
frequency are used as inputs, and the desired physical parameters are used
as the outputs as shown in Figure 5.14. This is an inverse modeling problem
because the inputs and outputs are interchanged. This mapping can often
cause multi-valued outputs with respect to the one input. In addition, since
the input space is (most likely) not characterized fully, the ANN model can
produce incorrect results due to the absence of training data for particular
regions of input data. In order to overcome this problem associated with the
inverse mapping, the outputs of the synthesis ANN model are reconnected to
the inputs of the analysis model as shown in Fig 5.16. K \ and K 2 calculated
from the outputs of the analysis model are then compared to those obtained
from the circuit specifications which have been used as inputs to the synthesis
model. In this way, a determination can be made as to the accuracy of the
synthesis model for a given region of input space. If the model is not accurate
for a given set of K \ and K 2, they are altered by selecting different set of Z 0N's.
5.4.3
A N N M odels
The Design of Multilayer End-Coupled Filters Using
Both synthesis and analysis models for a gap coupled sec­
tion have been developed using 875 simulations performed on HP-Momentum
which have been used for training/testing data for ANN models. W\, W2, g and
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91
Commercial
microwave
circuit simulator
Model input
variables
User-defined linear
model subroutine
EM-ANN
EM-ANN
model inputs
model outputs
Feed-forward
ANN subroutine
EM-ANN
model data
EM-ANN
model file
Figure 5.15. Flow of data for linking EM-ANN models to commercial mi­
crowave circuit simulators
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92
Circuit specifications
J-parameters
Change Z ^ s
No
Design parameters
(K p iq )
Synthesis ANN
Compare
Acceptable,
W , , W2 and g
Analysis ANN
Figure 5.16. A synthesis procedure for gap coupled sections using ANN models
frequency have been repeatedly altered using a uniform grid. One end-coupled
band-pass filter has been developed using ANN models in two layer structure.
For comparison, the specifications used in Section 5.3 are again selected for
the design example. Starting with these circuit specifications, physical param­
eters obtained using synthesis and analysis models for gap coupled sections are
shown in Table 5.5.
Using these physical dimensions, this filter is analyzed on a circuit
simulator which incorporates the analysis ANN models of gap and transmission
lines. Figure 5.17 illustrates filter performance of this filter. Simulation results
from Momentum using the physical geometry without ANNs are repeated here
for comparison with these performances. Table 5.6 gives the center frequency,
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93
Table 5.5. Physical dimensions of a two-layer end-coupled band-pass filter
(units in mm) with ANNs (Design A)
Section #
Wi
W2
9
I
1
1.6212
1.8035
4.88
28.854
2
1.8035
1.6212
3.35
32.2224
3
1.6212
1.8035
2.89
30.8876
4
1.8035
1.6212
2.89
32.2224
5
1.6212
1.8035
3.35
28.854
6
1.8035
1.6212
4.88
-
0 dB
—
—
-—
-10 dB
IS111(Momentum)
IS211 (Momentum)
IS111(ANN)
IS211 (ANN)
-20 dB
-30 dB -
-40 dB
-50 dB
1.5
2.5
3.5
4.5
frequency (GHz)
Figure 5.17: Performance of a two-layer end-coupled filter using ANNs
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94
Table 5.6. Center frequency, bandwidth and ripple for a two-layer end-coupled
band-pass filter with ANNs
Specification
M om entum simulation
ANN analysis
Center
Frequency
(GHz)
3
3.07
3.08
3 dB
Bandwidth
(%)
30
27.65
28.90
Ripple
Level
(dB)
0.5
< 1.017
<1.084
bandwidth and ripple level of the designed filter with ANNs. The filters de­
signed with ANNs and without ANNs are comparable. The ripple level for the
ANN design is slightly larger than desired. Besides, overall shapes are slightly
deviated from the filter designed without ANNs. However, the advantage of
using ANN models for filter design is a large savings in required CPU time
as shown in Table 5.7. In this table, the CPU time on an HP700 workstation
and the number of altering physical geometry is compared. The optimization
time without ANNs is also presented for comparison. The optimization time of
the complete circuit using the linked analysis ANN models on HP-MDS [71]
shows an efficiency in the filter design.
5.5
Discussion
Two examples of end-coupled band-pass filters in a two-layer con­
figuration have been designed using the design procedure developed in this
Chapter.
Overlapping gaps between resonators make it possible to design
wideband filters, and these overlapping gaps can only be realized in multi­
layer configurations. In addition to wide bandwidth, more design flexibility
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95
Table 5.7. Design times and required iterations for end-coupled filters with
ANN modeling and without ANNs
Section
ANN
# iterations
1
2
3
ANN optimization
using HP-MDS
W ithout ANN
1
2
3
6
4
4
CPU
0.83
0.55
0.55
time
sec.
sec.
sec.
6
58 sec.
84
64
52
84 min. 25 sec.
50 min. 04 sec.
45 min. 12 sec.
has been obtained with multilayer structure. Taking the shunt capacitances
of gap coupled sections into account, we characterize the gap geometry bet­
ter than the conventional method which does not consider those capacitances.
Newly derived design parameters have been used as criteria for optimization
of gap geometry.
Due to the huge amount of time for optimization process, ANN mod­
els have been developed. The ANN models reduce the required CPU time
drastically in comparison with the way used earlier in this Chapter. Once the
ANN models are set up, new designs with different circuit specifications can
easily be carried out in a very small fraction of the time.
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CHAPTER 6
MODELING FOR THREE-LINE BALUNS IN MULTILAYER
CONFIGURATIONS
6.1
Introduction
Many microwave applications need the balun which transforms a bal­
anced transmission signal to an unbalanced transmission signal and vice versa.
These include double balanced mixers [72-78], push-pull amplifiers [79-81],
antenna feed networks [82-90], frequency doublers [91-93] and etc. A large
number of balun configurations have been reported in literature. Among them
a planar version of Marchand balun has been adapted for a long time by using
microstrip lines [8 , 20, 40-42], and applications of planar Marchand baluns
have steadily increased in microwave integrated circuits (MIC) and microwave
monolithic integrated circuits (MMIC).
For use in MIC and MMIC, wide bandwidth and compactness of
baluns are of high interest. Multilayer configurations make MIC/MMIC more
compact and can exhibit wide bandwidths due to inherent tight coupling in
coupled-line compensated baluns. Besides, flexible design can be realized by
using multilayer configurations.
A compact configuration of 3-line balun reported recently in litera­
ture [43] is shown in Figure 6.1. This 3-line balun has more compactness than
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97
planar Marchand baluns which combine two identical coupled lines with differ­
ent termination. However, a design procedure for implementing 3-line baluns
in single layer or two-layer geometry has not been available.
In this Chapter, we describe a generic approach [94] suitable for de­
signing this 3-line balun configuration for single-layer and two-layer structure.
We show that this 3-line balun configuration can be represented as a combi­
nation of two identical directional couplers each consisting of a 2 -coupled line
section. This representation is a key step in the design procedure developed.
The procedure has been used for designing single-layer and two-layer 3-line
baluns. The approach is verified by comparing the results with full-wave sim­
ulation results. In addition, a two-layer 3-line balun has been fabricated and
measured to verify the design procedure developed.
Zout
Z in •
• z out
I = A/4
Figure 6 .1 : The general configuration of a 3-line balun
6.2
Description of Design Procedure
6.2.1
Couplers
Representation of a Balun by Two Coupled-Line
When the two balanced terminations of a balun are considered as
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98
two ports, a balun circuit can be considered as a 3-port network as shown in
Figure 6.2. The characteristics of baluns can generally be expressed in terms of
the reflection coefficient (Su = 0 ), and the sum of £>21 and S 31 (S2i + S 3 1 = 0 ).
3-port S-parameters of an ideal balun are given by:
0
- e ~ i 9/y/2
e~ie/y/2
- e~ i29/2
-e ~ i29l2
- e~ i29/2
—e~i29/2
[*5] Balun —
e~i9/ y/2
The 3-port block diagram (Figure 6.2) of a balun can be divided into
two separate blocks as shown in Figure 6.3 where the S-parameters of the two
sub-circuits are:
,-jO
—e~j9
[5] CircuitA
—e~i9
IN
(i)
( 6.2)
CircuitB —
—
0
i~>9
0
(2)
OUT+
(3)
OUT-
Balun
Figure 6.2: The block diagram of baluns
One of the possible methods of realizing circuits A and B is by use
of appropriately terminated coupled-line directional couplers as shown in Fig­
ure 6.4. This configuration can behave like a balun when:
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99
IN
Circuit A
OUT+
Circuit B
OUT-
(1)
Figure 6.3: The bifurcated block diagram of baluns
CIRCUIT A
CIRCUIT B
Figure 6.4: A 3-line balun composed of two 2-line couplers
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100
3
0
[S]cir«.«A(0 = 90°) =
0
~3
-3
0
>[S']CircuitB^ = 90°) =
3 0
(6.3)
when 9 is the electrical length of the two couplers.
The combination of these two 2-line coupler circuits yields the fol­
lowing S-parameters and functions as a balun:
0
j / V 2 -j/y /2
j/y /2
1/2
1/2
-j/y /2
1 /2
1 /2
•
(6.4)
To use the design procedure for asymmetric directional couplers re­
ported earlier [9, 10, 20], [Y] matrices for the circuit A and the circuit B
need to be represented in terms of the coupling factor (/?) and the coupler port
admittances (Yen, Y02) where Y01 = 1/Z0i ,Y 02 = l / % 2, as:
0
[y\ CircuitA
—
-3
~3
PVYqiYqi
(6.5)
0y/Yp i Yqz
0
yfiHP
and
~3
CircuitB —
Vqi —0y/Yp 1Yot
(6.6)
: Yo1 —0VY q1 Vq2
~3
0
The corresponding [S] matrices with the input impedance (2Zin) and
the output impedance (Zout) are calculated using [Y] matrices obtained in
Eq. (6.5) and Eq. (6 .6 ) as:
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101
Table 6.1. Some choices of Zoi, Z$2 for balun input/output impedances Zin =
Z ^ = 50Q
Z q2(£1)
20.42
40.825
100
Zoi(fi)
38
40.825
50
/?(Coupling factor)
0.367
0.5
0.707
I | 2(1—P)
[•S']C ircuitA
1 T
—
j 2 0 y /2 ( 1- P
)y01Y o iZ in Zout
X
(6.7)
j 2 0 ^ 2 ( l - P 2 )Yol Yo2Z in Z out
X
[<5] Circuits —
y
^
l - 0 2 + * 0 Y Oiy / Y 5 i Y m Z i n Z o . t - 2Ym lY 0i + 0 2 YO2 ) Z i n Z ou,
>2^1 - 0 2i-Yoi + SV Y ^Y m )V *Z inZ °~■
> 2 ^ 1 - /9=(—Vbi + 0 v 'V o iV O2 )v '2 Z i n Z (>u ,
1 - /32 + 4 ^ y o iv ^ i'V o :Z ,„ Z 0„. - 2y0i(Voi + tfaVo2)^i«
( 6 .8 )
where X — l+/?2(—l+2Yoi5'o2^in^out) and ^ — 1—/22—4/?Yol^/^ol^o2^m^out^■
2yo1(Kol + / ^ ^ o u t Equating [S]circmM in Eq. (6.3) to [S]c«r««M in Eq. (6.7), and [S ]cw :ts
in Eq. (6.3) to [5]CircuttB in Eq. (6.8),
H t /S
( 6 -9 )
and
Z02 = 4Z01 -
^01
(6.10)
We note th at for a given set of balun impedances at input and output
ports Zin and Zmt, the values of coupled line parameters Z qi and Z 02 are not
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102
unique. For example when Zin = Zmt = 50ft, any of the combinations shown in
Table 6.1 will satisfy Eq. (6.9) and Eq. (6.10). It is found that different choices
for the values of coupler impedances (ZqX and Z02) lead to different bandwidths
for the balun. Network simulations were carried out for two baluns, one using
symmetrical directional coupler with Z Qi = Z 02 = 40.825ft, and the other
with Z 0i = 38Q and Z Q2 = 20.42ft. For the symmetrical case, S u bandwidth
(1‘S'nl < -10 dB) is 48.4 %, the amplitude imbalance is within 0.91 dB, and
phase error is 0°. For the non-symmetrical case, S n bandwidth is 20.9 %, the
amplitude imbalance is less than 1.68 dB, and phase error is 0°. Thus we note
th at among the cases studied, the symmetrical case yields better performance.
For this design, Z 0 1 = Z 02 = Z 0, then /? = 0.5 and Z 0 = yj2ZinZmit/Z.
6.2.2
D esign o f 3 -L in e B alu n s
Design of the 3-line balun
shown in Figure 6.1 is based on finding an equivalence between a 6-port section
of 3 coupled lines (shown in Figure 6.5 (a)) and a 6-port combination of two
couplers as shown in Figure 6.5 (b). The normal mode parameters of the 3coupled lines shown in Figure 6.5 (a) can be found by equating 6-port [Y]
m atrix of these 3-coupled lines to the [Y] matrix of the 6-port circuit shown in
Figure 6.5 (b). For the circuit shown in Figure 6.5 (b), the two sets of identical
2-coupled lines shown enclosed by the dotted lines are perfectly isolated. For
finding out this equivalence, three different phase velocities of the coupled line
in Figure 6.5 (a) are assumed to be equal. This approximation is similar to that
commonly used for design of microstrip directional coupler. Our experience in
this research project shows that good balun designs can be arrived at even
when using this approximation. This procedure leads to the following four
relations among the normal mode parameters of the structure in Figure 6.5 (a)
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103
• 4
•
6
(a)
1 •
3 »
(b)
Figure 6.5. Equivalence between (a) a section of 3-coupled lines and (b) a
6-port network combination of two couplers
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104
and the c - and 7r-mode parameters of two identical couplers in Figure 6.5 (b).
ml
R irY c 1 — R cY ttI
p
itrr
( 6 . 11 )
-q
lie
Yp, - ¥„, _ ¥ c l - ¥ , :
R v 1 - R v2
Rts
(6.12)
Rc
Rv2Yp\ —Ry\Yn\ _ RcYcl — R^Yni
RviRv2{Ypl - Ynl) ~ R cR„(Yci - ywl)
(6.13)
(6.14)
where R y 1, R v 2 are the voltage ratios and Ym1, ynl, Ypi are the admittances of
3 normal modes (m ,n ,p modes) for 3-coupled lines [95], and R c, R n,Yci, Y^i
are c- and 7r-mode voltage ratios and admittances for 2-line couplers [57]. It
may be noted th at we have only 4 equations (6.11-6.14) for 5 independent
values (i?vi, R vi, F'mi, F„i and Ypl) of NMPs of 3-coupled lines. Thus one of
these parameters needs to be selected independently and this choice leads to
different designs for the balun. These NMPs for the 3-line structure are used
to find the geometry of the 3-line balun.
6.2.3
P h y sical G e o m e try for th e 3 -L in e B a lu n
geometry is determined by an optimization process. This process compares
iteratively the desired NMPs for 3-coupled lines (evaluated as indicated in
Section 6.2.2) with NMPs calculated from selected dimensions for 3-coupled
lines. A quasi-static field analysis program SBEM [9, 10] has also been used
to calculate inductance and capacitance matrices for specific geometries.
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Physical
105
Balun specifications
Initial guess for
W! ,W2 and s
(^ in ’ ^om ’ 5) )
SB E M f
Coupler specifications
(13=0.5,2^) o r (p,
, 7q2)
Calculate [L] & [C]
NM P for the coupler
Calculate NM P
SBEM
RVi chosen
NM P for the 3-line balun
(Ryi’Kyz’ %ii ■Y m» Ypi)
Electrical
Design
Change RVI,
Change
,V£ ,S
Bad
Compare
Good
Final ^
^
,S
for the 3-line balun
Design of
Physical
Dimensions
Figure 6.6: A design procedure for 3-line baluns
The design procedure discussed in this section is summarized in the
flow diagram of Figure 6.6. The electrical design part in the left hand column
yields NMPs for 3-coupled lines, and the physical design part in the right
hand column leads to the physical dimensions appropriate for realizing the
NMPs calculated in the electrical design part. For the physical design part,
physical parameters (Wi, W2 and S) are altered iteratively for optimization. In
addition, an intermediate parameter (‘a’) used in the design of 2-line couplers
(explained in Section 4.1.3) can be altered, and R v i can also be altered for
optimization of the physical parameters.
The design is verified by simulating the optimized geometry on a fullwave electromagnetic simulator and measuring the performance of a two-layer
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106
Table 6.2: Parameters for the design example of a single-layer 3-line balun
Inputs
h
15 mil
10
Zin 50 ft
Zout 50 ft
Outputs
Z qi
Z 02
Coupling factor(/?)
Wx
W2
S
40.825 ft
40.825 ft
-6.0 dB
0.348 mm
1.086 mm
0.018 mm
3-line balun designed and fabricated using the design procedure reported here.
6.3
D esig n E x am p les
We illustrate the procedure developed by an example of a single-layer
3-line balun shown in Figure 6.7 and two examples of two-layer 3-line baluns
shown in Figure 6.8 and Figure 6.9.
OUT(3)
OUT(2)
I N(l)
Figure 6.7: The physical layout of a single-layer 3-line balun
6.3.1
S in g le-L ay er 3 -L in e B aiu n s
Input parameters and op­
timized output parameters for the single-layer design example axe shown in
Table 6.2. In this case, the spacings between the adjacent lines are so narrow
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107
Table 6.3. Parameters for the design example of a two-layer 3-line balun
(Topology A)
Inputs
20 mil
hi
h2
20 mil
2.2
^rl
2.2
Cr2
Zin 50 ft
Zaut 50 ft
Outputs
Zoi
Zo2
Coupling factor(/3)
Wi
W2
S
Length(at 3 GHz)
40 ft
35 ft
-6.6 dB
4.280 mm
3.643 mm
1.710 mm
17.749 mm
(0.018 mm in this example) that it is difficult to fabricate this design. Therefore
we need to use two-layer circuits for this purpose.
OUT(3)
OUT(2)
IN(1)
Figure 6.8: The physical layout of a two-layer 3-line balun (Topology A)
6.3.2
T w o -L ay er B aiu n s
Input parameters and optimized out­
put parameters for the two-layer design examples are shown in Table 6.3 and
Table 6.4, respectively. For the 3-line structure used for the balun, the wave­
length is taken as the arithmetic mean of phase velocities of 3 normal modes
divided by the design frequency.
Using the physical geometry obtained, the two-layer 3-line balun
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108
OUT(3)
OUT(2)
IN(1)
Figure 6.9: The physical layout of a two-layer 3-line balun (Topology B)
Table 6.4. Parameters for the design example of a two-layer 3-line balun
(Topology B)
Inputs
20 mil
hi
20 mil
h2
2.2
frl
2.2
Cr2
Zin 50 ft
Zout 50 ft
Outputs
Zoi
Zo2
Coupling factor (/?)
W1
W2
S
Length (at 3 GHz)
43 ft
55.7 ft
-4.9 dB
1.343 mm
5.771 mm
0.506 mm
17.243 mm
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109
0.0 dB
-10.0 dB
-20.0 dB
IS111(Momentum)
IS211 (Momentum)
IS311 (Momentum)
IS111 (ideal)
IS21I (ideal)
IS31I (ideal)
-30.0 dB
-40.0 dB
1.0
1.5
2.0
2.5
3.0
3.5
frequency (GHz)
4.0
4.5
Figure 6.10. The performance of two-layer 3-line balun (Topology A) designed
by the procedure developed and comparison with an ‘ideal’ balun
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110
0.0 dB
-10.0 dB
-20.0 dB
IS111(Momentum)
IS211 (Momentum)
IS311 (Momentum)
IS111 (ideal)
IS21I (ideal)
IS311 (ideal)
-30.0 dB
-40.0 dB
1.0
1.5
2.0
2.5
3.0
3.5
frequency (GHz)
4.0
4.5
5.0
Figure 6.11. The performance of two-layer 3-line balun (Topology B) designed
by the procedure developed and comparison with an ‘ideal’ balun
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Ill
210.0
205.0
Momentum, topology A
Momentum, topology B
200.0
195.0
6> 190.0
0}
2- 185.0
co, 180.0
175.0
170.0
165.0
160.0
155.0
150.0
1.0
1.5
2.0
2.5
3.0
3.5
frequency (GHz)
4.0
4.5
5.0
Figure 6.12. The phase imbalances of two-layer 3-line baluns designed by the
procedure developed
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112
Vias to ground
<i ----------X __
.
....
— ..........\
IX. ..
V
Via to upper layer
(a)
(b)
Figure 6.13. (a) The layout of a two-layer 3-line balun fabricated on Duroid
RT5880, (b) the photograph of a two-layer 3-line balun fabricated on Duroid
RT5880
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113
0.0 dB
-10.0 dB
-20.0 dB — IS111(Momentum)
— IS21I (Momentum)
— IS311 (Momentum)
— e !S111(measured)
— * |S211 (measured)
— « IS311 (measured)
-30.0 dB -
-40.0 dB
2.5
3.0
3.5
frequency (GHz)
4.5
5.0
Figure 6.14. The measured performance of a two-layer 3-line balun (Topol­
ogy B) designed by the procedure developed and comparison with a full-wave
simulation
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114
210.0
205.0
Measured, topology B
200.0
195.0
(•6sp) 10S /-I-3S /
190.0
185.0
180.0
170.0
165.0
160.0
155.0
150.0
1.0
1.5
2.0
3.5
2.5
3.0
frequency (GHz)
4.0
4.5
5.0
Figure 6.15. The measured phase imbalance of a two-layer 3-line balun de­
signed by the procedure developed
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115
Table 6.5: Summary of a two-layer 3-line balun performance (Topology A)
Ideal
M om entum
Center
frequency
(GHz)
3
2.86
n \s u \
< -10 dB)
(GHz)
2.67~3.33
2.26~3.45
IS21ICO
1^311(/)
I S 21 — z s 31
(dB)
-3.45~-3.01
-3.22~-2.48
(dB)
-3.45~-3.01
-4.44~-3.48
180°
169.6° ~ 173.5°
structures have been simulated on a full-wave EM simulator (Momentum).
S-parameters obtained from an EM simulation are compared with those for
an ‘ideal’ balun in Figure 6.10 and Figure 6.11. The performance of the ‘ideal’
balun is calculated using the desired NMPs and the phase velocities for the
three modes assumed to be equal. The phase imbalance (ZS2i — ZS31) is plot­
ted in Figure 6.12. The performances of simulation and measurement are
summarized along with an ideal response in Table 6.5 and Table 6 .6 . We note
th at for topology A, the center frequency is shifted to 2.86 GHz, the actual
transmission coefficients are in -4.44 - -2.48 dB range, the amplitude imbalance
at the balanced output ports is within 1.96 dB and the phase error is less than
10.4° over the frequency range of 2.26 - 3.45 GHz where |5 u | < -10 dB. For
topology B, the center frequency is shifted to 2.98 GHz, the actual transmis­
sion coefficients are in -4.44 - -2.56 dB range, the amplitude imbalance at the
balanced output ports is within 1.88 dB and phase error is only 0.2° over 2.14
- 3.78 GHz where |S n | < -10 dB. Thus we note that the topology B yields
simulated performance close to the ideal performance. Moreover, through sev­
eral simulations we find that the topology B allows 0.5 mm misalignment in
the metallizations on the two layers.
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116
Table 6.6: Summary of a two-layer 3-line balun performance (Topology B)
Ideal
M om entum
M easured
Center
frequency
(GHz)
3
2.98
3.08
f{\S n \
< -10 dB)
(GHz)
2.33~3.67
2.01~3.81
2.14~3.78
l& iK /)
\SM )
ZS21 —lS z\
(dB)
-3.46~-3.01
-3.78~-2.56
-4.31~-2.87
(dB)
-3.46~-3.01
-4.44~_2.98
-4.99~-2.69
180°
180° ~ 180.2°
180.3° ~ 184.1°
It may be noted that, as in other synthesis procedures at microwave
frequencies, procedure developed here does not take into account via induc­
tances, discontinuity reactances, difference in the phase velocities of 3 normal
modes, and dispersion in coupled lines. One needs to compensate for these
effects by an optimization of the initial design obtained. However, the method
developed provides an efficient tool for initial design.
A balun using topology B was fabricated on the Duroid RT5880 sub­
strate. The layout is shown in Figure 6.13 where the lines to the input and
the output ports are extended to locate connectors easily. Its performance is
measured and plotted in Figure 6.14 and Figure 6.15. As shown in Figure 6.14
and Figure 6.15, the design frequency is shifted to 3.10 GHz, |S n | is less than
-10 dB over 2.13 - 3.78 GHz. In this frequency range, the actual transmission
coefficients varies from -4.99 dB to -2.2 dB, the amplitude imbalance is within
2.12 dB and the phase error is less than 4.51°. These measurement results
agree fairly well with the simulation results. Some of the possible reasons for
lack of better agreement are : the air gap between two layers, the lead in­
ductance of vias used to connect ground and two layers, non-identical physical
lengths of the two extended output ports, misalignment between two substrates
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117
and inaccurate calibration process (because of input and output connections
at different levels).
6.4
Discussion
A design procedure for the three-line balun (using the design of two-
line couplers) has been presented.
The analytical procedure yields normal
mode parameters for the coupled lines. Physical dimensions are obtained by
optimization using a quasi-static analysis program. Alternatively an EM-ANN
(Electromagnetic Artificial Neural Network) model could be developed for this
procedure.
This method was verified by designing single-layer and two-layer 3line baluns. The single-layer version produces very narrow spacing between
three strips, therefore, two-layer versions (that provide more design flexibility)
have been implemented. A two-layer 3-line balun was fabricated and mea­
sured to verify the design procedure. Experimental results are compared to
those obtained from a full-wave EM simulation. This kind of balun showed a
good performance in spite of the use of imperfect fabrication facilities leading
to a misalignment between the two substrates. Thus, this design allows a con­
siderable flexibility in the design procedure and yields reasonable tolerances for
fabrication.
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CHAPTER 7
SUMMARY AND FUTURE WORK
7.1
Multilayer Microwave Circuit Design M ethodology
A systematic approach for establishing efficient design methodologies
of multilayer passive microwave circuits such as filters and baluns has been
presented in this thesis. The determination of design parameters, the synthesis
process, and the verification of the design comprise three parts for designing
these multilayer circuits. Various equivalent networks have been utilized to
derive the design equations for filters and baluns. Admittance inverter models
and transmission line models play a key role in building the design equations
for filters. Balun circuits have employed a design method used earlier for twocoupled line directional couplers for deriving the design equations. A multilayer
multi-conductor transmission line model provides a comer stone for analyzing
two-coupled lines and three-coupled lines to be used in setting up desired
normal mode parameters. An analysis from the circuit configurations to net­
work parameters (i.e. S-, Y -, Z - or ABCD-parameters) makes it possible to
establish these desired NMPs. These NMPs are then used as parameters to
be optimized in the synthesis process part. The synthesis process finds phys­
ical dimensions for circuits using an optimization algorithm. A quasi-static
field analysis program, (SBEM), has widely been used together with Simplex
method, a commonly used optimization algorithm, for parallel coupled-line
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119
filters and three-line baluns. End-coupled filters employed an ANN model for
optimizing physical geometry. Once the ANN models have been developed,
a large amount of time can be saved in finding physical parameters and in
simulating circuits on a commercial microwave simulator. For the third part
of the design methodology, a verification is needed using physical parameters
obtained from the synthesis process. A network simulation and a full-wave
electromagnetic simulation are available tools in computers for verifying the
developed design procedures. Experimental measurements have also been per­
formed to confirm these design procedures.
An important part of a whole design process is the optimization of
physical geometry. Two main potential problems in the optimization process
are: a possibility of stalling into local minima and a considerably large amount
of required CPU time. As shown in the design of end-coupled band-pass filters,
ANN models shorten the CPU time requirement and possibly avoid the local
minima which can arise with conventional optimization algorithms.
In summary, the general methodology th at have been developed generically in this thesis can be applicable to any circuits/components th at make
use of multilayer multiconductor transmission lines. For instance, directional
couplers, filters, planar baluns, spiral inductors and capacitors can be designed
using this methodology. However, as we examined in this thesis, every circuit
has its special features th at translate to specific design steps that are not con­
tained in the generic methodology. For parallel coupled-line filters, a special
procedure to obtain the desired NMPs from the filter specifications is needed.
Well known g - and J-param eters are used for this special purpose. For endcoupled band-pass filters, two design parameters other than NMPs are used
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120
for the desired design values to be optimized. For 3-line baluns, the design of
coupled-line couplers as an intermediate step to obtain the desired NMPs is
utilized. Research reported in this thesis brings out these specific design details
for these circuits.
7.2
M u ltila y e r M icrow ave C irc u it E x am p les
7.2.1
P a ra lle l C o u p le d -L in e B a n d -P a s s F ilte rs
A design
methodology has been developed to design multilayer parallel coupled-line
band-pass filters. The main purpose of using multilayer structure in this fil­
ter is to design filters with a wide bandwidth. Since tightly coupled lines are
necessary for a wide bandwidth, multilayer structure facilitate the physical lay­
out. Asymmetrical geometries for coupled lines are also employed to provide a
design flexibility in multilayer configurations.
Three different physical environments have been explored to realize
this class of filters. Those are homogeneous (stripline), inhomogeneous(microstrip
line), and CPW configurations. Because the homogeneous medium results in
equal phase velocities for all normal modes, explicit expressions have been de­
rived for the desired NMPs. In inhomogeneous media, phase velocities are
different for the different normal modes. In this case, one additional design
freedom for optimizing the physical geometry exists. The CPW configurations
can be implemented using design procedures for homogeneous and inhomoge­
neous cases.
Two design examples have been carried out for homogeneous filters
using 3 layers and 4 layers, respectively. For these filters (using 20 mil sub­
strates with er = 2.2), a 40 % bandwidth, 3 resonator configuration and 0.5 dB
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121
pass-band ripple level have been realized at the center frequency of 10 GHz. A
full-wave EM simulation has been performed over 2 - 1 8 GHz frequency range.
Both of these examples show a close agreement with the circuit specifications.
Also, two design examples have been carried out for inhomogeneous
filters using 3 layers and 5 layers, respectively. 50 % bandwidth, 3 resonators
and 0.5 dB pass-band ripple level were used as the specifications for 6 GHz
center frequency filters. The substrates used in homogeneous filters were also
utilized for inhomogeneous configurations. Designs were verified with full-wave
EM simulations and experimental measurements. The results over 1 - 1 1 GHz
frequency range have been shown to yield a good agreement with the filter
specifications.
The CPW configurations have also been used to create two different
topologies of filters. Both of examples have been performed using 3 layers to
realize 30 % bandwidth, 2 resonators, 0.5 dB pass-band ripple and 4 GHz
center frequency. These designs were verified by full-wave EM simulations
performed over 1 - 7 GHz range.
These design examples implemented in the three different environ­
ments for multilayer parallel coupled-line band-pass filters show th at the de­
sign methodologies developed axe valid for any kind of different physical config­
urations and those can be applied to other circuits employing parallel coupled
lines.
7.2.2
E n d -C o u p le d B a n d -P a s s F ilte rs
A systematic design
methodology has been developed to design multilayer end-coupled band-pass
filters. Since the single-layer end-coupled filters are not suitable for obtain­
ing a wide bandwidth, multilayer structures were employed to overcome this
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122
restriction in the bandwidth. These filters consist of gap coupled sections and
the half-wavelength transmission lines. A full-wave simulator has been used
to optimize the gap coupled section placed through multiple substrates. Since
this approach requires a large amount of CPU time to optimize physical ge­
ometry for each gap coupled section, an ANN model has been developed to
reduce the required CPU time. Once the ANN models are derived using the
simulation data from an EM simulator, the optimization of each gap coupled
section and even of the complete circuit is much faster than that performed
directly on an EM simulator. Only a small fraction of CPU time is necessary
to design this filter with ANN models.
Two design examples have been created using two substrate layers.
One is realized for 30 % bandwidth, 0.5 dB pass-band ripple level, 5 resonators,
and 3 GHz center frequency. The other is for 35 % bandwidth, 0.5 dB passband ripple level, 4 GHz center frequency, and 5 resonators. Both designs have
been carried out using 10 mil substrates with er = 2.2. Full-wave simulations
and measurements show a good agreement to the circuit specifications for both
cases.
One of two designs has been carried out by using ANN models de­
veloped. The simulation results from ANN models also show an agreement
to those designed using full-wave EM simulations without ANN models. The
ANN models can be applied to any other circuit designs that require a huge
amount of CPU time.
7.2.3
T h re e -L in e B alu n s
A methodology for designing two-
layer three-line baluns has been developed. This class of baluns are more com­
pact than the planar Marchand balun developed earlier. Single-layer three-line
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123
baluns presented a difficulty in obtaining reasonable spacing dimensions. The
two-layer three-line baluns developed here provide physically realizable geom­
etry and a design flexibility. Characterization of three-coupled lines are based
upon an analysis of two-coupled line directional couplers. Since 4 equations
are established for the 5 desired NMPs, an enhanced freedom in obtaining the
physical parameters is available.
Two design examples have been carried out using two layer substrates
of 20 mil and e = 2.2. Two different topologies have been investigated by plac­
ing the conducting strips differently. Full-wave simulations and measurements
were presented over 1.5 - 4.5 GHz frequency range. One design shows a better
performance than the other design. Thus, one can choose a topology leading
to a better design performance.
7.3
F u tu re W o rk
7.3.1
C o m p a c tio n o f F ilte rs
Various parallel coupled sections
in multilayer structures have been connected together in a straight forward
direction to implement circuit specifications. This kind of layout topology
does not provide compactness in comparison to the single-layer coupled-line
filters. More compaction could be obtained if the coupled sections on two
adjacent layers are connected bent at an angle as shown in Figure 7.1. Many
possibilities of selecting physical topology exist. The characterization of each
coupled section used in this thesis may be used for establishing the design
procedure for this circuit. A full-wave field analysis program needs to used for
analyzing modified parallel coupled sections.
Also, end-coupled filters can be made more compact by bending the
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124
OUT
layer 1
Figure 7.1. A possible layout of a more compact parallel coupled-line band­
pass filter
half-wavelength transmission lines or placing the gap coupled section at some
angle. For this circuit to work, a different characterization of bent transmission
lines and/or gap coupled sections with some angle needs to be performed.
More compact end-coupled band-pass filters could be obtained with this kind
of physical layout as shown in Figure 7.2. ANN models could alleviate the
complexity of designing modified physical layout.
m
out
layer 1
layer 4
layer 2
layer 3
Figure 7.2. A possible layout of a more compact end-coupled band-pass filter
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125
7.3.2
B alu n s
B a n d w id th C o n sid era tio n s in D esigning T h re e -L in e
Although two-layer three-line baluns provide more compact and
flexible design topology than the planar Marchand balun and single-layer
three-line baluns, one aspect that was not taken into account in developing
the design procedure is the bandwidth consideration. Since the bandwidth is
an important factor for balun design, a procedure for designing baluns with a
specified bandwidth needs to be investigated. In addition, cascaded three-line
baluns as shown in Figure 7.3 could be explored to see if these can yield a
wider bandwidth.
Figure 7.3: A possible layout of a cascaded three-line balun
7.3.3
O th e r M u ltilay er C irc u its
In this thesis, a methodol­
ogy has been developed for filters and balun circuits. In addition to filters
and baluns, many other potential applications of this methodology needs to be
explored for other multilayer circuits such as spiral inductors, capacitors and
couplers. Continued investigations of these circuits will be helpful in develop­
ment of systematic design procedures for multilayer circuit designs.
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eling a Three-Element Printed Dipole Antenna Array Using the FDTD
Technique,” IEEE Antennas and Propagation Society International Sym­
posium, pp. 1062-1065, 1997.
[83] Y.-D. Lin and S.-N. Tsai, “Coplanar Waveguide-fed Uniplanar Bow-Tie
Antenna,” IEEE Transactions on Antennas and Propagation, Vol. 45, No.
2, pp. 305-306, Feb. 1997.
[84] A. Nesic and S. Dragas, “Frequency Scanning Printed Array Antenna,”
IEEE Antennas and Propagation Society International Symposium, pp.
950-953, 1995.
[85] N. I. Dib, R. N. Simons, and L. P. B. Katehi, “New Uniplanar Transitions
for Circuit and Antenna,” IEEE Transactions on Microwave Theory and
Techniques, Vol. 43, No. 12, pp. 2868-2873, Dec. 1995.
[86] M. W. Numberger and J. L. Volakis, “A New Planar Feed for Slot Spiral
Antennas,” IEEE Transactions on Antennas and Propagation, Vol. 44,
No. 1, pp. 130-131, Jan. 1996.
[87] J. J. Van Tonder and J. K. Cloete, “A Study of an Archimedes Spiral
Antenna,” IEEE Antennas and Propagation Society International Sympo­
sium, pp. 1302-1305,1994.
[88] K. Tilley, X.-D. Wu, and K. Chang, “Dual Frequency Coplanar Strip
Dipole Antenna,” IEEE Antennas and Propagation Society International
Symposium, pp. 928-931, 1994.
[89] D. Hofer and V. K. Tripp, “A Low-Profiie, Broadband Baiun Feed,” IEEE
Antennas and Propagation Society International Symposium, pp. 458-461,
1993.
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[90] M.-Y. Li, K. Tilley, J. McCleary, and K. Chang, “Broadband Coplanar
Waveguide-Coplanar Strip-Fed Spiral Antenna,” Electronics Letters, Vol.
31, No. 1, pp. 4-5, Jan. 1995.
[91] S. A. Maas and Y. Ryu, “A Broadband, Planar, Monolithic Resistive
Frequency Doubler,” IEEE M T T -S International Microwave Symposium,
pp. 443-446, 1994.
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1633-1636, 1994.
[93] R. Bitzer, “Planar Broadband MIC Balanced Frequency Doubler,” IEEE
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[94] C. Cho and K. C. Gupta, “A New Design Procedure for Single-Layer
and Two-Layer 3-Line baluns,” IEEE M T T -S International Microwave
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Circuits,” IEEE Transactions on Microwave Theory and Techniques, Vol.
25, No. 9, pp. 726-7292, Sept. 1977.
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APPENDIX A
AN OPTIMIZATION OF PHYSICAL GEOMETRY USING “SIMPLEX”
ALGORITHM
A .l
Main function
This main function provides input/output interface for necessary pa­
rameters to optimize physical dimensions, and calls “Simplex” algorithm.
^*************************************************************
* Finding optimized values for w l, w2 and s *
* until the error function gets a minimum value *
* using an optimization or a minimization algorithm *
* (Amoeba) along with ”SBEM” software *
*************************************************************j
#inciude <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include ”nr.h”
#include ”nrutil.h”
#include ”sbem.h”
#define sqr(x) ((x)*(x))
#define LP 10
#define MP 4
#define NP 3
#define N 500
#define FTOL 1.0e-6
#define PI 3.141592654
int k=0;
char rs;
double func(double *);
double Rc, Rp, Zcl, Zpl, vpc, vpp;
double w l, w2, s;
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139
double k id , k2d, k3d;
/* ------------- (BEGIN MAIN)---------------------------------- */
int main (void)
{ int i, nfunc, j, ndim=NP;
int Ns, Ni;
double J, zOl, z02, bw, zOi, zOo, zOlp, z02p;
double *x, *y, **p;
double fO, lambda;
double initl, init2, init3;
FILE *fpo;
char *foname = "soptd.out”;
double g[13][13] = { { 0, 0, 0, 0, 0 },
{ 0, 0.6986, 1.0000 },
{ 0, 1.4029, 0.7071, 1.9841 },
{ 0, 1.5963, 1.0967, 1.5963,1.0000 },
{ 0, 1.6703, 1.1926, 2.3661, 0.8419, 1.9841 },
{ 0, 1.7058, 1.2296, 2.5408, 1.2296, 1.7058, 1.0000 },
{ 0, 1.7254, 1.2479, 2.6064,1.3137, 2.4758, 0.8696, 1.9841 },
{ 0, 1.7372, 1.2583, 2.6381,1.3444, 2.6381, 1.2583, 1.7372, 1.0000 },
{0, 1.7451, 1.2647, 2.6564, 1.3590, 2.6964, 1.3389, 2.5093, 0.8796, 1.9841 },
{0, 1.7504, 1.2690, 2.6678, 1.3673, 2.7239, 1.3673, 2.6678, 1.2690, 1.7504, 1.0000 },
{0, 1.7543, 1.2721, 2.6754, 1.3725, 2.7392, 1.3806, 2.7231, 1 3485, 2.5239, 0.8842,1.9841} };
printf(”*****************************************************\n”)'
printf(”* Finding the optimized values *\n”);
printf(”* of w l, w2 and s for Rc, Rp, Zcl and Zpl *\n”);
print.f(w*******************************
do { printf(”N = ”); scanf(”%i”, &Ns);
} while(Ns < = 0);
do { printf(”Which coupled section = ”); scanf(”%i”, &Ni);
} while(Ni < = 0 || Ni > Ns+1);
do { printf(”Band width = ”); scanf(”%lF, &bw);
} while(bw < = 0);
do { printf(”Z01 = ”); scanf(”%lF, &z01);
} while(z01 < 10 || zOl > 100);
do { printf(”Z02 = ”); scanf(”%lF, &z02);
} while(z02 < 10 || z02 > 100);
do { printf(”Is the actual geometry same as that of ‘sbem’?(y/n) ”);
scanf(”%s”, &rs);
} while(!(rs==’n’ || rs= = ’N’ || rs= = ’y’ || rs= = ’Y’));
if((fpo=fopen(foname, ”w”))==NULL) {
printf(”Unable to open %s for writing\n”, foname);
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exit(l); }
x = dvector(l,NP);
y = dvector(l,MP);
p = dmatrix(l,MP,l,NP);
if(N i==l) zOi = zOl;
if(Ni==Ns+l) zOo = z02;
zOlp = 2/z02; z02p = 2/z01;
if(N i==l) J = z0i/sqr(z01) *sqrt(PI*z01p*bw*z0i/(4*g[Ns][Ni]));
else if(Ni==Ns+l) J = l/z02*sqrt(PI*bw*z0o*z02p/(4*g[Ns][Ni-l] *g[Ns][Ni]));
else J = PI*bw/4 *sqrt(z02p*z01p/(g[Ns][Ni-l]*g[Ns][Ni]));
kid = J*z01+l/(J*z02);
k2d = J*z01*z02;
k3d = J*z02+l/(J*z01);
f0 = 6e9;
do { printf(”Initial values for (wl,w2,s) = ”);
scanf(”%lf %lf %lf”, &initl, &init2, &init3);
} while(initl <=0.0 || init2 <=0.0);
for(i=l; i<=MP; i+ + ) {
for(j=l; j<=NP; j+ + ) {
if (i= = l || i==j) p[i][j] = initl;
if (i= = (j+ l)) p[i][j] = fabs(init3);
if (i!=l && i==(j-l)) p[i][j] = init2;
if (i==0+2)) p[i][j] = init2;
if (i==(j+3)) p[i][j] = initl;
p[MP][NP] = init3;
x[j] = p[i][j];}
y[i] = func(x); }
amoeba(p, y, ndim, FTOL, func, &nfunc);
printf(”Outputs: w l w2 s Rc Rp Zcl Zpl Error\n”);
printf(”%14.6f %8.6f %8.6f %8.6e %8.6f %8.6e %8.6f %8.6f %%\n”,
wl,w2,s,Rc,Rp,Zcl,Zpl,y[MP]*100);
fprintf(fpo
fprintf(fpo,”* Inputs *\n”);
fprintf(fpo,”N = %i\n”, Ns);
fprintf(fpo,”Coupled section %i\n”, Ni);
fprintf(fpo,”J = %f\n”, J);
fprintf(fpo,”ZOl = %.2f\n”, zOl);
fprintf(fpo”Z02 = %.2f\n”, z02);
fprintf(fpo,”BW = %.2f %%\n”, bw*100);
fprintf(fpo
ft)rintf(fpo,”* Results *\n”);
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141
fprintf(fpo ”* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ) *
fprintf(fpo,”wl = %.6f\n”, wl);
fprintf(fpo,”w2 = %.6f\n”, w2);
fprintf(fpo,”s = %.6f\n”, s);
fprintf(fpo,"shift = %.6f\n”, wl/2+s-w2/2);
fprintf(fpo,”Rc = %.6e\n”, Rc);
fprintf(fpo,”Rp = %.6e\n”, Rp);
fprintf(fpo,”Zcl = %.6e\n”, Zcl);
fprintf(fpo,”Zpl = %.6e\n”, Zpl);
fprintf(fpo,”vpc = %e\n”, vpc);
fprintf(fpo,”vpp = %e\n”, vpp);
lambda = (vpc+vpp)/(2*f0);
fprintf(fpo,”Iambda/4 at %.0f GHz = %f mm\n”, f0/le9, lambda/4* le3);
fprintf(fpo,”Function value at the minimum point: %f %%\n”,y[MP]*100);
free.dmatrix(p, 1,MP, 1,NP);
free.dvector(y,l ,MP);
free.dvector (x, 1,NP);
printf(”Output written to %s\n”, foname);
fclose(fpo);
return 0;
}
A.2
Link to SBEM
This function computes the normal mode parameters using [C] matrix
returned by “SBEM” function.
/ * ------------- (func)--------------------------------- */
double func(double *x)
{ double val;
double LI, L2, Lm;
double Cl, C2, Cm;
double D, D l, D2;
double **C, **L;
double ms;
double kl, k2, k3;
C = dmatrix(l,MP,l,MP);
L = dmatrix(l,MP,l,MP);
w l = x[l];
w2 = x[2];
s = x[3];
if(wl<=0.0 || w2<=0.0 || s<0) { w l = fabs(wl);
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142
w2 = fabs(w2);
s = fabs(s); }
k++;
sbem(&wl, &w2, &s, C, L);
Cm = (C[l][2]+C[2][l])/2.0*le-12;
Lm = (L[l][2]+L[2][l])/2.0*le-9;
if(rs==’n’ || rs= = ’N’) {
C2 = C[l][l]*le-12;
Cl = C[2][2]*le-12;
L2 = L[l][l]*le-9;
LI = L[2][2]*le-9; }
else { Cl = C[l][l]*le-12;
C2 = C[2][2]*le-12;
LI = L[l][l]*le-9;
L2 = L[2][2]*le-9; }
D = sqr(L2*C2-Ll*Cl) + 4*(Lm*Cl+L2*Cm)*(Lm*C2+Ll*Cm);
D1 = Ll*Cl+L2*C2+2*Lm*CnH-sqrt(D);
D2 = Ll*Cl+L2*C2+2*Lm*Cm-sqrt(D);
if(D<0 || D 1<=0 || D2<=0) { printf(”Error in D, D1 or D2\n”);
val = k*10;
goto L20; }
Rc = (L2*C2-Ll*Cl+sqrt(D))/(2*(Lm*C2+Ll*Cm));
Rp = (L2*C2-Ll*Cl-sqrt(D))/(2*(Lm*C2+Ll*Cm));
vpc = sqrt(2)/sqrt(Ll*Cl+L2,,tC2+2*Lm*Cm+sqrt(D));
vpp = sqrt(2)/sqrt(Ll*Cl+L2*C2+2*Lm*Cm-sqrt(D));
Zcl = vpc*(Ll-Lm/Rp);
Zpl = vpp*(Ll-Lm/Rc);
kl = (Rp*Zcl-Rc*Zpl)/(Rc*Rp*(Zcl-Zpl));
k2 = Rc*Rp*(Zcl-Zpl)/(Rp-Rc);
k3 = (Rc*Zcl-Rp*Zpl)/(Zcl-Zpl);
veil = sqrt(sqr((kl-kld)/kld)+sqr((k2-k2d)/k2d)+sqr((k3-k3d)/k3d));
free_dmatrix(C,l,MP,l,MP);
free.dmatrix(L,l,MP,l,MP);
L20:
printf(”w l = %6.5f w2 = %6.5f s = %6.5f vpc = %4.2f vpp = %4.2f Err = %6.7f %% N =
%i\n”,
wl,w2,s,vpc/le8, vpp/le8, val* 100, k);
return val;
}
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143
A.3
“Simplex” function
This C code finds a minimization function based on “Simplex” algo­
rithm using the physical parameters passed from the Main function.
/ * ------------------ (Simplex Function)-------------------------*/
#include <math.h>
#define NMAX 5000
#define ALPHA 1.0
#define BETA 0.5
#define GAMMA 2.0
#define GET.PSUM for (j=ly<=ndimj+-l-) { for (i=l,sum=0.0;i<=mpts;i++)
sum + = p[i][j]; psum[j]=sum;}
void amoeba(p,y,ndim,ftol,funk,nfunk)
double **p,y[],ftol,(*funk)();
int ndim,*nfunk;
{ int ij,ilo,ihi,inhi,mpts=ndim-l-l;
double ytry,ysave,sum,rtol,tol, amotry(),*psum,*dvector();
void nrerror(),ffee.dvector();
psum=dvector( 1,ndim);
*nfiink=0;
GETJPSUM
for (;;) { ilo=l;
ihi = y[l]>y[2] ? (inhi=2,l) : (inhi=l,2);
for (i=l;i<=m pts;i++) {
if (y[i] < y[ilo]) ilo=i;
if (y[i] > y[ihi]) {
inhi=ihi;
ihi=i;
} else if (y[i] > y[inhi])
if (i != ihi) inhi=i; }
tol = fabs(y[ihi])<fabs(y[ilo])? fabs(y[ihi]):fabs(y[ilo]);
rtol=2.0*fabs(y[ihi]-y[ilo])/(fabs(y[ihi])+fabs(y[ilo]));
if (rtol < ftol || tol<ftol) break;
if (*nfunk > = NMAX) nrerror(”Too many iterations in AMOEBA”);
ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,-ALPHA);
if (ytry < = y[ilo])
ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,GAMMA);
else if (ytry > = y[inhi]) {
ysave=y[ihi];
ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,BETA);
if (ytry > = ysave) {
for (i=l;i<=m pts;i++) {
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
if (i != ilo) {
for (j=lj<=ndim ;j++) {
psum[j]=0.5*(p[i][j]+p[ilo][j]);
p[i][j]=psum[j]; }
y[i]=(*funk)(psum); } }
*nfunk + = ndim;
GET_PSUM } } }
free_dvector(psum, 1,ndim);
}
double amotry(p,y,psum,ndim,funk,ihi,nfunk,fac)
double **p,*y,*psum,(*funk)(),fac;
int ndim,ihi,*nfunk;
{ int j;
double facl,fac2,ytry,*ptry,*dvector();
void nrerrorQ ,free.dvector();
ptry=dvector (1 ,ndim);
facl=(1.0-fac)/ndim;
fac2=facl-fac;
for (j=ly<=ndim y++) ptry[j]=psum[j]*facl-p[ihi]p]*fac2;
ytry=(*funk)(ptry);
++(*nfunk);
if (ytry < y[ihi]) {
y[ihi]=ytry;
for (j=ly<=ndima+4-) {
psump] + = ptry [j]-p[ihi] [j];
P[ihi][j]=ptry[j]; } }
free_dvector(ptry, 1,ndim);
return ytry,
}
#undef ALPHA
#undef BETA
#undef GAMMA
#undef NMAX
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX B
DATA FLOW FROM EM-ANN MODELS TO HP-MDS
B .l
User-defined linear m odel
Instructions of how to integrate an EM-ANN model into HP-MDS is
given to help one create his or her own EM-ANN model library. This library
is linked to HP-MDS whenever it calls the user-defined model.
B.1.1 Creating and preparing a directory The purpose of
this step is to create and prepare a directory to copy necessary files onto for
user-compiled linear model development.
Example :
mkdir models
cd models
run /usr/...{system dependent path}.../hp85150/lib/mnsmodels/modelprepare
B .l. 2 Run the “makemod” This program will create a Ccode template for user’s own model. Several questions will be given to user
about the model to be developed.
B.1.3 Editing the C-code tem plate file The only function to
be modified is the “u_mode/name_eval()” . In this function, S- or Y-parameters
are calculated. In the following example, the “u_modeiname_eval” function calls
the feed-forward ANN function which is linked to the weight values from the
file “endgap_dat”.
J%
************************************************************************
* File: endgap.c
* Description: Model code for the user-compiled linear model: "enddgap”
* Created: 08 Oct 1998 11:37:59
* RCS: H ea d er:
************************************************************************
* The function ”ujendgap_eval()” is the function that
* calculates Y-parameters.
*
* The function ”u_endgap_query()” returns the value for
* ”read-only” parameters. (Non-read-only parameters are handled elsewhere.)
* If you do not have any "read-only” parameters, you do not need to modify
* this procedure.
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146
*
* The function ”u,endgap-dispose()” frees any memory
* allocated by u_endgap-eval().
*
************************************************************************
7
#define DEBUG 1 /* Define this to be zero to turn off
debugging. */
/* * usermodel.h includes stdio.h, math.h, string(s).h, ctype.h, sys/types.h,
* and malloc.h */
#include "usermodel.h”
#include <stdlib.h>
#include ”nnjsub-gap”
^***********************************************************************
* Here is a list of preprocessor macros which are used to access the
* parameters of this device: */
#define PARAM.wl 0
#define PARAM_w2 1
#define PARAM_g 2
#define PARAM_endgap_dat 3
static int u.endgap_eval();
static int u_endgap.query();
static void u_endgap_dispose();
^***********************************************************************
* The USER_PARAM data structure describes the parameters used by this
* device. */
static USER-PARAM u.endgap_params[| = {
{ "wl”, /* name */
NULL,
NULL,
DP-READABLE—IP-DIFFERENTIABLE—IP.SETTABLE—IP-MODIFIABLE— IP-REQUIRED,
REAL-TYPE,
0 .001 ,
0, /* default value if real or integer */
0, /* default imag value if complex */
/* default string if string (next line) */
NULL },
{ ”w2”, /* name */
NULL,
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147
NULL,
IP .READABLE—IP .DIFFERENTIABLE—IP .SETTABLE—IP .MODIFIABLE— IP-REQUIRED,
REAL.TYPE,
0 . 001 ,
0, /* default value if real or integer */
0, /* default imag value if complex */
/* default string if string (next line) */
NULL },
{ ”g”, /* name */
NULL,
NULL,
IP .READ ABLE—IP_DIFFERENTLABLE—IP.SETTABLE—IP-MODIFIABLE— IPJREQUIRED,
REAL.TYPE,
0 . 001 ,
0, /* default value if real or integer */
0, /* default imag value if complex */
/* default string if string (next line) */
NULL },
{ ”endgap-dat”, /* name */
NULL,
NULL,
IP .READABLE—IP .SETTABLE—IP-MODIFIABLE—IPJREQUIRED,
STRING-TYPE,
0,
0, I* default value if real or integer */
0, /* default imag value if complex */
/* default string if string (next line) */
NULL }
};
^***********************************************************************
* The USER_MODEL data structure describes the device, and any parameters
* used by it. */
USER-MODEL u.endgap = {
1,
”endgap”,
NULL,
2,
u-endgap.params,
sizeof(u.endgap.params) / sizeof(USER_PARAM),
MODEL-EVALUATES.Y,
u-endgapjeval,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
u.endgap.query,
u-endgap.dispose
};
^***********************************************************************
* u.endgap.eval() calculates Y-parameters. This is the
* main model evaluation routine. */
static int u.endgap_eval(Name, Flags, Omega, Matrix, NumberOfPorts,
Parameters, Substrate, SavedData)
char *Name;
int Flags;
RealNumber Omega;
ComplexNumber *Matrix;
int NumberOfPorts;
USERJDATA *Parameters;
struct SubstrateModelData *Substrate;
void **SavedData;
|
y ******************************************************************J
* Add code to calculate Y-parameters here.
y******************************************************************
J
double I[10],O[10],pi,wl, w2, g,freq;
ComplexNumber param;
char ctmp[50];
pi=3.14159265358973;
wl=UGETJlEAL-VALUE(Parameters[PARAM-wl]);
w2=UGETJREAL_VALUE(Parameters[PARAM.w2]);
g=UGET_REAL_VALUE(Parameters[PARAM.g]);
freq=Omega/ (2.0*pi*1.0e9);
l[0]=wl;
I[l]=w2;
I[2]=g;
I[3]=freq;
strcpy(ctmp,UGET^TRING-VALUE(ParametersfPARAMjendgap.dat]));
neuraljiet_gap(l,0,ctmp);
/* param.Real=50.0;
param.lmag=0.0;
CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 1), param);
CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 2), param);*/
param.Real=O[0];
param.lmag=0[l];
CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,1), param);
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
param.Real=0 [2];
param.Imag=0[3];
CMPLX.ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,2), param);
CMPLX-ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 2,1), param);
param.Real=0 [4];
param.Imag=0[5];
CMPLX_ASSIGN(MATRIXlJELEMENT(Matrbc, NumberOfPorts, 2,2), param);
return (YES);
}
^***********************************************************************
* u.endgap_query() is used only if "read-only” parameters exist. If this
* model does not have any ’’read-only” parameters, this routine does not have
* to be modified. If there are "read-only” parameters, you must modify this
* procedure to return the value of the "read-only” parameter. */
static int u_endgap.query(ParameterID, NumberOfPorts, Parameters, Substrate,
SavedData, Value)
int ParameterID;
int NumberOfPorts;
USERJDATA *Parameters;
struct SubstrateModelData ^Substrate;
void **SavedData;
USERJDATA *Value;
{ /* Initialization */
USETJDATA_TYPE(* Value, UNKNOWN.TYPE); /* leave this alone! */
/* * To the following switch statement, add case statements to extract
* the value of read-only parameters (if any - if there aren’t any,
* just leave this procedure alone). */
switch (Parameter®) {
default:
/* * If this is parameter is not handled by this routine, just
* exit. */
break; }
return (YES);
}
* u.endgap.dispose() is used to free memory that was allocated and stored
* on the "saved.data” parameter of the u_endgapjeval() function.
* If you do not use the ”saved.data” parameter of u_endgap.eval(), you
* do not need to modify this routine. * */
static void u.endgap.dispose(SavedData)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
void **SavedData;
{ if (*SavedData) {
/* * Free any additional data here. */
free(*SavedData); } }
/* * Local Variables:
* c-indent-level: 4
* c-continued-statement-offset: 4
* c-brace-offset: -4
* c-argdecl-indent: 0
* c-label-offset: -4
* End: */
B.2
The feed-forward A N N function
neural .net.gap (1,0 ,ctmp)
double I[10],0[10];
char ctmp[50];
{ int ij,k,r,c,l;
double minmax[21][2], wl[50][ll],w2[10][51],IN[ll];
double sum, net[50],f[51],net2[10],ON[10];
float x;
FILE *fpt;
/* Read input file*/
fpt=fopen(ctmp,”r”);
fscanf(fpt,” %d%d%d:’,&i,&k,&j);
for(r=0;r<i+k;++r) {
for(c=0;c<2;-f+c){
fscanf(fpt,” %e”,&x);
minmax[r] [c]=x;}}
for(r=0;r<j;+-i-r){
for(c=0;c<=i;++c){
fscanf(fpt,”%e”,&x);
wl[r][c]=x;}}
for(r=0;r<k;-t-+r) {
for(c=0;c<=j;++c){
fscanf(fpt,”%e”,&x);
w2[r][c]=x;}}
fclose(fpt);
/* Normalize Inputs between 0 and 1 */
IN[0]=1.0;
for(r=k;r<i-t-k;++r){
IN[r-k+1]=(I[r-k]-minmax[r] [0]) / (minmax[r] [l]-minmax[r] [0]);}
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
/* Multiply normalized inputs by first set of weights and sigmoid*/
f[0]=1.0;
for(r=0;r<j;++r){
sum=0.0;
for(c=0;c<=i;++c){
sum=sum+wl[r][c]*IN[c];}
net[r]=sum;
f[r+1]=1.0/ (1.0+exp(-net [r]));}
/* Multiply by second set of weights, Sigmoid, denormalize */
for(r=0;r<k;++r){ sum=0.0;
for(c=0;c< =j;++c) { sum=sum+w2[r] [c]*f[c];}
net2[r]=sum;
ON[r]=1.0/(1.0+exp(-net2[r]));
0[r]=((ON[r]-0.2)*(minmax[r][l]-minmax[r][0])/0.6)+minmax[r][0];}
}
B.3
An EM -A N N weight file
4 /* number of inputs */
6 /* number of outputs */
12 /* number of neurons in the hidden layer */
/* Max and Min values for the outputs */
7.974182e-07 3.704246e-04
8.132715e-04 4.239201e-02
-2.674593e-04 -7.694745e-07
4.384907e-04 3.057494e-02
8.945518e-07 2.607813e-04
9.052016e-04 5.294224e-02
8.000000e-014.200000e+00
4.000000e-01 2.000000e+00
1.000000e+00 4.000000e+00
1.500000e+00 4.500000e+00
/* The weights between the input and the hidden layer */
-2.936455e+00 3.038668e-01 7.041506e-01 1.238946e+00 6.709919e-01
-3.292541e-01 -1.433612e-01 -2.736312e-02 -9.260146e-01 -2.899395e-01
-2.886026e+00 5.198771e-01 -2.793950e-02 1.342801e+00 -4.452597e-01
-7.513946e+00 -4.724797e+00 2.844372e+00 1.828593e+00 2.468859e+00
-2.738880e+00 -4.925343e-02 -2.290847e-01 -3.586707e-01 -4.73001 le-01
-4.998860e+00 8.719739e-01 9.786560e-01 -1.240659e-01 2.165266e+00
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
1.173558e+01 9.464445e-02 -2.368811e+00 -3.73115tJe+00 -5.036164e+00
-5.500352e+00 1.296099e+00 -2.421762e-01 1.393999e+00 2.269715e+00
-2.895616e+00-3.112258e-01 5.363251e-01 1.253820e+00 -7.669684e-01
-3.455950e+00-9.192074e-01 1.131245e-01 9.544331e-01 1.661224e+00
-3.356013e+00 5.031830e-02 -1.454407e+00 1.159295e+00 1.390404e+00
4.017048e+00 -2.575329e-01 -8.039668e-01 -2.025872e+00 -2.201498e+00
/* The weights between the hidden and the output layer */
3.859342e+00 -2.745112e+00 -1.360446e+00 -1.746495e+00 -1.639044e+00
-1.552682e+00 1.312729e+00 -3.075470e+00 4.647749e+00 1.823731e+00
-1.892173e+00 -9.283437e-01 -1.331090e+00
3.851617e+00 1.410064e+00 -2.662861e+00 -7.582046e-01 -2.033446e+00
-2.386133e+00 -2.099265e+00 -2.327482e+00 2.026903e+00 -3.300690e+00
-3.055536e+00 -7.966869e-01 -1.451613e+00
-5.967424e+00 1.318110e+00 8.776059e-01 1.013951e+00 2.540218e+00
1.592350e+00 -9.007094e-01 4.992166e+00 -3.339734e-01 5.225501e-02
1.123291e+00 1.209594e+00 1.739809e+00
6.247129e+00 1.108459e+00 -1.782773e+00 -1.905597e+00 -3.701628e+00
-1.621191e-l-00 -1.998428e+00 -4.297600e+00 -1.419235e+00 -1.271881e+00
-1.145129e+00 -2.169320e+00 -2.319211e+00
7.034432e+00 -1.498197e+00 -1.378570e+00 -8.561791e-01 -1.333040e+00
-7.732884e-01 1.596873e-01 -5.521996e+00 -1.639091e+00 -4.638169e-01
-7.809489e-01 -1.365040e+00 -2.112312e+00
5.269771e+00 1.695510e+00 -2.380372e+00 -2.916158e+00 -1.494385e+00
-1.817080e+00 -2.322940e+00 -3.380170e+00 -8.619703e-01 -8.335024e-01
-7.763543e-01 -2.818443e+00 -1.993454e+00
B.4
Compiling and linking the model
Now add the name of the model file after “CFILES = ” in the Makefile
and run “make”. A new simulator file “mns” is created. Obtain the permission
from user’s system administrator to move the file “mns” into .../mns800.
B.5
Read design icons file into MDS
To use the newly installed models, the design icons file must be read
into MDS. One way to do this is to copy an existing design icon and to modify
it for user’s needs. The symbol and the scion page are mainly modified based
on the user’s intention. Finally execute “perform/add to menu” and one can
use his or her own model as other MDS model to create circuits by executing
“insert/component/u ser modeV.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B.6
N otes on m odel usage
Within MDS model :
(1) All inputs for W \, W 2 , G, I are in mm.
(2) Input correct path to ANN model file names.
(Ex. ‘usr/ferrari2/student/ choc/annmodel/ endgap_dat’)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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