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Artificial neural network modeling for computer-aided design of microwave and millimeter-wave circuits

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ARTIFICIAL NEURAL NETWORK M ODELING FOR COMPUTER-AIDED
DESIGN O F MICROWAVE AND M ILLIM ETER-W AVE CIRCUITS
by
PAUL MARTIN W ATSON
B.S., University o f Utah, 1991
M.Eng., University o f Utah, 1993
A thesis subm itted to the
Faculty of the Graduate School o f the
University of Colorado in partial fulfillment
o f the requirements for the degree of
Doctor of Philosophy
Department of Electrical and Com puter Engineering
1998
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This thesis for the Doctor o f Philosophy degree by
Paul Martin W atson
has been approved for the
Department o f
Electrical and Computer Engineering
By
K.C. Gupta
regory L. Creech
Date O & .-0
2.
The final copy of this thesis has been exam ined by the
signators, and we find that both the content and the form
meet acceptable presentation standards o f scholarly work in
the above mentioned discipline.
|
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Watson, Paul M artin (Ph.D. Electrical Engineering)
Artificial N eural Network Modeling for Computer-Aided Design o f Microwave and
M illimeter-W ave Circuits
Thesis directed by Professor K.C. Gupta
A
novel
approach
for
accurate
and
efficient
modeling
of
passive
microwave/mm-wave components by using electromagnetically-trained artificial
neural netw ork (EM-ANN) software modules is presented. Artificial neural networks
are employed to model complex relationships between physical parameters of a
component and the corresponding electrical response.
Full-wave EM analysis is
employed to characterize passive components. Structures for simulation are chosen
using design o f experiments (DOE) methodology.
Analysis EM-ANN models are
then trained using physical parameters as inputs and component response (i.e. Sparameters) as outputs.
In addition, synthesis models can be developed by
interchanging the inputs and outputs used for component characterization. Methods
for incorporation o f prior knowledge (existing models) for model development have
been explored. It has been dem onstrated that use of prior knowledge (when it exists)
reduces the num ber of EM simulations that are needed to characterize the component
to be modeled. Once trained, the EM -ANN models can be inserted into a commercial
microwave circuit simulator where they provide results approaching the accuracy of
the EM simulation tool used for characterization of the microwave/mm-wave
components without increasing the analysis time significantly.
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The proposed
iv
technique is capable of providing models for simulation and optimization o f
microwave/mm-wave components where models do not exist or are not accurate over
the desired region o f operation.
EM-ANN modeling o f microstrip vias and multilayer interconnects is
demonstrated.
An example of using EM-ANN models to optimize component
geometry is included for a stripline-to-stripline multilayer interconnect.
A
methodology for the synthesis (leading to physical dimensions) of multilayer
asymmetric coupled microstrip lines using ANN models is presented. Both synthesis
and analysis models have been developed. Models are appropriate for synthesis o f
multilayer structures like filters, baluns, and directional couplers.
EM-ANN
modeling has also been used for generating a library of component models for CPW
circuit design. Design and optimization o f a CPW folded double stub filter and a 50
Q, 3 dB power divider circuit, using the developed CPW EM-ANN models, has been
demonstrated.
Research has also been conducted on novel CPW patch antennas.
Using EM-ANN modeling techniques, a wide bandwidth CPW patch antenna has
been designed and validated by both EM simulation and measurements. A discussion
of these results and ideas for future research are presented.
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V
ACKNOWLEGEMENT
I would like to thank all o f those individuals who helped to make this
dissertation possible. I wish to thank Dr. K.C. Gupta, the dissertation advisor, for his
continued support, encouragement, and guidance.
Also, I thank Dr. Roop L.
Mahajan, Dr. Gregory L. Creech, and Manish Marwah for many helpful discussions
on artificial neural network techniques. I am grateful for the assistance provided by
Dr. Tom Jones, Mark Calcaterra, and Alan Tewksbury o f W right-Patterson Air Force
base in dealing with the Palace Knight program. I thank Dr. Melinda Piket-May and
Dr. Zoya Popovic for serving on my committee.
I wish to express my deepest gratitude to my wife, Mamie, for her continuing
love, support, and devotion without which none o f this work would have been
possible. Finally, I thank my children, Shea, Keegan, and Cloe for making my life
brighter when I get home.
ii
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TABLE OF CONTENTS
CHAPTER
1
INTRODUCTION...................................................................................................... 1
1.1
1.2
2
M otivation....................................................................................................... 1
1.1.1
M odeling for C A D ...........................................................................1
1.1.2
Artificial Neural Network M odels................................................4
Organization o f the T h esis...........................................................................5
INTRODUCTION TO MULTILAYER, FEED-FORWARD ARTIFICIAL
NEURAL N ETW O R K S.......................................................................................8
2 .1
ANN T opology................................................................................................9
2.2
ANN M odel Development (Training)........................................................12
2.2.1
Data Preprocessing........................................................................ 14
2.2.2
Error Back-Propagation.................................................................14
2.2.3
Error Functions...............................................................................16
2.2.4
2.3
3
2.2.3.1
Absolute Error............................................................. 16
2.2.3.2
Relative Error.............................................................. 17
Learning R u le s...............................................................................18
Model Generalization and O verfitting...................................................... 19
MODELING M E T H O D O LO G Y ......................................................................... 20
3.1
Selection o f Training Data by Design of Experiments (DOE)
T echniques................................................................................................. 20
3.2
ANN Training M ethodology......................................................................25
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3.3
4
5
6
3.2.1
Data P re-Processing.......................................................................25
3.2.2
Simultaneous Training and Testing.............................................. 26
Use o f Prior K now ledge.............................................................................. 27
ANN M ODELS FOR MICROWAVE/MILLIMETER-WAVE DESIGN.... 32
4.1
Selection o f Model Inputs and Outputs......................................................32
4.2
Training Data G eneration............................................................................ 33
4.3
Error M easures.............................................................................................. 34
4.4
Integration o f EM -ANN Models with CircuitS im ulators.......................35
4.5
Design and Optimization Using EM-ANN M odels................................ 37
EM-ANN M ODELS FOR VIAS AND MULTILAYER
IN TER C O N N EC TS............................................................................................... 38
5 .1
M icrostrip Transmission Line Model......................................................... 39
5.2
Broadband GaAs 1-port Microstrip V ia.................................................... 42
5.3
Broadband GaAs 2-port Microstrip V ia.................................................... 43
5.4
Stripline-to-Stripline Multilayer Interconnect...........................................45
5.5
M icrostrip-to-M icrostrip Multilayer Interconnect.................................. 47
5.6
Model Development Using Prior Knowledge...........................................49
5.6.1
Two-Port Broadband GaAs Microstrip Ground V ia .................49
5.6.2
Stripline-to-Stripline Multilayer Interconnect: Frequency
Range Extension............................................................................. 53
5.7
Integration o f EM -ANN Models with a Network Sim ulator.................57
5.8
Optimization o f Component Structure.......................................................59
M ULTICONDUCTOR MULTILAYER COUPLED TRANSM ISSION
LINE DESIGN USING ANN MODELS ...........................................................60
6.1
Synthesis of Asymmetrical Multilayer Coupled Line Sections............ 62
t
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6.2
6.3
6.4
7
ANN Modeling Methodology for M ultilayer Asymmetric Coupled
Lines ........................................................................................................... 64
6 .2 .1
Analysis Model............................................................................... 65
6.2.2
Synthesis M odel.............................................................................67
M ultilayer Filter Design using ANN M odels...........................................70
6.3.1
ANN Model Development for Coupled Line S ectio n s............71
6.3.2
Design Example: 2-Layer Coupled Line Filter........................ 74
6.3.3
Comparison o f 2-Layer Filter Design Using ANN M ethod
and Optimization M ethod.............................................................. 78
D iscussion..................................................................................................... 80
DESIGN AND OPTIMIZATION OF CPW CIRCUITS USING EM ANN
MODELS FOR CPW CO M PO N EN TS.............................................................. 82
7.1
EM-ANN Modeling of Chamfered CPW 90° Bends.............................. 84
7.1.1
Optimally Chamfered Conventional CPW B end......................86
7.1.2
Novel Compensated CPW B en d ................................................. 88
7.1.3
CPW Bend Comparisons.............................................................. 89
7.1.4
CPW 90° Bend with Air-Bridge Height as an Input
Parameter ........................................................................................91
7.2
EM-ANN Modeling o f CPW Transmission Lines.................................. 94
7.3
EM-ANN Models for CPW Opens and S h o rts....................................... 95
7.4
EM-ANN Modeling o f CPW Step-in-W idth...........................................97
7.5
EM-ANN Modeling of CPW Symmetric T-junctions.......................... 100
7.6
CPW Circuit Design Exam ples................................................................ 102
7.7
7.6.1
CPW Folded Double-Stub F ilter............................................... 102
7.6.2
CPW 50 Q, 3 dB Power D ivider............................................... 106
D iscussion................................................................................................... 110
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8
EM-ANN MODELS FOR DESIGN OF CPW PATCH A N TEN N A S
8.1
8.2
8.3
8.4
9
112
Radiation Characteristics o f CPW Line and Open E n d ....................... 113
8.1.1
Radiation from a Wide CPW L in e.............................................. 113
8.1.2
Radiation from CPW O pen-Ends................................................ 113
Transmission Line Equivalent o f a Rectangular CPW Patch............... 119
8.2.1
Transmission Line Model for CPW Antennas......................... 119
8.2.2
EM-ANN Model for CPW Transmission L in e..........................120
8.2.3
EM-ANN Model for CPW Open-End E ffects.......................... 122
8.2.4
CPW Patch Antenna Design Without Including Feed
Effects
......................................................................................127
CPW Patch Antenna Design Including Feed Discontinuities.............. 128
8.3.1
EM-ANN Model for Feed Discontinuities................................129
8.3.2
CPW Patch Antenna Design Using EM-ANN M o d els.......... 130
8.3.3
CPW Patch Antenna Design Optimization Using EM -ANN
Models
......................................................................................134
D iscussion.................................................................................................... 139
SUMMARY AND FUTURE W O R K .................................................................140
9.1
EM-ANN Modeling Methodology............................................................140
9.2
EM-ANN Modeling Examples.................................................................. 142
9.3
9.2.1
Microstrip Vias and Multilayer Interconnects.......................... 142
9.2.2
Multiconductor Multilayer Coupled Transmission Line
Models
......................................................................................143
9.2.3
EM-ANN Models for CPW Com ponents................................. 144
9.2.4
EM-ANN Models for Design o f CPW Patch A ntennas
145
Future W o rk ................................................................................................145
9.3.1
Nonlinear Active Device M odeling.......................................... 145
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9.3.2
ANN Model Development for Passive Components using
Measured Data................................................................................146
9.3.3
CPW Patch Antenna....................................................................... 146
9.3.4
ANN o f Complete Circuit M o d u les............................................146
9.3.5
Synthesis o f Com ponents.............................................................. 147
BIBLIOGRAPHY.................................................................................................................148
APPENDIX A ........................................................................................................................159
A. 1 User-Defined Linear Model Subroutine...................................................159
A.2 Feed-Forward ANN Subroutine................................................................ 165
A.3 Sample EM-ANN Model Input F ile ......................................................... 167
APPENDIX B
USER-DEFINED LINEAR M ODEL LIBRARY FOR CPW
COMPONENTS.............................................................................168
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LIST OF FIGURES
FIGURE
2.1
Artificial neural network architecture........................................................ 10
2.2
Logistic activation function used in hidden layer and output layer
neurons............................................................................................................13
3.1
DOE 2k factorial design............................................................................... 23
3.2
DOE central composite design................................................................... 24
3.3
Modified DOE central composite design..................................................24
3.4
Modified DOE central composite design with additional interior
points.............................................................................................................. 25
3.5
Schemes for using prior knowledge (existing models) for artificial
neural network training, (a) difference method and (b) PKI method. 31
4.1
R ow of data for linking EM-ANN models to commercial microwave
circuit simulators..........................................................................................36
5.1
Cross-section o f microstrip transmission line geometry where W)
is the width o f the microstrip line, Hsub is the substrate height, and
er is the relative dielectric constant o f the substrate................................40
5.2
GaAs microstrip ground via geometry. Substrate thickness = 4
mil, £t=12.9, tan5=0.002, crmetai=4.1xl07, and tmetai=0.1 mil.................42
5.3
Two-port GaAs microstrip grounding via. Substrate thickness = 4
mil, £r=12.9, tan8=0.002, CmetaF^-lxlO7, and tmemi = 0.1 m il............... 44
5.4
Stripline-to-stripline interconnect structure with W|ine= 13.675 mil,
Zo = 50 ohms, £,= 2.94, tanS = 0.0012, tmetai= 1.4 mil, cy^ai =
5.7xl07, and H = 20 mil.............................................................................. 46
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5.5
Microstrip-to-Microstrip interconnect with Zo = 50 ohms, Wbol =
23 mil, W Iop = 125 mil, grl = 10.2, er2 = 2.2, tan5 = 0.0012, tmetal =
1.4 mil, CTmetai = 5.7x 107, and H = 25 mil...............................................47
5.6
Comparison o f EM-ANN model (NET1), HP-Momentum (HPMOM), HP-MDS via elem ent (msvia), and MSVIA with added
components (msvia + comp). GaAs via with er= 12.9, HSUb= 4 mil,
tmeupo.l mil, a metai=4.lx 107, tan5 = 0.002, W|/Wp= 0.3875,
Dvia/Wp =0.4, and W,/Hsllb = 0.3375.......................................................... 58
6.1
Example of a multiconductor multilayer coupled line geometries in
an inhomogeneous medium. Both layer-to-layer and same layer
coupling sections are shown...................................................................... 63
6.2
Procedure for the design o f asymmetric multilayer coupled line
sections using optimization [80]............................................................... 63
6.3
Analysis ANN model for asymmetric multilayer coupled line
sections.......................................................................................................... 66
6.4
Synthesis ANN model for asymmetric multilayer coupled line
sections.......................................................................................................... 66
6.5
Modified synthesis procedure for asymmetric multilayer coupled
line sections using ANN models in place o f optimization.................... 69
6.6
Top view of a 2-layer coupled line filter consisting of 3 coupled
line sections. Sections I and 3 couple from layer 1 to layer 2 and
section 2 couples from layer 1 to layer 1. Input and output ports
are on the top o f layer 2.............................................................................. 70
6.7
Two-layer filter response. Both ANN modeled (light solid lines)
and SBEM (dark dashed lines) results are shown...................................76
6.8
Two-layer filter response. Both ANN modeled (light solid lines)
and SBEM (dark dashed lines) results are shown...................................78
7.1
CPW 90° bend structures with Wa = 40 pm, Ha = 3pm, Hsub = 625
pm, £r = 12.9, and tanS = 0.0005. (a) Conventional chamfered
bend and (b) novel compensated bend (Ha is height o f air-bridge
above the substrate, Wa is the width of the air-bridge, and Hsub is
the substrate thickness.).............................................................................. 85
7.2
Optimal chamfer for return loss versus W/G for the conventional
CPW 90° bend. (Fig. 7. la .) ....................................................................... 88
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7.3
Com parison o f unchamfered (Comer), conventional (Opt. Chamf.),
and novel (Comp. Bend) CPW bends. W = 70 pm, G=20 pm,
8r=12.9, and Hsub=625 pm ...........................................................................90
7.4
CPW short circuit geometry........................................................................ 95
7.5
CPW open circuit geometry.........................................................................96
7.6
S-param eter response for CPW open and short circuits. W = 70
pm, G = 60 pm, and reference planes at the discontinuities................. 96
7.7
CPW step-in-width geometry....................................................................... 98
7.8
S-param eter response for a 71 Q. to 50 O CPW step-in-width
transition. W[ = 20 pm, W2 = 70 pm , G = 60 pm, and reference
planes at the discontinuity........................................................................... 99
7.9
CPW symmetric T-junction geom etry..................................................... 100
7.10
S-param eter response for a typical CPW symmetric T-junction.
W in = W out = 70 pm, Gin = Gout = 60 pm , and reference planes
at the air-bridge locations.......................................................................... 101
7.11
CPW folded double-stub filter geom etry................................................ 103
7.12(a)
Sii for CPW folded double-stub filter for the optimized EM-ANN
circuit (EM -ANN Opt.), the original EM -ANN circuit (EM-ANN
Org.), and EM simulation (EM sim .).......................................................104
7.12(b)
S 21 for CPW folded double-stub filter for the optimized EM-ANN
circuit (EM-ANN Opt.), the original EM -ANN circuit (EM-ANN
Org.), and EM simulation (EM sim .).......................................................105
7.13
CPW pow er divider geometry.................................................................... 107
7 .14(a)
S 11 for C PW power divider for the optimized EM-ANN circuit
(EM -ANN Opt.), the original EM -ANN circuit (EM-ANN Org.),
and EM simulation (EM sim.).................................................................. 108
7 .14(b)
S 21 for CPW power divider for the optim ized EM-ANN circuit
(EM -ANN Opt.), the original EM -ANN circuit (EM-ANN Org.),
and EM simulation (EM sim.).................................................................. 109
8.1
Open-end CPW geometry........................................................................... 114
8.2
Sim ulated radiation patterns (Ee and E^) o f a CPW line (W=1.5
cm, G=0.01 cm, L=3 cm and f = 5 GHz) without an open end. The
plane o f the pattern is perpendicular to the gaps (<J>= 90°)..................114
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8.3
Far-Field radiation patterns (Ee and E^) at 5 GHz for two openended CPW s with W = 1.5 cm, L=3 cm , Gend = 0.85 cm, and
different gap widths (<j) = 90°). (a) G = 0.5 cm and (b) G = 0.01
cm...................................................................................................................115
8.4
Far-Field radiation patterns (<j> = 90°) at 5 G H z for two open-ended
CPW s with G = 0.05 cm, Gend = 0.85 cm , L=3 cm, and different
conductor widths (W). (a) W = 1.5 cm and (b) W = 2.0 cm............ 117
8.5
M agnetic current distributions for two CPW open-ends with W =
1.5 cm , Gend = 0.85 cm, L=3 cm, and different gap widths at 5
GHz. (a) G = 0.5 cm and (b) G = 0.1 cm ............................................. 118
8.6
Ideal C PW patch antenna geometry and corresponding
transmission line equivalent circuit m odel............................................. 119
8.7
Typical trends for Zo and p (phase constant) with (a) f = 5 GHz, G
= 0.05 cm , and W variable, (b) f = 5 G Hz, W = 1.5 cm, and G
variable, and (c ) W = 1.5 cm, G = 0.05 cm, and frequency
variable......................................................................................................... 121
8.8
Trends o f the radiation conductance, G r, and capacitance, C, for a
CPW open-end with Gend=0.85 cm at 5 GHz. (a) G variable and
W=1.5 cm . (b) W variable and G=0.05 cm ..........................................125
8.9
Trends o f the radiation conductance, G r, and capacitance, C, for a
CPW open-end with Gend=0.8 cm versus frequency, (a)W=1.5
cm and G=0.05 cm. (b) W =i cm and G =0.05 cm ................................126
8.10
CPW patch fed on the radiating edge and its corresponding
transm ission line model............................................................................. 129
8.11
Layout o f CPW patch antenna design. Electrical parameters
referenced to the resonant frequency o f 4.99 G H z............................... 131
8.12
Comparison o f return loss for the CPW patch antenna shown in
Fig. 8.11........................................................................................................132
8.13
Far field radiation patterns for the antenna shown in Fig. 8.11. (a)
E-plane (<|) = 0°) and (b) H-plane (<|> = 90°)............................................. 133
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XV
8.14
Effects of radiating edge feed section and line on CPW patch
antenna (W=1.5 cm G=0.1 cm and Gend=0-85 cm) S 1 1 response.
(Al) Ideal patch with no feed (Lpaich= 1-6465 cm). (Bl) Addition
o f feed section. (Cl) Addition o f incoming feed line..........................135
8.15
Effects of increasing the patch length (Lpa(ch=1.937 cm). (Al: La=0
cm and B 1: La=3.4 c m .)......................................................................... 135
8.16
Layout for CPW patch antenna with longer than ideal patch length.
All dimensions are in cm. Electrical parameters referenced to the
resonant frequency of 5.56 GHz.............................................................. 137
8.17
Comparison o f return loss for the longer than ideal patch length
CPW patch antenna....................................................................................137
8.18
Far field radiation patterns, measured and EM simulation, (a) Eplane (tj) = 0°). Only E_theta is shown due to antenna damage
during measurement, (b) H-plane (<j> =90°)...........................................138
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LIST OF TABLES
TABLE
5.1
Variable input parameters for microstrip transmission line model.............. 40
5.2
Error results (average and standard deviation) between the EM-ANN
model and linecalc for the
m icrostrip transmission line for absolute
error training.....................................................................................................41
5.3
Error results (average and standard deviation) between the EM-ANN
model and linecalc for the m icrostrip transmission line for relative
error training.....................................................................................................41
5.4
Variable input parameters for GaAs microstrip ground via modeling........ 42
5.5
Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the 1-port microstrip via............................... 43
5.6
Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the 2-port microstrip via............................... 44
5.7
Variable parameters for stripline-to-stripline multilayer interconnect
m odel....................................................................................................................46
5.8
Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the stripline-to-stripline multilayer
interconnect......................................................................................................... 46
5.9
Variable parameters for microstrip-to-microstrip interconnect m odel........ 48
5.10 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the microstrip-to-microstrip multilayer
interconnect......................................................................................................... 48
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5.11
Error results for the 2-port microstrip via using regular training. (7
train structures, 4 inputs, 4 outputs, 5 hidden neurons, 49.w eights).......... 51
5.12
Error results for the 2-port microstrip via, difference method. (7
train structures, 4 inputs, 4 outputs, 8 hidden neurons, 76.w eights).......... 51
5.13
Error results for the 2-port microstrip via, PKI method. (7 train
structures, 8 inputs, 4 outputs, 5 hidden neurons, 69 w eights)...................51
5.14
Error results for the 2-port microstrip via, regular training. (15 train
structures, 4 inputs, 4 outputs, 13 hidden neurons, 121 w eights)...............52
5.15
Error results for the2-port microstrip via, difference method. (15
train structures, 4 inputs, 4 outputs, 12 hidden neurons, 112 weights)
53
5.16
Error results for the 2-port microstrip via, PKI method. (15 train
structures, 8 inputs, 4 outputs, 11 hidden neurons, 147 w eights).............. 53
5.17
Error results for the stripline-to-stripline interconnect frequency
extension model, regular training. (5 train structures, 3 inputs, 4
outputs, 10 hidden neurons, 84 weights).........................................................55
5.18
Error results for the stripline-to-stripline interconnect frequency
extension model, difference method. (5 train structures, 3 inputs, 4
outputs, 13 hidden neurons, 108 weights)...................................................... 55
5.19
Error results for the stripline-to-stripline interconnect frequency
extension model, PKI method. (5 train structures, 7 inputs, 4 outputs,
8 hidden neurons, 102 weights)........................................................................55
5.20
Error results for the stripline-to-stripline interconnect frequency
extension model, regular training. (9 train structures, 3 inputs, 4
outputs, 11 hidden neurons, 92 weights).........................................................56
5.21
Error results for the stripline-to-stripline interconnect frequency
extension model, difference method. (9 train structures, 3 inputs, 4
outputs, 13 hidden neurons, 108 weights)...................................................... 56
5.22
Error results for the stripline-to-stripline interconnect frequency
extension model, PKI method. (9 train structures, 7 inputs, 4 outputs,
10 hidden neurons, 124 weights)......................................................................56
5.23
Comparison of simulation times for the GaAs via described in Fig.
5.6. The tim es for MSVIA and NET1 are averaged over 100 frequency
points. HP-M omentum results are for 1 frequency point............................57
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6.1
Variable input parameters and corresponding ranges for the layer 1 to
layer 2 coupling section model........................................................................ 7 1
6.2
Variable input parameters and corresponding ranges for the layer 1 to
layer 1 coupling section m odel......................................................................... 71
6.3
Error results for the layer 1 to layer 2 coupling line section analysis
model. (725 train/test examples, 25 verify; 3 inputs, 6 outputs, 15
hidden neurons, 156 weights)........................................................................... 72
6.4
Error results for the layer 1 to layer 1 coupling line section analysis
model. (645 train/test structures, 25 verify; 3 inputs, 6 outputs, 15
hidden neurons, 156 weights)........................................................................... 72
6.5
Error results for the layer I to layer 2 coupling line section synthesis
model. (725 train/test examples, 25 verify; 4 inputs, 3 outputs, 13
hidden neurons, 107 weights)........................................................................... 73
6.6
Error results for the layer I to layer 1 coupling line section synthesis
model. (645 train/test examples, 25 verify; 4 inputs, 3 outputs, 14
hidden neurons, 115 weights)........................................................................... 73
6.7
Filter specifications used for the design o f a 2-layer asymmetric
coupled line filter................................................................................................ 74
6.8
Physical dimensions obtained from ANN models for the 2-layer Filter
example. Filter specifications are given in Table 6.7.................................. 75
6.9
Comparison o f two-layer filter responses........................................................76
6.10 Optimized physical dimensions obtained from ANN models for the 2layer filter example. Filter specifications are given in Table 6.7............... 77
6.11 Comparison o f optimized two-layer filter responses..................................... 77
6.12
Physical dimensions obtained from optimization method for the 2layer filter example. Filter specifications are given in Table 6.7............... 79
6.13
Center frequency and bandwidth parameters for the 2-layer filter
designed using the optimization method. Also, the response of the
filter using A NN modeling is repeated here for comparison purposes
79
6.14 Two-layer filter design times and required iterations for ANN
modeling and the optimization method of [80]............................................. 80
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x ix
7.1
Variable param eter ranges for CPW components............................................87
7.2
Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the optimally cham fered CPW
bend....................................................................................................................... 87
7.3
Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the compensated bend.........................89
7.4
Comparison of return loss for the conventional optimally chamfered
bend and the novel compensated bend for several structures.
(Frequency = 50 G H z)....................................................................................... 91
7.5
Variable input param eter ranges for the CPW 90° bend................................ 92
7.6
Error results for the variable air-bridge height CPW bend model,
regular training. (5 train structures, 4 inputs, 4 outputs, 14 hidden
neurons, 130 w e ig h ts)....................................................................................... 93
7.7
Error results for the variable air-bridge height CPW bend model,
difference method. (5 train structures, 4 inputs, 4 outputs, 15 hidden
neurons, 139 w e ig h ts)....................................................................................... 93
7.8
Error results for the variable air-bridge height CPW bend model, PKI
method. (5 train structures, 8 inputs, 4 outputs, 13 hidden neurons,
179 w eights)........................................................................................................ 93
7.9
Error results (average and standard deviation) between the EM-ANN
model and EM sim ulation for the CPW transmission line........................... 94
7.10 Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the CPW short circuit..........................97
7.11 Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the CPW open circuit..........................97
7.12 Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the step-in-width.................................. 98
7.13 Error results between the EM-ANN model and EM sim ulation for the
CPW symmetric T-junction (average and standard deviation). Input
branchline port is Port 1, and the output ports on the main line are
Ports 2 and 3....................................................................................................... 102
8.1
Input variables and ranges for CPW transmission line m odel.....................120
8.2
Error results (average and standard deviation) for the CPW line model. 120
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XX
8.3
Error values (average and standard deviation) for the C PW open-end
m odel...................................................................................................................123
8.4
Ideal CPW patch antenna designs.................................................................... 128
8.5
Error results (average and standard deviation) for the CPW feed
discontinuity model........................................................................................... 130
8.6
Comparison of resonant frequency and bandwidth for EM-ANN
modeling, EM simulation, and measurement................................................131
8.7
Comparison of resonant frequency and bandwidth for EM-ANN
modeling, EM simulation, and measurement. CPW patch antenna with
longer than ideal patch length..........................................................................137
|
t
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CHAPTER 1
INTRODUCTION
1.1
Motivation
1.1.1
Modeling for CAD
Computer-aided design (CAD) of microwave/mm-wave integrated circuits
and monolithic microwave/mm-wave integrated circuits relies heavily upon models
developed for passive circuit components. Accurate characterization and modeling o f
passive circuit com ponents and discontinuities is vital for accurate circuit simulation
and increased first-pass design success.
The degree o f accuracy to which the
performance o f a microwave/mm-wave circuit can be predicted by CAD depends on
the accuracy o f characterization and modeling o f components. Passive components
can be categorized as either lumped or distributed in nature. Lumped elements (via
holes, discontinuities, spiral inductors, etc.) are considered small with respect to the
operating wavelength, w hile distributed elem ents (microstrip transmission lines,
coplanar waveguide transmission lines, coupled lines, etc.) have sizes comparable to
the wavelength.
G enerally, microwave circuit design requires both lumped and
distributed elements.
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2
Distributed elements are modeled using sections o f transmission lines [1-4].
As an example, transmission lines can be described by their characteristic impedance,
Zo, and complex propagation constant, y. Discontinuities associated with distributed
elements (bends, steps-in-width, open and shorted stubs, junctions etc.) and lumped
elements are generally modeled by networks o f equivalent circuit parameters (ECPs),
consisting of resistors, inductors, and capacitors [1-5].
Models can be developed using analytical, electromagnetic (EM) and
measurement based techniques [5]. Analytical models, when they exist, are generally
based on assumptions that are valid only over a certain limited range o f operation.
Also, analytical models require a high level o f expertise and a long development time.
Electromagnetic
simulation
can
provide
accurate responses.
However, the
computational expense required does not make practical interactive circuit design
using EM simulations feasible, especially when the circuit response must be
optimized. Measurement-based models are developed by measuring the S-parameter
characteristics of the element, requiring costly mask designs, fabrication, and testing.
Although this method can be accurate, it is generally limited to the specific structures
that are fabricated and measured.
Since analytical models require prohibitive assumptions to be made and
require a high level of expertise and knowledge to develop, empirical modeling
techniques are attractive alternatives.
Empirical models for passive circuit
components may be developed by using EM simulation or measured data.
Even
when accurate numerical data is available, efficient use o f these results for CAD is
not straightforward. Empirical models for distributed components (microstrip lines,
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3
CPW lines, etc.) have generally been developed by curve-fitting responses to
specialized functions [1]. The choice o f function requires some degree of expertise
about the data to be modeled. This expertise may be lacking for novel components.
The most common method for developing empirical models for lumped components
has been using equivalent circuit parameter (ECP) models [1-6].
Equivalent circuit
models are developed by first extracting ECP values from numerical data for different
component geometries and at different operating points, if needed. These results can
then be stored in look-up tables [7] or used for obtaining empirical expressions for
each ECP based on curve-fitting [2]. However, accurate results are dependent on
having adequate equivalent circuit representations, extraction routines, and fitting
functions. This approach may be adequate for previously explored structures, which
are well understood, but may not be adequate for novel structures for which limited
knowledge is available. Therefore, common modeling techniques suffer from the
necessity o f having to choose an appropriate function or equivalent circuit to fit the
numerical data.
As an alternative to the above mentioned modeling techniques, it may be
desirable to directly model (or map) the input/output relationships that exist between
characteristic parameters (input variables) o f a component and the corresponding
response (output variables).
Conventional methods used for this purpose are
polynomial regression, for exam ple [8, 9], and look-up table models, for example [7].
With these methods, separate models are required for each output variable.
Also,
prior knowledge about the input/output mapping, which may not be available, is
needed in order to select the order o f the model for polynomial regression and the
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4
interpolating functions for look-up table models. Therefore, a more general modeling
technique is necessary, capable o f modeling nonlinear and linear mappings between
multiple input variables and multiple output variables.
Artificial neural networks
(ANNs) offer such an alternative.
1.1.2
Artificial Neural Network Models
Artificial neural networks (ANNs) have emerged as a powerful technique for
modeling general input/output relationships. In the past, ANNs have been used for
many complex tasks. Applications have been reported in areas such as control [10],
telecommunications [11], biomedical [12], remote sensing [13], pattern recognition
[14], and manufacturing [15], just to name a few. However, until recently, ANNs
have been used only to a very limited extent in the area o f microwave/mm-wave
design.
Applications reported in literature include: automatic impedance matching
[16], microstrip circuit design [17], microwave circuit analysis and optimization [18,
19], active device modeling [20-22], and modeling of passive components [23-31],
Note that a majority o f the papers on passive component modeling are a result of the
research reported in this thesis.
Artificial neural network models can be more accurate than polynomial
regression models [32-37], allow more dimensions than look-up table models [37],
and allow multiple outputs for a single model. Models using ANNs are developed by
providing sufficient training data (i.e. EM simulation or measured data) from which it
learns the underlying input/output mapping.
Several valuable characteristics are
offered by ANNs [38]. First, no prior knowledge about the input/output mapping is
required for model development. Unknown relationships are inferred from the data
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5
provided for training. Therefore, with an ANN, the fitted function is represented by
the network and does not have to be explicitly defined.
Second, ANNs can
generalize, meaning they can respond correctly to new data that has not been used for
model development. Third, ANNs have the ability to model highly nonlinear, as well
as linear input/output mappings. In fact, it has been shown that ANNs are capable of
forming an arbitrarily close approximation to any continuous nonlinear mapping [39].
The prim ary objective o f this research is to demonstrate the feasibility o f and
provide a general methodology for the developm ent o f accurate and efficient
electromagnetically-trained
ANN
(EM-ANN)
models
for
use
in
CAD
of
microwave/mm-wave circuits. These models are capable o f providing EM simulation
accuracy within a microwave circuit simulator environment and thus lead to an
accurate and efficient CAD.
1.2
Organization o f the Thesis
This thesis begins with an overview o f the methodology used for developing
EM-ANN models for microwave/mm-wave circuit components.
general concepts concerning ANNs are discussed.
In Chapter 2,
The ANN architecture, training
algorithm, data pre-processing, and error formulation are reviewed.
presents the specific methodology used throughout this thesis.
Chapter 3
Attention is paid to
the selection of ANN training data and the methods used for obtaining optimal ANN
architecture for a given component to be modeled. Also, methods for simplifying the
input/output mapping that needs to be learned by the ANN, through incorporation o f
prior knowledge (existing models), are discussed [31]. Specific issues related to the
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6
development of EM -ANN models for microwave components are covered in Chapter
4.
Selection of model inputs and outputs and generation o f training data for
microwave components are discussed. Also, methods for linking EM-ANN models
to commercial microwave circuit simulators are detailed.
The remaining chapters of this thesis contain various examples and uses of
EM-ANN models for the CAD of microwave/mm-wave circuits. EM-ANN modeling
o f microstrip vias and multilayer interconnects is considered in Chapter 5 [25,26].
Models are developed for microstrip line characteristic impedance, one- and two-port
microstrip vias, a stripline-to-stripline multilayer interconnect, a microstrip-tomicrostrip multilayer interconnect, and a microstrip-to-CPW multilayer interconnect.
An example of using EM-ANN models to optimize the component geometry is
included. Use of prior knowledge (existing models) for model development is also
demostrated in Chapter 5.
Chapter 6 presents a methodology for the synthesis
(leading to physical dimensions) of multilayer asymmetric coupled microstrip lines
using artificial neural ANN models [27].
Both synthesis and analysis models are
developed. Models are appropriate for synthesis of multilayer structures like filters,
baluns, and directional couplers. Accuracy comparable to other optimization methods
for multilayer filter design is achieved, but in a small fraction o f the time.
The
proposed methodology is demonstrated by the design of a 2-layer coupled line filter.
Chapter 7 is concerned with generating a library o f EM-ANN models for CPW circuit
design [28,29]. M odeled components include: CPW transmission lines (frequency
dependent Zo and ere), 90° bends, short circuit stubs, open circuit stubs, step-in-width
discontinuities, and symmetric T-junctions.
Design and optimization o f a CPW
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7
folded double stub filter and a 50 Q , 3 dB power divider circuit, using the developed
CPW EM-ANN models, are demonstrated. Chapter 8 deals with developing EMANN models for novel CPW patch antenna design [30]. Models are developed for
wide strip CPW lines, CPW open-end effects including radiation conductance, and
feed interactions. Since this is a novel antenna, no design information was available
in the literature. However, using EM-ANN modeling techniques, a couple of wide
bandwidth CPW patch antennas have been designed and validated by both EM
simulation and measurements. The thesis concludes with a discussion o f results and
directions for future research in Chapter 9.
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CHAPTER 2
INTRODUCTION TO MULTILAYER, FEED-FORWARD
ARTIFICIAL NEURAL NETWORKS
Multilayer, feed-forward artificial neural networks consist of parallel, highly
interconnected layers o f computational nodes termed neurons. These networks can be
viewed as providing a general framework for representing nonlinear functional
mappings between a set o f input variables and a set of output variables. Mapping is
achieved by representing the nonlinear function of many variables in terms of
compositions of nonlinear functions o f a single variable, called activation functions.
In a related matter, Kolmogorov [40] has shown that every continuous function of
several variables can be represented as the superposition o f a small num ber o f
functions of one variable. Supervised training o f the ANN is provided by adjusting
adaptive weights which provide connections between neurons, using the error backpropagation algorithm.
Two-layer networks, containing one hidden layer and an
output layer of neurons are the most popular. Both layers have sigmoidal activation
functions for the neurons. It has been shown that two-layer networks of this form can
arbitrarily approximate any continuous mapping from one finite-dimensional space to
another, provided the num ber of hidden layer neurons is sufficiently large [39].
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9
This chapter reviews the architecture and corresponding equations for twolayer ANNs using error back-propagation training. Issues related to ANN training,
including data selection and pre-processing, error formulation, the error backpropagation algorithm, and generalization are discussed.
For a more detailed
discussion of ANN concepts refer to [38].
2.1
ANN Topology
The topology o f the ANN used for this work is shown in Fig. 2.1. It is a two-
layer network, consisting o f an input (non-computing) layer, a hidden layer of
neurons, and an output layer o f neurons. It is fully connected, which means that each
neuron is connected to every neuron in the next layer.
All connections have an
adjustable weight associated with them. Each com puting neuron has, associated with
it, a nonlinear activation function. The number o f neurons in each layer is problem
dependent and is decided upon during training.
One can write down the analytical function corresponding to the network of
Fig. 2.1 as follows. The input, Uj, of the y'th hidden neuron is obtained by forming a
weighted linear combination o f the / input variables, ,v„ and the corresponding
connection weight,
, to give
i=i
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10
Input Layer
Hidden Layer
Output Layer
w1<5
-yi
j1 wj0
r k l wk0
-yk
-►yK
i=1,2....1
j=1,2
J
k=1,2
K
Fig. 2.1 Artificial neural network architecture.
where
is the additional bias input to the jth neuron.
This input, Uj, can be
written as
t
(i)
Uj = Z
W j i
X
,
( 2 .2 )
i= 0
where jc0=1 . The output, Zj, of hidden neuron j is then obtained by transforming the
linear sum of (2.2) using the activation function o f the neuron g(») to give
Z j = S(U j )-
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(2.3)
11
The network outputs are obtained by transforming the outputs o f the hidden layer
neurons in a sim ilar manner.
Thus, for each output unit k, a weighted linear
combination o f the outputs of the hidden layer neurons is formed to give
v k = 'LJj=0w ^ z J
<2 -4 )
where the bias weight has again been absorbed into the sum by setting z0= 1. The
output of the network is then obtained by transforming (2.4) by the activation function
of the output layer neurons to give
(2-5)
y k= s(vk)
Combining (2.2), (2.3), (2.4), and (2.5) one obtains the output o f the network shown
in Fig. 2.1 as
y k=
•
( 2 -6 )
Equation (8.6) can be written in vector-matrix form as
Y = i ( w 2-«(w,*x))
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(2.7)
where X is the input vector, Y is the output vector, and W j and W 2 are the weight
connection matrices between the input and hidden layer and between the hidden layer
and output layer, respectively.
The activation functions, for both the hidden layer neurons and the output
layer neurons, are sigmoidal. The specific sigmoidal function used for this work is
the logistic function given by
g(u) =
-tit-
(2.8)
l +e
Sigmoidal activation functions have several desirable properties.
First, a sigmoid
function is bounded. Second, the value o f a sigmoid function is monotonic. Third, a
sigmoid function is continuous and smooth and is therefore differentiable anywhere.
The logistic activation function o f (2.8) is shown in Fig. 2.2 and varies from 0 to 1 as
u varies from -oo to +oo. The values o f the weights determine the slope and shift o f the
logistic function.
2.2
ANN M odel Developm ent (Training)
Network training (or learning) is accomplished by adjusting the weights o f the
network based upon some error criteria between the actual outputs o f the network, _v’k,
and the target output values, tk- To start with, the weights are initialized to small
random values. Then input vectors are passed forward through the neural network
I
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13
0.75 --
0.5
0 . 2<
10
-7.5
-5
-2.5
0
2.5
5
7.5
10
u
Fig. 2.2 Logistic activation function used in hidden layer and output layer neurons.
and the corresponding outputs are computed. In the beginning, the actual outputs will
not be close to the target outputs. Actual network outputs are then compared to target
output values and the derivative o f the error between them with respect to each o f the
weights, is calculated. Error derivatives with respect to each weight are summed for
all input/output vectors, which is termed batch processing. Weights are then adjusted
based upon their contribution to the error such that overall network error decreases.
These steps of calculating the error derivatives for all the training data and then
updating the weights is termed an epoch.
This “gradient descent” procedure
continues in an iterative manner until overall error is reduced to an acceptable level.
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14
2.2.1
Data Preprocessing
Data selection is crucial for the development o f ANN models. Data must be
selected to capture important input/output mapping relationships. Once data has been
selected, it is generally separated into training, testing, and independent verification
datasets. Training data is used for model development while testing data is used to
determine when training should halt.
Verification data is used for final model
validation.
An important form o f data preprocessing consists o f a simple linear rescaling
of the input/output data. This is useful when different variables have typical values
which differ significantly.
Data is generally scaled from 0 to 1 or from -1 to 1
depending upon the activation function used. With linear rescaling, each variable is
assigned the same importance (errors are o f the same magnitude) for model
development and determined weights should not be markedly different.
Another form of data preprocessing is the use of prior knowledge.
Prior
knowledge about the mapping to be learned can be incorporated into network training
by altering the input/output data. This alteration can reduce the complexity of the
mapping and therefore require less training data to capture. This is discussed in more
detail in Chapter 3.
2.2.2
Error Back-Propagation
Error back-propagation refers to the propagation o f errors backward through
the network to find the error derivatives with respect to each weight. Once the error
derivatives are determined, they can be used in conjunction with a method such as
gradient descent to update the network weights.
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15
Using differential calculus the derivatives of the error, £", with respect to each
weight for a single input vector, n, can be found as
dw
.dE n
-m > —
'/
<2-9 >
for the second layer of weights between the hidden layer and the output layer, and
where Sk = g (vv)
<?E
(2.10)
for the first layer of weights between the input layer and the hidden layer. Note that
when multiple network outputs are present, EP, is the combination of the errors from
all the outputs so that
r
= r ( y ,
y K)-
( 2 - 11 )
Error derivatives are then summed for all input vectors and used to update the weights
of the network.
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16
2.2.3
Error Functions
2.2.3.1 Absolute Error
Training to reduce the absolute error from the network is accomplished by
using the condition of least squared error between the target output, tk, and the
network output, yk. The error function for a single input vector is given by
( 2 . 12 )
This choice of error function is convenient since it is differentiable and provides a
positive error surface which is used in conjunction with gradient search techniques.
As one can see from (2.12), this choice o f error function is aimed at reducing the
absolute error from the network, placing em phasis on reducing the largest errors.
Using this error measure, the error back-propagation equations become
(2.13)
for the second layer o f weights , and
<3En
-
—
•
ri
= 8 (Uj)2^wk A xi
where 4 = g (vk )(yk - t k )
for the first layer of weights.
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(2.14)
17
2.2.3.2 Relative Error
Many times the absolute error is not as important as the relative error. For
example, when creating a model for the characteristic impedance of a microstrip line,
the output values may range from 10 Q to 100 Cl. A 1 f i absolute error corresponds
to a 10% error at 10 Q but only a 1% error at 100 Q . In this situation it would be
beneficial to put more emphasis on reducing the relative error.
To perform network training on relative error, we have modified the error
function o f (2.12) as follows
(2.15)
Using this error measure, the error back-propagation equations become
(2.16)
for the second layer o f weights , and
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18
/
where Sk = g \ v k ) — L r
{ tl
(2.17)
J
for the first layer o f weights. An example o f training on relative error is given in
Chapter 5 for the characteristic impedance o f microstrip lines.
2.2.4
Learning Rules
The most common learning rule used to update the weights of the network is
the steepest gradient descent method and is used extensively in this work. The name
“steepest descent” implies that weight changes move the weights in a direction in
which the error declines most quickly. The weight update rule is given below as
•+i
t
(2.18)
where t is the epoch number, r\ is the learning rate, and p. is the momentum. Error
derivatives given in the previous section may be used in conjunction with (8.18) for
network training. Other error minimization algorithms may be used for learning such
as adaptive steepest gradient and conjugate gradient methods.
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19
2.3
M odel Generalization and Overfitting
The goal o f neural network modeling is to produce a model that is valid not
only for the training data but for data (within the range o f the input variables) that the
network has never seen before. This is referred to as the generalization capability o f
the network.
It is possible for the network to fit the training data too closely or even exactly.
This is termed overfitting and occurs when the network learns the noise in the data in
addition to the underlying function to be modeled.
In this case, the models
generalization capabilities will be poor.
The number of neurons in the hidden layer is crucial to the ANNs ability to
generalize. Too many neurons in the hidden layer tend to lead to overfitting, while a
network with too few hidden layer neurons may not be able to learn the desired
input/output mapping.
Therefore, one needs a method to monitor whether overtraining has occurred
and to determine the optimal number o f neurons in the hidden layer for a given
problem. Methods used for this work are discussed in detail in Chapter 3.
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CHAPTER 3
MODELING METHODOLOGY
This chapter reviews the methodology used for development of ANN models
throughout this work. Attention is paid to selection o f training data and methods for
obtaining the optimal ANN model for a given component.
Also, methods for
simplifying the input/output mapping that needs to be learned by the ANN through
incorporation o f existing knowledge are demonstrated.
3.1
Selection of Training Data by Design o f Experiments (DOE) Techniques
In order to train the ANN models, input/output relationship data (termed
examples) needs to be collected. In many situations, this data is not readily available
and can be very time-consuming to obtain.
In these cases, a minimum number of
training points need to be chosen so that important input/output relationships are
presented to and learned by the ANN model.
Simple models require less training
data, while highly nonlinear models require an increased number o f training data
points.
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21
For some components, analytical models are possible and input/output
relationships may be expressed in closed forms. W hen the input/output relationships
are too complex, experimental data may need to be obtained to characterize the
component.
For many complex relationships, design o f experiments (DOE)
methodology is used to systematically study the input/output relationships o f a
component or process [41].
A designed experiment is a test or a series of tests in which purposeful
changes are made to the input variables of a process or system so that the causes of
changes in the output response can be observed and identified. Experimental results
are then used to build the model of the input/output relationship using response
surface methodology (RSM).
In RSM problems, the input/output relationships are unknown. The first step
is to approximate the input/output relationships. This is usually done using low-order
polynomials or other fitting technique over a small portion o f the input variables’
ranges.
However, when the process is influenced by a large number of input
variables, is highly nonlinear, has more than one output variable, or when a global fit
to the response surface is needed, these conventional fitting methods are limited
[19,42],
An alternative approach for modeling o f the response surface is the use of
ANNs [42], ANNs are able to deal with highly nonlinear and multiple input/output
variables effectively, providing excellent interpolative capabilities [38]. This allows
development of a global model representing a component.
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22
Although response surface methods have been developed for regression
analysis, they can be used to determine simulation points which effectively cover the
region of interest. W hen building a model, one would like to reduce the training time
by providing as little training data as necessary, for achieving a desired accuracy.
This implies starting w ith a low-order experimental design and sequentially building
up to higher-order designs by adding additional training data.
The simplest experimental designs for fitting first-order response surfaces are
2k factorial designs, where k is the number o f input variables as shown in Fig. 3.1 [41]
for a two variable case.
For the design, only minimum and maximum values of each
input parameter are used.
Minimum and maximum input parameter values are
represented as -1 and +1, respectively. This design requires 2k comer points. Because
there are only two levels for each input variable, this design is useful for
characterizing output responses that are approximately linear over the range o f the
input variables.
If a first-order design is not sufficient for capturing the input/output
relationships of the component, then additional simulation points are added to capture
the higher-order nonlinearities. The most widely used experimental design for fitting
second-order response surfaces is the central composite design [41].
Central
composite designs are advantageous in that they can be built up from 2k factorial
designs by adding axial points and a center point as shown in Fig. 3.2. The axial
points are positioned to provide a circular pattern.
Minimum and maximum
parameter values are represented by -1 and +1, respectively.
One may also use a
modified central composite design as shown in Fig. 3.3. For this design, all points are
l|
i
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23
shifted inward so that there are no simulation points outside the input variable space.
Central composite designs require 2k com er points, 1 center point, and 2(k) axial
points, where k is the num ber o f variable parameters.
If the nonlinear input/output relationships have still not been sufficiently
captured, simulation points spaced midway between the central com posite points, as
shown in Fig. 3.4, are then added to capture higher-order nonlinearities.
In this
manner, design of experim ents is built up sequentially, adding more sim ulation points
if increased model accuracy is desired.
0 d.D
H.i) 0
0
(1.-D
Fig. 3.1 DOE 2k factorial design.
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(0. t.4 )
( 1. 1)
> 1 . 1)
(0 . 0 )
(-1 .4 . 0)
(1.4. 0)
(-1.-D
(0.-1.4)
Fig. 3.2 DOE central composite design.
( 0 . 1)
(0.7.0.7) £
(0 .0 )
( - 1 .0 )
Q
( 1 .0 )
(0.7.-0.7) Q
(-0.7.-0.7)
(0 .- 1)
Fig. 3.3 Modified DOE central composite design.
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25
i
*2
(0.1)
Q
(0.7.0.7) ^
00.7.0.7)
•
•
II
•
A
W
------9
X1
|
•
•
0
0 .0 )
(0.0)
(0.7.-O.7) £
(-0.7.-0.7)
(0.-1)
'
Fig. 3.4 Modified DOE central composite design with additional interior points.
3.2
ANN Training Methodology
Training o f the ANNs for this work has been accomplished using CU-ANN*, a
user-friendly software developed at the University o f Colorado at Boulder by Marwah
et al. [43]. This section briefly describes the methodology used and its advantages.
3.2.1
Data Pre-Processing
To begin with, training data is separated into two datasets, one for training and
one for testing. Model validation data is kept separate and is not used in any capacity
for training the ANN. The inputs are linearly normalized between 0 and 1. Outputs
are linearly normalized between 0.2 and 0.8 so that output neurons operate in the
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26
relatively linear portion of the logistic function. If the range o f any o f the inputs or
outputs is large, they can be logarithmically normalized before training.
3.2.2
Sim ultaneous Training and Testing
One advantage of using the methodology o f [43] is the ability to perform
simultaneous training and testing. Testing dataset errors can be monitored as training
progresses to avoid overfitting o f the training data. In this way, a model with good
generalization capabilities is developed.
Before training begins, all network weights are randomly initialized to small
values near zero. After each pass through the training data, or epoch, the correlation
coefficient, R 2, and the normalized mean-squared error,
£ Ms e
are calculated for the
training dataset and for the testing dataset after R 2 reaches 0.8 [43].
£m se
is
a
measure
of the absolute error while R2 is a relative measure ranging from 0 to 1. The two error
measures together give an indication of the quality of the model and are given below
(3.1)
R- = l n=U =l
and
(3.2)
w here
N is the number of input/output examples,
K is the number o f output variables,
y nt is the predicted output of the model,
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27
is the target output, and
t is the target output mean.
W henever E mseuu decreases, the weights are stored.
Therefore, the model
with the lowest testing dataset errors is saved, providing a model with the best
generalization capabilities.
Another feature o f CU-ANN is the ‘simple to complex’ procedure used to
determine the neural network architecture. A network with too few neurons will not
be able to map complex input/output relationships, while a network with too many
neurons tends to overfitt the training data [38]. First, a simple network architecture is
chosen, usually containing one hidden layer with a small number o f neurons.
If
learning is slow or desired accuracy is not achieved, additional neurons are added to
the hidden layer.
In the CU-ANN software, the process o f changing the network
architecture has been automated. The best network architecture is saved, identifying
the optimal network.
3.3
Use o f Prior Knowledge
A potential drawback o f ANN modeling is the amount o f training data that
needs to be provided in order to obtain an accurate model. Training data must be
provided to characterize the component to be modeled over a desired range of
operation and for different combinations o f geometrical and physical model inputs.
The difficulty arises when training data is expensive or difficult to obtain.
The
amount of data needed to train an ANN model can be reduced by using design of
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28
experiment (DOE) techniques. However, even with the use o f DOE techniques, the
required amount of data needed for model development can still be too large. An
approach to reducing this data is through reducing the complexity o f the input/output
mapping that must be learned by the ANN.
To this end we propose using prior
knowledge (existing models) about the component to be modeled. Prior knowledge,
for example, can be in the form o f analytical equations, empirical models, already
trained ANN models, or some available experimentally measured data.
These
existing models are models which contain information about the component to be
modeled but do not give the required accuracy over the desired range o f operation.
Use o f prior knowledge for microwave design has been shown to be an
effective means of reducing the amount o f training data needed to obtain desired
model accuracy [26, 44]. In [44], prior knowledge is incorporated into a knowledge
based neural network structure, consisting o f 7 layers, in the form of empirical
functions or analytical approximations as activation functions in “ knowledge layers”.
Drawbacks of this approach are the more complicated structure o f the network for
which conventional error backpropagation training is not applicable, the restriction o f
having prior knowledge in equation form, and the possible restriction of only having
one network output.
For a chemical vapor deposition in a horizontal reactor, Marwah [45] and
M arwah and Mahajan [46] propose using different model transfer techniques to
convert a previously trained physical neural network model (called the source model)
to an equivalent model (called the target model). Three different techniques, namely
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29
difference method, source weights method, and prior knowledge input method (PKI)
are evaluated. The PKI method was shown to out perform the other two methods.
To get better insight into the dynamics of the above mentioned model modifier
techniques, the output/input behavior was monitored during the training process. It
was noted that in the difference method, the difference between the source and the
target was not a simpler function of the inputs as compared to the target. As a result,
no benefit was expected to result from this modifier approach. This was supported by
the training results, which showed that the percent relative error on the target points
was the same as that obtained by training the target model without the help o f the
source model. The source weight technique resulted in a similar performance. With
the PKI method, on the other hand, the source function converged towards the target
function continuously as the training proceeded. Trained on one-fourth of the points
used for the source model, the target model achieved the same accuracy as the source
model. These techniques have not been investigated thoroughly for their performance
in modeling of microwave components.
In this section, we present two of the three techniques mentioned above for
incorporating prior knowledge (or existing models) into ANN model development
using EM simulation. These are the difference method and the PKI method.
In the
difference method, the ANN is trained on the difference between the target model
output and the existing model (source model) output, shown in Fig. 3.4a.
This
method is expected to give good results when the difference has a simpler
input/output mapping as a function of the inputs than the target data.
A simpler
input/output mapping requires less training data to characterize. An example o f the
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30
use o f the difference method has previously been reported in [26]. In the PKI method,
the source model outputs are used as inputs for the ANN model in addition to the
other inputs, shown in Fig. 3.4b.
In this case, the input/output mapping that m ust be
learned by the ANN is that between the output response o f the existing model and that
of the target model. For the case when the target outputs are the same as the existing
model outputs, the learning problem is reduced to a one-to-one mapping. Note that
conventional two-layer neural networks along with error backpropagation training are
used with both the difference and PKI methods, which is advantageous for a user.
Applications o f the difference m ethod and the PKI method for developing
electromagnetically-trained
ANN
(EM -ANN)
models
for
microwave
design
encompass new ANN model development, range extension of existing ANN models,
and the addition o f input parameters to existing ANN models.
Examples o f using
prior knowledge for ANN model developm ent are presented in following chapters. A
2-port microstrip via model is developed in Section 5.7.1 with the aide o f an
analytical expression for inductance o f the via. In Section 5.7.2. the frequency range
of a stripline-to-stripline multilayer interconnect model is extended using an already
developed ANN model as prior knowledge. As a final example, in Section 7.1.4, an
input parameter (air-bridge height) is added to an existing ANN model (CPW 90°
bend), again using an existing ANN model as prior knowledge.
I
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31
Existing
Prior
Knowledge
Physical Param eters
Frequency
■AS
EM
Simulation
T raining
Signal
Physical Param eters
Frequency
ANN
M odel
Error
(a)
Existing M odel Outputs
Physical Param eters
Frequency
Existing
Prior
EM
Simulation
K n o w le d g e
EM O utput
A N N O utput
ANN
Model
Physical Parameters
Frequency
Error ( Training l Signal
(b)
Fig. 3.5 Schemes for using prior knowledge (existing models) for artificial neural
network training, (a) difference method and (b) PKI method.
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CHAPTER 4
ANN MODELS FOR MICROWAVE/MILLIMETER-WAVE DESIGN
This chapter discusses some general issues related to the developm ent of
ANN models for passive microwave/mm-wave components.
model developed are given in the following chapters.
Specifics for each
In this chapter, selection of
model inputs and outputs, as well as generation of training data are discussed. Also,
error measures for model validation are given. After the ANN models are developed,
they are linked to a commercial microwave simulator where they can be used for
circuit design and optimization.
4.1
Selection of Model Inputs and Outputs
Selection of input parameters for microwave/mm-wave passive components is
relatively straight-forward.
Inputs are generally important physical (geometrical)
parameters of the component, which one would like to vary, and frequency. Input
variables’ ranges are determined by desired model usage requirements.
In the design of microwave/mm-wave circuits, it is often desirable to
interconnect many active and passive elements together. This can be accomplished
by representing model outputs in the form o f S-parameters, which are related to the
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33
power reflected and transmitted by a given component.
S-parameters are also a
convenient way to link developed models with commercial microwave simulators for
design and optimization. For this work, most ANN model outputs are given as Sparameters.
The magnitude and phase o f each S-parameter is a separate output.
Therefore, if the component to be modeled is a one-port device, the output parameters
would be ISnI and Z S n .
For a more detailed discussion of S-parameter theory and
applications refer to [47].
For transmission line models, the outputs o f the ANN model are the
characteristic impedance, Z„, and the propagation constant, p.
Knowing these two
parameters, and the length o f the line, the S-parameters o f a section o f the line can be
found. In this way, the length o f the line is not included as a variable input parameter
for the ANN model.
4.2
Training Data Generation
Training data for passive microwave/mm-wave component models generally
comes from measurements o f actual components or from electromagnetic (EM)
simulation.
Using actual measurements can be costly since it requires design and
fabrication of many components for characterization.
However, by using actual
measurement data, one may obtain a model that is valid for their specific fabrication
process, which may be desirable.
EM simulation is the alternative to using measured data for model
development and is used throughout this work.
The EM simulator used for this
purpose is HP-Momentum [48], except for the development of models for multilayer
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34
coupled line design which are discussed in detail in Chapter 6. The EM sim ulator
yields S-parameters for given com ponent geometries, which are then used to train
ANN models.
These models trained by EM simulations are therefore term ed
electromagnetically-trained artificial neural network (EM-ANN) models.
One drawback of using EM simulation for the generation o f training data is
that EM simulation can be very time-consuming. Therefore, DOE techniques and
prior knowledge, as discussed in the previous chapter, should be used in order to
reduce the number of EM simulations necessary for model development.
4.3
Error Measures
Error measures can either be absolute or relative in nature. The choice o f
w hich error measure to use is determ ined by the type of accuracy desired and model
usage requirements.
Most EM-ANN model errors reported in this work are presented as the
absolute average and the standard deviation of error for each output.
For S-
parameters, this is useful since it allows a designer to determine the amount o f signal
reflection and/or transmission o f the model on average and to estimate some useful
error bounds.
In some cases, relative errors are important, as with the characteristic
impedance, Zq, of a transmission line. W hen Zq is small, a small absolute error can
produce large mismatch errors w hen impedance matching is carried out. However, a
larger absolute error is allowable for higher Zo values. Therefore, relative errors are
considered in this case.
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!
35
4.4
Integration of EM-ANN Models with Circuit Simulators
Once the EM-ANN models have been trained and their accuracy determined,
they can either be used in stand-alone mode or they can be integrated with a
commercial microwave circuit simulator depending on the type and desired usage o f
the model.
These models then provide accuracy approaching that o f the EM
simulator used for generating the training data.
As shown in Fig. 4.1, EM-ANN models have been integrated into HP-MDS
[49], a commercially available microwave circuit simulator. Models can be inserted
into other circuit simulators in a similar manner. During simulation, HP-MDS passes
input variables, such as frequency and the physical parameters of a component, to the
user-defined linear model subroutine used for linking models to the circuit simulator.
This subroutine is then responsible for returning S-parameters of the component back
to HP-MDS for further processing. The input variables are passed to a feed-forward
ANN subroutine, by the user-defined linear model subroutine, for computation of
model S-parameters or the data required for com puting them. The feed-forward ANN
subroutine implements the algorithm o f Section 2.1 for finding the output o f a 2-layer
ANN. EM-ANN models are stored as files, w hich are read by the feed-forward ANN
subroutine. Each model file contains the num ber o f input parameters, the number of
output parameters, the number of neurons in the hidden layer, the maximum and
minimum values (used for normalization) for each o f the input and output parameters,
and the weight connection matrices.
An exam ple of a user-defined linear model
subroutine, the feed-forward ANN subroutine, and an EM-ANN model input file are
given in Appendix A.
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36
Models can also be grouped into libraries. A library is a collection o f models
that can be linked to HP-MDS as a group. This offers a convenient way to create and
distribute models for use by others. An example o f a library o f coplanar waveguide
(CPW) components, created for model distribution, is given in Appendix B.
Commercial
microwave
circuit simulator
Model
S-param eters
Model input
variables
User-defined linear
model subroutine
EM-ANN
model outputs
EM-ANN
model inputs
Feed-forward
ANN subroutine
EM-ANN
model data
EM-ANN
model file
Fig. 4.1 Flow of data for linking EM-ANN models to commercial microwave circuit
simulators.
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37
4.5
Design and Optimization Using EM -ANN Models
Once EM-ANN models have been linked to the circuit simulator, they can be
used in the design and optimization o f microwave/mm-wave circuits.
EM-ANN
models are used just as any other m odel available within HP-MDS (or similar
network simulator).
The models can be simulated alone or combined w ith many
other models to form a complete circuit.
Circuit and/or component optimization, where the gradient o f a function is
needed, can also be performed using the routines available within the circuit
simulator.
Two-layer networks with sigmoidal hidden units have the ability to
simultaneously approximate both a function and its derivative [50].
This is due to
having continuous hidden layer and output layer neuron activation functions
(sigmoids), which are differentiable everywhere.
Examples of design and optimization o f microwave/mm-wave circuits and
components are presented in following chapters.
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CHAPTER 5
EM-ANN MODELS FOR VIAS AND MULTILAYER
INTERCONNECTS
Efforts to lower the cost and reduce the weight/volume of microwave circuits
have resulted in high-density and multilayer circuits where a large number of via
interconnects are used.
W ith this increased complexity and higher operating
frequencies, accurate and efficient characterizations o f via interconnect discontinuities
and single-layer ground vias m ust be carried out in order to achieve accurate
simulation results [51].
Several recent efforts have focused on the analytical and
numerical evaluation of via discontinuities using quasi-static and full wave techniques
[51-67],
Quasi-static models are valid only at lower frequencies. Full-wave EM
simulation and characterization can lead to accurate results, but at much higher
computational expense which prevents their use in practical interactive CAD.
Applications of the EM -ANN methodology for modeling via elements in
microstrip circuits and multilayer via interconnects are presented in this chapter.
Modeling examples include, m icrostrip transmission line, one- and two-port
microstrip vias, a stripline-to-stripline multilayer interconnect, a microstrip-to-
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39
microstrip multilayer interconnect, and a microstrip-to-CPW multilayer interconnect.
As a demonstration, use of prior knowledge, as discussed in Chapter 3, has been used
to develop models for a 2-port microstrip via and to extend the frequency range o f the
stripline-to-stripline multilayer interconnect model.
Results are compared with
normal training methods (no use of existing knowledge).
The developed EM-ANN models have been linked to HP-MDS [49] (a
commercial microwave circuit simulator) where they can be used for circuit
simulation and optimization. An example comparing the 1-port microstrip via model,
available in HP-MDS, to the EM-ANN 1-port microstrip via model is presented.
Also, component optimization, using the stripline-to-stripline multilayer interconnect
model, is demonstrated.
5.1
Microstrip Transmission Line Model
Many times a model for a microstrip transmission line is needed either as a
element or to provide useful data for a circuit designer. Therefore, an ANN model
has been created to provide the characteristic impedance
dielectric constant (e Cfr) for microstrip transmission lines.
(Z q )
and the effective
Another reason for this
modeling example is to demonstrate a situation where it is better to train on relative
error rather than on absolute error as discussed in Chapter 2. For example, when
creating a model for the characteristic impedance of a microstrip line, the output
values may range from 10 Q to 100 Q. A 1 Q absolute error corresponds to a 10%
error at 10 Q but only a 1% error at 100 Q. In this situation it would be beneficial to
put more emphasis on reducing the relative error.
The goal for this model was to
!
j
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40
have the sum o f the average and standard deviation o f the residual errors for Zq be less
than 1%.
Figure 5.1 shows the geometry of the microstrip line to be modeled. Variable
input parameters and corresponding ranges are given in Table 5.1. Output parameters
Training data has been provided using linecalc [68].
are Zo and 8eff.
Since the
training data was not time-consuming to obtain, DOE techniques were not used.
Instead, a uniform grid of points was simulated to provide the training data.
The
training/test dataset consisted of 155 examples while the verification dataset
contained 100 examples.
Models were trained using both absolute and relative error
criteria for comparison.
The final models were trained using all 155 training/test
examples and both required 10 hidden layer neurons.
Table 5.1 Variable input parameters for microstrip transmission line model.
Input Parameter
Minimum Value
Maximum Value
Frequency
1 GHz
-1
2
18 GHz
1
13
Iogio(W|/HSUb)
er
W
Hs u b |
I
£r
ground
/////////////////////? //
Fig. 5.1 Cross-section of microstrip transmission line geometry where
W] is the
width of the microstrip line, HSUb is the substrate height, and Sr is the relative dielectric
constant of the substrate.
i
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41
The residual error results for both absolute error training and relative error
training are given in Table 5.2 and in Table 5.3, respectively.
Looking at the Zo
results, notice that the training on absolute error provides lower absolute error, but
higher relative (percentage) error. The highest relative errors are at low Z q values as
expected and do not meet the goal o f having the average and standard deviation
results sum to less than 1%. W hen using relative error measures during training,
lower relative errors are obained and our accuracy goal is achieved.
Table 5.2 Error results (average and standard deviation) between the EM-ANN
model and linecalc for the microstrip transmission line for a bsolute e rro r training.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
Zo(tt)
Zo (%)
S e fT
£ e ff ( % )
0.206
0.205
1.161
1.157
0.012
0.012
0.377
0.376
0.338
0.520
0.774
0.875
0.015
0.013
0.293
0.223
Table 5.3 Error results (average and standard deviation) between the EM-ANN
model and linecalc for the microstrip transmission line for relativ e e rro r training.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
Zo(Q)
Zo (%)
S e rf
S e ff ( % )
0.300
0.344
0.456
0.334
0.014
0.015
0.244
0.186
0.399
0.679
0.518
0.464
0.011
0.011
0.186
0.150
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42
5.2
Broadband GaAs 1-port M icrostrip Via
Figure 5.2 shows the structure and some parameters o f the one-port via under
consideration. The height of the substrate (HSUb). the dielectric constant (£r). and all
loss parameters are considered constant for this example. The width o f the incoming
microstrip line. Wi, the side o f the square shaped via pad. W p. and the diameter of the
via hole. D via. are the three variable design parameters. Input variables for the EMANN model and their ranges are given in Table 5.4.
Output variables aie the
magnitude and phase of Sn referenced to 50 Q port termination.
REFERENCE
PLANE
via
Fig. 5.2 GaAs microstrip ground via geometry. Substrate thickness = 4 mil, 8r=12.9,
tan5=0.002, crm«ai=4-l.x.l07, and
1 mil.
Table 5.4 Variable input parameters for GaAs m icrostrip ground via modeling.
Input Parameter
Frequency
W,/WD
DviaAVp
W|/Hsub
M inimum Value
5 GHz
0.3
0.2
0.1
M axim um Value
55 GHz
1.0
0.8
2.0
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43
EM simulations were performed from 5 to 55 GHz in 10 GHz steps using a
commercially available full-wave electromagnetic simulator (HP-Momentum [48]).
Via structures for 15 DOE central composite points, as well as for 14 additional
training/testing points spaced midway between the previous points, were simulated.
In addition, 16 structures were simulated for independent verification o f the model
after com pletion o f the training.
Best results were obtained by using 10 neurons in the hidden layer and the 15
central composite points, as well as the 14 interior points for training the network.
Residual error results for the EM-ANN model are given in Table 5.5. We note that an
excellent accuracy has been achieved.
Table 5.5 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the 1-port microstrip via.
ISul
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
5.3
z s^
n
0 .0 0 1 0 2
0 .4 5 6
0 .5 2 2
0 .0 0 1 6 2
0 .5 3 7
0 .0 0 2 2 5
0 .5 3 6
0 .0 0 1 0 5
Broadband GaAs 2-port Microstrip Via
In addition to the one-port via described above, a two-port via has also been
modeled. The same training points were used as for the 1-port via. The structure o f
the via is shown in Fig. 5.3 and the input variables and corresponding ranges are
given in Table 5.4. Output variables are the magnitudes and phases of Sn and S 2 1 ,
j
i
!
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44
again referenced to 50 Q. As with the one-port via, best results were obtained by
using 15 central composite points and the 14 interior points for training. Ten neurons
were required for the hidden layer. Residual error results are given in Table 5.6.
Again, an excellent accuracy has been achieved.
REFERENCE
PLANE
70
1 W,
T
iH
Fig. 5.3 Two-port GaAs microstrip grounding via. Substrate thickness = 4 mil,
e=12.9, tanS=0.002, a meaI=4.1x107, and tmeIal = 0.1 mil.
Table 5.6 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the 2-port microstrip via.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
ISnl
Z S „(■)
IS2 1 I
0.00361
0.00334
0.413
0.402
0.00680
0.00492
0.442
0.474
0.00420
0.00385
0.434
0.356
0.00881
0.00920
0.771
0.774
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45
It may be noted that the EM-ANN via models are able to achieve accuracy
comparable to EM simulation over the entire 5-55 GHz range. Since a full-wave
analysis is used, all the dielectric, conductor, and radiation losses, as well as all
parasitic effects, are included. The developed models may now be used in linear
analysis and in nonlinear analysis where harmonic frequency components are
generated.
5.4
StripIine-to-Stripline Multilayer Interconnect
Figure 5.4 shows the structure of a 50
stripline-to-stripline multilayer
interconnect for which an EM-ANN model has been developed. Reference planes are
set at Wiine/2 from the center of the via.
The variable design parameters are the
diameter of the via, Dvia, and the diameter o f the ground access opening, Dgnc]. All
other parameters are fixed. Model input variables and their ranges are given in Table
5.7. Output variables are the magnitudes and phases o f Si i and S2iEM simulations were performed from 1 GHz to 26 GHz in 5 GHz steps.
Interconnect structures for 9 central composite points and 8 additional training/testing
points were simulated.
In addition, 12 structures were simulated for model
verification purposes.
Using the 9 central composite points plus the 8 additional points for training
the model yielded the best results.
Nine neurons were used in the hidden layer.
Residual error results are given in Table 5.8. As with the GaAs ground vias, excellent
results have been obtained.
!
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R eference Planes
ine
50 oh m strip
via
gnd
ground
Fig. 5.4 Stripline-to-stripline interconnect structure with W|ine= 13.675 mil, Zo = 50
ohms, 8r= 2.94, tanS = 0.0012, tmetai = 1.4 mil, Ometai = 5.7xl07. and H = 20 mil.
Table 5.7 Variable parameters for stripline-to-stripline multilayer interconnect model.
Input Parameter
Freauencv
Dyia/Wune
_____Dmd/Dyia
M inimum Value
1 GHz
0.365
1.25
Maximum Value
26 GHz
0.8
6
Table 5.8 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the stripline-to-stripline multilayer interconnect.
ISnl
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
z s i,n
IS2 1 I
z s 21n
0.00172
0.00164
1.043
0.855
0.00069
0.00087
0.238
0.230
0.00151
0.00128
1.540
1.306
0.00057
0.00054
0.220
0.160
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47
5.5
Microstrip-to-Microstrip Multilayer Interconnect
Figure 5.5 shows the structure o f a 50 O microstrip-to-microstrip multilayer
interconnect for which an EM-ANN model has been developed. Reference planes are
set at Wbot/2 and WIop/2 from the center of the via for the bottom and top microstrip
lines, respectively. The variable design parameters are the diameter of the via. DV13.
and the length o f the overhang for the top microstrip line. LoH. All other parameters
are fixed. Model input variables and their ranges are given in Table 5.9.
Output
parameters for this ANN model are the magnitudes and phases of Sn, S i|, and Sii.
Reference Planes
/ \
L oh
50 o h m strip
i
c r2
r
r1
—►
t
c
5 0 o h m stri p
'via
H
H
Fig. 5.5 Microstrip-to-Microstrip interconnect with Zo = 50 ohms, W ^, = 23 mil,
W Iop = 125 mil, eri = 10.2, era = 2.2, tan5 = 0.0012, t^u ] = 1.4 mil, Ometai = 5.7xl07,
and H = 25 mil.
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48
EM simulations were performed from 2 GHz to 12 GHz in 2 GHz steps.
Interconnect structures for 9 central composite points and 8 additional training/testing
points were simulated.
In addition, 16 structures were simulated for model
verification purposes.
Using the 9 central composite points plus the 8 additional interior points for
training the model yielded the best results. Eight neurons were used in the hidden
layer.
Residual error results are given in Table 5.10.
As with the previously
developed models, excellent results have been obtained.
Table 5.9 Variable parameters for microstrip-to-microstrip interconnect model.
Input Parameter
Freauencv
Dvia/^Vbot
Loh
Minimum Value
2 GHz
0.2
1 mil
Maximum Value
12 GHz
0.9
15 mil
Table 5.10 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the microstrip-to-microstrip multilayer interconnect.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
ISnl
ZSuH
IS2 1 I
ZS2i H
IS22I
z s 22(°)
0.0009
0.0008
0.745
0.493
0.0003
0.0002
0.083
0.082
0.0011
0.0009
0.798
0.645
0.0010
0.0009
0.752
0.659
0.0003
0.0003
0.083
0.082
0.0013
0.0010
0.813
0.768
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49
5.6
Model Development Using Prior Knowledge
In this section, EM-ANN models are developed using prior knowledge
(existing models) about the component to be modeled. The first example is a 2-port
broadband GaAs microstrip ground via like the one discussed in Section 5.3.
However, when developing the model this time, prior knowledge about the microstrip
line characteristic impedances, and knowledge about the inductance o f the via are
used. The second example concerned with using a developed EM-ANN model to
extend one of its own input parameter ranges.
For this purpose, the stripline-to-
stripline multilayer interconnect model is used. The prior model is the stripline-tostripline model developed previously, but only the data from 1 GHz to 16 GHz is
assumed available. A new model is developed extending the frequency range to 26
GHz.
5.6.1
Two-Port Broadband GaAs Microstrip Ground Via
The geometry o f the two-port broadband GaAs microstrip via is shown in Fig.
5.3.
As with the previously developed model, the height of the substrate, the
dielectric constant, and all loss parameters are considered constant for this example.
Frequency, the width of the incoming microstrip lines, W), the side o f the square
shaped via pad, W p, and the diameter o f the via hole to ground, Dvia, are the variable
input parameters for the EM-ANN model. Input variable ranges are given in Table
5.4. Model outputs are the magnitudes and phases o f Sn and Sit-
However, the
reference impedances for the S-parameters are now the characteristic impedances of
the microstrip lines, eliminating reflection at the ports.
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50
An existing model in an equation form for the inductance o f a microstrip
grounding via is given in [53], The existing model was found to give reasonable
results at lower frequencies (<15 GHz), but as frequency increased, errors between the
model and EM simulation also increased.
Inaccuracies o f the model, especially at
higher frequencies may be due to pad inductance, pad capacitance, discontinuity
effects, and radiation from the via-hole [51, 69].
EM simulations were performed from 5 GHz to 55 GHz in 10 GHZ steps on
the same 45 via structures of Section 5.3. Originally, fifteen vias were simulated for
training, 14 for simultaneous testing or additional training, and 16 for verification.
However, with the use of prior knowledge, it was found that less training data is
sufficient for model development. Therefore, more of the simulated data has been
used for simultaneous testing. Initial model development used only 7 via structures
for training, 22 via structures for testing, and 16 via structures for model verification.
EM-ANN models were developed using regular training methods (no use of existing
knowledge), the difference method, and the PKI method.
The different training
methods have been discussed previously in Chapters 2 and 3.
Model average error and standard deviation are shown in Table 5.11, Table
5.12, and Table 5.13 for regular training, difference training, and PKI training,
respectively. Looking at verification dataset errors, both the difference method and
the PKI method provide more accurate models than using regular training methods.
In addition, the PKI method provides better accuracy for ISnl and comparable
accuracy on other parameters.
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51
Table 5.11 Error results for the 2-port microstrip via using regular training.
(7 train structures, 4 inputs, 4 outputs, 5 hidden neurons, 49 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
ISUI
Z S U (°)
IS2 1 I
z s 21 (°)
0.0076
0.0114
2.000
2.275
0.0314
0.0389
2.575
3.000
0.0066
0.0085
1.677
1.831
0.0226
0.0244
2.104
2.197
Table 5.12 Error results for the 2-port microstrip via, difference method.
(7 train structures, 4 inputs, 4 outputs, 8 hidden neurons, 76 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS.,1
Z S n (°)
IS2 1 I
Z S 2I (°)
0.0042
0.0058
1.313
1.803
0.0094
0.0089
2.084
3.174
0.0041
0.0043
0.941
0.908
0.0083
0.0061
1.477
1.387
Table 5.13 Error results for the 2-port microstrip via, PKI method.
(7 train structures, 8 inputs, 4 outputs, 5 hidden neurons, 69 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS 1 |l
Z S ,, (°)
IS2 1 I
Z S 21 (°)
0.0035
0.0087
1.209
1.780
0.0092
0.0122
1.587
1.890
0.0023
0.0023
0.949
1.011
0.0066
0.0077
1.526
1.426
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52
To further demonstrate the advantages o f incorporating existing knowledge
into training, EM-ANN m odels were developed using 15 training vias, 14 test
structures, and again 16 verification structures.
Model average error and standard
deviation are shown in Table 5.14, Table 5.15, and Table 5.16 for regular training,
difference training, and PK I training, respectively.
W ith more training data, error
results for regular training improve. However, verification dataset error results using
the difference method and PK I method improve also and still provide better accuracy
than regular training. W hat is more important is that when com paring verification
dataset errors, the accuracy o f the models trained with only 7 via structures using the
difference method and PKI method show comparable or better accuracy than the
model developed using 15 training via structures and regular training. Also, note that
regular training errors have im proved over those of Section 5.3. The difference in this
case is that the characteristic impedances of the connecting microstrip lines are used
as terminating impedance. Therefore, when existing knowledge is used for model
development, fewer EM sim ulations are needed for a required model accuracy.
Table 5.14 Error results for the 2-port microstrip via, re g u la r tra in in g .
(15 train structures, 4 inputs, 4 outputs, 13 hidden neurons, 121 weights)
O
N
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
00
ISiil
IS2 1 I
z s 2I n
0.0020
0.0023
0.528
0.448
0.0065
0.0059
0.620
0.544
0.0041
0.0049
0.714
0.504
0.0105
0.0089
1.061
0.929
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53
Table 5.15 Error results for the2-port microstrip via, difference method.
(15 train structures, 4 inputs, 4 outputs, 12 hidden neurons, 112 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS,,I
Z S „ ( 0)
IS21I
Z S 2i (°)
0.0013
0.0014
0.628
0.502
0.0036
0.0035
0.731
0.526
0.0026
0.0032
0.709
0.524
0.0047
0.0038
0.983
0.839
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
5.6.2
StripIine-to-StripIine
Extension
K
w
Table 5.16 Error results for the 2-port microstrip via, PKI method.
(15 train structures, 8 inputs, 4 outputs, 11 hidden neurons, 147 weights)
z s n (°)
IS2 1 I
0.0017
0.0014
0.538
0.563
0.0032
0.0026
0.662
0.742
0.0021
0.0024
0.782
0.604
0.0038
0.0026
1.087
0.947
Multilayer
Interconnect:
t-J
O
IS.il
Frequency
Range
For this example, existing knowledge in the form o f an already trained EMANN model is used to extend the range o f one o f its own input variables, frequency.
The structure of the 50 Q stripline-to-stripline multilayer interconnect has been
discussed in Section 5.4.
Suppose an EM-ANN model has been developed for the frequency range of I
GHz to 16 GHz, but it is desired to extend the models frequency range up to 26 GHz.
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54
In this case, prior knowledge is in the form of the S-parameter response o f the
existing EM-ANN model up to 16 GHz. To extend the frequency range, the regular
training method, the difference method, and the PKI method have been employed.
EM simulations have been performed on 29 interconnect structures for the 16
GHz to 26 GHz range in 5 GHz steps. Five structures were used for training, 12
structures for simultaneous testing, and 12 structures for final model verification. As
with the 2-port microstrip via model, data that was originally simulated for training
has been placed in the testing dataset.
Model average error and standard deviation are given in Table 5.17, Table
5.18, and Table 5.19 for the regular training method, the difference method, and the
PKI method, respectively. Significant improvements in verification dataset errors are
observed for both the difference method and the PKI method over regular training,
especially for ISnl and Z S n - Also, the PKI method provides lower error results on
ISiiI, Z S n , IS2il. Results on Z S 21 are comparable.
As with the 2-port microstrip via model, addition of further data points to the
training dataset leads to increased accuracy for all training methods.
EM-ANN
models were developed using 9 training vias, 8 test structures, and again 12
verification structures.
Model average error and standard deviation are shown in
Table 5.20, Table 5.21, and Table 5.22 for regular training, difference training, and
PKI training, respectively. Again, use o f existing knowledge allows more accurate
model development with fewer EM simulations than regular training.
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55
Table 5.17 Error results for the stripline-to-stripline interconnect frequency extension
model, regular training. (5 train structures, 3 inputs, 4 outputs, 10 hidden neurons,
84 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS,,I
Z S „°
IS2 1 I
Z S 2i°
0.00411
0.00666
3.802
3.847
0.00142
0.00160
0.443
0.416
0.01640
0.02021
7.540
7.862
0.00441
0.00455
0.845
0.841
Table 5.18 Error results for the stripline-to-stripline interconnect frequency extension
model, difference method. (5 train structures, 3 inputs, 4 outputs, 13 hidden
neurons, 108 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
is ,, i
Z S ,,°
IS2 1 I
Z S 21°
0.00470
0.00366
1.984
1.618
0.00171
0.00156
0.481
0.315
0.00906
0.01121
3.360
3.205
0.00336
0.00436
0.638
0.521
Table 5.19 Error results for the stripline-to-stripline interconnect frequency extension
model, PKI method. (5 train structures, 7 inputs, 4 outputs, 8 hidden neurons, 102
weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS,,I
Z S ,,°
IS2 1 I
ZS210
0.00322
0.00073
2.609
2.498
0.00089
0.00057
0.267
0.227
0.00849
0.00845
2.903
3.149
0.00275
0.00273
0.609
0.773
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56
Table 5.20 Error results for the stripline-to-stripline interconnect frequency extension
model, regular training. (9 train structures, 3 inputs, 4 outputs, 11 hidden neurons,
92 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
is,,i
ZSn°
IS2 1 I
Z S 2i°
0.00178
0.00207
2.069
2.320
0.00093
0.00080
0.211
0.196
0.00611
0.00732
4.583
4.154
0.00197
0.00262
0.422
0.435
Table 5.21 Error results for the stripline-to-stripline interconnect frequency extension
model, difference method. (9 train structures, 3 inputs, 4 outputs, 13 hidden
neurons, 108 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS,,I
^S n°
IS2 1 I
Z S 2i°
0.00216
0.00202
0.896
0.579
0.00082
0.00060
0.294
0.217
0.00584
0.00661
2.318
1.821
0.00193
0.00269
0.373
0.348
Table 5.22 Error results for the stripline-to-stripline interconnect frequency extension
model, PKI method. (9 train structures, 7 inputs, 4 outputs, 10 hidden neurons, 124
weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS 1 ,1
Z S ,,0
IS2 1 I
Z S 2i°
0.00139
0.00194
1.279
1.559
0.00055
0.00066
0.144
0.108
0.00470
0.00545
2.367
1.524
0.00173
0.00241
0.419
0.320
I
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57
5.7
Integration o f EM -ANN Models with a Network Simulator
After training, the EM-ANN models were integrated into a microwave
network simulator (HP-MDS [49]). Fig. 5.6 compares the new EM-ANN one-port
via model (NET1) with HP-Momentum results and the current MSVIA element
available in HP-MDS. Note that the MSVIA reference plane is at the center o f the
hole, while our reference plane is at the edge o f the pad. Therefore, a more accurate
model, also shown in Fig. 5.6, may be constructed by adding additional HP-MDS
elements such as MSSTEP, MSTL, and MSOC to account for the pad length and the
step in width.
However, the constructed HP-MDS model cannot accurately
characterize the via hole over the entire range o f the input variables, whereas the EMANN via model can. Excellent results are achieved by the EM-ANN models when
compared to HP-M omentum [48] simulations. Simulation times for NET1, MSVIA,
and HP-Momentum on an HP 700 workstation are shown in Table 5.23. Note that the
new EM-ANN model does not require a significant increase in simulation time over
the current HP-MDS model.
Table 5.23 Comparison of simulation times for the GaAs via described in Fig. 5.6.
The times for MSVIA and NET1 are averaged over 100 frequency points. HPMomentum results are for 1 frequency point.
M odel
HP-MDS, MSVIA
HP-M omentum
N etl (EM-ANN Model)
Simulation Time
0.37 sec
12.48 min
0.54 sec
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58
1
t
—
■
0.98
------------- II
0.96
(/)
0.94
--
msvia + comp
NET1
msvia
HP-MOM
0.92
0.9
15
25
35
FREQUENCY (GHZ)
45
55
45
55
(a)
190
180
170
5 160
LU
° 150
msvia + comp
NET1
msvia
HP-MOM
140
130
120
5
15
25
35
FREQUENCY (GHz)
(b)
Fig. 5.6 Comparison of EM-ANN model (NET1), HP-Momentum (HP-MOM), HPMDS via element (msvia), and MSVIA with added components (m svia + comp).
GaAs via with cr = 12.9, HSUb= 4 mil, tmetai=0.1 mil, CTmelai=4.1xl07, tan5 = 0.002,
W„Wp= 0.3875, Dvia/Wp =0.4, and W,/Hsub = 0.3375.
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59
5.8
Optimization of Component Structure
Once an EM-ANN model has been developed, it can be used to find the
optimal physical structure o f a component for a given application.
This can be
accomplished by using standard techniques such as random and gradient optimization
[49]. To demonstrate the usefulness o f optimization, an example is considered.
Example: Stripline-to-Stripiine Multilayer Interconnect
For this EM-ANN model, two variable physical parameters are: the diameter
of the via and the diameter o f the ground access opening. This structure has been
considered in [62] and it was found that good performance was obtained as long as
the diam eter of the via was large and the ratio o f the diameter o f the ground access to
that o f the via was near 4.2:1. In fact, this ratio is the same as that o f the inner and
outer conductors of a 50 £2 coaxial line with £r = 2.94. However, only a limited
number of structures were simulated.
One would expect that the ratio for the
stripline-to-stripline interconnect might be less than for a coaxial line, increasing the
capacitance of the structure in order to compensate for only having a partial outer
conductor.
Initial values for the physical parameters were set at 0.3 for Dyi/Wi and 6.0
for Dgnd/Dyia. These are clearly not optimal values. Optimization was completed by
maximizing the transmission coefficient yielding DVja/Wi = 0.77 and Dgnd/Dvia = 3.4.
These results agree well with our expectations as mentioned previously.
1
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CHAPTER 6
MULTICONDUCTOR MULTILAYER COUPLED TRANSMISSION
LINE DESIGN USING ANN MODELS *
The use of multilayer circuit configurations is increasing due to the
compactness and the increased design flexibility that may be achieved.
Although
multilayer circuit configurations have been widely used for digital and low frequency
systems, their use at RF and microwave frequencies is limited. Directional couplers
and baluns, implemented in multilayer configurations, have appeared in recent years
[70-74].
In addition, the design o f filters in multilayer configurations has been
demonstrated, but they are limited to broadside coupled symmetrical
strip
configurations [75-77].
In the past, RF and microwave circuits have generally been fabricated in
single-layer configurations [78, 79]. Often, very tightly coupled lines are needed, but
are difficult to fabricate in single-layer configurations.
Multilayer configurations
overcome this difficulty because o f the flexibility in overlapping coupled lines on
different layers. This makes it convenient to design tightly coupled sections. Also,
' This work has been carried out in collaboration with Choonsik Cho w hose project is aimed at
synthesis o f multilayered circuits.
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61
multilayer circuits can be implemented in both homogeneous and inhomogeneous
layered dielectric media.
Recently, a methodology for the design o f multilayer asymmetric coupled line
circuits has been proposed [80]. In this approach, network modeling and synthesis
procedures are used to derive normal mode parameters (NMPs) for various multilayer
coupled line sections, which constitute the circuit to be designed.
Evaluation of
physical geometry to realize the NMPs for each coupled section is not straight­
forward. An optimization procedure is used to arrive at physical dimensions for the
coupled line sections by comparing desired NMPs with those obtained by analysis of
the physical geometry. A problem associated with this optimization approach is the
presence of local minima, which can cause the optimization routine to stall instead of
finding the desired global minimum. Also, optimization can be very time consuming
and depends heavily on the selection of initial physical dimensions.
This chapter focuses on the use o f ANNs, in place o f time consuming
optimization routines, for evaluation o f the physical geometry for multiconductor
multilayer coupled line sections. Both synthesis (NMPs to the physical geometry)
and analysis (physical geometry to NMPs) ANN models have been developed.
Problems associated with synthesis using ANNs are discussed. As an example o f the
proposed methodology, the design of multilayer coupled line filters, using ANNs, is
demonstrated.
i
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62
6.1
Synthesis of Asymmetrical M ultilayer Coupled Line Sections
The synthesis procedure takes NMPs (desired response) and provides the
physical geometry required to achieve this response. An example o f a multilayer
coupled line configuration is shown in Fig. 6.1.
It consists of an asymmetrical
coupled line section in an inhomogeneous dielectric medium. Both layer-to-layer
coupling and same layer coupling are shown. A synthesis approach for the geometry
of multilayer coupled line sections for use in multilayer filter design, proposed in
[80], is shown in Fig. 6.2.
Beginning with circuit specifications, J-parameters
(admittance inverter parameters) are derived for each coupled line section.
selected values of Z0l,
For
(impedances at two ends of a coupled line section), and
another design parameter, ‘a’, related to coupling, NMPs are derived. NMPs are the
different voltage ratios (Rc and R J , mode impedances (Zci, Z*i, Z ^, and Z ^ ), and
phase velocities for the two normal modes, known as c- and n- modes, used to
characterize asymmetrical coupled line sections [81-83]. Four o f the NMPs (Rc, R*.
Zd and Z ,i) are utilized to obtain the physical dimensions (for selected substrate, h,
and £r values) of each coupled line section by using an optimization routine. This
optimization process compares the NMPs obtained from specifications with those
calculated from the physical geometry by evaluating capacitance and inductance
matrices [81-83] as an intermediate step. The capacitance and inductance matrices,
for a specific coupled line geometry, are determined using Segmentation and
Boundary Element Method (SBEM) analysis [84]. This process (contained inside the
dotted block A in Fig. 6.2) continues in an iterative manner until desired results are
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63
Same Layer
Layer-to-Layer
I
I
| W*
W
1I
I
w1( ,w2
I
air
£r2
T
I I
I
I
£ r1
/ / / / / a / / / / / / / / / / / / ///A//y/ / / / / / /
—►is r*—
—i►is
Fig. 6.1 Exam ple o f a multiconductor multilayer coupled line geometries in an
inhomogeneous medium. Both layer-to-layer and same layer coupling sections are
shown.
Circuit Specifications
.(•parameters
Choose Zot and Zq2 for
each coupled line section
( or 'a' reselected)
Nonnal mode parameters
lor each coupled section
SBEM
Optimize for physical dimensions
NMPs
acceptabli
No
Yes
and
Results
Fig. 6.2 Procedure for the design o f asymmetric multilayer coupled line sections
using optim ization [80].
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64
obtained. If the desired agreement with NMPs is not obtained, Zoi, Z ^ , and ‘a' are
altered to obtain a new set of NMPs, which yield the same circuit performance. The
optimization procedure is repeated with this new set of parameters. Thus we have
two levels of iterations involved in this design procedure.
Optimization is used to determine the physical geometry o f the coupled line
sections because no closed-form expressions for deriving physical dimensions from
NMPs are available. Also, the solution to the problem is not unique. In other words,
different coupled line sections can produce the same values o f the 4 selected NMPs.
It should also be noted that the choice o f NMPs for a desired circuit response is not
unique because of selection of parameters Zq|, Z 0 2 , and ‘a’. Therefore, as shown in
Fig. 6.2, the terminating impedances, Zoi and Z 0 2 , and ‘a’, for each coupled line
section can be chosen to provide realizable physical dimensions. For a more detailed
discussion see [80, 84],
One problem associated with optimization procedures is the likelihood of
finding a local minimum instead o f the desired global minimum.
In this case,
selection of initial physical values for the coupled line sections is very important.
Also, optimization can be very time-consuming as will be shown.
6.2
ANN M odeling Methodology for M ultilayer Asymmetric Coupled Lines
In order to bypass the problems associated with optimization, ANN models
may be used. ANN models can be used to effectively determine physical values for
coupled line sections from given NMPs (synthesis).
ANN models may also be
Ji
1
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65
developed which give the correct S-parameter response based upon the physical
geometry (analysis) for use in commercial microwave circuit simulators. The SBEM
method is used to provide the training data for both the synthesis and analysis models.
Training data is obtained by specifying physical parameters and their ranges for the
multilayer coupled line sections under consideration. Simulations are carried out to
obtain the L and C matrices corresponding to the physical geometry. These L and C
matrices can then be easily converted into NMPs by analytical techniques [84],
Therefore, a set of NMPs, corresponding to a specific physical geometry, is obtained.
This data can be used to develop both synthesis and analysis models for the design of
asymmetric multilayer coupled line circuits.
6.2.1
Analysis Model
The development o f the analysis model is straightforward.
Models are
developed for each type o f coupled line section using the methodology discussed in
Chapters 2 and 3. Physical parameters, such as the width o f each line and the spacing
between their edges, are used as ANN models inputs as shown in Fig. 6.3.
The
outputs are the elements o f the L and C matrices corresponding to the coupled line
configuration. Once the L and C matrices have been obtained, they can be used to
determine the NMPs and consequently the S-parameters o f a given coupled line
section. Analysis models m ay be linked to commercial microwave circuit simulators
for circuit analysis and optimization.
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66
► Ln
W,
► l 12
Wo
Analysis ANN model for a
single coupled line section
for a selected set of £r1,
h1t and h2
► L 22.
► Cn
► C-|2
C 22
Fig. 6.3 Analysis ANN model for asymmetric m ultilayer coupled line sections.
-► W1
Synthesis ANN model for
a single coupled line section
for a selected set of s r1, s^,
and h2
►s
Fig. 6.4 Synthesis ANN model for asymmetric multilayer coupled line sections.
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67
6.2.2
Synthesis Model
The synthesis model is developed by using normal mode parameters as inputs
to the ANN model as shown in Fig. 6.4. The desired physical parameters for the
coupled line section are the outputs. This is known as an inverse modeling problem
because the input and output variables are interchanged from characterization. For
such problems there exists a well-defined forward (analysis) problem which is
characterized by a single-valued mapping.
However, for inverse problems, the
mapping can often be multi-valued, with values o f the inputs for which there are
several valid values for the outputs. In this case, if a least-squares error approach is
used, the neural net tends to approximate the average o f the target data [38]. This can
lead to poor network performance since the average o f several solutions is not
necessarily itself a solution.
Another problem associated with inverse modeling is the coverage o f the
input variable space by the selected training data.
For the forward problem, it is
possible to select points for ANN training which characterize the entire space spanned
by the input variables. However, when the roles o f the input and output variables are
interchanged for inverse modeling, full characterization o f the new input space most
likely is not achieved. Therefore, there can be valid input vectors (within the input
space) for the ANN model which produce incorrect results due to the absence of
training data for particular regions o f input space.
The problem for asymmetrical coupled line design, as mentioned previously,
is that the mapping from physical parameters to NMPs is single-valued, while the
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68
inverse mapping from normal mode parameters to physical parameters can be multi­
valued. For problems involving many input and output variables, where visualization
o f the data is not straightforward, it can be very difficult to determine whether there
are regions of input space for which the target data is multi-valued. It can also be
difficult to determine if and where there are regions o f input variable space which
have not been characterized by the available training data. Therefore, a method for
determining the accuracy o f the model outputs is needed.
The method for verifying the accuracy of the synthesis model outputs is
shown in Fig. 6.5. First, the desired normal mode parameters are used as inputs for
the synthesis ANN model, giving physical parameters as outputs. The outputs o f the
synthesis model are then used as inputs to the analysis model, which is a single­
valued mapping, to determine the L and C matrices for the geometry obtained from
the synthesis model.
From the L and C matrices, NMPs are calculated and
transformed to 4-port S-parameters [84].
These 4-port S-parameters are then
compared to the 4-port S-parameters obtained from the NMPs 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 o f NMPs (input variables), the NMPs are altered by changing
Zoi, Zq2 , and/or ‘a’.
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69
Circuit specifications
C hange Zoi and Z02 to
modify J-parameters
J-param eters
Normal m ode param eters
for e ach coupled section
C hange ‘a‘ to
modify NMPs
No
Com pare
sp ecs
Y es
acceptable
Stop
Analysis ANN
Synthesis ANN
for
verification
m odel
R esu lts
Fig. 6.5 Modified synthesis procedure for asymmetric multilayer coupled line
sections using ANN models in place o f optimization.
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70
6.3
Multilayer Filter Design using ANN Models
As an example o f the proposed methodology, the design o f multilayer coupled
line filters, using ANN models, is presented in this section. The geometry of the type
o f filter under consideration is shown in Fig. 6.6.
Specifically, it is a two-layer
asymmetric coupled line filter in an inhomogeneous medium consisting o f 3 coupled
line sections. There are two types of open-ended coupling sections, each o f length
UA at the desired center frequency of the filter. Sections 1 and 3 couple layer I to
layer 2, while section 2 couples from layer 1 to layer 1. The height and dielectric
constant of each layer are taken as h i= 3 1 mils, hi=lO mils, and erI= srz = 2.2 (refer to
Fig. 6.1).
Fig. 6.6 Top view of a 2-layer coupled line filter consisting o f 3 coupled line
sections. Sections 1 and 3 couple from layer 1 to layer 2 and section 2 couples from
layer 1 to layer 1. Input and output ports are on the top o f layer 2.
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71
6.3.1
A N N Model Development for Coupled Line Sections
Both synthesis and analysis models have been developed for layer-to-layer
coupling and same layer coupling on layer 1 for the design of 2-Iayer coupled line
Filters. Variable parameters for the model inputs and their corresponding ranges are
given in Table 6.1 for layer-to-layer coupling, and in Table 6.2 for same layer
coupling on layer 1. Parameter ranges were chosen based on previous work on
multilayer coupled line filters [85].
SBEM analysis has been used to provide the
training data for ANN model developm ent.
Also, since SBEM analysis for this
geometry is not time consuming (1000 simulations take 40 minutes on an HP700
workstation), DOE techniques were not used to choose simulation points. Instead, a
uniform grid of points was chosen to provide the training data.
Table 6.1 Variable input parameters and corresponding ranges for the layer 1 to layer
2 coupling section model.
w,
w 2
s
Min.
1 mm
1 mm
-1 mm
Max.
5 mm
5 mm
1 mm
Table 6.2 Variable input parameters and corresponding ranges for the layer 1 to layer
1 coupling section model.
W,
W,
S
Min.
1 mm
1 mm
0.25 mm
Max.
5 mm
5 mm
2 mm
i
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72
Analysis ANN model error results and model specifics are given in Table 6.3
for layer-to-layer coupling and in Table 6.4 for same layer coupling on layer 1. Each
model has 3 inputs (W |, W 2, and S) and 6 outputs (C n, Q 2, C22, L n, L |2, and L22)
which constitute the L and C matrices for a given input geometry. Relative errors are
given in addition to absolute errors for better interpretation o f results. Low errors are
achieved confirming the accuracy o f the developed models.
Table 6.3 Error results for the layer 1 to layer 2 coupling line section analysis model.
(725 train/test examples, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156
weights)___________________________________________________________________
Train/test
A vg. Error
Std. Dev.
% A vg. Error
7c Std Dev.
Verification
A vg. Error
Std. Dev.
7c Avg. Error
7c Std. Dev.
c„
C|2
c„
(pF/m.)
(pF/m)
(pF/m)
Lu
(nH/tn)
(nH/m)
(nH/m)
0.933
0.768
0.346
0.299
0.886
0.734
1.630
1.406
0.899
0.862
2.340
1.811
0.790
0.567
2.084
1.390
0.970
0.687
0.759
0.554
2.249
2.290
0.922
0.660
0.792
0.500
0.346
0.313
1.059
0.577
1.167
0.851
0.856
0.619
2.816
1.885
0.695
0.476
2.185
1.496
1.207
0.501
0.596
0.395
2.403
2.624
1.110
0.714
L-22
Table 6.4 Error results for the layerl to layer 1 coupling line section analysis model.
(645 train/test structures, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156
w e i g h t s ) ______ ______ ______ ____________________________________________
c„
Train/test
Avg. Error
Std. Dev.
(pF/m)
Cn
(pF/m)
C 22
(pF/m)
Lit
(nH/m)
L|2
(nH/m)
L 22
(nH/m)
0.516
0.451
0.139
0.089
0.457
0.372
1.788
1.518
0.445
0.588
1.639
1.563
7c A vg. Error
7c Std. Dev.
Verification
A vg. Error
Std. Dev.
0.447
0.322
2.075
2.061
0.419
0.313
0.813
0.592
2.277
2.643
0.743
0.612
0.373
0.290
0.181
0.119
0.346
0.231
1.409
1.168
0.426
0.438
1.489
1.331
7c A vg. Error
7c Std. Dev.
0.313
0.206
2.360
1.407
0.366
0.289
0.653
0.429
2.385
2.252
0.679
0.588
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73
Synthesis ANN model error results and model specifics are given in Table 6.5
for layer-to-layer coupling and in Table 6.6 for same layer coupling on layer 1. These
models each have 4 inputs (Rc, l/R*, Zc, and Z*) and 3 outputs (W[, W2, and S). Note
that instead of using R* as an input, 1/R* has been used. This is due to discontinuities
which tend to ±oo as R* changes sign.
Using 1/R* reduces the effects o f the
discontinuities and allows an accurate model to be developed.
Since good model
accuracy has been achieved, there does not seem to be a significant problem with
multi-valued outputs for the same inputs.
Table 6.5 Error results for the layerl to layer 2 coupling line section synthesis model.
(725 train/test examples, 25 verify; 4 inputs, 3 outputs, 13 hidden neurons, 107
weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
W,
(mm)
W2
(mm)
S
(mm)
0.036
0.028
0.061
0.049
0.024
0.021
0.034
0.027
0.079
0.046
0.015
0.015
Table 6.6 Error results for the layerl to layer 1 coupling line section synthesis model.
(645 train/test examples, 25 verify; 4 inputs, 3 outputs, 14 hidden neurons, 115
weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
W,
(mm)
W2
(mm)
S
(mm)
0.023
0.018
0.056
0.047
0.034
0.028
0.023
0.019
0.044
0.029
0.036
0.024
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74
6.3.2
Design Example: 2-Layer Coupled Line Filter
The developed ANN models have been used to design a 2-layer coupled line
filter having the specifications given in Table 6.7.
Physical dimensions, obtained
from the ANN models, for each coupled line section are given in Table 6.8.
To
determine the accuracy o f the ANN model outputs, comparisons were made between
the modeled 4-port S-parameters o f each coupled line section with those obtained
from specifications at the desired center frequency. Again, these 4-port S-parameters
are for general coupled lines and have been used to determine whether the output of
the synthesis model is valid for the given input NMPs.
Error bounds for an
acceptable solution have been set at 0.01 for magnitude and 5° for angle. Angle error
was not considered when the magnitude o f a given S-parameter was below 0.01. The
4-port S-parameters can then be transformed into the appropriate 2-port S-parameters,
which characterize the open-ended, UA coupling sections used for filter design.
Table 6.7 Filter specifications used for the design o f a 2-layer asymmetric coupled
line filter.
C enter frequency
Ripple Bandwidth
Ripple Level
N um ber o f coupled sections
Sri = Sr2
hi
h2
2 GHz
7.5 %
0.5 dB
3
2.2
31 mil
10 mil
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75
Table 6.8 Physical dimensions obtained from ANN models for the 2-layer filter
example. Filter specifications are given in Table 6.7.
Section #
1
2
3
W | (mm)
1.50803
1.71022
2.95975
W 2 (mm)
2.93213
3.06325
2.79627
S (mm)
0.05418
0.79071
-0.08822
3.2259
W„ W0 (mm)
Zoi (SI)
60
60
40
Zo2 (J2)
50
40
50
The modeled filter response is shown in Fig 6.7 along with the response
obtained from SBEM analysis o f the coupled line sections as given in Table 6.8.
Also, center frequency, ripple bandwidth, ripple level, and 3 dB bandwidth are given
in Table 6.9. Analysis ANN models for each coupled line section have been linked to
a commercial microwave circuit sim ulator (HP-MDS [49]) to obtain the filter
response.
Excellent agreement is obtained confirming the accuracy of the ANN
coupled line models.
If the 0.7 dB ripple level is unacceptable, the filter response may be optimized
to obtain the desired 0.5 dB ripple using the ANN analysis models. The optimized
filter dimensions are given in Table 6.10. Filter response is given in Table 6.11 and
shown in Fig. 6.8.
Note that only small changes in physical parameters were
necessary to achieve the desired response. These changes are on the order of the
errors for the ANN models given in Table 6.5 and in Table 6.6.
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76
Table 6.9 Comparison of two-layer filter responses.
3 dB
Bandwidth
(%)
-
Ripple Level
Specification
Center
Frequency
(GHz)
2
(dB)
0.5
Ripple
Bandwidth
(%)
7.5
ANN
l.98
11.11
0.702
7.87
SBEM
1.98
10.86
0.748
7.83
1.25
1.5
Frequency (GHz)
1.75
2
2.25
2.5
2.75
-10
-20
■o
Su_ANN
-30
-40
-50
Fig. 6.7 Two-layer filter response. Both ANN modeled (light solid lines) and SBEM
(dark dashed lines) results are shown.
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77
Table 6.10 Optimized physical dimensions obtained from ANN models for the 2layer filter example. Filter specifications are given in Table 6.7.
Section #
1
2
3
W ( (mm)
1.52068
1.70905
3.00076
W 2 (mm)
2.94101
3.06157
2.69997
S (mm)
-0.00732
0.75217
-0.10564
3.2259
Wi? W0 (mm)
Zoi (H)
60
60
40
Zo2(Q)
50
40
50
Table 6.11 Comparison o f optimized two-layer filter responses.
3 dB
Bandwidth
(%)
-
Ripple Level
Specification
Center
Frequency
(GHz)
2
(dB)
0.5
Ripple
Bandwidth
(%)
7.5
ANN (opt.)
1.98
11.61
0.456
8.08
SBEM (opt.)
1.98
11.36
0.501
8.02
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78
Frequency (GHz)
1.25
1.5
2.25
1.75
2.5
2.75
-10
-20
-30
Sn_SBEM
-40
Si i_ANN
-50
Fig. 6.8 Two-layer filter response. Both ANN m odeled (light solid lines) and SBEM
(dark dashed lines) results are shown.
6.3.3
Comparison o f 2-Layer Filter
Optimization Method
Design
Using
ANN
Method
and
A filter w ith the same specifications given in Table 6.7 has also been designed
using the optimization method discussed in Section 6.1. Table 6.12 gives the physical
dimensions, while Table 6.13 gives the center frequency and bandwidth parameters of
the designed filter.
The filter performance param eters obtained by using ANN
modeling are also repeated here for comparison.
I
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79
Table 6.12 Physical dimensions obtained from optimization method for the 2-layer
filter example. Filter specifications are given in Table 6.7.
Section #
1
2
3
W | (mm)
1.4928
1.7078
2.9706
W 2 (mm)
2.9259
3.1520
2.7987
S (mm)
0.0535
0.7880
-0.0904
Wj, W 0 (mm)
3.2259
Zo, (£2)
60
60
40
Z o2(Q)
50
40
50
Table 6.13 Center frequency and bandwidth parameters for the 2-layer filter designed
using the optimization method. Also, the response of the filter using ANN modeling
is repeated here for comparison purposes.
3dB
Bandwidth
(%)
-
Ripple Level
Specification
Center
Frequency
(GHz)
2
(dB)
0.5
Ripple
Bandwidth
(%)
7.5
OPT.
1.98
10.86
0.539
7.68
ANN
1.98
11.11
0.702
7.87
The filter designs using the optimization method and ANN modeling are
comparable.
The ripple level for the ANN design is slightly larger than desired.
However, optimizing the physical geometry slightly, using the analysis ANN models,
resulted in the correct response. Note that no analysis models are available when
using the optimization method.
I
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80
The advantage of using ANN models for the filter design is a large savings in
required CPU time. Table 6.14 gives the CPU time on an HP700 workstation and the
number of design iterations (changes in physical geometry) required to arrive at the
final filter dimensions. Also given is the amount o f time required for optimization of
the filter response using ANN analysis models linked to HP-MDS [49]. It is evident
that using ANN models for the filter design results in a much more efficient process
than using optimization methods.
Both designs were carried out on an HP700
workstation. For the design comparison, only ‘a’ was allowed to change. Zoi and Zo2
were held constant for each section.
Table 6.14 Two-layer filter design times and required iterations for ANN modeling
and the optimization method o f [80],
# iterations
CPU time
1
4
0.0379 sec.
2
8
0.0758 sec.
3
3
0.0284 sec.
2
0.76 sec.
1
4212
64 min. 11 sec.
2
1634
125 min. 4 sec.
3
1285
19 min. 1 sec.
Section
ANN:
ANN optimization
using HP-MDS:
Optimization:
6.4
Discussion
It has been demonstrated that ANN modeling offers an accurate and efficient
alternative to optimization methods for the design of multilayer coupled line circuit
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81
components. Circuit elements can be designed in a small fraction o f the time using
ANN models.
Another advantage o f the ANN modeling approach for m ultilayer circuit
design is the availability o f analysis models, which can be linked to com m ercial
microwave simulators. These analysis models can be used in conjunction with other
component
models
and
optimization
routines,
available
within
com m ercial
microwave circuit simulators, for the design and optimization o f larger circuits.
Analysis models are not available when using the optimization method for m ultilayer
coupled line circuit design.
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CHAPTER 7
DESIGN AND OPTIMIZATION OF CPW CIRCUITS USING EMANN MODELS FOR CPW COMPONENTS
Use o f coplanar waveguides (CPW) in micro wave/mm-wave integrated
circuits offers several advantages due to the physical configuration o f the CPW line.
These include: the ease o f mounting shunt and series lumped components, low
radiation losses, low dispersion, and the avoidance o f the need for thin fragile
substrates. These advantages make CPW an attractive choice for development o f
M MICs. Currently, design software available for C PW circuits is inadequate because
o f the non-availability of accurate and efficient models for CPW discontinuities such
as bends, T-junctions, steps-in-width, short and open stubs, etc.
Accurate
characterization and modeling o f these components are vital for accurate circuit
simulation and increased first-pass design success.
Much effort has been expended in developing accurate and efficient methods
for electromagnetic (EM) simulation o f CPW discontinuities [86-118]. However, the
time-consuming nature of EM simulation limits the use o f these tools for interactive
CAD and circuit optimization.
Equivalent circuit models generally available for
CPW discontinuities require certain assumptions to be made which may or may not be
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83
valid over the desired range of operation.
CPW discontinuities have also been
characterized by measurements [119, 120], generating a library of data, which is
generally valid only for the structures measured. This method of characterization is
also very time-consuming.
As an alternative to the above, EM -ANN models for CPW components
suitable for use in interactive MMIC design and optimization have been developed.
No assumptions about component behavior are made when developing the EM-ANN
models.
Full-wave EM simulation has been employed to characterize the CPW
components.
EM -ANN models have been developed for CPW transmission lines
(frequency dependent Z q and £re), 90° bends, short circuit stubs, open circuit stubs,
step-in-width discontinuities, and symmetric T-junctions.
Air-bridges are included
where needed to suppress the unwanted slot-line mode [121]. All models have been
developed using HP-Momentum [48] for EM simulation and its adaptive frequency
sampling (AFS) feature, with the exception o f the CPW transmission line model.
This was due to the unavailability of Zo information for CPW lines in the particular
version of Momentum available at the time this work was completed.
Common
parameters for all models are the substrate parameters (£r = 12.9, HSUb = 625 pm, tanS
= 0.0005) and air-bridge parameters (Ha = 3 pm and W a = 40 pm). Once developed,
these EM-ANN models are linked to a commercial microwave circuit simulator
where they provide accuracy approaching that o f the EM simulation tool used for
characterization o f the CPW components over the entire ranges of the model input
variables.
In addition, the developed models allow for very fast, accurate
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84
electromagnetic/circuit optimization within the framework of the circuit simulator
environment.
Circuit design using the developed EM-ANN CPW models is demonstrated by
two exam ples: a CPW folded double stub filter and a 50 Q, 3 dB power divider
circuit. Optimization of circuit responses have been performed and compared to the
full-wave simulation results o f the entire circuits, showing excellent agreement.
7.1
EM -ANN Modeling o f Chamfered CPW 90° Bends
In this section, EM-ANN models are developed for two different chamfered
CPW bend structures as shown in Fig. 7.1. Air-bridges are placed near CPW bends in
order to reduce the unwanted slot-line mode which tends to radiate [121]. The slotline m ode is generated in CPW bends due to the path length difference for the two
slots. The inclusion of air-bridges, however, adds unwanted capacitance, which can
degrade the performance of the bend. In addition to compensating for the reactances
associated with the bend, chamfering provides a simple way to partially compensate
for the effects of the air-bridges. This section investigates the effects o f chamfering
on the S-parameters for the CPW 90° bends shown in Fig. 7.1. Optimal chamfering
values are determined for the different bend structures.
CPW bends of the type shown in Fig. 7. la have been studied in [88], but only
for b=0 and b=W+G. The work reported in [88] is extended by determining the
optimal chamfer for each bend structure. The compensated CPW bend shown in Fig.
7.1b is a novel structure which has been shown, by EM simulation, to improve upon
the return loss and the insertion loss o f the conventional chamfered bend o f Fig. 7.1a.
I
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85
(a)
-«S- W
(b)
Fig. 7 .1 CPW 90° bend structures with W a = 40 pm, Ha = 3pm, HSUb = 625 pm, er =
12.9, and tan8 = 0.0005.
(a) Conventional chamfered bend and (b) novel
compensated bend (Ha is height o f air-bridge above the substrate, Wa is the width of
the air-bridge, and HSUb is the substrate thickness.)
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86
EM-ANN models are developed for the CPW bends and are used to determine
optimal chamfer values.
All air-bridge parameters are held constant in order to
concentrate on the effects caused by the chamfering of the bends.
7.1.1
Optimally Chamfered Conventional CPW Bend
An EM-ANN model has been developed for the CPW bend structure shown in
Fig. 7.1a. Variable inputs for the EM-ANN model are W, G, b/bmax, and frequency.
Model outputs are S-parameters. Substrate material used is GaAs (£r = 12.9), and the
thickness is 625 pm for all results included here. Air-bridges are 40 pm wide (Wa), 3
pm (Ha) above the GaAs surface, and are positioned at the bend discontinuity as
shown. Note, all air-bridge parameters are held constant in order to concentrate on
the effects caused by the chamfering of the bends.
EM simulations were performed on 17 bend structures, included within the
range o f parameters given in Table 7.1. Characteristic impedances used for port
terminations have been determined from linecalc [68].
Five different values of
chamfer were simulated for each bend, with b/bmax ranging from 0 to I. The strip
comer was chamfered by a proportional amount given by bW/(W+G). EM simulation
data was separated into training/test (165 examples) and verification (300 examples)
datasets for model development. Ten neurons were used in the hidden layer. Error
results (EM-ANN model compared to EM simulation) are shown in Table 7.2.
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87
Table 7.1 Variable parameter ranges for C PW components.
Max.
50 GHz
120 pm
60 pm
Min.
1 GHz
20 pm
20 pm
Frequency
W
G
Table 7.2 Error results (average and standard deviation) between the EM-ANN model
and full-wave simulation for the optimally chamfered C PW bend.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
ISml
ZS „(•)
IS2 1 I
Z S2i(°)
0.000701
0.000632
0.102
0.104
0.000293
0.000270
0.034
0.029
0.000966
0.001058
0.124
0.141
0.000354
0.000339
0.048
0.039
It was determined that indeed there exists an optimal chamfer for each
structure, especially when analyzing the return loss, 201ogiolSnL The developed EMANN model can reproduce the trends in S-parameters determined by the changes in
the physical structure of the CPW bend. Using this model, the optimal chamfer for
each bend is determined. Fig. 7.2 shows the optimal chamfer, b/bmax, versus W/G for
minimum return loss, as determined by the EM-ANN model. The optimal chamfer as
a function of W /G is given by
b/bmax = 0.2102 ln(W/G) + 0.7677
= 1
for 0 < W/G <2
for W/G > 2.5
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(7.1)
88
0.8
X
n
CQ
E
^
0.6
0 .4
b/bmax
'm a x = 0 .2 1 0 2 ln (W /G ) + 0 .7 6 7 7
0.2
0
0 .5
1
1 .5
2
2 .5
W/G
Fig. 7.2 Optimal chamfer for return loss versus W /G for the conventional CPW 90°
bend. (Fig. 7.1a.)
7.1.2
Novel Compensated CPW Bend
An EM-ANN model has been developed for the novel compensated CPW
bend structure, proposed here, shown in Fig. 7.1b. This novel bend is capable of
improving upon the performance o f the already discussed optimally chamfered CPW
bend.
Variable input parameters for the model are W, G, and frequency.
Model
outputs are S-parameters. For this novel bend, the optimum chamfer for the strip is
found to be the maximum allowable by air-bridge placement.
EM simulations have
been performed on 17 bend structures, included within the range o f parameters given
in Table 7.1, to provide training/test (45 examples) and verification (35 examples)
i
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89
datasets for model development. Ten neurons were used in the hidden layer. Error
results for the developed EM-ANN model are shown in Table 7.3.
Table 7.3 Error results (average and standard deviation) between the EM -ANN model
and full-wave simulation for the compensated bend.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
7.1.3
ISnl
Z S „(°)
IS21 I
Z S 2i(°)
0.000784
0.000518
0.680
0.513
0.000584
0.000390
0.363
0.261
0.001390
0.000861
1.022
0.759
0.000705
0.000365
0.447
0.380
CPW Bend Comparisons
The novel compensated CPW bend structure is found to improve the return
loss over the optimally chamfered conventional bend, as shown in Table 7.4. This is
believed to be due to a decrease in capacitance as the slot width at the com er is
increased, thereby compensating for the increase in capacitance due to the air-bridges.
Improvements are also seen in the insertion loss.
Note that all air-bridge parameters
remain the same as in the case for the optimally chamfered CPW bend.
Comparisons between unchamfered CPW
comer, optimally chamfered
conventional bend, and the novel compensated bends are shown in Fig. 7.3 for CPW
bend structures with W = 70 pm and G= 20 pm, corresponding to Zo=35 Q .
Note that
all air-bridges and reference planes are at the same positions. Based on the results
shown in Fig. 7.3 and in Table 7.4, the new compensated bend provides significant
improvements in return and insertion loss over the other CPW bend structures.
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90
Improvements are also seen when comparing the optimally chamfered bend results to
the comer (unchamfered) bend.
-10
-20
- -
-30 - -4 0 - -
5
C om er
-50 - -
Opt. Chamf.
-60
Comp. Bend
-70
17
6.5
34
50
Frequency (GHz)
0
2 “ -0 .0 5 --
«T -0.1 +
(0
o
^
-0 .1 5 +
o
'■E
0)
(0
£
-
0.2
Corner
- -
Opt. Chamf.
-0 .2 5 +
Comp. Bend
-0 .3
6.5
17
34
50
Frequency (GHz)
Fig. 7.3
Comparison of unchamfered (Comer), conventional (Opt. Chamf.), and
novel (Comp. Bend) CPW bends. W = 70 pm, G=20 pm, 8,= 12.9, and HSUb=625 pm.
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91
Table 7.4 Comparison of return loss for the conventional optimally chamfered bend
and the novel compensated bend for several structures. (Frequency = 50 GHz)
w
G
(pm)
(pm)
70
120
70
35
105
105
70
7.1.4
60
40
20
55
55
25
40
Optimally
Chamfered bend
Return loss (dB)
Novel bend
Return loss (dB)
-13.89
-12.96
-21.51
-17.27
-12.50
-15.76
-16.36
-20.92
-16.36
-26.94
-20.18
-17.02
-19.33
-21.41
Improvement
(dB)
7.03
3.40
5.43
2.91
4.52
3.57
5.05
CPW 90° Bend with Air-Bridge Height as an Input Parameter
As an example of using prior knowledge (existing models) for ANN model
development, an input parameter is being added to an existing EM-ANN model using
regular training methods, the difference method, and the PKI method. The structure
of the CPW 90° bend under consideration is shown in Fig. 7.1a.
Variable input
parameters for the original EM-ANN model are frequency, W, and G. Model outputs
are S-parameters. Substrate material used is GaAs (£r = 12.9) and the thickness (Hsub)
is 625 pm for all results included in this section. Air-bridges are 40 pm wide (Wa)
and are positioned at the bend discontinuity as shown.
Originally, the height o f the air-bridge (Ha) was held constant at 3 pm. For the
new model, Ha is to be added as an input parameter. The new model variable input
parameters and corresponding ranges are given in Table 7.5. EM simulations have
been performed over the 1 GHz to 50 GHz frequency range for various air-bridge
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92
heights on 5 training structures (120 examples), 6 simultaneous test structures (140
examples), and 6 model verification structures (140 examples).
Table 7.5 Variable input parameter ranges for the CPW 90° bend.
Frequency
W
G
Ha
Min.
1 GHz
20 pm
20 pm
3 pm
Max.
50 G H z
120 pm
60 pm
9 pm
Model average error and standard deviation are given in Table 7.6, Table 7.7,
and Table 7.8 for the regular training method, the difference method, and the PKI
method, respectively.
Both the difference method and the PKI method show
increased accuracy over regular training for the same num ber o f training points. Also,
the PKI method gives slightly better accuracy than the difference method.
This example demonstrates the advantage o f using prior knowledge for adding
new input parameters to existing ANN models.
For the model developed using
regular training methods, more data would be required to obtain lower errors.
However, when using prior knowledge, information about old input parameters is
present, allowing additional EM simulations to be concentrated on capturing the
trends of the new input parameter.
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93
Table 7.6 Error results for the variable air-bridge height CPW bend model, regular
training. (5 train structures, 4 inputs, 4 outputs, 14 hidden neurons, 130 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
ISul
ZS„0
IS2il
Z S 2I°
0.0047
0.0042
2.871
3.718
0.0027
0.0024
0.917
0.657
0.0049
0.0043
2.592
2.432
0.0027
0.0025
1.080
0.882
Table 7.7 Error results for the variable air-bridge height CPW bend model,
difference method. (5 train structures, 4 inputs, 4 outputs, 15 hidden neurons, 139
weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
is , , i
ZSn°
IS21I
z s 2,°
0.0017
0.0014
1.213
1.744
0.0006
0.0005
0.197
0.126
0.0018
0.0015
1.886
2.463
0.0009
0.0011
0.271
0.253
Table 7.8 Error results for the variable air-bridge height CPW bend model, PK I
method. (5 train structures, 8 inputs, 4 outputs, 13 hidden neurons, 179 weights)
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
IS.,1
ZSn°
IS2,I
Z S 21°
0.0011
0.0010
1.161
1.285
0.0006
0.0004
0.227
0.114
0.0015
0.0012
1.559
1.787
0.0006
0.0001
0.227
0.215
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94
7.2
EM-ANN Modeling of CPW Transmission Lines
An
EM-ANN
model
characteristics of CPW
has
been
transmission
developed
lines.
for
frequency
dependent
Variable input parameters
and
corresponding ranges are given in Table 7.1. Model outputs are frequency dependent
Zq and 8re. The EM-ANN model has been trained using PCAAMT* [122], a program
which provides full-wave solutions for printed transmission lines and general
multilayer geometries. The training/test dataset consisted o f 265 examples, while the
verification dataset contained 51 examples. Twenty neurons were used in the hidden
layer.
Error results between the developed EM-ANN model and the full-wave
solution for the trainmg/test and verification datasets are shown in Table 7.9.
Table 7.9 Error results (average and standard deviation) between the EM-ANN
model and EM simulation for the CPW transmission line.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
Zo (a)
Zo (%)
£re
0.105
0.098
0.234
0.224
0.00283
0.00248
0.111
0.112
0.243
0.238
0.00341
0.00240
' Momentum (ver. A .02.20) could not be used for this purpose because value o f Zo is not available for
CPW.
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95
7.3
EM-ANN Models for CPW Opens and Shorts
Open and short circuit stubs are important components for many circuit
designs such as filters and impedance matching networks.
The geometries o f the
short and open components considered are shown in Fig. 7.4 and in Fig. 7.5,
respectively.
Variable input parameters and corresponding ranges for model
development are given in Table 7.1. Model outputs are S-parameters. Typical output
responses for an open and a short circuit with reference planes at the discontinuities
are shown in Fig. 7.6. For each model, EM simulations have been performed on 17
structures over the 1 G H z to 50 GHz frequency range. For the short circuit model
development, 71 examples were used in the training/test dataset and 46 examples for
the verification dataset, requiring 5 neurons in the hidden layer. Open circuit model
development was accomplished using 95 examples in the training/test dataset, 53
examples for the verification dataset, and 6 neurons in the hidden layer. Error results
for the training and verification datasets are given in Table 7.10 for the short circuit
and in Table 7.11 for the open circuit.
G
A
W
V
G
Fig. 7.4 CPW short circuit geometry.
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96
G_
A
W
JL
G
Fig. 7.5 C PW open circuit geometry.
10
-
20
30
40
50
0.1
-
0.2
-
0.3
-
0.4
£■o -0-5
CD
-
0.6
-
0.7
-
0.8
-
0.9
frequency (GHz)
180
150
120
90
60
-op en .S li
-shoft_Stt
30
0
10
20
-r
-*r
-30
-60
fre q u e n c y (GHz)
Fig. 7.6 S-parameter response for CPW open and short circuits. W = 70 pm, G = 60
pm, and reference planes at the discontinuities.
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97
Table 7.10 Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the CPW short circuit.
T rain/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
ISnl
Z S in (°)
0.000248
0.000350
0.396
0.271
0.000381
0.000412
0.964
0.867
Table 7.11 Error results (average and standard deviation) between the EM-ANN
model and full-wave simulation for the CPW open circuit.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
7.4
ISnl
Z S n (°)
0.000481
0.000633
0.332
0.373
0.000520
0.000892
0.634
0.676
EM -ANN M odeling o f C PW Step-in-W idth
CPW step-in-width discontinuities are used extensively in circuit design for
introducing impedance changes. The geometry of the step-in-width, for which an
EM-ANN model has been developed, is shown in Fig. 7.7. Variable input parameters
are frequency, Wi, W2, and G. Also, only structures where Wi < W 2 were used for
model development due to the nature o f the step. Parameter ranges are given in Table
7.1. Model outputs are S-parameters. A typical output response is shown in Fig. 7.8.
EM simulations have been performed on 30 structures over the 1 GHz to 50 GHz
frequency range, providing 95 training/test examples and 55 verification examples.
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98
Eight neurons were used in the hidden layer. Residual errors are shown in Table 7.12
and (as for other models developed) are negligible for design applications.
X
i
G
A
G
A
Wo
W 1
i
G
f
G
A
Fig. 7.7 CPW step-in-width geometry.
Table 7.12 Error results (average and standard deviation) between the EM -ANN
model and full-wave simulation for the step-in-width.
Train/test dataset
Average error
Standard dev.
Verification dataset
Average error
Standard dev.
ISnl
^S n(°)
IS2 1 I
ZS2i(°)
0.000864
0.000721
0.435
0.454
0.000792
0.000840
0.321
0.286
0.001214
0.001023
0.553
0.579
0.000986
0.001032
0.457
0.390
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99
50
-8
- -
d B (S 1 1 )
TJ
-12
d B (S 2 1 );
-1 6 --20
frequency (GHz)
180
150--
a n g (S 1 1 )
a n g (S 2 1 )
05
30 --
-30
40
50
frequency (GHz)
Fig. 7.8 S-parameter response for a 71 Q to 50 Q CPW step-in-width transition. W (
= 20 pm, W2 = 70 pm , G = 60 pm, and reference planes at the discontinuity.
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100
7.5
EM-ANN Modeling of CPW Symmetric T-junctions
The symmetric T-junction under consideration is shown in Fig. 7.9. Variable
model input parameters are frequency. Win, Gjn, Wout, and Gout. Param eter ranges are
given in Table 7.1. Model outputs are S-parameters. A typical output response is
shown in Fig. 7.10. EM simulations have been performed on 25 structures over the 1
GHz to 50 GHz frequency range, providing 155 training/test examples and 131
verification examples. Fifteen neurons were used in the hidden layer. Model error
results are shown in Table 7.13 for both the training/test and verification datasets.
out
out
out
out
©
Fig.7.9 CPW symmetric T-junction geometry.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
II
20
-2
40
50
-•
1k
dB(S11)
dB(S33) i
db(S13) I
dB(S23) |
-10
• •
-12
frequency (GHz)
180
120
TO
--
ang(S11)
ang(S33)
ang(S13)
ang(S23);
60 ••
O)
-60
frequency (GHz)
Fig. 7.10 S-parameter response for a typical CPW symmetric T-junction. Win =
W out = 70 pm, Gin = Gout = 60 pm, and reference planes at the air-bridge locations.
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102
Table 7.13 Error results between the EM-ANN model and EM simulation for the
CPW symmetric T-junction (average and standard deviation). Input branchline port is
Port I, and the output ports on the main line are Ports 2 and 3.
IS„I
4S„ °
ISI3I
Z S 13°
ISijI
Z S 23 0
IS33 I
Z S 33°
Train
Avg.
Stdev.
0.00150
0.00128
0.754
0.696
0.00071
0 .0 0058
0 .1 7 6
0 .1 7 2
0.00084
0.00097
0.246
0.237
0 .0 0 1 0 6
0.00109
0.633
0.546
Verify
Avg.
Stdev.
0.00345
0.00337
0.782
0.674
0 .0 0 0 8 8
0 .0 0 0 8 5
0.141
0 .1 2 5
0.00126
0.00105
0.177
0.129
0.00083
0.00068
0.838
0.717
7.6
CPW Circuit Design Examples
7.6.1
CPW Folded Double-Stub Filter
The first CPW circuit design example is a CPW folded double-stub filter as
shown in Fig. 7.11. For this design W = 70 pm and G = 60 pm, yielding Zq = 50 Q.
CPW EM-ANN models used are CPW transmission line, 90° compensated bends,
short circuit stubs, and symmetric T-junctions. The filter has been designed for a
center frequency of 26 GHz. Ideally, the length of each short circuit stub and the
section of line between the stubs should have a length of X74 at 26 GHz. However,
due to the presence of discontinuities, these lengths need to be adjusted. Design and
optimization have been accomplished using HP-MDS [49] network simulator and
EM-ANN models for various components.
Parameters to be optimized are
l SWb
and
lmjd.
Initial values for these lengths
were determined and the structure simulated, showing a less than ideal response. The
circuit was then optimized, using gradient descent, to provide the desired circuit
response.
The effect of optimization was reductions in line lengths.
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Results are
103
shown in Fig. 7.12 for the original design, optimized design, and full-wave EM
simulation of the entire optimized circuit. Excellent agreement is obtained betw een
the optimized EM -ANN circuit design and the full-wave EM simulation over the 1
GHz to 50 GHz frequency range.
This demonstrates applications of EM -ANN
models in CPW circuit design.
i
G_
A
W
jr.
G_
fI
Fig. 7.11 CPW folded double-stub filter geometry.
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104
0
^
-10
--
-20
- -
10
20
30
40
50
to
S’
■° - 3 0 - Opt. EM-ANN i
-40 - - - Org. EM-ANN
-50
frequency (GHZ)
200
150 ■*
100
o>
o>
<a
--
50 --
53
-50 --100
EM-ANN Opt.
-150
- - EM-ANN Org.
-200
frequency (GHz)
(a)
Fig. 7.12(a) S|i for C PW folded double-stub filter for the optimized EM-ANN
circuit (EM-ANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM
simulation (EM sim.).
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I
105
0
<2.
■O
-10
- -
-20
--
10
20
30
40
50
EM-ANN Opt.
-30
g
EM sim.
■ - - EM-ANN Org.
-40
frequency (GHz)
200
150
- - EM-ANN Org.
100
50 -20
-50- ■
-100
5D
\
- -
-150 - -200
frequency (GHz)
(b)
Fig. 7.12(b) S 21 for CPW folded double-stub filter for the optimized EM-ANN
circuit (EM-ANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM
simulation (EM sim.).
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106
7.6.2
CPW 50 £2,3 dB Power Divider
The second CPW circuit design example is a 50 Q , 3 dB power divider,
shown in Fig. 7.13. For this design, EM -ANN models for CPW transmission lines,
90° compensated bends, T-junctions, and step-in-width transitions are used.
The
power divider has been designed for a 3 dB pow er split between the output ports at 26
GHz.
Ideally, 7JA, 70.7 Q line sections are used to transform the 50 Q output
impedance at Ports 2 and 3 into 100 £2 loads at the T-junction. Due to the presence of
discontinuities, the lengths of the transformers need to be adjusted. Input and output
lines are 50 Q (W = 70 pm, G = 60 pm) and transformer lines are approximately 71 £2
(W = 20 pm , G = 60 pm).
Again, HP-MDS [49] has been used for design and
optimization.
The optimizable parameter for this design is the length of the transformer line
section, ltrans. An initial value for 1 ,^ was determined. After the initial design failed
to meet the prescribed design criteria, optimization was performed, resulting in a
shorter iine length than initially determined. Resuits are shown in Fig. 7.14 for the
original design, optimized design, and full-wave EM simulation o f the entire
optimized circuit. As with the double-stub filter design, excellent agreement has been
obtained between the optimized EM-ANN circuit design and EM simulation results
over the entire 1 GHz to 50 GHz range.
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107
trans
trans
G l< W H G
©
Fig. 7.13 CPW power divider geometry.
I
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108
0
10
20
30
40
50
EM-ANN Opt.
|
EM sim.
- - EM-ANN Org.
^
-
10-1
CO
m
■° -1 5 - -
-
20--
-25
frequency (GHz)
180
150 --
120
--
90 -U)
60 -EM-ANN Opt.
g
30 --
EM sim
■ - - B/t-ANN O rg .:
20
30
40
frequency (GHz)
(a)
Fig. 7.14(a) Sn for CPW power divider for the optimized EM-ANN circuit (EMANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM simulation (EM
sim.).
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109
0
10
20
30
40
50
0
■1
2
-3
-4
-5
-6
-7
-8
-9
-10
frequency (GHz)
200
150
100
a>
EM-ANN Opt. :
g
EM Sim.
• - -EM-ANNOrg.
50
-50
20
5)
-100
-150
-200
frequency (GHz)
(b)
Fig. 7.14(b) S 21 for CPW power divider for the optimized EM-ANN circuit (EMANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM sim ulation (EM
sim.).
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110
Use of EM-ANN models for CPW components has allow ed accurate and
efficient design and optimization o f the CPW filter. Thus, we note that the EM-ANN
modeis provide EM optimization capabilities. Optimization time for the EM -ANN
circuit was only 3 minutes and required 7 circuit analyses.
T he am ount o f time
required to provide EM simulation results for 17 frequency points for the entire filter
circuit was approximately 14 hours on the same HP 700 workstation. Optimization
time for the power divider circuit was only 2 minutes and required 6 circuit analyses.
EM simulation time for the entire power divider, at 15 frequency points, totaled
almost 11 hours on this HP 700 workstation. This confirms that substantial savings in
time are achievable by using EM-ANN component models, especially when
optimization is desired, requiring numerous circuit solves and when these components
are to be used over and over in different circuit designs.
It should be mentioned that even larger and more com plex circuits can be
designed using the developed EM-ANN models. EM simulation o f large, complex
circuits is limited by the computer resources available, and in many cases is not
practical. With EM-ANN component modeling, these difficulties are overcome.
7.7
Discussion
Results presented in this chapter demonstrate clearly the application o f the
EM-ANN modeling approach for developing efficient and accurate models for
various CPW components and discontinuities.
Models developed for CPW lines,
open-ends, shorts, steps-in-width, bends, and T-junctions can be conveniently used
for efficient and accurate design o f various kinds o f CPW circuits. The two examples
I
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
of circuit design and optimization reported in this chapter and verification o f final
design by comparing with electromagnetic simulation results validate the modeling
and design approach developed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 8
EM-ANN MODELS FOR DESIGN OF CPW PATCH ANTENNAS
This chapter explores the use of radiating elements using open-ended coplanar
waveguide (CPW) resonators to provide an alternative for printed slot antennas and
microstrip patch antennas. Motivation for exploring these antenna structures arises
from the ease of connecting CPW resonators to CPW lines, which have received
much attention due to several advantages of CPW lines over microstrips as discussed
in Chapter 7. Further investigation of these radiating structures requires development
of simple network models (like the transmission line model for microstrip patch
antennas) which may be used for designing these antennas. However, unlike in the
case for microstrip antennas, no work has been reported in the literature on wide strip
CPW lines or open-end discontinuities and their radiating properties.
Therefore, the
focus o f this chapter is on the development of accurate and efficient EM-ANN models
for wide strip CPW lines, CPW open-end discontinuities (including radiation
conductance modeling), and feed discontinuities used for connecting CPW resonators
to CPW lines. These models are then used within commercial microwave simulators
for CPW patch antenna design.
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113
8.1
Radiation Characteristics o f CPW Line and Open End
The radiation characteristics o f the CPW line open-end shown in Fig. 8.1 have
been studied, using HP Momentum [48], to determine the effects o f varying the strip
width, W, and the gap spacing, G. The substrate used is Duroid 5880 (8r = 2.2 and
HSUb = 31.25 mil). The open-end geometry lies in the x-y plane as shown. The polar
angle, 0, is measured from the z-axis towards the x-y plane and the azim uthal angle,
(j), from the x-axis towards the y-axis in the x-y plane.
8.1.1
Radiation from a Wide CPW Line
Figure 8.2 shows the simulated radiation pattern of a CPW line (W =1.5 cm,
G=0.01 cm, and L=3 cm) terminated at two ends by matched loads (without an open
end). The length, L, is A72 (CPW wavelength) at 5 GHz. The plane o f the pattern is
perpendicular to the gaps (<|) = 90°). The fields in the gaps are 180° out o f phase and
Ee contributions from the two gaps cancel in the broadside direction. However, since
W+2G is large, perfect cancellation does not occur for values of 0 away from 0°.
This radiation from a line section is different from that in a microstrip patch antenna
where the dominant radiation is only from the two open ends.
8.1.2
Radiation from CPW Open-Ends
A large width, W, is needed to increase the radiation from the CPW open ends
as with microstrip patch antennas. Therefore, rough guidelines for this work are that
G needs to remain small and W should be as large as possible as long as the radiation
from the line is at an acceptable level. To illustrate this, several CPW open ends have
been simulated. Figure 8.3 shows the effects o f increasing G on the H-plane (<{>= 90°)
i
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'end
y
X
Fig. 8.1 O pen-end CPW geometry.
ca
Broadside
r u
B1
Cl
JC
ou
i
L tJ
Fig. 8.2 Simulated radiation patterns (E q and E^) o f a CPW line (W =1.5 cm, G=0.
cm, L=3 cm and f = 5 GHz) w ithout an open end. The plane o f the pattern
perpendicular to the gaps (<j>= 90°).
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115
( u r \j
i
(a)
a
uj
(b)
Fig. 8.3 Far-Field radiation patterns (Ee and E^) at 5 GHz for two open-ended CPWs
with W = 1.5 cm, L=3 cm, Gend = 0.85 cm, and different gap widths ((j) = 90°). (a) G
= 0.5 cm and (b) G = 0.01 cm.
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116
radiation pattern o f the open-ended line. The strip width, W, is kept at X j A for these
simulations and the spacing, Gemi, is held constant. As G is increased, the radiation
from the CPW line increases (Eg) until it is as strong as the radiation from the openend (H^), Fig. 8.3a. Lines with smaller gaps show less radiation, Fig. 8.3b. Figure 8.4
shows the effects o f increasing W. The gap, G, is held constant for these simulations,
along with the spacing, Gen(j. We note from this figure that as W is increased, the
radiation from the line increases also. Therefore, for this modeling effort, small gaps
will be used along with smaller conductor widths to reduce the radiation from the
line.
Another reason for using small gaps is the presence of higher order modes on
the CPW line at the open-end discontinuity. Figure 8.5 illustrates the effects o f gap
width by showing the magnetic current distribution within the gaps. For the desired
CPW mode, the magnetic currents within the slots o f the line should be in opposite
direction and contain only x-directed, not transverse (y-directed), components.
Notice that for the open-end with wider gaps, higher order modes extending well into
the CPW line are present and contribute to the far field radiation since the transverse
magnetic current components are in phase in the two gaps and thus add in the far
field. For the open-stub with smaller gaps, higher order modes are not as visible.
Since the transmission line model assumes only one mode (TEM) on the line, it is not
a good candidate for modeling CPW antennas using CPW lines with wide gaps.
However, y-directed magnetic current components, in the gaps near the open-end.
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117
have the same polarization as the magnetic current at the open-end and are therefore
not undesirable from a radiation point o f view.
s)
C9
(a)
o
(b)
Fig. 8.4 Far-Field radiation patterns ((J) = 90°) at 5 GHz for two open-ended CPWs
with G = 0.05 cm, Gend = 0.85 cm, L=3 cm, and different conductor widths (W). (a)
W = 1.5 cm and (b) W = 2.0 cm.
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118
(a)
111 tiax£03r
(b)
Fig. 8.5 Magnetic current distributions for two CPW open-ends with W = 1.5 cm,
Gcnd = 0-85 cm, L=3 cm , and different gap widths at 5 GHz. (a) G = 0.5 cm and (b) G
= 0.1 cm.
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119
8.2
Transmission Line Equivalent o f a Rectangular CPW Patch
8.2.1
Transm ission Line Model for CPW Antennas
Transmission line models for microstrip patch antennas have been studied
extensively [123]. In the same manner, a transmission line model for CPW antenna
design can be developed. Figure 8.6 shows the antenna structure without the feed line
and an equivalent transmission line model. The transmission line model consists of a
length of CPW transmission line open-circuited at the two ends. Thus, the patch can
be represented by a uniform length of transmission line o f characteristic impedance Z q
and phase velocity u p (or propagation constant, (3=co/up).
For this model, the
assumption is that the line is operating in the TEM CPW mode and is lossless, which
is a fair assumption when the conditions o f Section 8.1 (small values o f G) are met.
The fringing fields associated with
the open ends are represented by lumped
admittances, consisting of a radiation conductance, Gr, and an edge capacitance, C.
’end
C
>
Fig. 8.6 Ideal CPW patch antenna geometry and corresponding transmission line
equivalent circuit model.
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120
8.2.2
EM-ANN Model for CPW Transmission Line
An EM-ANN model for wide conductor CPW transmission lines on Duroid
5880 (£r = 2.2 and Hsub = 31.25 mil) has been developed for use in C band antenna (4
GHz to 7 GHz) design. Model input variables and corresponding ranges are given in
Table 8.1. Outputs o f this ANN model are Zq and (3 for the CPW line.
Since the training data was relatively inexpensive to obtain for this
component, EM simulations were performed, using HP Momentum [48], for a
uniform distribution over the input variables’ ranges.
HP-Momentum is able to
provide values for Re(Zo) and P for CPW lines. The train/test dataset consisted of
140 input/output examples and the verification dataset contained 62 examples. The
optimal ANN structure contained 6 hidden layer neurons (38 weights). Error results
for the training and verification datasets are given in Table 8.2, and show excellent
accuracy. Typical trends for Zo and p are shown in Fig. 8.7 and are consistent with
those reported elsewhere for CPW lines with smaller strip widths [1].
Table 8.1 Input variables and ranges for CPW transmission line model.
Input Parameter
Maximum Value
Minimum Value
Frequency
4 GHz
7 GHz
W
0.5 cm
2 .0
cm
G
0.05 cm
0 .2
cm
Table 8.2 Error results (average and standard deviation) for the CPW line model.
Z olQ )
Train/test
A verage error
Standard dev.
Verification
Average error
Standard dev.
3
(rad/m)
0.109
0.075
0.147
0 .150
0.145
0.0 9 4
0.138
0.126
1
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121
124
68
■•123
122
■ *
- ■ 121
S
58 ■■
118
0.5
1.25
0.75
1.5
W (cm )
(a)
120.5
■•120
+ 119.5
£
■•119
g
■■118.5 ca.
N 60--
117.5
0.07
0.09
G (cm )
(b)
180
160
60 - ■
• ■140
58 ■■
■• 120
57 ■>
■ ■
56
100
80
Frequency (GHz)
( C)
Fig. 8.7 Typical trends for Zo and p (phase constant) with (a) f = 5 GHz, G = 0.05
cm, and W variable, (b) f = 5 GHz, W = 1.5 cm, and G variable, and (c ) W = 1.5 cm,
G = 0.05 cm, and frequency variable.
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122
8.2.3
EM-ANN Model for CPW Open-End Effects
An EM-ANN
model for CPW
open-end effects, including
radiation
conductance, has been developed. Substrate parameters are the same as those for the
CPW transmission line model.
Variable input parameters and their corresponding
ranges are given in Table 8.1. For this model, the open-end spacing, Gend. is set equal
to 0.5(W+2G). EM -ANN model outputs are the magnitude and phase o f S n . The
reflection coefficient, S n , for the open-end is obtained by simulating a Xl2 line and
finding input impedance at the far end.
This choice of output parameters allows
easier insertion of the m odel into commercial microwave simulators.
A DOE central composite design, as discussed in Chapter 3, was used to
obtain the EM simulation data for training. The parameters for the central composite
design were frequency, W , and G. Frequency is needed in the experim ents’ design
due to the fact that }J2 lines are needed for open-end characterization. Initially, 15
examples were used for training, 14 for testing, and 10 for verification.
However,
errors were not as low as desired. Therefore, the 14 test examples were added to the
training dataset for a total o f 29 examples. The final model contained 10 hidden layer
neurons (62 weights). Error values for the final model are given in Table 8.3. We
note that excellent accuracy has been achieved.
Radiation Conductance and Capacitance
The radiation conductance and capacitance o f the open end may be obtained
from the EM-ANN model by noting that S n is the reflection coefficient o f the open-
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i
123
Table 8.3
model.
Error values (average and standard deviation) for the CPW open-end
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
ISnl
Z S „(°)
0.0032
0.0029
0.493
0.418
0.0043
0.0037
0.728
0.623
end. When the line length used to characterize the open end is )J2 long and the line is
lossless, the load (that is, the open-end) impedance may be found as
Zl
1+ Su
= Z j-— —
1—on
(8.1)
Taking the inverse o f ZL to obtain YL yields the radiation conductance as
Gr = R c (Y l )
(8.2)
C = h !^
(8.3)
and the end capacitance as
CO
As noted, this technique for finding the load impedance is valid only for
lossless transmission lines.
Therefore, when radiation from the line increases, as
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124
described in Section 8.1, the values o f Gr and C are not only for the open-end, but also
include the effect of radiation from the line. However, the EM-ANN model with Sn
as the output still gives useful results, but Gr and C for the open-end alone cannot be
extracted using this sim ple method.
Using the guidelines for values of W and G given in Section 8.1, trends for Gr
and C have been determ ined and are shown in Fig. 8.8 and in Fig. 8.9. For the results
shown, the value o f the spacing, Gend, at the open end has been held constant. Notice
in Fig 8.8a that Gr increases slightly and C decreases as the gap width, G, is increased.
These results are expected due to the slight increase in radiating area at the top and
bottom of the open-end and the added distance between conductor and ground plane.
Both Gr and C increase as the center strip width, W, is increased, due to the increase
in radiating area, as shown in Fig. 8.8b. Fig. 8.9 shows the behavior of Gr and C
versus frequency for two different values of W. In Fig. 8.9a, the capacitance remains
fairly constant over m ost of the frequency range and then decreases sharply. Since it
is expected that C should only have a slight frequency variation, the extraction
technique, as described earlier, may not be valid for the points that show a sharp
decrease.
The reason for this is that as frequency increases, the patch becomes
electrically wider (W = "kJA at 5 GHz), increasing radiation from the line used to
characterize the stub. Therefore, for this case, the results up to only about 5.5 GHz
are reasonable for the open-end characterization (i.e., not affected significantly by
radiation from the CPW line itself)-
Fig. 8.9b shows results o f Gr and C versus
frequency for a lower value o f W (1cm). Notice that C remains fairly constant over
the entire frequency range as one would expect.
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125
0.3
- - 0.25
4 -=
- ■
3 --
0.2
-- 0.15
2
IT
B
-- -
0.1
- - 0.05
0.01
0.03 0.05
0.07 0.09
0.11
G (cm)
(a)
0.3
- - 0.25
2.5
- -
0.2
O)
-- 0.15
1.5
d
- -
0.1
-- 0.05
0.5
1 1.1 1.2 1.3 1.4 1.5 1.6
W (cm)
(b)
Fig. 8.8 Trends o f the radiation conductance, Gr, and capacitance, C, for a CPW
open-end with Gend=0.85 cm at 5 GHz. (a) G variable and W=1.5 cm . (b) W
variable and G=0.05 cm.
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126
0.35
-■ 0.3
- - 0.25
--
0.2
LL
a.
-- 0.15
"
0.1
- - 0.05
4.5
5
5.5
6
6.5
Frequency (GHz)
(a)
0.3
2 .5
0.25
0.2
u.
1.5
-- 0.15
--
0.5
0.1
■* 0.05
Frequency (GHz)
(b)
Fig. 8.9 Trends o f the radiation conductance, G r, and capacitance, C, for a CPW
open-end with Gend=0.8 cm versus frequency, (a) W=1.5 cm and G=0.05 cm. (b)
W=1 cm and G=0.05 cm.
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127
8.2.4
CPW Patch Antenna Design W ithout Including Feed Effects
Now that models for the CPW line and the CPW open-end have been
developed, the ideal CPW patch antenna design (ignoring feed discontinuities) may
be carried out. Again, the geometry under consideration is shown in Fig. 8.6.
For the ideal case, if the ends o f the patch are perfect open circuits, the length
of the patch, L, for resonance would need to be Xl2, providing maximum and equal
voltages at the patch ends and a real input impedance.
M aximum values o f the
voltage at the patch ends corresponds to the maximum radiated power.
W hen the ends of the patch are not perfect open circuits, the length of the
patch is reduced below X/2 due to the edge susceptance. The resonant patch length,
in this case, is determined by the condition o f having a real input impedance along the
patch, which also provides equal and maximum voltages at the patch ends [123J.
Using the EM-ANN models for CPW line and open-end (developed earlier in
this chapter) within a commercial microwave simulator, the patch length, L, is
determined by optimization and the patch antenna can be simulated . Voltage probes
may also be used to check the voltages at the patch ends. Results o f several ideal
CPW patch antenna designs are given in Table 8.4.
The results include antenna
designs with wide impedance bandwidths (ISnl < -10 dB) in the range of 7.7% to
14.2% for W =1.5 cm. As discussed previously, some o f the results (when W is wide)
may include radiation from the CPW line also, but an attempt has been made to keep
this to a minimum.
As will be demonstrated in the next section on practical
realization o f these CPW antennas, wide bandwidths can be achieved. Note that the
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128
bandwidth of a conventional microstrip patch antenna with W =
1.5 cm is
approximately 1%.
Table 8.4 Ideal CPW patch antenna designs.
Antenna
W = 1.0 cm
G = 0.05 cm
f = 5 GHz
W = 1.0 cm
G = 0.1 cm
f = 5 GHz
W = 1.5 cm
G - 0.05 cm
f = 5 GHz
W = 1.5 cm
G = 0.1 cm
f = 5 GHz
W = 1.0 cm
G = 0.05 cm
f = 4.5 GHz
W = 1.5 cm
G = 0.05 cm
f = 4.5 GHz
8.3
G r (mS)
C (pF)
L (cm)
BW (%)
0.878
0.201
2.052
36
0.978
0.193
1.989
4.9
3.015
0.296
1.767
12.0
3.575
0.294
1.648
14.2
0.682
0.205
2.337
3.0
2.049
0.294
2.103
7.78
CPW Patch Antenna Design Including Feed Discontinuities
Practical realization o f a CPW patch antenna design requires inclusion o f a
way to feed the antenna. Feed discontinuities can alter antenna performance and need
to be included and compensated for during design. The feed arrangement used for
this work is shown in Fig. 8.10. The patch is fed by a high impedance line on the
radiating edge. A radiating edge feed has been chosen to keep the design symmetric
in order to avoid excitation o f slot line mode on the patch. Also, ease o f fabrication is
a consideration. If a feed on the non-radiating edge is desired, it needs to be a dual­
feed in order to keep symmetry.
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129
7 ////////////A
Fig. 8.10 C PW patch fed on the radiating edge and its corresponding transmission
line model.
8.3.1
EM -ANN M odel for Feed Discontinuities
Variable input parameters for the model are given in Table 8.1. The incoming
feed line has to be kept narrow in width in order to minimize interference with
radiation from the radiating edge, but has to be wide enough to be realizable using
available fabrication facilities. Therefore, the incoming line has been chosen to have
W = 0.1 cm , G = 0.05 cm, and Z<, » 96 Q. The output parameters for this model are
the magnitudes and phases of S n , S 2 1 , and S 2 2 - EM simulations have been performed
on 27 structures over the 4 GHz to 7 GHz frequency range providing 111 training/test
examples and 42 verification examples. The optimal ANN structure contained 15
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!
1
130
hidden layer neurons (156 weights). Error results are given in Table 8.5. As with the
other models, excellent accuracy is obtained.
Table 8.5
Error results (average and standard deviation) for the CPW feed
discontinuity model.
Train/test
Average error
Standard dev.
Verification
Average error
Standard dev.
8.3.2
IS„I
Z S „(°)
IS2il
Z S 21 (°)
IS22I
Z S 2 2 (°)
0.0034
0.0032
0.596
0.621
0.0032
0.0029
0.654
0.529
0.0035
0.0028
0.824
0.921
0.0046
0.0041
0.794
0.761
0.0040
0.0039
0.699
0.550
0.0046
0.0034
1.215
1.225
C PW Patch A n ten n a Design Using EM -ANN M odels
CPW patch antennas may now be designed using the EM-ANN models
developed for the CPW open-end, CPW line, and feed discontinuities.
As an
example, a CPW patch antenna has been designed at 5 GHz with W = 1.5 cm and G =
0.1 cm. The ideal patch length for this antenna has been determined in Section 8.2.3
and is given in Table 8.4 (fourth row). The layout o f the antenna is shown in Fig.
8.11. CPW section ‘a’ was designed by optimization using ANN models to yield a
real value of impedance at its input. Impedance at the input of this section was found
to be 821 Q. Three matching sections have been included to transform the input
impedance from 821 Q to 50 Q for measurement purposes.
The option o f stub
matching was not selected because that would need incorporation o f air-bridges.
Table 8.6 and Fig. 8.12 compare return loss for the EM -ANN model (EM-ANN), EM
simulation using H P’s M omentum [48] (EMsim), and measurement (meas).
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131
Excellent accuracy is achieved by the EM -ANN model design when compared with
EM simulation and measurement. Note that the bandwidth (ISnl < -10 dB) is much
less than for the ideal patch (2.7% versus 14.2%) with no feed discontinuities.
Therefore, some alternative feed arrangement may be able to yield wider bandwidth
from this class of antennas.
the EM-ANN models.
What needs to be stressed, however, is the accuracy of
Other feeding arrangements, such as a feed on the non-
radiating edge, can be designed and m odeled in the same manner. Radiation patterns
from EM simulation and measurement are shown in Fig. 8.13.
radiation (z>0, above the metallized layer) is shown.
Only top-side
Bottom-side (below the
substrate) radiation is o f comparable magnitude.
Fig. 8.11 Layout o f CPW patch antenna design. Electrical parameters referenced to
the resonant frequency of 4.99 GHz.
Table 8.6 Comparison o f resonant frequency and bandwidth for EM-ANN modeling,
EM simulation, and measurement.
Center Frequency
% Bandwidth
EM-ANN
4.99 GHz
2.6%
EM simulation
5.01 GHz
2.6%
Measured
5.09 GHz
2.7 %
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132
4
4.5
5
5.5
6
0
_
-10
00
s
(0
-20
tf >
°
-30
c
EM-ANN |
3 -40
EMsim |
a>
cc
m ea& ^j
-50
-60
F r e q u e n c y (GHz)
Fig. 8.12 Comparison o f return loss for the CPW patch antenna shown in Fig. 8.11.
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133
-100
50
-50
03
2,
100
10
O
5
o
Q.
■o
0N>
30
-40
75
E
E _ th eta_ sim
E.phi.slm
E _ th e » a _ m e a s
E _ p h l_ m e a s
56
-66
Angle_Theta (degrees)
(a)
-100
m
2,
w
0)
50
-50
100
10
3
o
Q.
TJ
0)
N
75
E
-40'
50
E _ th e t a _ s l m
E .p h L sIm
E _ th e t a _ m e a s
E _ph l_m ecn
-66
Angle_Theta (degrees)
(b)
Fig. 8.13 Far field radiation patterns for the antenna shown in Fig. 8.11. (a) E-plane
(<(>= 0°) and (b) H-plane (<j>=90°).
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134
8.3.3
CPW Patch Antenna Design Optimization Using EM-ANN Models
To show the usefulness o f the EM-ANN modeling approach, we are able to
investigate the effects of changing certain design parameters on the response o f the
C PW patch antenna. An exam ple o f this is changing the patch length from its ideal
length.
The effects o f changing the patch length will be demonstrated using the
antenna o f the previous section.
It has been noted that for several values of the patch length a loop forms in the
S n plot on the Smith Chart due to the nature of the CPW patch antenna (curve A l)
and the effects of the feed structure (curve B l) as shown in Fig. 8.14. The ideal patch
w ith no feed structure is labeled as A l. As the feed section (FS in Figs. 8.11 and
8.16), which is effectively a high impedance CPW line, is added, a loop forms another
resonance created by the feed section length. The response after the feed section (FS)
is added is labeled B 1. Next, adding the incoming feed line, which has an impedance
o f 96 Q, the response is rotated around the smith chart to the real axis for matching
purposes. C 1. Note that the loop has effectively been pulled out.
By experimentation it has been found that increasing the patch length
increases the size of the loop as shown in Fig. 8.15. If the antenna can be designed at
a frequency where the loop appears, a wider bandwidth can be achieved.
For this
purpose, the length of the incoming feed line can be adjusted, rotating the loop to the
real line. One thing to note, however, is that increasing the patch length may effect
the radiation pattern as will be shown.
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135
B1
Al
Fig. 8.14 Effects o f radiating edge feed section and line on CPW patch antenna
(W=1.5 cm G=0.l cm and Gentj=0.85 cm) S u response. (A l) Ideal patch with no feed
(Lpatch=l.6465 cm). (B l) Addition of feed section. (C l) Addition o f incoming feed
line.
Al
Fig. 8.15 Effects of increasing the patch length (LpatCh= 1.937 cm). (A l:L a= O cm and
B l: La=3.4cm.)
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136
A CPW patch antenna has been designed, fabricated, and measured with a
longer than ideal patch length in order to increase the bandwidth. The layout o f the
antenna, designed using EM-ANN models, is shown in Fig. 8.16.
No impedance
transforming sections were required since a match directly to 50 Q was possible.
CPW length ‘a’ acts as a matching section between patch input point T where Zjn=
169.7 Q + j4 1 .14
at 5.56 GHz. Impedance o f section ‘a ’ is 96 Q.
A wide bandwidth has been achieved for this antenna as seen in Table 8.7 and
in Fig. 8.17. The return loss for the EM simulated antenna is only down about -2 0 dB
at resonance due to a slight mismatch.
For a perfect match (according to EM
simulation), the length of section ‘a’ (La) needs to be reduced by 0.025?i (0.123 cm).
However, La was left at the ANN model result (3.4 cm) for fabrication and
measurement. EM-ANN modeling, EM simulation and measurements agree well.
The EM simulated and measured E-plane and H-plane radiation patterns are
shown in Fig. 8.18. Only the top-side radiation pattern is shown. Radiation from the
bottom side is comparable. Note that the radiation from the line (Eq) is only down at
about -1 0 dB at points. This radiation can be reduced by decreasing the strip width
(W) and the gap width (G), as discussed previously. The radiation pattern for this
case shows more of a main lobe shift than the ideal case.
For the ideal case, the main
lobe shift was approximately 9°, while it is around 15° for the antenna o f Fig. 8.16.
The modeling using EM -ANN models compares well with EM simulation and
measurement, validating the approach.
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137
0.85 cm
0.85 cm
Fig. 8.16 Layout for CPW patch antenna with longer than ideal patch length. All
dimensions are in cm. Electrical parameters referenced to the resonant frequency of
5.56 GHz.
Table 8.7 Comparison of resonant frequency and bandwidth for EM-ANN modeling,
EM simulation, and measurement. CPW patch antenna with longer than ideal patch
length.
Center Frequency
% Bandwidth
4.5
Measured
5.49 GHz
14.5 %
EM simulation
5.54 GHz
11.69 %
EM-ANN
5.56 GHz
14.03 %
5.5
6.5
7.5
S ' -10
-20
• •
_i
meas
EMsim
DC -40 ••
EM-ANN
-50
Frequency (GHz)
Fig. 8.17 Comparison of return loss for the longer than ideal patch length CPW patch
antenna.
1
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I
I
138
-90
-60
30
-30
-10
CL
--
-15 - -
-20
-
-25 -
- E _1heta_m eos
'E _ th e ta_ slm
Angle_theta (degrees)
(a)
-100
-50
0
50
100
0 -o
3
oQ.
TS
0)
N
E
o
z
E _ p h l_ slm
-40
-
“ E _ th eta_ slm
*"“
E _ p h l _ m 0a s
►““
E_th eta_ m eaj
Angle_theta (degrees)
(b)
Fig. 8.18 Far field radiation patterns, measured and EM simulation, (a) E-plane (<(> =
0°). Only E_theta is shown due to antenna damage during measurement, (b) H-plane
(<J)=90°).
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139
8.4
Discussion
This chapter has presented a novel antenna configuration, the CPW patch
antenna, designed by using EM-ANN modeling approach. The radiation properties of
the CPW open-end with a wide center strip have been studied. Recommendations for
antenna design resulting from this study may be summarized as follows:
•
•
•
Use small gap widths (G) to reduce CPW line radiation
Strip width (W) should be as large as possible to increase radiation from
the ope:, end, but not large enough where cross-polarization radiation from
the CPW line becomes a problem
Length o f the CPW patch may be adjusted to increase radiation bandwidth
EM -ANN models have been developed for design and optimization o f CPW patch
antennas.
Designed antennas show excellent agreement with EM simulation and
measurement.
This chapter has mainly been concerned with the modeling aspect o f the CPW
patch antenna.
Several interesting observations, including the wide bandwidth
observed theoretically as well as experimentally, call for continued detailed
investigations.
Radiation properties of wide strip CPW lines also warrant further
study. Also, different feeding arrangements, such as on the non-radiating edge, need
to be studied in order to explore if such a feed can lead to the wide bandwidth shown
by the ideal case with no feed.
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CHAPTER 9
SUMMARY AND FUTURE WORK
9.1
EM-ANN M odeling Methodology
A novel approach for accurate and efficient modeling of microwave and mm-
wave passive components by using electromagnetically-trained Artificial Neural
Network (EM-ANN) software modules has been presented in this thesis. The
proposed technique uses the Design o f Experiments (DOE) methodology to identify
various component parameter values for which electromagnetic simulations need to
be carried out in order to capture characteristic input/output relationships. Use of the
DOE approach allows for a minimum number o f EM simulations that need to be
performed. Simulation results are then used to train the ANN model, using physical
parameters as inputs, to provide the correct component response (i.e. S-parameters)
over the desired frequency range.
Simultaneous training and testing, as well as a
‘simple-to-complex’ approach is used for obtaining optimal ANN architectures.
Since ANNs have been shown to have the ability to learn from data, to generalize
patterns in data, and to model highly nonlinear relationships, the trained model is
valid for the entire ranges of the input variables.
It may be noted that no circuit
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141
models (in terms of lumped elements etc.) are involved in the derivation o f ANN
models.
Once EM-ANN models have been created, they are easily inserted into a
commercial microwave circuit simulator. It has been shown that EM-ANN models
provide accuracy approaching the EM simulation tool used for providing training
data, but at much less computational expense.
Optimization techniques can also be
used with the trained EM-ANN models to find optimal component structures for
given circuit design applications.
Optimization is performed within the circuit
simulator environment, which is very fast compared to EM simulation.
This is
advantageous for interactive CAD o f microwave circuits.
Prior knowledge in the form o f existing models (analytical, empirical, EMANN, etc.) has been used for ANN model development.
The advantage o f using
prior knowledge is the reduction o f training data (EM Simulations) that needs to be
supplied to the ANN in order to capture the desired input/output mapping accurately.
This implies that the input/output mapping is simplified by the use o f prior
knowledge.
A reduction in the amount o f training data needed for model
characterization is very advantageous since EM simulation accounts for a major
portion of the EM-ANN model development time.
Two simple methods, the
difference method and the PKI method, for incorporation of prior knowledge into
ANN training have been discussed and demonstrated in this thesis.
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142
9.2
EM-ANN Modeling Examples
9.2.1
M icrostrip Vias and M ultilayer Interconnects
An ANN model has been developed to provide microstrip line characteristic
impedance (Zo) and effective dielectric constant, £re.
The main purpose o f this
example was to show a situation where training the ANN on relative error
is more
desirable than training on absolute error. When training on relative error, the average
model error and standard deviation summed to less than 1%. This was not the case
when training on absolute error.
EM-ANN models have been created for I- and 2-port microstrip grounding
vias.
While models for microstrip vias exist, they were found to be lacking in
accuracy at high frequencies.
The EM-ANN microstrip via models have been
developed for the 5 GHz to 55 GHz frequency range.
Therefore, the EM-ANN
models may be used for high frequency design or in nonlinear circuit design where
harmonics are present.
As an example of modeling o f multilayer interconnects. EM-ANN models
have been created for a stripline-to-stripline interconnect and a microstrip-tomicrostrip interconnect. Models for these two interconnects did not exist previously.
However, with the EM-ANN modeling methodology presented in this thesis, accurate
and efficient models have been created which can be used for design and optimization
of multilayer circuits.
Prior knowledge has been used to create two models. Both the difference
method and the PKI method (discussed in Chapter 3) were used for model
development and comparisons have been made. The first model was for a 2-port
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14 3
microstrip via. The prior knowledge, in this case, was an equation for the inductance
o f the via.
In the second exam ple, a previously developed stripline-to-stripline
multilayer interconnect model was used as prior knowledge to extend one o f its own
input parameters’ range. In both situations, use o f prior knowledge resulted in lower
error than regular training (no prior knowledge) on the same training data. Therefore,
use of prior knowledge has been shown to be an effective means for reducing the
amount o f data needed for ANN model development. This is very important when
data is costly/time-consuming to obtain as is the case with EM simulation.
The developed models have been linked to a com m ercial microwave circuit
simulator where they can be used for circuit design and optim ization. Component
optimization has also been demonstrated.
9.2.2
M ulticonductor M ultilayer Coupled Transmission Line Models
A methodology for the synthesis (leading to physical dimensions) of
multilayer asymmetric coupled microstrip lines using ANN models has been
presented.
Both synthesis and analysis models have been developed. Models are
appropriate for synthesis o f m ultilayer circuits like filters, baluns, and directional
couplers. Accuracy comparable to other optimization methods for multilayer filter
design has been achieved, but in a small fraction o f the time.
The proposed
methodology has been dem onstrated by the design o f a 2-layer coupled line filter.
Synthesis of these multilayer m icrowave circuit components has not been reported
elsewhere.
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144
9.2 3
EM-ANN Models for CPW Components
Accurate and efficient EM -ANN models, valid from 1 GHz to 50 GHz. have
been developed for the purpose o f forming a library o f coplanar waveguide (CPW )
circuit components.
M odeled components include: CPW transmission
lines
(frequency dependent Z q and ere), 90° bends, short circuit stubs, open circuit stubs,
step-in-width discontinuities, and symmetric T-junctions.
These models can be
conveniently used for efficient and accurate design of various kinds of CPW circuits.
Design and optimization o f a CPW folded double stub filter and a 50 G , 3 dB power
divider circuit, using only the developed CPW EM-ANN models, has been
demonstrated.
Results were compared to EM simulation o f the same structures,
showing excellent agreement over the entire 1 GHz to 50 GHz frequency range. This
is the first report of using only ANN models for the design o f larger circuits.
Considerable attention has been paid to the modeling of various CPW 90°
bend structures. EM-ANN models have been developed for optimally chamfered
CPW 90° bends and a novel compensated CPW 90° bend. It has been shown that
chamfering the com er of 90° CPW bends provides a simple way to improve their
performance. The optimal cham fer for a conventional CPW bend, where both the slot
and strip comers are chamfered, has been determined and reported for the first time.
Also, a novel compensated CPW bend structure, where only the strip is chamfered,
has been developed as part o f this research. This novel compensated CPW bend has
been shown to reduce the return loss from that
in the conventional optimally
chamfered CPW bend by 3 to 7 dB.
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145
As an example o f the use o f prior knowledge, an EM-ANN model has been
developed for a bend where the air-bridge height is added as an input parameter. An
EM-ANN CPW bend model, without air-bridge height as an input parameter, has
been used as prior knowledge.
Again, less EM simulation data was required for
model development for desired model accuracy.
9.2.4
EM-ANN M odels for Design o f CPW Patch Antennas
A novel antenna configuration, the CPW patch antenna, designed by using
EM-ANN modeling approach, has been presented in this thesis. The radiation
properties of the CPW open-end with a wide center strip have been studied. EMANN models have been developed for the design and optimization o f CPW patch
antennas. Using the developed EM-ANN models, CPW patch antenna geometry has
been optimized to provide a wide bandwidth response.
In fact, much wider
bandwidths than those reported results for single-layer microstrip patch antennas have
been demonstrated. This portion o f research clearly demonstrates the usefulness o f
ANN modeling for the design o f novel components where little or no information is
known.
9.3
Future Work
9.3.1
Nonlinear Active Device Modeling
A potential application o f ANNs, which has not been explored to date, is
modeling of nonlinear active microwave devices (HBTs, MESFETs, HEMTs),
including thermal effects.
The devices could be characterized by making time-
domain current and voltage measurements.
Training o f the ANN would be
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146
accomplished using this data.
The resulting model could then be used in
commercially available microwave circuit simulators for the design of nonlinear
circuits, such as pow er amplifiers, oscillators, and mixers.
9.3.2
ANN M odel Development for Passive Components using Measured Data
ANN models could be created using measured data instead of EM simulation.
The result would be fabrication process specific models, which in many instances
may be desirable.
However, measured data inherently contains noise. ANNs are
ideal for this situation since they have the ability to model complex input/output
relationships, even in the presence o f noise [9.1].
9.3.3
CPW Patch Antenna
Several interesting observations about CPW patch antennas, including the
wide bandwidth observed theoretically as well as experimentally, call for continued
detailed investigations. Radiation properties of wide strip CPW lines also warrant
further study.
Also, different feeding arrangements, such as on the non-radiating
edge, need to be studied in order to explore if such a feed can lead to the wide
bandwidth shown by the ideal case with no feed.
9.3.4
ANN of Complete Circuit Modules
In this thesis, models have been developed for certain passive components and
then the components are combined to form larger circuits.
This is an acceptable
method when interactions (couplings) between components are not significant.
However, as circuits become more compact, interactions between components will
inevitably increase. In this situation, ANN models could be developed for complete
circuit topologies, such as amplifiers, filters, etc.
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147
9.3.5
Synthesis of Components
Synthesis o f components has problems associated with it as discussed in
Chapter 6. If the inverse mapping is multi-valued and a least-squares error approach
is used, the neural net tends to approximate the average o f the target data. Also, It
can be difficult to determine if and where there are regions o f input variable space
which have not been characterized by the available training data. Future work in this
area should be directed at solving these problems.
i
i
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I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX A
A.1
User-Defined Linear Model Subroutine
This C code subroutine links a generic ANN model, consisting o f up to
inputs and 10 outputs, to HP-MDS. The majority o f the code is a template. Cc
added by the user to define a model is shown in bold.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
File:
Description:
net2p.c
Model codefor the user-compiled linear model:
"net2 p"
Created:
16 Nov 1995
RCS:
SHeader S
13:29:12
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
The function ,,u_net2p_evalO" is the function that
calculates S-parameters.
The function ”u_net2p_query0" 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.
The function "u_net2p_dispose()” frees any memory
allocated by u_net2 p_eval().
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
#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.
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
* and malloc.h
*/
#include "usermodel.h"
#include <stdlib.h>
#include ”nn_sub2p"
y * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* Here is a list o f preprocessor macros which are used to access the
* parameters of this device:
*
*/
#define PARAM_il
#define PARAM_i2
#define PARAM_i3
#define PARAM_i4
#define PARAM_i5
#define PARAM_i6
#define PARAM_i7
#deftne PARAM_i8
#define PARAMJ9
#define PARAM_i 10
#define PARAM_data_ftle
0
1
2
3
4
5
6
7
8
9
10
static int u_net2 p_evai():
static int u_net2 p_query():
static void u_net2 p_dispose():
/* * * « * * * * * * * * * * * * * * * * * * * * * * * * * M a t* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* The USER_PARAM data structure describes the parameters used by this
* device.
*
*1
static USER_PARAM
u_net2p_params[ ] = {
{ "il",
/* name */
NULL,
NULL.
IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEI[P_REQUlRED.
REAL.TYPE.
. 00001.
/* default value if real or integer */
/* default imag value if complex */
/* default string if string (next line) */
NULL },
( "i2 ".
/* name */
NULL.
NULL.
IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEIIP_REQUIRED.
REAL.TYPE,
0
0
.
,
.00001 .
/* default value if real or integer */
/* default imag value if complex */
I* default string if string (next line) */
NULL }.
{ ”i3".
/* name */
NULL.
NULL.
IP_READABLE!lP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEIIP_REQUIRED.
REAL_TYPE,
0
0
.
,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.0 0 0 0 1 .
.
/* default value if real or integer */
0,
/* default imag value if complex */
/* default string if string (next line) */
NULL I,
{ "i4".
/* name */
NULL.
NULL,
0
ip
_ r e a d a b l e iip _ d if f e r e n t ia b l e iip _ s e t t a b l e iip _ m o d if ia b l e iip _ r e q u ir e d .
REAL.TYPE.
.0 0 0 0 1 ,
0.
/* default value if real or integer */
0.
/* default imag value if complex */
/* default string if string (next line) */
NULL ),
{ "i5",
/* name */
NULL,
NULL,
IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED.
REAL.TYPE.
.0 0 0 0 1 .
0,
/* default value if real or integer */
0,
/* default imag value if complex */
/* default string if string (next line) */
NULL ).
{ ”i6 ",
/* name */
NULL.
NULL.
IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIlP_MODIFIABLElIP_REQUIRED.
REAL.TYPE,
.0 0 0 0 1 .
0,
/* default value if real or integer */
0.
/* default imag value if complex */
/* default string if string (next line) */
NULL }.
{ ”i7".
/* name */
NULL,
NULL.
IP_READABLE!IP_DIFFERENTIABLEIIP_SETTABLEI1P_V10DIFIABLEIIP_ REQUIRED,
REAL.TYPE,
.0 0 0 0 1 ,
0,
/* default value if real or integer */
0.
/* default imag value if complex *1
/* default string if string (next line) */
NULL ),
( "i8 ",
/* name */
NULL,
NULL.
IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIHABLEIIP.REQUIRED.
REAL.TYPE,
.0 0 0 0 1 ,
0.
/* default value if real or integer */
0,
/* default imag value if complex */
/* default string if string (next line) */
NULL ),
{ "i9",
/* name */
NULL.
NULL,
IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED.
REAL.TYPE,
.0 0 0 0 1 ,
0,
/* default value if real or integer */
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i
/* default imag value if complex */
/* default string if string (next line) */
NULL },
{ "ilO".
/* name */
NULL.
NULL.
IP_READABLEIIP_DlFFERENTIABLEIIP_SETTABLEIIP_MODIRABLEIIP_REQUIRED,
REAL.TYPE,
0
.
.00001.
/* default value if real or integer */
/* default imag value if complex */
/* default string if string (next line) */
NULL }.
{ "data.file",
/* name */
NULL.
NULL.
IP.READABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED,
STRING.TYPE.
0
0
.
.
0,
/* default value if real or integer */
/* default imag value if complex */
/* default string if string (next line) */
NULL }
0
0
.
.
):
^ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* The USER.MODEL data structure describes the device, and any parameters
* used by it.
tic
*/
USER.MODEL
u_net2p = {
1.
''net2 p'\
NULL,
2,
u_net2 p_params.
sizeof(u_net2p_params) / sizeoftUSER.PARAM),
MODEL.EV ALU ATES.S,
u_net2 p_eval,
u_net2 p_query,
u_net2 p_dispose
1:
^* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* u_net2p_eval() calculates S-parameters. This is the
* main model evaluation routine.
*
*/
static int u_net2p_eval(Name, Rags, Omega, Matrix. NumberOfPorts,
Parameters, Substrate, SavedData)
char
*Name;
int
Rags;
RealNumber
Omega;
ComplexNumber
*Matrix;
int
NumberOfPorts;
USER.DATA
‘ Parameters:
struct SubstrateModelData ‘ Substrate;
void
“ SavedData;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
{
RealNumber I[10],0[10],pi,theta;
CompIexNumber param;
char
ctmp[50];
pi=3.14159265358973;
I[0i=0mega/(2.0*pi*1.0e9);
* Get input parameters fro m sim ulator *
I[lI=UGET_REAL_VALUE(Parameters[PARAMJl]);
I[21=UGET_REAL_VALUE(Parameters[PARAM_i21);
I[31=UGET_REAL_VALUE(Parameters[PARAM_i3]);
I[4]=UGET_REAL_VALUE(Parameters[PARAMJ41);
I[5]=UGET_REAL_VALUE(Parameters[PARAM_i5]);
I[6]=UGET_REAL_VALUE(Parameters[PARAM_i6]);
I[7]=UGET_REAL_VALUE(Parameters[PARAM_i7]);
I[8]=UGET_REAL_VALUE(Parameters[PARAM_i8]);
I[9)=UGET_REAL_VALUE(Parameters[PARAM_i9]);
I[10]=UGET_REAL_VALUE(Parameters[PARAMJ10]);
strcpy(ctmp,UGET_STRING_VALUE(Parameters[PARAM_data_filel));
* Call feed-forw ard A N N routine *
neural_net2p(I,0,ctmp);
* Process A N N outputs and send S-parameters back to circuit sim ulator
theta=(0[ 1]*pi)/180.0;
param.ReaI=O[0]*cos(theta);
param.Imag=O[0]*sin(theta);
CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,1), param);
CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 2,2), param);
theta=(0[3]*pi)/180.0;
param.Real=0[21*cos(theta);
param.Imag=0[2]*sin(theta);
CMPLX_ASSIGN(MATRIXl_ELEMENT(MatrLx, NumberOfPorts, 2,1), param);
CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,2), param);
param.Reai=50.0;
param.lmag=0.0;
CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 1), param);
CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 2), param);
return (YES);
}
/******************************************************************************
*
* u_net2 p_query() is used only if "read-only” parameters exist. If this
* model does not have any "read-only" parameters, this routine does not have
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
* 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_net2p_query(Parameter!D, NumberOfPorts, Parameters, Substrate,
SavedData. Value)
int
ParameterlD;
int
NumberOfPorts;
USER_DATA
‘ Parameters;
struct SubstrateModelData ‘ Substrate;
void
“ SavedData;
USER_DATA
‘ Value;
(
/* Initialization */
USET_DATA_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 (ParameterlD) {
default:
/*
* If this is parameter is not handled by this routine, just
* exit.
*/
break;
I
return (YES);
I
/* * * * * * * * « * * * c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* u_net2 p_dispose() is used to free memory that was allocated and stored
* on the "saved_data" parameter of the u_net2 p_eval() function.
* If you do not use the ''saved_data” parameter o f u_net2p_eva!(), you
* do not need to modify this routine.
*
*/
static void u_net2p_dispose(SavedData)
void
“ SavedData;
{
if (‘ SavedData) (
/*
* Free any additional data here.
*/
free( ‘ SavedData):
}
}
/*
* Local Variables:
* c-indent-levcl: 4
* c-continued-statement-offset: 4
* c-brace-offset: -4
* c-argdecl-indent: 0
* c-labcl-offset: -4
* End;
*/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A.2
Feed-Forward ANN Subroutine
neural_net2p(I,0,ctmp)
double I[L0],O[10];
char ctmp[50];
{
int i,j,k,r,c,l;
double minmax[21 )[2], w l[5 0 ][l l],w 2[10][51],IN [l 1];
double sum, net[50],f[511,net2[I0],ON[10|;
float x;
FILE *fpt;
*
Read input file containing E M -A N N model information *
fpt=fopen(ctmp,,’r");
fscanf(fpt,”9fcd%d%d".&i,&k,&j);
for(r=0;r<i+k;++r) {
for(c=0;c<2;++c){
fscanf(fpt,”%e",&x);
minmax[r][c]=x;}}
for(r=0;r<j;++r){
for(c=0;c<=i;++c) {
fscan f( fpt,"■
% e " ,& x);
wl[r][c]=x;>}
for(r=0;r<k;++r){
for(c=0;c<=j;++c) {
fscanf(fpt.’’%e",&x);
w 2[r][c]=x;n
fclose(fpt);
* Normalize Inputs between 0 and 1 *
IN[0]=1.0;
for(r=k;r<i+k;++r) {
IN[r-k+I l=(I[r-k]-minmax[r][0])/(minmax[r][l]-minmax[r][0]);}
* Multiply normalized inputs by first set o f weights and pass through logistic
activation function *
f[0]=1.0;
for(r=0;r<j;++r){
sum=0.0;
for( c=0 ;c<=i;+ +c) {
sum=sum+w 1[r][c]*IN[c];}
net[r]=sum;
f[r+1]= 1,0/C 1.0+exp(-net[r]));}
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166
* M ultiply by second set o f weights, and pass through logistic activation function
*
for(r=0;r<k;++r){
sum=0.0;
for(c=0;c<=j ;++c){
sum=sum+w2[r][c]*f[c];}
net2[rl=sum:
ON[rj=l.0/(1.0+exp(-net2[r]));
* Denormalize outputs
*
0[rl=((ON[r]-0.2)*(minmax[r][l]-minmax[r][0])/0.6)+minmax[r][0];}
}
i
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167
A.3
Sample EM-ANN Model Input File
The following EM-ANN model file is that o f a CPW short circuit stub.
3
2
5
* # o f inputs *
* # o f outputs *
* # o f neurons in the hidden layer *
* Max. and Min. values for outputs *
9.870000e-01
1.057610e+02
I.000000e+00
1,786330e+02
* Max. and Min. values for inputs *
to to
1.000000e+00
.000000e+01
.000000e+01
5.000000e+01
1.200000e+02
6.000000e+01
* First layer of weights between the input and hidden layers
3.762740e+00
-3.657379e-0I
1.029619e+00
5.309179e+00
2.I92086e+00
-4.328468e+00 -2.988256e-01 -2.771775e-01
-5.236892e+00 4.126552e-02 -1.223319e-02
-5.204754e+00 1.435307e+00 8.790260e-0l
-1.41749 le+00 -1.898849e+00 -1.391095e+00
-4.185616e+00 1.659987e+00 9.686552e-01
* Second layer of weights between the hidden and output layers *
-3.219908c+00 2.860686e+00
-2.718878e+00 1.958229e+00
-3.04206le+ 00 3.117409e+00 3.816633e-rOO -3.497359e+00
2.358216e+00 3.028646e-02 8.417108e-01 3.96I452e-01
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I
APPENDIX B
USER-DEFINED LINEAR MODEL LIBRARY FOR CPW
COMPONENTS
Appendix B contains instructions for installing a distributable user-defined
linear model library for use with HP-MDS [49]. The library consists o f various CPW
passive component EM -ANN models useful for microwave design. Refer to Chapter
7 for a description o f available CPW models. The CPW library is available for
distribution with instructions provided for installation. References contained in the
instructions refer to the reference manuals provided with HP-MDS.
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169
Installing the CPW Library of Components
1)
Creating and preparing a directory (Ref. DTR-V9 Creating Device and
Model Libraries, p. 5-8
The purpose o f this step is to create and prepare a directory to copy necessary
files into for user-compiled linear model development.
Example:
mkdir models
cd models
run
/usr/..appropriate path..7hp85150/lib/mnsmodels/modelprepare
note: The path for the modelprepare program is dependent on your specific
software installation path.
2)
Copy library file, icon file and ANN model files to models directory
a) copy cu_cpw.a (library file) and cpw jm ods (icon file) to models
directory
b) create a directory under your models directory for the CPW ANN models
ex. mkdir /...Vmodels/cpw_models
c) copy CPW A N N models to cpw_models directory
1) cpw_line, use as Zo_mod for all models except for cpw_bend
2) cpw_bend_line, use as Zo_mod for all models except for
cpw_bend
3) cpw_open, CPW open circuit model
4) cpw_short, CPW short circuit model
5) cpw jbend , CPW compensated bend model
6) cpw_step,
CPW step model (port 1 always has the smaller W)
7) cpw_tee,
CPW symmetric T-junction (port 1 is the input port,
ports 2 and 3 are the symmetric ports)
8) cpw_cap_ab, air-bridge capacitance model used with T-junction
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170
3)
Edit libraries file
(Ref. DTR-V9 Creating devivce and model libraries, pp. 5-38 to 5-44)
Initially the libraries file will contain:
m m tttttiiitiiiitm tttittiiiiiu itiiiiitiittitttititiiiiim iiiiiiiiiiiiiiiiiiH itiiitiitiiu iitiiiitt
# Description
user-compiled linear models,
C function name
declare_user_models
Edit the file to look as follows:
MmtittittttittittitMtmtnttttttitiitttiiiiitittiiittititimifHiiittiitiuiiimttnmittttitit
# Description
#user-compiled linear models,
declare_user_models
CU CPW models,
4)
C function name
cu_cpw_install
Edit M akefile
Edit OTHER_LIBRARIES to look as follows:
OTHER_LEBRARIES= cu_cpw.a
5)
Type make and press return
At this point you will have an executable program called inns, which is the
simulator with the desired library.
This simulator file must be switched with the one currently in use.
copy /..Vmodels/mns
to
/usr/
/hp85150/lib/mns800
note: save the old mns800 file as mns800.old for example.
note: make sure to change permissions so that everyone can use the newly
created simulator file.
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171
6)
Read design icons file into MDS
To use the newly installed models, the design icons file must be read into
MDS. Once these design icons are created, they can be used in the same
manner as other MDS components.
run mds
click Browse/open
click unix system
change to directory where cpw_mods has been stored (models)
click on cpw_mods
click OK
A design file cpw_mods should appear on your mds screen. This design file
contains the icons for all cpw models.
To use these models single click on each one to highlight them. Then execute
perform/add to menu.
To place these models into a schematic, execute insert/component.
A list o f the new cpw components should appear. Click on the desired model
and use as you woud any other mds model.
7)
Notes on model usage
Within MDS model:
•
All inputs for W, G, 1, etc. are in pm. (Ex. W= 20, W equal 20 pm)
•
Input correct path to ANN model file names
( Ex. ‘usr/local/watson/mds/models/cpw_models/cpw_line’)
•
Step model: Port 1 is always the side with the smaller metal width
(Wl)
•
T-Junction: This is a symmetric T-junction. Port 1 is the port at the
bottom o f the T. Ports 2 and 3 are the symmetric ports.
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IMAGE EVALUATION
TEST TARGET ( Q A - 3 )
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