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Evolutionary generation of microwave line-segment circuits by genetic algorithms

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U
n iv e r s it y
of
C
a l if o r n ia
L os Angeles
Evolutionary Generation of Microwave
Line-segment circuits by Genetic Algorithms
A d is s e rta tio n s u b m itte d in p a r tia l s a tis fa c tio n
o f the re q u ire m e n ts fo r th e degree
D o c to r o f P h ilo s o p h y in E le c tric a l E n g in e e rin g
by
Tamotsu Nishino
2002
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 3045558
___
®
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©
C o p y rig h t by
T a m o ts u N ish in o
2002
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T h e d is s e rta tio n o f T a m o ts u N is h in o is a pproved.
2 ^
.
E rn e st A be rs
J ^ ^ r T V andenberghe
^
Tatsuo Ito h . C o m m itte e C h a ir
U n iv e rs ity o f C a lifo rn ia , Los Angeles
2002
ii
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To m y family.
iii
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T
1
o n ten ts
1.1
B a c k g ro u n d o f th e re s e a rc h ............................................................................
1
1.2
B r ie f re v ie w o f p re v io u s w o rks o f th e G A s in m icrow ave e ng in e e rin g s
1.3
Features o f o u r w o r k .......................................................................................
7
1.3.1
2 -D lin e -se gm en t c i r c u i t s .................................................................
8
1.3.2
2 -D co up le d lin e -se g m e n t c i r c u i t s ................................................
8
1.3.3
3 -D lin e -se gm en t c i r c u i t s ..................................................................
9
O rg a n iz a tio n o f th is d is s e r t a t io n .................................................................
9
3
T h e g e n e t ic a l g o r i t h m s ............................................................................................11
T h e general flo w o f th e g en e tic a l g o r i t h m s .............................................
11
2.1.1
'‘M a te ” p r o c e d u r e ................................................................................
11
.1 . 2
“ E v a lu a te ” p r o c e d u r e .........................................................................
14
C o n clu sio n s o f th is c h a p t e r ............................................................................
16
2
2 . 2
4
C
1
2.1
3
o f
I n t r o d u c t i o n ................................................................................................................
1.4
2
a b le
A p p lic a t io n s t o 2 -D lin e - s e g m e n t c ir c u its
..................................................17
3.1
E xpression o f a c ir c u it b y a set o f param eters
......................................
18
3.2
O p tim iz a tio n b y G A ......................................................................................
23
3.3
D esign exam ples
..............................................................................................
24
3.4
C o n clu sio n s o f th is c h a p t e r ...........................................................................
37
E x t e n s io n s o f 2 -D c i r c u i t s ....................................................................................38
iv
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4.1
C o n s id e ra tio n o f c o u p lin g e ffe c ts .................................................................
4.1.1
4.2
4.3
5
38
A n exam ple o f L P F w ith c o u p lin g e f f e c t ..................................... 44
C o m b in a tio n w ith lu m p e d e le m e n ts ..........................................................
46
4.2.1
Techniques to express lines w ith lu m p e d e le m e n t s ................
46
4.2.2
A n e xam ple o f L P F w ith lu m p e d e le m e n t s .............................
48
C o n clu sio n s o f th is c h a p t e r ............................................................................
51
A p p lic a t io n s t o 3 -D lin e - s e g m e n t c ir c u it s
............................................... 52
5.1
G e n e tic expressions o f g ro w in g th re e -d im e n s io n a l c i r c u i t s ................
54
5.2
M o d e ls o f elem ents in a m u ltila y e r s t r u c t u r e .........................................
55
5.2.1
M o d els o f v i a s .......................................................................................
55
5.2.2
M o d e ls o f b ro ad -sid e co up le d lin e s ...............................................
57
5.3
V e rific a tio n o f th e m o d e l ................................................................................
69
5.4
D e sig n E xa m p le s o f M icrow ave C ir c u i t s ....................................................
78
5.4.1
B and-P ass F i l t e r ................................................................................
78
5.4.2
B a n d -S to p F i l t e r ................................................................................
80
C o n c lu s io n s .........................................................................................................
82
5.5
6
C o n c l u s i o n s ....................................................................................................................83
A
T h e S p a r a m e t e r s o f t h e c ir c u it
B
P a r a m e t e r s o f th e im p le m e n te d p r o g r a m .................................................. 89
.....................................................................86
R e f e r e n c e s ................................................................................................................................91
v
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L
is t
o f
F
ig u r e s
1.1
C o n ve n tio n a l p la n a r filte r design p r o c e d u r e s .........................................
2
1.2
C o n ve n tio n a l p la n a r b ro a d -b a n d filte r design procedures
3
1.3
G A design o f ( M ) M IC co m p on e nts co m bined w ith 2.5D s p e c tra l
d o m a in approach by A .J o h n and R .H .Jansen
................
....................................
7
2.1
G A flo w ch a rt. G A consists o f tw o m a in p a rt, "M a te ” and '‘E v a lu a te ” . 12
2.2
Crossover exchange p a rts o f chrom osom es between parents.
• • •
14
2.3
M u ta te flip s some genes in chrom osom es o f c h ild r e n ............................
14
2.4
E va lu a te procedure operates on five states o f (a) chrom osom es,
(b) sets o f param eters, (c) c ir c u it p a tte rn s , (d ) responses, and (e)
fitn e s s e s ................................................................................................................
3.1
A set o f param eters expresses a c irc u it,
15
(a) The firs t th re e pa­
ram eters express th e size o f the c ir c u it and the n um ber o f lin e s to
be added, (b) A set o f three p aram ete rs x 4, x 5, x 6 expresses th e
a d d itio n a l firs t lin e to th e base c irc u it, (c) A set o f three p a ra m e ­
ters X 7 , x 8, X9 expresses the a d d itio n a l second line to the p re vio u s
c irc u it, (d) T he la st 3.'Vmax + 4 p aram ete rs in d ica te the lin e s to be
re m o v e d ................................................................................................................
3.2
19
F a brica te d tra d itio n a l fo u r stage lo w pass filte r. Pass band is b elow
2.1
G H z and stop ban d is above 3.8 G H z.
M easured responses.
(a) P a tte rn and (b )
......................................................................................
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25
3.3
F a b ric a te d fo u r stage lo w pass G A filte r. Pass b a n d 1.9 to
2 . 1
GHz
and s to p bands are fro m 3.8 to 4.2 G H z and 5.7 to 6.3 G H z . (a)
P a tte rn and (b ) Measured r e s p o n s e s .................................................. 27
3.4
F a b ric a te d fo u r stage low pass G A filte r w it h one s to p b a n d below
th e pass band.
Pass band 1.95 to 2.05 G H z a n d s to p bands are
fro m 1.4 to 1.5 G H z, fro m 3.9 t o 4.1 G H z a n d 5.85 to 6.15 G H z.
(a)
3.5
P a tte rn and (b) M easured r e s p o n s e s ......................................... 29
C o m p a riso n o f results o f G A design and responses by f u ll wave E M
s im u la tio n fo r F ig . 3 . 4 ( a ) ...........................................................................30
3.6
F a b ric a te d G A filte r w ith tw o pass bands and tw o s to p bands a l­
te rn a tiv e ly . Pass bands are fro m 3.4 to 3.6 G H z and fro m 5.4 to
5.6 G H z and sto p bands are fro m 2.4 to 2.6 G H z a n d 4.4 to 4.6
G H z. (a ) P a tte rn and (b) M e asured re s p o n s e s ................................ 32
3 .7
F a b ric a te d G A pow er d iv id e r.
P ow er fro m p o r t 2 to p o r t 1 is
30% and th a t fro m p o rt 2 to p o r t3 is 70% . (a) P a tte rn and (b)
M easured re s p o n s e s ......................................................................................34
3.8
F a b ric a te d G A m a tc h in g c ir c u it w ith m a x im u m g a in fro m 2.3 to
2.7 G H z ........................................................................................................... 36
3.9
(a) C a lc u la te d response, (b) M easured r e s p o n s e ...........................36
4.1
C o u p le d three l i n e s ..................................................................................
4.2
C o u p le d th re e lines m o d e l .......................................................................39
4.3
P ro p o s in g coupled three lines m o d e l.................................................... 40
4.4
E v e n /O d d m ode m odels fo r F E M ........................................................ 41
v ii
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38
4.5
N odes a n d elem ents (a) w ith o u t c o u p lin g effect, (b ) w ith c o u p lin g
e f f e c t s .........................................................................................................................43
4.6
D esigned G A L P F filte r w ith c o u p lin g lin e effects. Pass b a n d s are
fro m 4.0 to 4.2 G H z, and s to p b ands are fro m 4.8 to 5.0 G H z . (a)
P a tte rn and (b ) re s p o n s e s .................................................................................. 45
4.7
4.8
A c ir c u it exam ple w ith S h u n t C .................................................................
47
D esigned G A L P F filte r w ith c o u p lin g lin e effects and sh u n t Cs a t
g e n e ra tio n o f 50. Pass bands are fro m 4.0 to 4.2 G H z, a n d s to p
bands are fro m 4.8 to 5.0 G H z . (a) P a tte rn and (b ) responses.
4.9
• •
49
D esigned G A L P F filte r w ith c o u p lin g lin e effects and sh u n t Cs a t
g e n e ra tio n o f 250. Pass b ands are fro m 4.0 to 4.2 G H z, a n d s to p
bands are fro m 4.8 to 5.0 G H z . (a) P a tte rn and (b) responses.
5.1
• •
50
Process g ro w in g th re e -d im e n s io n a l c irc u its in the case o f fo u r-la y e r
s tru c tu re , (a) C re a tio n o f 2 -D P -c irc u it p a tte rn , (b ) C o p y o f th e
P -c irc u it p a tte rn to a ll layers, (c) R e m o val o f lines c o rre s p o n d in g
to ” 0.:’ (d ) R em oval o f via s c o rre s p o n d in g to ” 0 .”
5.2
..............................
56
T h re e type s o f d is c o n tin u itie s o f in te rs e c tio n p o in ts in P -c irc u it,
a nd fo u r type s o f c o m b in a tio n s o f v ia connections in th re e -la y e r case 57
5.3
Cross se ction o f a ty p ic a l m -c o n d u c to r tra n sm issio n lin e in an N laver s t r u c t u r e .....................................................................................................
v iii
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58
5.4
T w o d iffe re n t views o f th e same m -c o n d u c to r tra n s m is s io n lin e te r­
m in a te d by
a t a ll p o rts as an e xa m p le o f m = 3 .
(a) T h e m
co n d u cto rs are considered as one tra n s m is s io n lin e and te rm in a ­
tio n s are co llected in to tw o com m on te rm in a tio n s a t b o th ends.
(b ) m co nd u cto rs w ith im pedance o f m x Z k are te rm in a te d by
Z f Q a t 2m t e r m in a ls ......................................................................................
5.5
64
D ia g ra m to e x p la in d e riv a tio n o f th e s c a tte rin g p aram ete rs. The
s c a tte rin g param eters are o b ta in e d b y su p e rp o sin g re fle c tio n coef­
ficie n ts o f modes w ith s h o rt o r open b o u n d a ry c o n d itio n s a t the
m id d le p o in t o f the lines, (a) T h e m -c o n d u c to r tra n sm issio n line.
(b )
T h e re fle ctio n w ith s h o rt c o n d itio n s a t m id d le p o in ts , (c) T he
re fle c tio n w ith open co n d itio n s a t m id d le p o in ts .
.............................
6 8
5.6
A n exam ple o f th re e -c o n d u c to r tra n sm issio n lin e m o d e l .................
69
5.7
E x c itin g voltages fo r each s y s t e m .............................................................
70
5.8
S l l responses o f th e exam ple
.....................................................................
73
5.9
S21 responses o f th e exam ple
.....................................................................
74
5.10
S41 responses o f th e e xam ple
.....................................................................
75
5.11
S12 responses o f the exam ple
.....................................................................
76
5.12
S2
.....................................................................
77
2
responses o f th e exam ple
5.13 B and-pass filte r whose pass-band is 4.9 to 5.1 G H z, and stop-bands
are fro m 4.4 to 4.5 G H z and fro m 5.5 to 5.6 G H z.
(a) C irc u it
p a tte rn s in three -laye r s tru c tu re , (b ) Responses o f th e band-pass
f i l t e r ......................................................................................................................
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79
5.14 B a n d -sto p filte r whose s to p -b a n d is 5.0 to 5.1 G H z, a n d pass-bands
are fro m 4.6 to 4.8 G H z and fro m 5.3 to 5.5 G H z.
(a ) C ir c u it
p a tte rn s in th re e -la ye r s tru c tu re , (b ) Responses o f th e b a n d -sto p
f i l t e r ...................................................................................................................
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L
is t
o f
T
ab le s
2.1
G A t e r m in o lo g y ...................................................................................................
13
B .l
P a ra m e te rs o f the p r o g r a m .............................................................................
90
xi
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A
c k n o w le d g m e n ts
T h e a u th o r w o u ld lik e to express th e sincere g ra titu d e to a d v is o r P rofessor
T a tsu o Ito h fo r h is g uida n ce, encouragem ent a n d discussions. A d e b t o f g ra titu d e
is also owed to P ro fe sso r N ico la o s G . A le x o p o u lo s , w ho was a d v is o r u n til he
moved to U C Irv in e , fo r e n co u ra g in g me s tro n g ly w ith a p p ro p ria te suggestions.
A p p re c ia tio n m u s t to be expressed to P rofessor A ts u s h i Is h iy a m a , w h o was m y
a d v is o r o f M .S . p ro g ra m in W aseda U n iv e rs ity and suggested me th e G A was
w o rth y to be in v e s tig a te d in e le c tric a l e ng in e ering fields. A lso , I w a n t to show m y
a p p re c ia tio n to P rofessor F ranco De F la v iis , D r. R a u l R a m irez and D r. W illia m
M . M e r r ill fo r useful discussions. M y a p p re c ia tio n m u st be exte n de d to Professor
T a kash i K a ta g i, w h o was fo rm e r general m anager o f M its u b is h i I T R & D center,
fo r e n co u ra g in g me a ll th e tim e . I also express th a n kfu ln e ss to D r. S h u ji U rasaki,
D r. O sa m i Is h id a , D r. T a d a sh i T a k a g i and D r. K e n ji Ito h , fo r th e ir kindness to
back u p m y P h .D research in M its u b is h i. A lso , I w a n t to th a n k . D r. M o riy a s u
M iy a z a k i, D r. N o rih a ru S ue m a tsu, M r. H id e v u k i O ohashi, M r. T e ts u O hw ada
and M r. Takeshi O h s h im a fo r useful discussions.
x ii
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V
it a
1965
B o rn , Osaka, Japan
1989
B .S .,E le c tric a l E n g in e e rin g D e p t., W aseda U n iv e rs ity , T o kyo ,
Ja pa n
1991
M .S .,E le c tric a l E n g in e e rin g D e p t., W aseda U n iv e rs ity , T o kyo ,
Ja pa n
1991-2002
In fo rm a tio n and T e ch n o lo g y R & D center. M its u b is h i E le c tric
C o., Japan
199 6 -1 99 7
V is it in g Researcher, E le c tric a l E n g in e e rin g D e p t., U C L A
1997-2002
P h .D . S tu d e n t, E le c tric a l E n g in e e rin g D e p t., U C L A
P
u b l ic a t io n s
T a m o ts u N ish in o , F ra n co De F la viis, N ico la o s G . A le x o p o u lo s and T a tsu o Ito h
, E v o lu tio n a r y g e n e ra tio n o f m icrow ave lin e -se gm en ts c irc u its b y g e n e tic algo­
rith m s , E u rop e an M icro w a ve Conference 2000. D ig e st V o l.3, pp296-299
T a m o ts u N is h in o and T a tsu o Ito h , E v o lu tio n a r y g e n e ra tio n o f m icrow ave lin e segm ents c irc u its b y g e n e tic a lg o rith m s, M icro w a ve T h e o ry and Techniques, IE E E
T ra n s a c tio n s on, w ill be published in S eptem ber, 2002
xm
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T a m o ts u N is h in o and T a ts u o Ito h , E v o lu tio n a r y g e n e ra tio n o f 3 -D lin e -se gm en ts
c irc u its w ith a b ro a d -sid e c o u p le d m u ltic o n d u c to r tra n sm issio n lin e m o d e l, M i­
crowave T h e o ry a n d Techniques, IE E E T ra n s a c tio n s on, s u b m itte d and u n d e r
re vie w
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A
b s tr a c t
o f
th e
D
is s e r t a t io n
Evolutionary Generation of Microwave
Line-segment circuits by Genetic Algorithms
by
Tamotsu Nishino
D o c to r o f P h ilo s o p h y in E le c tric a l E n g in e e rin g
U n iv e rs ity o f C a lifo rn ia , Los A ngeles, 2002
P rofessor T a tsu o Ito h , C h a ir
E v o lu tio n a ry g e n e ra tio n o f m icro w a ve lin e -se gm en t c irc u its is presented. T o p o l­
ogy and d im e n sio n s o f lin e -se gm en t c irc u its are expressed by sets o f param eters,
w h ich d escribe th e w ay o f s tr u c tu r a l g ro w th o f line-segm ent c irc u its . T h e n , the
sets o f p a ra m e te rs are o p tim iz e d b y genetic a lg o rith m s (G A ) to s a tis fy specifica­
tio n s. U s in g lin e-segm ents, we can o b ta in n o t o n ly sm a ll co m p on e nts fo r lim ite d
space a p p lic a tio n s b u t also la rg e co m p on e nts fo r w id e band fre q u e n cy specifica­
tio n s w ith o u t in cre a sin g c o m p u ta tio n a l c o m p le x ity . In th e G A process, to reduce
c o m p u ta tio n tim e , a c ir c u it is decom posed in to lin e s and d is c o n tin u o u s elem ents.
T h e n , th e S p a ra m e te rs are synthesized to o b ta in th e response o f th e c irc u it.
F ilte rs , a p o w e r-d iv id e r and a m a tc h in g c ir c u it were designed and teste d . T he
re su lts v a lid a te d o u r p ro p o s in g p rocedure.
xv
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CHAPTER 1
Introduction
1.1
Background of the research
E xpa n sio n o f th e c o m m u n ic a tio n m a rk e t requires m icrow ave co m p on e nts to be
h ig h ly c o m p e titiv e .
W h ile new m o d u la tio n system has been sta n d a rd iz e d fo r
every g e n e ra tio n , size re d u c tio n techniques rem ain fo r each m a ke r as key issues
to d o m in a te th e m a rk e t. T h e purpose o f th is d isse rta tio n is to c o n trib u te m in ia ­
tu r iz a tio n o f th e m icrow ave com p on e nts such as filte rs , d iv id e rs , com biners and
m a tc h in g c irc u its by p ro p o sin g a novel o p tim iz a tio n technique c o m b in in g c irc u it
theories a n d g e n e tic a lg o rith m s (G A s ).
O ne o f th e concrete measures to m in ia tu riz e m icrow ave co m p o n e n ts is adop­
tio n o f a m u lti-c h ip -m o d u le (M C M ). C o m p o s itio n o f m icrow ave c irc u its in m u l­
tila y e r s tru c tu re s such as low te m p e ra tu re co-fired ce ram ic (L T C C ) packages
has been in v e s tig a te d b y a lo t o f researchers. M ost o f such stu d ie s ado p te d the
d is trib u te d -lin e -ty p e c irc u its fo r filte rs o r couplers. B u t few o f lu m p e d -e le m e n tty p c ones.
O n e o f th e reasons is th e d iffic u lty o f design o f lu m p e d elem ent
c irc u its in th in m u ltila y e r s tru c tu re s w ith co nside ra tion o f und e sire d p a ra s itic
effects.
E s p e cia lly, fo r the b ro a d -b a n d specifications such as h a rm o n ics e lim i­
n a tio n filte rs , th e elem ents do n o t act as p u re ly lu m p e d ones.
O n the o th e r
hand, th e d is trib u te d -lin e -ty p e c irc u its are designed as re la tiv e ly s im p le config-
1
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u ra tio n s such as step -im p ed a nce , s tu b -ty p e , side-coupled o r edge-coupled filte rs
o r h y b rid co up le rs w ith quarter-vvave-length lines.
Design p rocedures fo r such
c ir c u it s ta rte d fro m th e p ro to ty p e lu m p e d -e le m e n t c irc u its and re p lace d th e el­
em ents w ith a p p ro p ria te line-segm ents, a d ju s tin g th e ir im pedances a n d d im e n ­
sions. F ig . 1 . 1 shows co n ve n tio n a l p la n a r f ilt e r design procedures.
Translated
theoretically
(XT) ^ f fT)
z Jt -
77I7Frequency
O ptim ize to
desired
characteristics
b y E M sim.
F ig u re
1
I
. 1 : C o n ve n tio n a l p la n a r filte r design procedures
For th e b ro a d -b a n d sp ecifications, whereas c o m p u ta tio n o f the responses can
be done w ith o u t d iffic u lty , design o f such sp e cifica tio n s requires n e w ly-d e vise d
elem ents o r procedures fo r each a p p lic a tio n .
In o rd e r to o b ta in a m icrow ave c ir c u it w h ich has a b ro a d -b a n d sp ecified re­
sponses as w e ll as co m p a ct size, we give up the idea o f s ta rtin g fro m p ro to ty p e
lu m p e d -e le m e n t c irc u its and re p la cin g th e m b y line-segm ents. In s te a d , we syn­
thesize a c ir c u it by co n n e ctin g line-segm ents sca tte re d in tw o -d im e n s io n a l (2 -D )
o r th re e -d im e n s io n a l (3 -D ) space. T h e w ay to connect line-segm ents can n o t be
2
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0-
n
Devise the circuit
add L to
shunt C
m ore than one stop bands
Frequency"
Optimize to
desired
characteristics
by EM sim.
Transform
to physical
dimensions
resonator
F ig u re 1.2: C o n v e n tio n a l p la n a r b ro a d -b a n d filte r design procedures
express as a c o n tin u o u s fu n c tio n o f p a ra m e te rs . T h e fa c t says th a t we need to
a d o p t new te ch n iq u e s to solve d is c o n tin u o u s p ro ble m s.
T he G A s m a y be a c a n d id a te fo r such a d is c o n tin u o u s problem solver.
1.2
B rief review of previous works of the GAs in mi­
crowave engineerings
G A was in tro d u c e d b y H .J .H o lla n d in 1975 [1], as a s u b je c t o f c o m p u te r science.
B u t recently, i t began to be a p p lie d to o p tim iz a tio n p ro b le m s o f d iscrete a n d /o r
d isco n tin u o u s m ic ro w a v e co m p on e nts.
T h e m o st p o p u la r a p p lic a tio n o f G A s is th a t fo r a n te n n a a rra y design s ta rte d
by R .L .H a u p t t o th in a rra y elem ents [2 , 3], to o b ta in q u a n tiz e d phase ta p e r[4 ] and
q ua n tized a m p litu d e ta p e r [5], o r to o b ta in a d a p tiv e phase-only n u llin g [6 , 7,
8
],
w ith Y .C .C h u n g [9]. A lso , Y .C .C h u n g a p p lie d G A to sp he rica l arrays th a t con­
fo rm to th e su rfa ce o f a sphere [10,
1 1
], A g ro u p o f D .M a rc a n o is a n o th e r a c tive
3
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g roup. T h e ir firs t s tu d y was to o b ta in a ra d ia tio n p a tte rn specified by shaped
beams and n u lls in given d ire c tio n s [12, 13]. T h e y a p p lie d the G A s to varia bles
in a co m p le x p la ne o f th e S ch e lku n o ff m e th o d to synthesize a rra y p a tte rn s [14].
A p e n a lty fu n c tio n was used in [15, 16]. These stu d ie s were su m m a rize d in [17].
M a n y o th e r researches have been p e rfo rm e d on a n te n n a arrays. A .T e n n a n t s tu d ­
ied n u ll-s te e rin g in phased a nd a d a p tive a rra y s [18].
B .C ham bers designed an
e nd -fire a rra y a n te n n a w ith b o th a d a p tiv e n u llin g and ra d ia tio n p a tte rn enve­
lope as w ell as c y lin d ric a l ra d a r absorbers [19]. B .P .K u m a r used a m a th e m a tic a l
re la tio n o f th e L egendre p o ly n o m ia ls and s im p lifie d the a rra y fa c to r re la te d to
c u rre n t d is trib u tio n o f th in n e d arrays [20, 21]. R .J .M itc h e ll o perated th e G A s on
the ro o ts o f th e a rra y p o ly n o m ia l in th e c o m p le x p lane to o b ta in p a tte rn n u llin g
and showed advantages on th e tr a d itio n a l o p e ra tio n on the co m p lex w eights o f th e
a rra y fa c to r [22, 23]. F .A re z co m bined G A s w it h th e sim u la te d a n n e a lin g tech­
niques to search p a tte rn s w ith n u ll- fillin g [24]. L u Y ilo n g and K ee n -K eo n g Y a n
used d ecim al o p e ra tio n to deal w ith real o r c o m p le x coefficients d ire c tly [25, 26].
B e n g -K io n g Yeo pro po se d fo r a rra y fa ilu re c o rre c tio n in d ig ita l b e a m fo rm in g .
T h e b e a m fo rm in g w e ig h ts o f an a rra y were represented d ire c tly by a v e c to r o f
co m p lex num bers. F o r th e d e c im a l co d in g , th e y proposed three m a tin g schemes,
a d ja c e n t-fitn e s s -p a rin g ( A F P ), b e s t-m a te -w o rs t (B M W ) , and e m p eror-selective
(E M S ), and showed th e ir advantages [27]. K .F .S a b e t developed a m odel co nsider­
in g c o u p lin g effect betw een a n te n n a elem ents. T h e m o d el was e xtra c te d fro m fu llwave e le c tro m a g n e tic s im u la tio n s [28]. K .N .S h e rm a n o p tim iz e d ante nn a beam s
fo r shaped p o ly g o n a l coverage areas fo r m u ltib e a m co m m u n ic a tio n system [29].
A .P etosa in v e s tig a te d a p p lic a tio n s to p re ve n t in te rfe re n ce fro m adjace n t cells in
Io c a l-m u lti-p o in t c o m m u n ic a tio n s system (L M C S ) [30]. O th e r researches on ap­
p lic a tio n s to a n te n n a a rra ys are found in [31, 32. 33, 34, 35. 37, 38, 39. 40, 41].
4
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W ire a n te n n a design is one o f th e p o p u la r to p ics o f shape o p tim iz a tio n s by
th e G A s . A .B o a g o p tim iz e d lo a d e d elem ents disposed in a w ire a n te nn a as w e ll
as a m a tc h in g c irc u it [42]. Z .A ltm a n e xte n de d B o a g ’s technique to o th e r a n te nn a
shapes [43, 44]. E .E .A lts h u le r designed a w ire-segm ents a n te n n a fo ld in g a t some
in te r io r p o in ts [45]. P .L .W e rn e r in v e s tig a te d an a p p lic a tio n to stacked a nte nn a
system s [46]. D .S .L in d e n e xte n de d th is app ro a ch to the real code G A s [47]. A lso ,
he a p p lie d G A s to antennas in th e presence o f s a te llite stru c tu re s . T h e in te rfe r­
ence o f the s u rro u n d in g s tru c tu re s were considered d u rin g the o p tim iz a tio n [48],
B .S .S a n d lin developed techniques to e valua te e rro r s e n s itiv itie s o f w ire antennas
designed by th e G A s [49]. B. A .A u s tin co m b ine d G A s w ith th e m e th o d o f m o m e n t
(M o M ) to design o f a v e h icle -m o u n te d lo o p a n te nn a [50], and Y a g i-U d a arrays
[51]. A ls o , D .C o rre ia in ve stig a te d a p p lic a tio n s to Y a g i-U d a antennas [52] as w ell
as E .A .Jo n e s [53]. B .G .P o rte r proposed a p p lic a tio n s to th e developm ent o f the
p o la riz a tio n -a g ile m u ltip le -re s o n a n t w ire a n te n n a [54]. R .S chlub developed d u a l
ban d s w itc h e d -p a ra s itic w ire a nte nn a s fo r co m m u n ic a tio n s ban d in 900 and 1900
M H z [55, 56]. A .D .C h u p rin designed s m a ll folde d w ire antennas by th e G A s [57].
O ne o f th e o th e r a p p lic a tio n s o f shape o p tim iz a tio n is a design o f m u ltila y e r
s tru c tu re s such as filte rs o r absorbers. E .M ich ie lssen , w ith J.S aje r, S. R a n jith a n
and R .M ittr a , a p p lie d the G A to o p tim iz a tio n p ro ble m s o f m u ltila y e re d s tru c tu re s
such as frequency selective surfaces o r m icrow ave absorbers in 1993 [58, 59, 60].
T h e G A s was used to select a p p ro p ria te m a te ria ls as w ell as to o b ta in o p tim a l
thicknesses o f th e m . These are th e e a rlie st a p p lic a tio n s o f th e G A s to m icrow ave
e ngineering.
F o llo w in g th is w o rk , D .S .W e ile w orked on m u ltila y e re d absorbers
w ith m u ltio b je c tiv e fu n c tio n s [61, 62]. A ls o , A .R .F oroo ze sh w orked on absorbers
by a d a p tiv e G A s [63], and S .C h a h ra v a rty designed m icrow ave m u ltila y e re d filte rs
5
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by choosing la y e r m a te ria ls a n d th e ir thicknesses [64, 65,
6 6
].
In te re s tin g a p p lic a tio n s to shapes o f m icrow ave c o m p o n e n ts are d ire c t o p ti­
m iz a tio n o f t h e ir d im e n sio n s. J .K im o p tim iz e d a T - ju n c t io n o f H -p la n e waveg­
uide. He d isp o se d several p o in ts a t th e w a ll o f th e T - ju n c tio n . T h e w a ll changed
shape a c c o rd in g to p o in ts w h ic h were d isplaced by th e G A s [67]. J .M .J o h n s o n op­
tim iz e d a n te n n a p a tte rn s a lo n g w it h th e m e th o d o f m o m e n t (M o M ) . He reduced
its c o m p u ta tio n tim e b y re p la c in g some elem ents o f an a lre a d y -m a d e im pedance
m a trix o f M o M w it h zeros a c c o rd in g to an a ntenna sh ap e , in s te a d o f c a lc u la t­
ing the w h o le im p e d a n ce m a tr ix each tim e [6 8 . 69].
R .M .E d w a rd s o b ta in e d a
p rin te d s p ira l a n te n n a w it h d u a l o b je c tiv e s o f a u n ity a x ia l r a tio a n d a b oresight
m a in lobe [70, 71].
Y ilo n g L u designed an o p tim a l a p e rtu re fie ld d is trib u tio n
based on th e v e rs a tile th re e -p a ra m e te r (3 -P ) m odel [72]. H .M o s a lla e i a p p lie d the
G A s to s yn th e sis o f L u n e b u rg lens antennas w ith G re e n ’s fu n c tio n o f s p h e ric a lly
m u ltila y e re d s tru c tu re [73, 74].
H .C h o o o p tim iz e d p a tc h shapes fo r m ic ro s trip
antennas [75]. L i-C h u n g o b ta in e d a n u ltra v v id e -b a n d w id th ta p e re d h o rn a ntenna
[76]. B . A ljib o u r i designed a d u a l-fe e d c irc u la r p o la riz e d p a tc h a n te n n a by o p ti­
m iz in g e ig h t p a ra m e te rs by th e G A s [77]. L o g -p e rio d d ip o le a rra y was in v e s ti­
gated by Y .C .C h u n g [78]. A sm a ll-size d w aveguide p o la r iz a to r was designed by
B .V .S e s tro rc ts k y [79]. M u ltib a n d fra c ta l antennas was designed b y D .H .W e rn e r
[80].
A s the m o st im p re ssive w o rk fo r me, A .J o h n and R .H .J a n s e n have developed
an excellent w a y to design ( M ) M I C com ponents by G A co m b in e d w ith 2.5D
sp ectra l d o m a in a pp ro a ch (S D A ) [81].
Even th o u g h th is ena b le d th e m to o b ta in co m p o n e n ts w it h u n c o n v e n tio n a l
shapes fo r c e rta in s p e c ific a tio n s , th e c o m p u ta tio n tim e to o k 5 seconds fo r one
6
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F ig u re 1.3:
G A design o f ( M ) M IC com ponents co m b in e d w ith 2.5D s p e c tra l
d o m a in a p p ro a c h b y A .J o h n and R .H .Jansen
c o m p o n e n t w ith 100 patches b y D E C a lp ha 2 00 /23 3 because o f 2 .5 D S D A based
on p atch -se gm en ts. T h is was goo d fo r sm a ll size co m p o n e n ts b u t n o t e fficie n t fo r
large co m p o n e n ts.
A s t u t o r ia l m a te ria ls , J .M .J o h n and Y R a h m a t-S a m ii [82] is good to read,
and re ce n tly, th e y have been co m p ile d a lo t o f a p p lic a tio n s in th is fie ld [83].
Fo r a n a lo g c irc u its ' design, J .R .K o z a synthesized lin e a r and n o n -lin e a r c ir ­
cu its , c o m b in in g g e n e tic p ro g ra m m in g w ith S P IC E [84]. He is one o f th e le a d in g
persons w h o are in v o lv e d in th e gen e tic p ro g ra m m in g a p p lic a tio n s .
In th is d is s e rta tio n , we a p p ly th e G A to design m icro w a ve co m p o n e n ts such
as filte rs o r d iv id e rs b y a d o p tin g line-segm ents in ste a d o f p atch -se gm en ts. T h e n
we believe d to o b ta in o p tim iz e d c irc u its w ith c o m p lic a te d c o n fig u ra tio n s w ith in
p ra c tic a l c o m p u ta tio n tim e .
1.3
Features of our work
We a p p ly th e G A s to designs o f m icrow ave c irc u its to o p tim iz e th e ir to p o lo g y and
dim e nsion s. T h e G A s o pe ra tes on a set o f param eters, th e re fo re c ir c u it ’s to p o lo g y
7
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and dim ensions m u s t be expressed by a set o f param ete rs. T h e set o f param eters
can be o p tim iz e d b y G A , even th o u g h the responses are n o t contin u ou s fun ctio ns
o f the p aram ete rs. T h e fa c t is indispensable to o p tim iz e to p o lo g y o f a c irc u it.
U n like th e case o f o p tim iz a tio n s using e le ctrom ag n etic-b a se d patch-segm ents,
o u r approach o p tim iz in g line-segm ents as c ir c u it ’s elem ents does n o t require large
n um be r o f p a ra m e te rs fo r large c irc u it size. T h is enables us to achieve n o t o n ly
n a rro w band sp e c ific a tio n s fo r s m a ll com ponents b u t also w ide band specifications
fo r la rg er ones.
1 .3 .1
2 -D lin e - s e g m e n t c ir c u its
T h e firs t s tu d y has been done fo r a p p lic a tio n s to 2 -D line-segm ent c irc u its . T he
n o ve lty o f th e s tu d y is d evelopm ent o f the expression o f a c irc u it p a tte rn by a
set o f param eters, th a t describes c irc u it to p o lo g y as w ell as lengths o f the linesegments.
T h e set o f param ete rs describes s tru c tu ra l g ro w th o f the c irc u it by
in d ic a tin g how new lines w ill be added inside the o u te rm o s t c irc u it successively.
T o reduce th e c o m p u ta tio n tim e fo r e v a lu a tio n o f th e frequency responses
o f m any c irc u its , each c ir c u it is decomposed in to sim p le elements such as T ju n c tio n s , corners and open-ends, and th e ir S param ete rs are synthesized again
to o b ta in the responses o f th e c irc u it. T h e average c o m p u ta tio n tim e was a b o u t
3 seconds fo r 100 c irc u its b y PC w ith C eleron 400 M H z.
1 .3 .2
2 -D c o u p le d lin e -s e g m e n t c ir c u its
T h e second s tu d y was a p p lic a tio n s to 2-D co up le d line-segm ent c irc u its .
T he
n o ve lty o f th e s tu d y is d eve lo p m en t o f a m o d e l o f an a djacent coupled lines
section using v o lta g e tra n sfo rm e rs.
T h is enables us to o b ta in the responses o f
8
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coupled lin e sections w ith o u t e le c tro m a g n e tic c o m p u ta tio n s w h ich required lo n g
c o m p u ta tio n tim e . T h e w hole c ir c u it p a tte rn is decom posed in to p a irs o f a djacent
lines o f equal le n g th b y u sing o u r d e v e lo p in g e la b o ra te procedure.
1 .3 .3
3 -D lin e - s e g m e n t c ir c u it s
T h e last s tu d y has c o n trib u te d to 3 -D m icro w a ve c ir c u it design. T h e o b je c tiv e
is to design c o m p a c t line-segm ent c ir c u it in a m u ltila y e r s tru c tu re . W hen lines
are stacked u p in th e m u ltila y e r s tru c tu re , co u p lin g s between th e lines can n o t
be n e g lig ib le e sp e cia lly fo r design o f fre q u e n c y se n sitive co m p on e nts such as f il­
ters. We in tro d u c e d m odels o f m u ltic o n d u c to r tra n sm issio n lines to reduce th e
c o m p u ta tio n tim e th a t w o u ld be u n p ra c tic a lly lo n g i f th e fu ll-w a ve ele ctrom ag ­
n e tic c a lc u la tio n was used. C o n s tru c tio n o f th e m o d e l is done by su p e rp o s itio n
o f the modes, w h ic h correspond to th e e igenvectors o f the ca pa cita nce m a tr ix
o f u n it-le n g th tra n s m is s io n lines. O u r p ro p o s in g p ro ce d u re is d escribed so as to
be im p le m e n te d easily in to C A D p ro g ra m s. T h e m o d e l is a vailab le to any k in d
o f m u ltic o n d u c to r tra n sm issio n lines whose cross sections are u n ifo rm along the
p ro p a g a tin g d ire c tio n .
1.4
Organization of this dissertation
T h e o rg a n iz a tio n o f th is d is s e rta tio n is in tro d u c e d as follow s. C h a p te r
2
presents
the b rie f in tro d u c tio n o f G A th a t is used in th is d is s e rta tio n .
C h a p te r 3 presents th e a p p lic a tio n s o f th e G A to 2 -D line-segm ent c irc u its .
T h e procedure to c o n s tru c t a c ir c u it fro m a set o f ra n d o m num bers is described
w ith an e xa m p le .
T h en design exam ples o f filte rs , a d iv id e r and a m a tc h in g
9
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c ir c u it fo r F E T are d e m o n s tra te d .
C h a p te r 4 presents th e e xte n d e d a p p lic a tio n s o f th e 2 -D line-segm ent to c ir­
c u its w ith c o u p le d -lin e sections. In a d d itio n , th e a p p lic a tio n o f th e line-segm ent
m o d e l w ith a lu m p e d elem ent is discussed as well.
T w o exam ples are dem on­
s tra te d .
C h a p te r 5 presents th e a p p lic a tio n s to 3 -D line-segm ent c irc u its .
lin e -se g m e n t c ir c u it in tro d u c e d in th e c h a p te r
2
T h e 2-D
is copied to each la ye r, and is
co nnected b y via s disposed betw een c o rre sp o n d in g in te rse ctio n s. T h e n some lines
a n d some via s are rem oved a c c o rd in g to th e co rre sp o n d in g gen e tic codes. N e w ly
d e riv e d m u ltic o n d u c to r tra n s m is s io n lin e m o d el helps th e c o m p u ta tio n tim e to
decrease d ra m a tic a lly .
D esign exam ple s o f a band-pass filte r and a b a n d -s to p
filt e r are d e m o n s tra te d .
C h a p te r
6
presents the co nclusio n s and suggestions fo r fu tu re w orks.
10
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CHAPTER 2
The genetic algorithms
In th is ch ap ter, the G A p ro c e d u re th a t is used in th is w o rk is described.
2.1
The general flow of the genetic algorithms
T h e flo w c h a rt o f th e G A used in th is w o rk is show n in F ig . 2.1. T h e a lg o rith m
consists o f tw o p a rts, n a m e ly “ M a te ” and “ E v a lu a te ” procedures. T h e “ M a te ”
is a co m m o n p ro ced u re o f G A , a n d th e “ E v a lu a te ” m u s t be developed fo r each
a p p lic a tio n .
We w ill g iv e a b r ie f e x p la n a tio n fo r th e “ M a te ” as th e com m on
p ro ced u re , the n go to o u r “ E v a lu a te ” p ro ced u re .
“ M a te ” can be fo u n d in th e reference [83].
F u rth e r e x p la n a tio n s fo r the
D efine te rm in o lo g y o f G A as ta b le
2 . 1;
2 .1 .1
“M a t e ” p r o c e d u r e
T h e “ M a te ” creates new chrom osom es th a t we ca ll “ c h ild re n ” in to th e n e x t gener­
a tio n . In each g e n e ra tio n , th e G A chooses chrom osom es as parents d e p e n d in g to
th e ir fitness. T h e chro m o som e t h a t has h ig h fitness w o u ld be chosen fre q u e n tly,
b u t th e one th a t has lo w fitne ss fa ils to be chosen. L et th e fitness o f chrom osom e
11
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Q START ^
Create Imax
Chromosomes
Randomly
Generation = I
Evaluate'
M ate'
Map jth chromosome
to a set of
parameters Gj
Map Gj to
Circuit Pattern
Choose Gk
Choose G1
Calculate
Circuit
Response
Perform
Crossover
Perform Mutate
Evaluate Fj
Put two offsprings
into next Generation
Fj > Fopt ?
]=Imax ?
j=j+l
Generation >
_ Gmax ?
END
Generation = Generation +1
F ig u re 2.1: G A flo w c h a rt. G A consists o f tw o m a in p a rt, “ M a te ” and “ E valua te ” .
12
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Table 2.1: GA term inology
Chromosome
a sequence o f b in a ry numbers, w h ich are decoded
in to real parameters
Gene
P opulation
Parent
C hild
Generation
a b in ary number com posing a chromosome
a num ber o f chromosomes in one generation
a chosen chromosome to create ch ild re n
a chromosome created from a couple o f parents
an ite ra tio n stage where G A creates children as much as
a certain p o p u la tion
Fitness
a certain value in d ica tin g how th e response o f a chromosome
is close to the goal
Crossover
a G A operation exchanging some genes between two chromosomes
M u ta tio n
a G A operation flip p in g some genes as “ 0” to “ l 77 or “ 1 ” to “ 0”
j be F j. T h e n th e p ro b a b ility fo r th e ch ro m o som e j to be chosen is defin e d as
F
P r o b a b ility o f j = -— -—
/ m ax
(2-1)
k= 1
w here / max is p o p u la tio n . T h e w ay to c a lc u la te fitne ss is described in th e c h a p te r
3.
“ C ro sso ve r 7 is p e rfo rm e d when tw o c h ild re n are cre a te d . L e t the tw o chosen
chrom osom es be C, and Cj as show n in F ig . 2.2. A p a ir o f crossover p o in ts is set
ra n d o m ly . T h e n th e b in a ry n um bers betw een th e m are exchanged. T h e created
tw o d iffe re n t chrom osom es in h e rit some fea tu re s o f th e ir parents som ew hat. T h is
is w h y we ca ll th e m “ c h ild re n 77.
“ M u ta te 77 is p e rfo rm e d on the cre a te d c h ild .
Som e m u ta tio n p o in ts are set
ra n d o m ly fo r each chrom osom e. Genes a t th e p o in ts are flip p e d as show n in F ig .
2.3. T h e created chrom osom es are e xp e cte d to have d iffe re n t ch a ra c te ris tic s fro m
th e o rig in a l ones. T h is causes th e d ivergence o f a v a rie ty o f c irc u it p a tte rn s .
13
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Crossover points
C i* o o io iix o iq o c io m c |io iio io o o o i
I
I
C j- io o io io iin iio io iiid o o o io io io ii
P e r f o r m C ro s s o v e r
o
Ci=0010111010ll010111Cl^0110100001
C]° 10010101 lljT o iO ll 1C|00 010101011
F ig u re 2.2: Crossover exchange p a rts o f chrom osom es between parents.
M u ta t io n
i
p o in ts
U
C i= 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1
P e rfo rm
M u ta tio n
C i = Q0101l[o|o 1000 lcjcjojio 10110100001
F ig u re 2.3: M u ta te flip s some genes in chrom osom es o f c h ild re n .
A fte r these tw o new c h ild re n are p u t in to n ext g en e ra tio n , th e tw o parents
are ta ke n back to th e o rig in a l set, and G A repeats the same p rocedure u n t il th e
n u m b e r o f c h ild re n o f th e n e x t g e n e ra tio n becomes / mnx. T h e o u te r lo o p c o n tro ls
ite ra tio n o f g enerations. G max is th e l im it o f th is ite ra tio n .
2 .1 .2
“E v a lu a t e ” p r o c e d u r e
W e w ill e x p la in each p rocedure in th e “ E v a lu a te ” o f F ig .2.1, using F ig .2 .4 . “ M a p
j t h ch rom osom e C j to a set o f p a ra m e te rs G j ' tra nslate s a sequences o f b in a ry
n u m b e rs in F ig .2 .4 (a ) to a set o f p a ra m e te rs o f real num bers in F ig .2 .4 (b ), fo l-
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lo w in g a ru le d efin e d in advance.
__________________
100X110101110010.'......
chraaoaos** to
~
0011001 0 1 0 0 0 0 1 0 1
"
00101100 0 1 0 1 0 1 1 0 .......
0 1 1 1 1 11010110000 .............
101 0 0 0 0 1 1 0 1 0 1 1 1 1 .......
1111001101111010
—
{0.6.0.87, 0.47, 0 . 2 ........>
}
of
to
circuit pottarn*
. {0 . 2 . 0 . 1 3 . 0 . 5 3 . 0 . 3 3
{ 0 . 1 3 , 0 . 8,0.33.0.4....... }
•{0.4S, 0 . 9 3 . 0 . 7 3 . 0 . 0 ...... >
1000001010000011........
-
« t . ol t u u . f r .
{ 1 . 0 . 0 . 2 . 0 ^ « ! o '.S6°.V.,!'.S 6 }1 '0 ....... }
‘
(0.53,0. 1 3 , 0 . 5 3 , 0 - 2 ...... >
U)
(b)
Pitn*** - 98
Pitn*** ■ 65
Pita***
Pitn*** • 42
T
-•l£ k
- N
'- f w r \
■f y y
- i n
¥
Pita*** - 91
Pita*** - 9
Pita*** ■ 25
(•)
r**poa*«* to
£ita*s*«*
1n m ,J
(c)
‘f n
circuit p*tt*ras to
r**poaa«*
(d)
F ig u re 2.4: E v a lu a te procedure operates on five states o f (a) chromosomes, (b)
sets o f p aram ete rs, (c) c irc u it p a tte rn s, (d ) responses, and (c) fitnesses.
“ M a p G j to c ir c u it p a tte rn ” , w h ich corresponds to F ig . 2 .4 (c), creates physical
c irc u it p a tte rn s fro m sets o f param eters, w it h th e procedure developed in the
fo llo w in g ch ap ters. “ C a lc u la te c irc u it response” , w h ich corresponds to F ig .2 .4 (d ),
calculates responses o f c irc u its .
“ E va lu a te F j ” , w h ich corresponds to F ig .2 .4 (e ), evaluates the fitness o f each
response o f th e c ir c u it by a specific fu n c tio n . W h e n F j — Fopt, where F ^ t is the
o p tim a l value o f th e fitness, the chrom osom e m eets a ll th e specifications.
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2.2
Conclusions of this chapter
A sim p le G A is used in th is d is s e rta tio n . D e ve lo p in g s o m e th in g new fo r G A s is n o t
th e o b je c t o f th is d is s e rta tio n . B u t tria ls to im p ro ve i t have been done som ew hat.
F o r e xam ple , c o m b in a tio n w ith th e co njug a te g ra d ie n t m e th o d was im p le m e n te d
in th e p ro g ra m . T h e re s u lt is n o t so efficient because th e n u m e ric a l d e riva tive s o f
the p a ra m e te rs take u n p ra c tic a lly lo n g tim e . A lso , th e som e fu n c tio n s o f fitness
were e xa m in e d . N o t o n ly lin e a rly p ro p o rtio n a l fu n c tio n s o f th e chosen p ro b a b ility
respect to th e fitness, b u t also s q u a re -p ro p o rtio n a l o r lo g a rith m ic p ro p o rtio n a l
fu n c tio n s are tested.
T h e convergence was depend on th e c ir c u it s tru c tu re s o r
th e sp e cifica tio n s. T h erefo re , in th is d isse rta tio n , th e s im p le G A is used to avoid
dependency o f such e x te rn a l c o n d itio n s .
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CHAPTER 3
Applications to 2-D line-segment circuits
O p tim iz a tio n s o f m icrow ave c irc u its have ty p ic a lly been c a rrie d o u t fo r th e ir
le n g th s o f lines by c o n v e n tio n a l m e tho d s such as q u a s i-N e w to n m e th o d , co n ju g a te
g ra d ie n t m e th o d o r ra n d o m search technique. T h e in it ia l values are o b ta in e d fro m
c o n v e n tio n a l lu m p e d -e le m e n t p ro to ty p e circu its. F o r c o m p lic a te d sp e cific a tio n s
w ith several pass bands and s to p bands, o r unbalanced p ow er d iv id in g ra tio s , we
designed and o p tim iz e d a c ir c u it to p o lo g y by t r ia l and e rro r because the re were no
s tra ig h tfo rw a rd ways to o b ta in in it ia l lengths and in it ia l to p o lo g y . T h e re fo re , we
have desired a o p tim iz in g m e th o d w h ic h can tre a t d iscre te a n d /o r d isc o n tin u o u s
p aram ete rs, such as c ir c u it to p o lo g y.
In th is c h a p te r, we a p p ly G A to p la n a r m icrow ave c irc u its to o p tim iz e th e ir
to p o lo g y and d im e nsion s.
U n lik e th e case o f o p tim iz a tio n s based on p a tc h -
segm ents, o u r a p p ro a ch o p tim iz in g line-segm ents does n o t re q u ire large n u m b e r
o f p aram ete rs fo r la rg e c ir c u it size. T h is enables us to achieve n o t o n ly n a rro w
band sp e cifica tio n s fo r sm a ll co m p on e nts b u t also w ide ban d sp e cifica tio n s fo r
la rg e r ones.
17
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3.1
Expression of a circuit by a set of parameters
In th e proposed p ro ce d u re , a c ir c u it is expressed b y a set o f p a ra m e te rs th a t
describe s tru c tu ra l g ro w th o f th e c ir c u it b y in d ic a tin g how new lin e s w ill be added
to an o rig in a l c ir c u it successively.
W e c a ll th e o rig in a l c ir c u it “ base c irc u it” ,
w h ich is th e o u te rm o s t re c ta n g u la r p a tte rn . T h e lin e -a d d in g -p ro ce ss chooses two
a d ja ce n t p a ra lle l lines in th e c irc u it. T h e n a new lin e is disposed to b rid g e these
tw o lines p e rp e n d ic u la rly . A f te r ite ra tio n o f th is process, some lines are e ve n tu a lly
rem oved fro m th e c ir c u it as we w ill see la te r.
H e re a fte r we w ill illu s tra te our
pro ced u re using an e xa m p le show n in F ig . 3.1(a) to 3 .1 (d ).
L e t a set o f p a ra m e te rs be G as
G
=
{ { x i , x 2, X3 }.
{X 4 , X 5 , Xg,
■, X 3 fc_j_i, X 3 fc4 _2 , ^'3fc+3>
{^ 3 V max—3?^3iVmax+4:
k —
‘ , ^3iVmax-r3 }
t 3'6A,max+7} } :
(3-1)
Y rnax •
1
G is com posed o f th re e p a rts ; firs t three p aram ete rs, N max sets o f th re e param eters
a nd la s t 3 N max 4- 4 p a ra m e te rs. Each p a rt fu n c tio n s d iffe re n tly . Each param ete r
has a value between 0 a n d
1
. N max specified in advance is the m a x im u m n u m b e r o f
lines to be added to a base c ir c u it, and th is corresponds ro u g h ly to the c o m p le x ity
o f the c irc u it.
In F ig . 3 .1 (a ), P o rt 1 and 2 are th e in p u t and th e o u tp u t p o rts . T h is c irc u it
consists o f d is trib u te d lines o f th e same w id th . F ir s t tw o p aram ete rs x \ and x 2
define th e x and the y d im e n sio n s o f a base c irc u it.
T h e th ir d p a ra m e te r x 3
defines th e n u m b e r o f lines to be added to th e base c irc u it. I f X max and Ymax are
18
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( in p u t 1
2 5 x 0 .5
S t r i p L in e
(a)Base Circuit
4 5 x 0 .7 * 3 1 . Sms
(c)Add Second line
13 . S an
(d)Remove three lines
F ig u re 3.1: A set o f param eters expresses a c irc u it, (a) T h e firs t th re e p aram ete rs
express the size o f the c irc u it a n d th e n u m b e r o f lines to be added, (b ) A set o f
th re e p aram ete rs x 4, x$.
expresses th e a d d itio n a l firs t lin e to th e base c irc u it,
(c) A set o f th re e param eters X 7 , x 8, x 9 expresses the a d d itio n a l second lin e to
th e p re vio u s c irc u it, (d) T h e la s t 3 A rmax + 4 param eters in d ic a te th e lines to be
rem oved.
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th e m a x im u m x d im e n sio n and th e m a x im u m y d im e n sio n o f th e
c irc u it, th e n
th e a c tu a l x a n d y dim ensions are X max ■x i a n d Ymax ■x 2 as show n. N o te th a t
th e d im e n s io n s are n o t la rg e r th a n X max x Ymax because X i and x 2 are less th a n
1. So, X max a n d Ymax are considered as s c a lin g fa c to rs th a t we can tu n e fo r each
p ro b le m . T h e n u m b e r N rnax - x 3 in d ic a te s h o w m a n y lin e s w ill be added to a base
c ir c u it u p to Nmax.
In th is exam ple, we sp e cifie d N max =
1 0
, w h ich in d ic a te d
tw o lin e s w o u ld be added because N max • x 3 = 10 • 0.2 = 2.
T h e N max sets o f three p aram ete rs o f x 3* +1, x 3 * + 2 and x 3 * + 3
1
, w here k =
, • • • N max? in d ic a te how th e Arth lin e is a d d e d to th e base c ir c u it successively.
T h is p ro c e d u re is e xp la in e d in F ig . 3 .1 (b ) a n d 3 .1 (c ).
T h e stage o f k = 1 corresponds to th e o p e ra tio n to choose the firs t lin e to be
add e d to th e base c irc u it. N o te th a t th e to t a l n u m b e r o f lines in th e base c ir c u it
is fo u r. T h e process chooses one lin e o u t o f th e fo u r e x is tin g lines as a s ta r tin g
p o in t o f new lin e , a ccordin g to x 4;
lin e
1
is chosen i f
0
< x4 <
lin e
2
is chosen i f
1
< x4 < |
lin e 3 is chosen i f
line 4 is chosen i f
In th e case o f x 4 = 0 . 1 , lin e
1
1
| < x4 < |
| < x4 <
1
.
(3 .2)
is chosen, a n d we c a ll th is lin e “ s ta r tin g lin e ".
C hoose a n o th e r lin e o u t o f th e lines fa c in g to th e s ta r tin g lin e a c co rd in g to
x 5, th a t is x 3 fc+
2
w hen k = 1. T h e m e a n in g o f “ fa c in g " is th a t we can m ake a
v e rtic a l o r h o riz o n ta l lin e fro m th e s ta r tin g lin e to th e chosen lin e . In th is case,
such a lin e is o n ly lin e 3.
lin e 3 is chosen i f
0 < x5 < 1 .
20
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(3-3)
C a ll th is lin e “ e n d in g lin e ” .
Xs in d ica te s p o s itio n o f th e new line. In th is e xam ple , th e y p o s itio n o f the
one end o f th e new lin e m u s t be the same as th a t o f lin e
, and the o th e r end
1
o f th e new lin e m u s t be th e same as t h a t o f lin e 3. T h e re fo re the x p o s itio n is
re m a in e d to be d e te rm in e d b y x§. I f the le ftm o s t p ossible p o s itio n o f th e lin e is
x = 0, and th e rig h tm o s t possible p o s itio n is x = X 1nax • x
x 6 indicates a p o in t
l7
between th e m . T h e x p o s itio n o f the new lin e is
*^new line = ('^max '
0) • X6 .
(3-4)
T h e to ta l n u m b e r o f lin e s increases by th re e because th e s ta r tin g lin e and th e
e n d in g lin e have been d iv id e d in to tw o p a rts as show n in
—> L in e
14- L in e 5,and L in e 3 —> L in e 3 + L in e
6
).
F ig . 3.1(b) (i.e. L in e 1
T h is process o f the firs t lin e
ends u p by re n u m b e rin g th e lines th is way.
T h e n we go to th e n e x t stage to add th e second lin e to
th e previous c irc u it.
R e p e a tin g th e same p ro ce d u re , we choose one lin e o u t o f th e seven lines, a c c o rd in g
to X 7 , th a t is X 3 *;+ i w h e n k =
2
.
lin e
1
is chosen i f
0
lin e
2
is chosen i f
j < x7 < j
lin e 7 is chosen i f
< x7 < £
f < x7 < 1 .
(3.5)
In th e case o f x 7 = 0.9, lin e 7 is chosen as “s ta r tin g lin e ” . F o r “ ending lin e ” , we
choose one lin e fro m th e tw o possible lines, lin e 2 and lin e 4.
lin e
2
is chosen i f
lin e 4 is chosen i f
0
< x8 < 4
\ < x8 < 1 .
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(3-6)
T h e to ta l n u m b e r o f th e lines becomes 10. T h e c ir c u it p a tte rn is shown in F ig .
3 .1 (c).
In th is e xam ple, the lin e -a dd in g -p roce ss ends w hen we add tw o lines
because N max ■x 3 = 2.
I f we need to a d d fcth lin e , re p e a tin g th e same p ro ced u re , we choose one lin e
o u t o f the 4 + 3(fc — 1) lines a cco rd in g to X 3 * + i.
lin e
1
is chosen i f
lin e
2
is chosen i f
0
< X3 * + i <
3
< x 3k+\ <
lin e 3 k + l is chosen i f
< x 3k +
1
^ 7 ,3 ^ 7
< 1 •
(3.7)
F o r “ ending lin e ” , we choose one lin e fro m lines fa c in g to th e s ta rtin g lin e th a t
are n o t always one o r two, b u t always less th a n 3 k.
T h e x p o sitio n o r th e y
p o s itio n is d e te rm in e d by the same way as m e n tio n e d before.
We repeat the
process N max ■x 3 tim e s , and fin a lly get 3 N max • x 3 + 4 lin e s in the c irc u it.
T h e last stage removes some lines o u t o f th e 3 N max ■x 3 -I- 4 lines. T h e firs t
3iVm aI-x 3 - f4 p aram ete rs o f the la s t 3 -jV m aI+ 4 p a ra m e te rs o f G are co rre sp on d ing
to the lines in th e c ir c u it and have values o f “ 0” o r “ 1” . O th e r param eters o f the
la s t set are n o t used. I f the value is ‘‘0” , the c o rre s p o n d in g lin e is removed fro m
th e c irc u it.
lin e 5, lin e
I f th e value is “ 1 ” , th e co rre sp o n d in g lin e rem ains. T h e case th a t
6
and lin e
8
are rem oved fro m F ig . 3 .1 (c) is show n in F ig . 3 .1 (d ).
The proposed procedure has th e fo llo w in g features.
( 1 ) The c irc u it m a y have loops a n d then m ay have a fre qu e ncy response u tiliz in g
phase in te rfe re n ce effect by d iffe re n t sig n al ro u te s, in w hich lo w in se rtio n
loss is expected because o f its non-resonance m echanism .
22
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(2 ) T h e fa ct th a t a ny set o f a r b it r a r y p a ra m e te rs corresponds to a c e rta in feasi­
ble c irc u it avoids c re a tio n o f a m eaningless set o f param eters th a t generates
an infeasible c irc u it. In c re a s in g o f th e n u m b e r o f such sets h in d e rs co nve r­
gence o f G A .
(3) T h e fa ct th a t c irc u it size is n o t re s tric te d b y th e n um ber o f p a ra m e te rs b u t
o n ly by the A 'maI and th e Ymax enables us to a p p ly the procedure to a la rg e
c ir c u it fo r w ide b a n d s p e c ific a tio n s as w e ll as a sm a ll co m p on e nt fo r lim ite d
space specifications.
3.2
Optimization by GA
T h e p rocedure o f th e proposed G A has been described in ch a p te r 2 th o u g h , th e
w a y to d e te rm in e the value o f th e fitness was le ft una tten d ed .
F o r designing a filte r, g en e ra l sp e c ific a tio n s are S u [d B ] <
V i[d B ] in pass
bands, i>2 i[d B ] < V^[dB] in s to p bands, w here V I, and V2 are specified S p a ra m e ­
ters in d B . T h e n th e fitness is d e fin e d as
.v
f it n e s s = ^ { m m [ - V c,n , ~ K ,n ] * W n}
n
(3 .8 )
w here V<.,„ is the S p a ra m e te r o f th e c ir c u it a t n th s a m p lin g frequency in d B , Ve^n
is th e expected S p a ra m e te r a t th e same fre q u e n cy in d B , and W n is a w e ig h tin g
value. T h e m inus signs are due to th e fa c t an S p aram ete r o f a passive e le m en t
is neg a tive in dB .
F o r a n o th e r exam ple o f d e s ig n in g a p ow er d iv id e r, we specify th a t
5 2 i[d B ]
<
^ 3 [dB ]
S 3 i[d B ]
<
V ;[d B ]
23
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S3 2 [dB ]
<
F 5 [d B ]
5 „[d B ]
<
V'etdBj
5 2 2 [dB ]
<
W [d B ]
S 3 3 [dB ]
<
U8 [d B ]
(3-9)
w here V3 to Vg are specified S -param eters in d B . W e define th e fitness as
f it n e s s =
mm
Szi ,S32
,5 3 2
S^l ySzi
^ n
51
(3.10)
( i l {minl
f ? 2 2 e?33 I H
3.3
Design examples
Several h a rm o n ic s tr ip lin e filte rs passing f 0 and s to p p in g 2 /
signed, fa b ric a te d and tested.
X max =
8
In a ll e xa m p le s, X max =
0
and 3 /o are de­
Ymax =
50m m , and
. T h e used C P U was C eleron 400 M H z .
A tr a d itio n a l fo u r-sta g e low-pass f ilt e r w it h a response o f passing below
2
.1 G Hz
and s to p p in g above 3 .8 G H z was fa b ric a te d to co m p a re w ith . F in a l c ir c u it p a t­
te rn was o b ta in e d b y a co n ve n tion a l o p tim iz a tio n by M D S 1. T h e size was 21.8 x
7 .6 m m 2 a n d th e wave le n g th is 8 7.5 m m a t 2 G H z on the su b stra te whose p e r­
m it t iv it y is 2.94 a n d thickness is
1
.0 m m . T h e c ir c u it p a tte rn and the fre q u e n cy
responses are show n in F ig . 3.2(a) and 3 .2 (b ). T h e in ve rte d s m a ll tria n g le s in d i­
cate th e s p e c ific a tio n s o f th e h a rm o n ic f ilt e r . T h e sp e cifica tio n s are b a re ly m e t.
T h e in s e rtio n loss was 0.50 d B a t 2G H z.
A gilen t Technologies M D S B7.20
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
P o rtl
P ort2
21.8
(a)
0
-10
m -20
'O - 3 0
-40
Spec
S ll[ d B ]
S 2 1 {d B l
-50
1
2
3
4
5
6
7
Freq[GHz]
(b)
F ig u re 3.2: F a b ric a te d tr a d itio n a l fo u r stage lo w pass filte r. Pass band is below
2.1
G H z and sto p b a n d is above 3.8 G Hz. (a) P a tte rn and (b ) M easured responses.
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig . 3 .3 (a ) shows th e c ir c u it p a tte rn o f a h a rm o n ic f ilt e r by G A in the same
s tr ip lin e s tru c tu re a nd F ig . 3 .3 (b ) is its frequency responses. T h e sp ecificatio n s
are .Su < —15 d B fro m 1.9 to 2.1 G H z and S 21 < —15 d B fro m 3.8 to 4.2 G H z
and fro m 5.7 to 6.3 G H z . T h e size o f the filte r was 13.1 x 11.5m m 2, th a t was
10% s m a lle r th a n th e tr a d itio n a l one. A ll sp ecificatio n s were m e t in th is exam ple.
T h e in s e rtio n loss was 0.52 d B a t 2G H z. The c o m p u ta tio n tim e was a b o u t five
h ou rs w ith 500 chrom osom es.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Port! ♦
Port2
13 .1
(a)
0
-10
T»T
m
Hi
if
■I
ll-
-20
CN
-30
-40
S p ec
S llt d B ]
S2LC dB l
-50
1
2
3
4
5
6
7
Freq[GHz]
(b)
F ig u re 3.3: F a b rica te d fo u r stage lo w pass G A filte r. Pass b a n d 1.9 to
2 .1
GHz
and sto p bands are fro m 3.8 to 4.2 G H z and 5.7 to 6.3 G H z. (a) P a tte rn a n d (b )
M easured responses.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig .s 3 .4 (a ), 3 .4 (b ) and F ig .
3.5 show a n o th e r e xa m p le w ith an a d d itio n a l
sto p b a n d b elow th e pass band, th a t was S2i < —15 d B fro m 1.4 to 1.5G Hz. T h e
o th e r s p e c ific a tio n s were S n < —15 d B fro m 1.95 to ‘2 .05 G H z, S2i < —15 d B
fro m 3.9 to 4.1 G H z a n d fro m 5.85 to 6.15 G H z . T h e size was 46.8 x 3 5.4m m 2.
T h e th in lines in th e F ig .
3.4(b) are th e responses o f c a lc u la tio n .
responses were s h iftin g 100M H z h ig h e r a t 4 G H z and 2 0 0 M H z a t
6
M easured
G H z. T h is was
caused b y a ir re g io n a ro u n d the s tr ip lin e c o n d u c to r. T h e region decreases th e
e ffe ctive p e r m it t iv it y . T h e c o m p u ta tio n tim e w as a b o u t 14 hours. F ig . 3.5 shows
th e responses o f o u r c a lc u la tio n and the responses o f a fu ll-w a v e e le ctro m a g n e tic
s im u la tio n , E M s ig h t2.
2A W R M icrow ave office 2001 Ver.4.01
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Porcl ♦
PorC2
in
46 .8
(a)
If
-10
®
-20
iH
CN
CO
CQ
T3
-1
-30
rH
H
-40
Spec
S ll[ d B ]
S 2 1 [d B ]
S l l ( D e s i g n ) [dBl
S 2 1 (D e s ig n ) [dB]
-50
1
2
4
5
6
7
F r e q [GHz]
F ig u re 3.4: F a b rica te d fo u r stage lo w pass G A filte r w ith one sto p ban d below
th e pass b a n d . Pass ban d 1.95 to 2.05 G H z and stop bands are fro m 1.4 to 1.5
G H z, fro m 3.9 to 4.1 G H z and 5.85 to 6.15 G H z. (a) P a tte rn and (b ) Measured
responses.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
V
-10
GQ - 2 0
T3
CN
CO
CQ
CO
-40
Spec
S l l ( D e s i g n ) [dB]
S 2 1 (D e s ig n ) [d B ]
S l l( E M ) [ d B ]
S 2 1 (E M )[d B ]
J lx
-50
1
4
2
5
7
Freq[G H z]
F ig u re 3.5: C o m p ariso n o f results o f G A design and responses by f u ll wave E M
s im u la tio n fo r F ig .3.4 (a )
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig .s 3 .6 (a ) and 3 .6 (b ) show a n o th e r e xa m p le o f m o re ch a lle n g in g sp e cifica ­
tio n s . A t 3.5 a nd 5.5 G H z. S u were specified below -15 d B . A t 2.5 and 4.5 G H z ,
»?2 i w ere specified below -15 d B . Each b a n d w id th was 0.2 G H z.
T h e size was
40.5 x 4 9 .2 m m 2. T h e fre qu e ncy response s h ift to h ig h e r frequency a ga in , a n d
some s p e c ific a tio n s were n o t m e t in its lo w e r edge o f th e frequency bands. T h e
c o m p u ta tio n tim e was a b o u t
1 0
hours.
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Portl ▲
Port2
4 0 .5
(a )
0
10
CO
T3
20
CM
CO
CO
TJ
30
CO
40
S pec
S ll[d B ]
S 2 1 [d B ]
50
1
2
3
4
5
6
7
F r e q [GHz]
(b )
F ig u re 3.6: F a b rica te d G A filte r w ith two pass bands and tw o s to p bands a lte r­
n a tiv e ly . Pass bands are fro m 3.4 to 3.6 G H z and fro m 5.4 to 5.6 G H z and stop
b ands are fro m 2.4 to 2.6 G H z and 4.4 to 4.6 G H z. (a) P a tte rn and (b ) M easured
responses.
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig .s 3 .7 (a ) and 3.7(b) show an e xa m p le o f pow er d iv id e r when p o rt 2 was the
in p u t te rm in a l. F ro m 2.9 G H z to 3.1 G H z , S 12 was specified a t -5.23 d B w ith in
e rro r o f 0.3 d B , a nd S32 was specified a t -1 .55 d B w ith in e rro r o f 0.15 d B . T h is
means th e in p u t pow er fro m p o r t 2 is d iv id e d in to 30% a t p o rt 1 and 70% a t
p o rt 3. A lso S 2 2 was specified b e lo w -15 d B . T h e size was 24.3 x 14m m 2. T h e
c o m p u ta tio n tim e was 30 m in u te s. In th is case, th e is o la tio n was n o t specified,
the re fo re i t was n o t very good.
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Porci,
Port2
Porc3
24 .3
(a)
S12
S32
S31
-5
-2
CO
I-*
to
&
CD
-10
-4
CO
OJ
CO
a
CQ
03
V: *./;
2
-6
CN - 1 5
V: /
CN
CO
co
OJ
a
03
-20
-8
S22
-25
-10
2.7
2.5
2.9
3 .1
3 .3
3.5
Freq[G H z]
( b)
F ig u re 3.7: F a b ric a te d G A p o w e r d iv id e r. P ow er fro m p o r t 2 to p o r t
a n d th a t fro m p o rt
2
1
is 30%
to p o r t3 is 70%. (a) P a tte rn a nd (b ) M easured responses
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig .3 .8 shows an e xam ple o f a p p lic a tio n fo r a m a tc h in g c ir c u it o f F E T . F o l­
lo w in g o u r design o f ro u g h p re -m a tc h in g c ir c u it fro m ra w d a ta o f an F E T , o u r
G A is a p p lie d to design th e in p u t a n d th e o u tp u t m a tc h in g c irc u its to o b ta in
m a x im u m gain at fre qu e ncy fro m 2 .3 to 2.7 G H z b y sp e cifyin g re fle ctio n s u n ­
d e r 10 d B . C a lc u la te d response o f th e c ir c u it show n in F ig .3 .9 (a ) co incides w e ll
w ith th e m easurem ent show n in F ig .3 .9 (b ).
T h e designed g a in is 14.3 d B fo r
th is F E T whose M A G is 15.0 d B . W e o b ta in e d th e g a in o f m ore th a n 13.3 d B in
m easurem ent.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u re 3.8: F a b rica te d G A m a tc h in g c ir c u it w ith m a x im u m gain fro m 2.3 to 2.7
GHz
(a)
(b )
F ig u re 3.9: (a) C a lcu la te d response, (b ) M easured response
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.4
Conclusions o f this chapter
W e have in tro d u c e d an e v o lu tio n a ry g e n e ra tio n o f m icrow ave lin e -se g m e n t c ir­
c u its u sin g G A . T h e developed p ro ce d u re o p tim iz e s a line-segm ent c ir c u it w ith a
v a rie ty o f top o lo gy, a n d ends u p w ith a c ir c u it th a t exceeds e x p e c ta tio n s . A lso ,
th e procedure g u a ra n tie s th e c ir c u it n o t to be la rg e r th a n th e size sp ecified in ad­
vance. Some exam ples o f u n c o n v e n tio n a l sp e cifica tio n s were teste d to v a lid a te the
p rocedure. I t is fo u n d th a t G A has a s tro n g design c a p a b ility fo r th e m icrow ave
line-segm ent c irc u its w ith sp e cifica tio n s fo r w h ic h no tr a d itio n a l a p p ro a ch can be
used.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 4
Extensions of 2-D circuits
4.1
Consideration, of coupling effects
In th e case o f th ic k s u b s tra te and n a rro w lin e space, c o u p lin g effects o f lines
c a n n o t be ig n o re d . T h is is happen when the c irc u its are b u ilt in L T C C o r M M IC
fo r exam ples. F o r such cases, we need to im p le m e n t a p ro ced u re to c a lc u la te th e
e ffect.
T h o u g h th e re a re m a n y researches on e v a lu a tio n o f the c o u p lin g effect
a m o n g m ore th a n tw o lines, m ost o f a ll are based on n u m e ric a l e le c tro m a g n e tic
c a lc u la tio n s .
T h is fa c t h in de rs p ra c tic a l G A o p tim iz a tio n because o f its huge
c o m p u ta tio n tim e .
GND
F ig u re 4.1: C oupled th re e lines
We in tro d u c e a novel c o u p lin g m odel c o n sid e rin g o n ly a djace n t lines. F ig .4 .1
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
GND
[C ff2
_L_
C f2 j
C k l2
I Cp,:!
T o *
iT^
~ ^ p' 2
cffi~f~ T e c ?
~!~C|v;
c r il
GND
F ig u re 4.2: C o u p le d th re e lines m o d el
shows th e m o d e l o f th re e s tr ip lin e s. T h e c o u p lin g effects betw een lin e
1
and lin e
2, and betw een lin e 2 a n d lin e 3 are considered. T h e c o u p lin g sections in Fig.4.1
have been m o d e le d as F ig .4 .2 . Cp is a ca pa cita nce ju s t u n d e r a n d above a line,
C f is a ca p a cita n ce o f frin g in g a t an edge and C * is a ca p a cita n ce between lines.
O u r p ro p o s in g m o d e l is as show n in F ig .4.3 . N o te th a t a ca pa cita nce between
lines is tw ic e as la rg e as th a t o f tw o coupled lines.
T h is is re q u ire d because
the tra n s fo rm e r dou b le s th e im p e d a n ce , th e n th e co rre sp o n d in g capacitances are
reduced to h a lf. A n S p a ra m e te r o f the c o u p lin g section is a 4 b y 4 m a trix . T h e
m a trix is b e tte r to be expressed b y e v e n /o d d p ro p e rtie s, n o t b y lu m p e d elements,
because th e fre q u e n c y dep e nd e ncy o f th e m a tr ix m ust be expressed exactly. Also,
lu m p e d e le m en ts re q u ire te d io u s processes to separate C p, C f a n d C V O n the
o th e r han d even and o d d m ode im pedances are easily d e riv e d by some technique
such as fin ite e le m e n t m e th o d ( F E M ) , and these are used to o b ta in th e S m a trix
d ire ctly.
F ig .4 .4 shows th e F E M
p ro p a g a tin g co e fficie n ts Z e,
m o d el to o b ta in e v e n /o d d im pedances and
j3e and [30. F o r the im p le m e n ta tio n in program ,
a lo o k -u p ta b le is used to o b ta in Z e, Z0, ,3e and 3a c a lc u la te d in advance. N ote
th a t the re are tw o m a g n e tic /e le c tric w a lls on b o th sides o f th e lin e fo r even/odd
modes. T h is is because we need to ca lc u la te th e p ro p e rtie s in case o f th e doubled
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Cfc. T h e n th e S p ara m e te r o f th e c o u p lin g section is d erived fro m th e o b ta in e d
p ro p e rtie s as follow s;
GND
GND
Line3
Coupled two lines with doubled Ck23
Coupled two lines with doubled Cki;
Line I
(b)
F ig u re 4.3: P ro p o s in g co up le d three lines m odel
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Magnetic wall
Even mode
half o f line space
O dd mode
Electric wall
F ig u re 4.4: E v e n /O d d m ode m odels fo r F E M
\
/
\
Sil
5 ,2
5 ,3
5 ,4
5u
5,2 5,3 5,4
521
So2
523
524
5.2
5,1 5,4 5,3
(4.1)
531
532
5 33
534
5.3
5,4 5 ,i
541
542
543 5,4
5.4
5,3 5,2 5 ,,
5,2
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
,where
5 i i — 5 ( 5 n 0 + 5 n e)
^12 =
i ( 5 l l o — S 'lie )
(4.2)
■^13 = $ (S l 2 o + S i 2 e)
“^14 = 5(5l2o ~ Si2e)
,and
C
= __________ Z lo - Z l
Z l a + Z I + 2Ze,oZRcath((3eJ )
Ue’°
s
_
12e’°
2Ze,gZflCSCh (/?e,0Z)
Z l „ + Z \ + 2 Z e,0Z * co th ( f o j ) •
A p p ly in g th e m o d e l to p re v io u s p ro ce d u re in section A , we can o b ta in the
response o f c ir c u its w ith c o u p lin g effects.
F ig .4 .5 (a ) and (b ) show s m o d ifie d
p rocedure to d o th is . F ig .4 .5 (a ) is a la s t c ir c u it m odel w ith o u t c o u p lin g effects.
E ve ry S p a ra m e te r o f d is c o n tin u itie s such as T -ju n c tio n o r L -c o rn e r, a re connected
a t th e ir p o rts b y e x te n d in g th e ir reference planes. Then th e p ro ced u re checks each
p airs o f a d ja c e n t lin e s w h e th e r th e d is ta n c e between th e m is less th a n a specified
value. I f it is so, th e p a ir is co nsidered as c o u p lin g section. In th e case th a t fo u r
p airs o f lines are co u p le d , the p ro ce d u re adds th e p o rts and in se rts th e co up le d
lin e m odels m o d e ls as show n in F ig .4 .5 (b ). N o te th a t the le ftm o s t lin e are d iv id e d
in to three segm ents because th e m o d e l needs to have lin e le n gth s sam e.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F ig u re 4.5: N odes and elem ents (a) w ith o u t c o u p lin g e ffe ct, (b ) w ith co u p lin g
effects
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4 .1 .1
A n e x a m p le o f L P F w it h c o u p lin g e ffe c t
F ig .4 .6 (a ) and (b) show an e xa m p le o f lo w pass filte r co n sid e rin g c o u p lin g lin e
effect.
T h e filte r sp e c ific a tio n s are passing fro m 4.0 to 4.2 G H z and s to p p in g
fro m 4.8 to 5.0 G H z.
T h e size is re s tric te d w ith in 2.0 m m by 6.0 m m .
The
difference between th e case o f c o n s id e ra tio n o f c o u p lin g effect (cp) and th e case
o f no co n sid e ra tio n o f th e e ffect (nc) is s m a ll. T h e reason seems to be t h a t the
ra tio o f thickness o f th e s u b s tra te to the lin e w id th , w h ich is 320 f im / 75 fim ,
is n o t enough to have th e e ffe ct to change th e responses. We need to a p p ly the
technique fo r th ic k e r s u b s tra te w ith th in n e r lin e such as M IC o r M M IC , to see
the advantage.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Input___________________________ Output
■
4^
1
<
>
5.11 mm
(a )
-1 0
u
c
u
c
&
- 30
(N
cn
&
Sll(C D )
S 21(cp)
-4 0
3 1 1 ir . c )
CO
▼
3
3.5
S21(nc)
Spec
4
5
4 .5
Freq
5 .5
6
7
6.5
[ Q lz ]
(b )
F ig u re 4.6: Designed G A L P F filte r w it h c o u p lin g lin e effects.
Pass bands are
fro m 4.0 to 4.2 G H z, and sto p b ands are fro m 4.8 to 5.0 G H z. (a) P a tte rn and
(b ) responses.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.2
Combination with lumped elements
F o r lo w fre q u e n cy a p p lic a tio n , th e c ir c u it size m ig h t be large. T o keep the c irc u it
size s m a ll, we in tro d u c e lu m p e d elem ents on th e lines. Since s h u n t ca p a cito rs
are o fte n used fo r c irc u its in M M IC , we im p le m e n te d a p ro ced u re to add sh un t
c a p a c ito rs to some lines in th e c irc u it a t th e ir m id d le p o in t.
4 .2 .1
T e c h n iq u e s t o e x p r e s s lin e s w it h lu m p e d e le m e n t s
R e m e m b e r th e p ro ce d u re re m o v in g lin e s in se ction A . A t th a t tim e o f re m o v in g
lines, we assigned “ 0 ” o r " 1 ” fo r each lin e to d e te rm in e ‘‘rem oved” o r “ re m a in e d ” .
T h e n u m b e r is exte n de d to have several values between 0 a n d 1. and the lin e
a ttr ib u te is d e te rm in e d as follo w s;
0 .0
< ^ 3 v m»x+3 +« <
0 .2
<
0 .2
• • - th e lin e i is rem oved
X 3 Nmax+ 3 + i < 0.3 • ■• 0 .5 p F sh u n t C is on th e lin e i
0.3 <
2 3
T Arm»x+ 3 +t < 0.4 • • • l.O p F sh u n t C is
on the lin e i
0.4 <
X 3 Nm*x+ 3 +i < 0.5 • • • l.o p F s h u n t C is
on th e lin e i
0.5 <
X 3 Nmnx+ 3 + i < 1.0 •• • th e lin e i rem ains as i t was
F ig .4 .7 shows an exam ple.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4-4)
1-3pF__,
m m
rWtt^ ^ P^vWiegg^Wigtoimsfteagya^K
F ig u re 4.7: A c ir c u it exam ple w ith S hunt C
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4 .2 .2
A n e x a m p le o f L P F w it h lu m p e d e le m e n ts
T h e fo llo w in g figures show th e re s u lt o f an exam ple design o f L P F . T h e speci­
fic a tio n s are pass bands fro m 4.0 to 4.2 G H z w ith in s e rtio n loss less th a n 2 d B ,
a n d s to p bands fro m 4.8 to 5.0 G H z w it h re tu rn loss m ore th a n
1 2
d B . F ig .4 .8
is th e re s u lt a t g en e ra tio n o f 50. T h e in s e rtio n loss in the pass ban d was n o t y e t
s a tis fie d . F ig .4 .9 is th e re su lt a t g e n e ra tio n o f 250. T h e in s e rtio n loss s a tis fie d
th e sp e cifica tio n s, and also th e size decreased even th o u g h it was n o t sp e cifie d to
b e m in im iz e d .
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
>
2.61 mm
(a)
LPF w i t h
shunt
C
( g e n e r a t io n = 5 0 )
o
-10
-20
-30
S l l [d 3 ]
S 21 [dB]
Spec.
-40
-50
3
3 .5
4
5
4.5
P req
5.5
6
6 .5
7
[GHz]
(b )
F ig u re 4.8: Designed G A L P F filt e r w ith c o u p lin g lin e effects a nd sh u n t Cs a t
g e n e ra tio n o f 50. Pass bands are fro m 4.0 to 4.2 G H z , and sto p bands are fro m
4.8
to 5.0 G H z . (a) P a tte rn a nd (b ) responses.
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.48 mm
(a)
LPF with shunt C (generation»250)
0
10
20
30
40
* - S 2 1 tdB]
Spec
-5 0
3
3 .5
4
4 .5
5
Freq
5 .5
6
6 .5
7
[GHz]
(b)
F ig u re 4.9: D e signed G A L P F filte r w ith c o u p lin g lin e effects and sh un t Cs at
generation o f 250. Pass bands are fro m 4.0 to 4.2 G H z , and sto p bands are fro m
4.8
to 5.0 G H z. (a) P a tte rn and (b) responses.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3
Conclusions of this chapter
A m o d e l o f closely disposed lines w ith c o u p lin g effects has been proposed. T h e
m o d el considered o n ly the effect betw een a djace n t lines to s im p lify th e d e riv a ­
tio n .
T o co m bine the even and th e o d d tra n sm issio n lin e p ro p e rtie s in to th a t
o f co up le d tra n sm issio n lin e sections, th e
1
to y/ 2
tra n s fo rm e r was in tro d u c e d .
T h e n th e w hole c irc u it p a tte rn was decom posed in to the coupled lin e sections
w ith e q u a l-le n g th lin e pairs, and th e tra n s fo rm e rs are disposed betw een th e m .
T h e proposed e xam ple showed d isp la ce m e n t o f the a tte n u a tio n fre qu e ncy s h ifte d
h ig he r. T h is is reasonable re s u lt, because th e coupled lin e section is seemed to
be s h o rt generally.
B u t the e ffe ct was weaker th a n w h a t was expected.
The
a p p lic a tio n s fo r in se nsitive fre qu e ncy sp e cifica tio n s do n ot have to co n sid e r th e
c o u p lin g effect. O n the o th e r h an d , fo r th e frequency sensitive sp e c ific a tio n s such
as n a rro w band re je c tio n filte rs , th e effects seem to be im p o rta n t.
In a d d itio n , th e G A does n o t alw ays o r m e re ly creates c irc u its th a t u tiliz e th e
c o u p lin g effect e ffe ctive ly to o b ta in th e eccentric frequency responses.
A lm o s t
a ll the tria ls o f designs, the d iffe re n ce between c irc u its w ith and w ith o u t the
coupled lin e m o d el are sm a ll o r are o n ly s h ift o f frequency responses in s te a d o f
d ra m a tic a lly changed ones. T o o b ta in th e super co m p act c irc u its u tiliz in g the
c o u p lin g effect m a x im a lly , th e new specific fu n c tio n s m ust be developed.
O n th e o th e r hand, the m o d e l w ith lines disposed a shunt c a p a c ito r a t the
m o d el shows a p o s s ib ility to m in im iz e c ir c u it size. T h e m odel o f th e c a p a c ito r
was ju s t lu m p e d clem ent one in th is d is s e rta tio n . T h erefo re we co u ld n o t p re d ic t
a w id e ban d ch ara cte ristics fo r such a p p lic a tio n s . I f the m odel is im p ro v e d and
w ith o th e r m odels such as sh u n t in d u c to rs , series ca p a cito rs and series in d u c to rs ,
the G A w o u ld propose very c o m p a c t c irc u its fo r special specifications.
51
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CHAPTER 5
Applications to 3-D line-segment circuits
R e ce nt m icrow ave system s re q u ire v e ry co m p a ct c irc u its o r very e cce n tric speci­
fic a tio n s , w h ich are d iffic u lt to be o b ta in e d by such co n ve n tion a l ways. To design
such co m pact c irc u its , we need to search s o lu tio n s n o t o n ly in p ro to ty p e la d d e r
lu m p e d -e le m e n ts c irc u its , b u t also in ways o f co n n e ctin g elem ents in tw o o r three
d im e nsion s.
In th is ch a p te r, e v o lu tio n a ry g e n e ra tio n o f thre e -d im e n sio n a l (3 -D ) m icrow ave
lin e -se gm en t c irc u its embedded in m u ltila y e r s tru c tu re is presented. C o n n e c tio n s
o f th e line-segm ents and th e ir le n g th s are expressed by sets o f p a ra m e te rs, w h ich
are e v o lu tio n a rilv o p tim iz e d by g e n e tic a lg o rith m s . P ra c tic a l o p tim iz a tio n tim e
is achieved by in tro d u c in g m o dels o f b ro a d -sid e coupled m u ltic o n d u c to r tra n s ­
m issio n lines in ste a d o f fu ll-w a ve e le c tro m a g n e tic ca lcu la tio n s.
T h e s c a tte rin g
p a ra m e te rs o f th e m odels are c o n n e cte d w ith th e sc a tte rin g p a ra m e te rs o f vias,
a n d are synthesized in to the w h o le c ir c u it.
U sing line-segm ents, we can o b ta in
n o t o n ly s m a ll com ponents fo r lim it e d space a p p lic a tio n s b u t also la rg e co m p o ­
n e n ts fo r w ide b a n d frequency s p e c ific a tio n s w ith o u t in creasing c o m p u ta tio n a l
c o m p le x ity .
A band-pass filte r a n d a b a n d -sto p filte r are designed a n d tested.
T h e results v a lid a te d o u r p ro p o s in g p ro ce d u re .
T o reduce th e c o m p u ta tio n tim e , a c ir c u it is decomposed in to v ia m odels
a n d broad-side co up le d m u ltic o n d u c to r tra n sm issio n lin e m odels.
52
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T h e re are a
huge n u m b e r o f works on tw o -c o n d u c to r tra n s m is s io n lin e m o d el and its a p p lic a ­
tio n s . A s fo r th re e -c o n d u c to r m o d els, several g re a t in v e stig a tio n s have been done.
D .P a v lid is has derived side coupled th re e -c o n d u c to r tra nsm issio n lin e m o d e ls w ith
m o d a l rep re sen tatio n s o f lines [85]. S .Y a m a m o to has in ve stig a te d n o t o n ly side
c o u p le d m odels b u t also has d e rive d a b ro a d -sid e coupled th re e -lin e m o d e l [8 6 ].
S everal books have been p u b lish e d on m u ltic o n d u c to r tra n sm issio n lin e m odels.
C .P a u l has in ve stig a te d th e m odels fro m a p o in t o f vie w o f tra n sm issio n lin e d iffe r­
e n tia l e q u a tio n s, w hich are d escribed b y u n it-le n g th capacitance, in d u c ta n c e and
resistance m a tric e s [87], N.Fache, F .O ly s la g e r and D .D e .Z u tte r have p u b lis h e d a
e xce lle n t w o rk [8
8
], T h e y discussed a b o u t th e c o n d itio n to m a tc h e le c tro m a g n e tic
re p re s e n ta tio n and c ir c u itr y re p re s e n ta tio n . T h is concept is h ig h ly suggestive fo r
o u r w o rk as w e ll.
In w h a t follo w s, we firs t e x tra c t th e ca pa cita nce m a trix o f an m -c o n d u c to r
tra n s m is s io n lin e o f u n it le n g th u sin g th e 2 -D fin ite elem ent m e th o d ( F E M ) . T h e
p ro ce d u re is described as a s u ita b le w a y to be em bedded in C A D p ro g ra m s. T h en
m in trin s ic tra n sm issio n m odes are c a lc u la te d .
Im pedance value o f each m ode
is c a lc u la te d using the 2 -D F E M b y e x c itin g m conductors w ith a p p ro p ria te
vo ltag e s, w h ich are n o t o n ly p ro p o rtio n a l to the m ode voltages b u t n o rm a liz e d to
s a tis fy th e c o n d itio n to equate energy co n s u m p tio n s between e le c tro m a g n e tic and
c ir c u it re p resentations. T h e o b ta in e d m o d e im pedances are sto re d in a lo o k -u p
ta b le , a nd used to ca lcu la te s c a tte rin g p a ra m e te rs (S p aram eters) o f m -c o n d u c to r
tra n s m is s io n lin e o f a r b itr a r y le n g th in th e G A process. T h e S p a ra m e te rs are
syn thesized w ith the S param ete rs o f via s th a t are p re -ca lcu la te d by th e M o M .
T h e c ir c u it responses are so c a lc u la te d t h a t th e c o m p u ta tio n tim e fo r one c irc u it
a t one fre q u e n cy is less th a n one second.
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A band-pass filte r a nd a b a n d -sto p filte r are designed a n d v e rifie d by full-w a ve
e le ctro m a g n e tic s im u la tio n s . T h e re su lt shows v a lid ity o f o u r proposed m odels
and effectiveness o f design by G A .
5.1
Genetic expressions of growing three-dimensional cir­
cuits
In th e c h a p te r 3, a 2 -D c ir c u it was expressed by a set o f p aram ete rs. T h e pa­
ra m e ters described s tru c tu ra l g ro w th o f the c ir c u it b y in d ic a tin g how new lines
w o u ld be added successively to o u te rm o st fra m e -c irc u its , w h ic h we called ‘base
c ir c u it / ’ T h e lin e -a d d in g -p ro ce ss chose tw o adjace n t p a ra lle l lines in th e c irc u it.
T h e n a new lin e was disposed to bridge these tw o lines p e rp e n d ic u la rly . A fte r
ite ra tio n o f th is process, some lines were e v e n tu a lly rem oved fro m th e c irc u it.
VVc extended th is p ro ce d u re to 3-D c irc u its com posed in a m u ltila y e r s tru c tu re .
F ig .5.1 shows th is process in th e case o f fo u r-la v e r s tru c tu re .
F irs t, o u r G A process generates a 2-D c irc u it p a tte rn as described in o u r
pre viou s w o rk, except no lin e is removed. L e t us ca ll th is c ir c u it p a tte rn a tw od im e n s io n a l p ro je c te d c irc u it (P -c irc u it) p a tte rn .
T h e process also assigns a
specific g enetic code to each lin e and to each in te rse ctio n p o in t (see F ig .5 .1 (a )).
T h e specific genetic code o f lin e is a N -b it b in a ry n um be r, a n d th e specific genetic
code o f in te rse ctio n p o in t is a ( N - l) - b it b in a ry n um ber.
T h e n th e P -c irc u it p a tte rn is copied to a ll layers in th e m u ltila y e r s tru c tu re
u n d e r s tu d y (sec F ig .5 .1( b ) ). T h e process uses th e specific code described above
to d e te rm in e existence o f lines w h ic h are copied fro m the sam e lin e o f th e P -c irc u it
p a tte rn .
54
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F ig .5 .1 (c) shows th e lin e s whose co rre s p o n d in g lin e in P - c ir c u it have a genetic
code “ 0
1 0 1
” re m a in in th e la y e r tw o and fo u r, and are rem o ve d in th e la y e r one
and three. In th is case, th e firs t “ 0” corresponds to re m o va l o f a lin e in th e firs t
la ye r (th e b o tto m m o s t o n e ), and th e la st “ 1 ” corre sp on d s t o e xistence o f a lin e
in the fo u rth la ye r (th e to p m o s t one), fo r exam ples.
F ig .5 .1 (d ) shows th e v ia s whose co rre sp o n d in g in te rs e c tio n p o in t in P -c irc u it
has a g enetic code “ O i l . ” These v ia s lie between th e second and th e t h ir d layer
and between the t h ir d a n d th e fo u rth layer. In th is e xa m p le , th e “ 0” corresponds
to rem oval o f a v ia betw e e n co rre sp o n d in g layers a n d th e “ 1 ” corresponds to
existence o f a v ia there.
These specific g e n e tic codes re p re se n tin g typ e s o f lines a n d v ia s are o p tim iz e d
b y the G A as w e ll as th e g e n e tic codes re p re sen tin g P - c ir c u it ’s to p o lo g y and d i­
m ensions. YVc do n o t m e n tio n a b o u t th e G A process in th is p a p e r. T h e processes
are th e same as w h a t we h ave proposed in th e c h a p te r 3.
5.2
Models of elem ents in a multilayer structure
T h e G A requires m o dels to c a lc u la te c ir c u it ’s responses q u ic k ly , since it tests
m ore th a n tens o f th o u sa n d s c irc u its before convergence. In th is se ctio n , m odels
o f via s and m odels o f lin e -se g m e n ts are described.
5 .2 .1
M o d e ls o f v ia s
A lo o k -u p ta b le m ade b y e le c tro m a g n e tic s im u la tio n is used fo r vias, since the
n u m b e r o f c o m b in a tio n s to co nn e ct layers th ro u g h via s is n o t large.
Inte rse c­
tio n p o in ts in a P -c irc u it p a tte rn have three type s o f d is c o n tin u itie s . T h e y are
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Port I
.Copy 2D-lines into all layers
in 3D
Port 2
Genetic code o f ^
Genetic code o f
this via= "011"
^
Iine=
101"
(a)
Port 1
Genetic codes o f lines
remove some lines
Port 2
Genetic codes o f Vias
remove some vias
Genetic code o f Via
= "011
Port 1
Port 2
Genetic code o f Lme= "0101
Port 1
Port 2
F ig u re 5.1: Process g ro w in g th re e -d im e n s io n a l c irc u its in the case o f fo u r-la y e r
s tru c tu re , (a) C re a tio n o f 2 -D P - c ir c u it p a tte rn , (b) C o p y o f the P -c irc u it p a tte rn
to a ll layers,
(c) R e m o val o f lin e s c o rre sp o n d in g to ” 0 ." (d ) R e m o val o f vias
co rre sp o n d in g to ” 0 .”
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T -ju n c tio n s , rig h t-a n g le corners and open ends.
In N -la ye r s tru c tu re , each in ­
te rse ctio n p o in t has 2 ; v - 1 c o m b in a tio n s o f v ia connections.
F ig .5 .2 shows fo u r
c o m b in a tio n s o f v ia connections in th re e -la ye r case. T herefore, we need to pre­
pare 3 x 23
-1
types o f frequency responses.
T Junction
<Jz] Right Comer
^Z) Single End
V ia G-code
= {0 0 }
V ia G-code
= { 01}
V ia G-code
= { 10}
V ia G-code
= { 11}
F ig u re 5.2: T h re e types o f d is c o n tin u itie s o f in te rs e c tio n p o in ts in P -c irc u it, and
fo u r types o f co m b in a tio n s o f v ia connections in th re e -la ye r case
5 .2 .2
M o d e ls o f b r o a d -s id e c o u p le d lin e s
Responses o f a lin c-se g m cn t va ry c o n tin u o u s ly as it s le ngth changes. T h erefo re ,
in ste a d o f lo o k -u p tables, tra n sm issio n lin e m odels are re q uired . In a m u ltila y e r
s tru c tu re , the co up lin g s between lines p la y an im p o rta n t role. E spe cia lly, lines
stacked up to v e rtic a l d ire c tio n have s ig n ific a n t b ro ad -sid e couplings.
In th is section, we propose a m u ltic o n d u c to r tra n sm issio n lin e m o d e l w ith
b ro a d -sid e c o u p lin g effects in X -la y e r s tru c tu re .
F ig .5 .3 shows a ty p ic a l m u lti­
c o n d u c to r tra n sm issio n lin e s tru c tu re in N -laver.
I t is n o t necessarv th a t a ll N
57
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c o n d u c to rs e xist. In th is figure, th e n u m b e r o f co n d u cto rs is m, c o u n tin g fro m
th e b o tto m m o s t one. B o th o f th e to p a n d b o tto m grounds are n u m b e re d as m + 1 .
A c c o rd in g to g enetic codes assigned to each lin e o f a P -c irc u it, th e n u m b e r o f con­
d u c to rs varies fro m 0 to N , and th e n u m b e r o f co m b in a tio n s o f such c o n d u c to rs
is
2
s.
Ground (m+1 st conductor)
r
.
i
:
"— i
----------
m th conductor
i
—i
----------
m- 1 st conductor
i
— -
!
i
—!
2
nd conductor
1
st conductor
Ground (m+1 st conductor)
F ig u re 5.3: Cross section o f a ty p ic a l m -c o n d u c to r tra n sm issio n lin e in an N -Ia ve r
s tru c tu re
T o o b ta in ch a ra c te ris tic modes o f th e m -c o n d u c to r s tru c tu re , we need to ob­
ta in th e capa cita nce C ^ , the ca pa cita nce betw een c o n d u c to r i and c o n d u c to r j.
N o te th a t th e n u m b e r o f c o n d u cto rs is m + 1 i f we consider th e g ro u n d is m + ls t
c o n d u c to r.
Since CY, = C j, and C „ = 0 fo r i , j =
is
1
, • • -, m +
1
, the n u m b e r o f u nkn o w n s
X he values o f th e u nknow ns are o b ta in e d by the 2 -D F E M . I f we take
58
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n otice o f the n u m b e r o f c o m b in a tio n s p ic k in g up tw o co n d u cto rs o u t o f m +
1
conductors b e in g also ,TIX(.™+1>, th e e fficien t c o m p u ta tio n a l procedure to o b ta in
a ll the capacitances w o u ld be as follow s.
F irs t, th e p ro ced u re chooses tw o c o n d u cto rs p and q o u t o f m + L c o n d u c to rs .
T h e n let the v o lta g e o f th e c o n d u c to rs p and q be
1
v o lt, and le t th e v o lta g e o f th e
others be zero. T h e n c a lc u la te th e energy E syslt;m o f th e system . T h e ca p a cita n ce
o f the system is d erived as C pq = 2 E systcm/ V
2
w ith V =
1
.
The re la tio n between C pq a n d C tJ is,
C pq = ^
C tJ —
^2
C tJ — C pq .
(5-1)
T h e second te rm in th e R .H .S . corresponds to ca pa cita nce between c o n d u c to rs
o f zero v o lt. T h e th ir d te rm co rre sp on d s to ca p a cita n ce between c o n d u c to rs o f 1
v o lt. We in tro d u c e a m a t r ix T w hose elem ents are,
=
1
if P e K i }
but 9 £ 0 ’ j }
but q € { i j }
r pq,ij
=1
i f P <£ { i j }
r pq,ij
=
0
i f P $ {*» J'} a n d 9 £ {*» j }
r pg,ij
=
0
i f P e U J } and ? e { ^ i } •
(5-2)
T h e n the m a tr ix e q u a tio n to c a lc u la te the elem ents o f th e capacitance m a tr ix is
o bta in ed .
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C I2
C 12
C]3
Cl3
Cu
=
Cu
r
-1
-m ,m — I
' m , m —1
\
c-
m,m+l
J
(
r ~ 2 , 12
r_
L 13,12
^ 1 4 ,1 2
^ 1 2 .1 3
^ 1 2 ,1 4
^ 1 3 .1 3
^ 1 3 ,1 4
r_
r1 —
14,14
1 14,13
r—
12 ,m m —1
r—
1 2 ,mra+l
C\Z
r_
14,m m —1
r_
1 4 ,rn m + l
m m —1,12
m m - 1 ,1 3
m m —1,14
m m —I , m m —I
m m -l,m m -rl
\ L m m + 1 ,1 2
m m + 1 ,1 3
mm-r- 1,14
m m — I ,rnm —1
m r n — I ,r n r n — I
(
X(
C l 4
"t
'/m ,m —1
J
y
C*m ,m +1
c12
0
1
1
• -
0
0
1
0
1
• -
0
0
Ci3
1
1
0
• -
0
0
C 14
0
0
0
• •
0
1
I 0
0
0
• •
1
o J
c
,m-f^
C 12
1
,m— 1
C m + l,m
j
(5.3)
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
y
In ve rsio n o f the m a tr ix T gives th e elem ents o f the ca p a cita nce m a trix .
\
/
' 12
c
\
f
13
Cm
-i
\
I
0
1
1
• ••
0
0
C, 2
1
0
1
•••
0
0
Cm3
1
1
0
0
0
C lT
(5.4)
c ,m . m — I
0
c,
• ••
0
0 0 0
m ,m + 1
V
0
0
1
1
0
c -m ,m —1
c____
/
\
T h e o n ly e xce p tio n o f th is tech n iq ue is th e case o f m = 4 . In th is case, C jj = C ^f
and also th e fie ld d is tr ib u tio n is th e sam e except th a t the e le c tric fie ld d ire cts
o p p o s ite d ire c tio n s . T h is m eans th e tw o c o n d itio n s are p h y s ic a lly th e same. T he
case o f C j j a nd CVq-, and th e case o f C j j and C 5 3 are in th e sam e m anner. Then,
th e m a tr ix becomes s in g u la r.
th e fo u r co n d u cto rs is
1
In th e case o f m = 4 , the c o n d itio n s th a t one o f
v o lt w h ile th e o th e r three are zero v o lt, as w e ll as the
c o n d itio n s th a t tw o c o n d u c to rs are
1
v o lt and the o th e r tw o are zero, can solve
th e p ro b le m .
N e x t, th e c h a ra c te ris tic m odes o f th e s tru c tu re are d erived . T h e capacitance
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
m atrix w ith the referenced ground co n d u cto r is,
/
Y C \k
—C\o
—C iz
—O n
'C u n
~C21
Y i C-2k
k= 1
—C03
— C24
-C 2m
—C 3 1
C3 2
'3 4
~Czm
k= 1
—C.ji
—C .1 2
J2 Czk
k= I
(5.5)
C'13
S C \k
~C\m
...
fc = l
\
~ C m1
—C m2
—c ,m'.i
-c,m
-1
rn
X) C m A:
fc=l
/
w here th e capacitance between c o n d u c to r i a n d th e g ro u n d is redefined as C a =
C i,m+i.
T h e c h a ra cte ristic m odes co rre s p o n d to th e eigenvectors o f th e above
m a trix . W e do n o t m e n tio n th e w a y to o b ta in eigenvectors, b u t place a reference
[89].
T h e c h a ra c te ris tic im p e da n ce o f a c e rta in m o d e is o b ta in e d by th e 2 -D F E M
a ga in . L e t V * to be th e k -th e ig e n ve cto r, w h ic h corresponds to k - th m ode.
(
\
H i
vk2
(5 .6)
\ V*T"
T h e n th e e x c itin g voltages fo r th e firs t c o n d u c to r to m -th c o n d u c to r m u st be
X k ^k i to XfcVfcm, where x k is a n o rm a liz in g c o e ffic ie n t o f the k -th m o d e to m a tc h
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
e le c tro m a g n e tic re p re s e n ta tio n w ith c ir c u it re p re s e n ta tio n . T h e ca p a cita n ce Ck
o f th e system e x c ite d b y th e voltages and th e ca p a cita n ce Cko o f the same system
w ith th e re la tiv e p e r m it t iv it y o f the m a te ria l set to one are used to o b ta in the
k - th m ode im pedance.
Zk
Cy/Ck X Ck 0
(5.7)
’
w here c is th e speed o f lig h t in free space.
F o r th e case t h a t a ll 2 m te rm in a ls o f m co u p le d c o n d u c to rs are te rm in a te d
by
f i , th e re are tw o ways o f a p p ro a ch in g th e p ro b le m . F ig .5 .4 is th e e x a m ­
ples o f these tw o v ie w w h e n m = 3 . F ig .5 .4 (a) shows th e v ie w th a t a lin e w ith
im p edance Z * is te rm in a te d by Z ^ / m Q a t b o th ends. T h is is considered th a t
th e m co n d u cto rs a ct as one transm ission lin e a n d te rm in a tio n s are co lle cte d in to
tw o co m m o n te rm in a tio n s a t b o th ends. O n th e o th e r han d , F ig .5 .4 (b) shows
th e v ie w o f th e m c o n d u c to rs w ith im p e da n ce o f m x Z * te rm in a te d b y Z ^ Q a t
2m te rm in a ls . In th is v ie w , we assumed a ll the lin e im pedances o f m c o n d u c to rs
are th e same as m x Zjt- T h is is tru e in th e case o f th e eigen m ode tra n s m is s io n .
I f n o t, the lin e a r ity o f th e voltages a t te rm in a ls a n d th e cu rre n ts o f lines fa ile d .
T h e vo lta g e a t th e te r m in a l
2
in F ig .5 .4 (a) is
m_________ v
\ r — _______ m
',=z \\
^ cos 31 + j Z k sin 31
,
(5.8)
and a t the te rm in a l 2 i in F ig .5 .4 (b) is
ZL
Z i cos 31 + jm Z k sin
V'l, =
Z V U - ZxkV ki ■
(5.9)
@1
T h e pow er c o n s u m p tio n s a t the lo a d is,
(5.10)
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3Zk
V 13
Zl
3Zk
V 12
3Zk
■Zl \
V:i
Vi!
F ig u re 5.4: T w o d iffe re n t view s o f the same m -c o n d u c to r tra nsm issio n lin e te r­
m in a te d by Z [S l a t a ll p o rts as an exam ple o f m = 3 . (a) T h e m co n d u cto rs are
considered as one tra n sm issio n lin e and te rm in a tio n s are collected in to tw o co m ­
m on te rm in a tio n s a t b o th ends, (b) m c o n d u c to rs w ith im pedance o f m x Z * are
te rm in a te d by Z^Q. a t
2
m te rm in a ls
in F ig .5 .4 (a ), and
in F ig .5 .4 (b ). T h e n th e e q u a tio n to d e te rm in e x k is.
Pi. = P'l ,
(5-12)
or,
m
mV? =
.
(5.13)
i
W h a t we need to o b ta in is the value o f Xk w hen \ \ =
1
so as to m a tch the
d e fin itio n o f im p e da n ce o f e le ctro m a g n e tic re p re se n ta tio n , w h ich are d e te rm in e d
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by E sy3tem, and c ir c u it re p re se n ta tio n .
m
m
Xk =
(5.14)
O nce a ll the m o d e im pedances are o b ta in e d , th e S p a ra m e te rs o f th e m c o n d u c to r tra n s m is s io n lin e can be derived by a co n v e n tio n a l w a y [90]. F ig.5.5
shows e x p la n a to ry d ia g ra m o f su p e rp o sing re fle c tio n co e fficie n ts o f modes w ith
s h o rt o r open c o n d itio n s a t th e m id d le p o in ts o f th e lines.
P ro p e rly chosen
co efficie n ts realize a c o n d itio n o f o n e -p o rt e x c ita tio n .
T o e xcite p o rt j b y one v o lt and th e o th e r p o rts b y zero v o lt, th e m ode i m u st
be e x c ite d a ^ tim e s o f x * V i, w h ich is the eigenvector co rre s p o n d in g to the m ode
i.
T h is c o n d itio n can be expressed as
/
\
/
\
0
1
02j
0
®m—1,j
(5.15)
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T h e e x c itin g co e fficie n ts
/
w ill be
\
(
a ij
\
o
CLoj
-i
IlV „
^2^2,
')
■E-in^n
0
\
\
/
(5.16)
L e t th e re fle c tio n co e fficie n t fo r e x c ita tio n o f m ode k w ith open c o n d itio n a t
m id d le p o in t o f th e lin e be r * 0, and w ith s h o rt c o n d itio n be r * a.
r
Zko — Zr,
i ko = —-----—
4 ko +
Z ks — Z L
Lfc, = —— — — ,
6 ks +
r?
^
Z ko = —j m Z k cot( — )
£
(5.17)
.
/3l
Z k 3 = j m Z k ta n ( — )
(5.18)
2
T h e n th e e x c ite d vo lta g e a t p o r t i is
^
m
k
m
(5.19)
ki^ko "F ^ . O-ki^k^ki^ks) = Sij
k
fo r th e e x c itin g side and
^i+m — ^ ( ^ P-ki^k^'ki^'ko
^ ! ^ki^-k^ki^'ka) —
k
k
•
(5.20)
fo r th e fa r side. T h e co m p le te S p a ra m e te rs are fo u n d by re p e a tin g th e e q u a tio n s
fro m (5.15) to (5.20) w ith j fro m 1 to m .
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T h e o b ta in e d S param ete rs o f m u ltic o n d u c to r tra n sm issio n lines are connected
to th e S param eters o f vias o b ta in e d in p re vio u s se ction .
T h e n the response
o f th e w h o le s tru c tu re is c a lcu la te d m u ch fa s te r th a n fu ll-w a v e e le ctro m a g n e tic
s im u la tio n s .
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Port m
'
Port 2m
Port m - 1 1
Port 2 m -1
Port 1
Port m+1
(a)
L /2
L /2
Short
Port m
Port 2m
h o rt
Port m - 1
—°
Port 2 m -1
77T
Short
Port 1
Port m + 1
(b)
L /2
L /2
Port m
Port m-1
Port 1
Open
Port 2m
Open
Port 2 m -1
Open
Port m+1
(c)
F ig u re 5.5:
D ia g ra m to e xp la in d e riv a tio n o f th e s c a tte rin g param eters.
The
s c a tte rin g p aram ete rs are o b ta in e d by s u p e rp o sin g re fle c tio n coefficients o f m odes
w ith s h o rt o r open b o u n d a ry c o n d itio n s a t th e m id d le p o in t o f the lines, (a) T h e
m -c o n d u c to r tra nsm issio n line, (b) T h e re fle c tio n w ith s h o rt co n d itio n s at m id d le
p o in ts , (c) T h e re fle ction w ith open c o n d itio n s a t m id d le points.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.3
Verification of the model
T h e m u ltic o n d u c to r tra n s m is s io n lin e m o d e l is v e rifie d b y an e xa m p le . T h e ex­
a m p le is a th re e -c o n d u c to r tra n sm issio n lin e . I t consists o f fo u r d ie le c tric layer
w ith re la tiv e p e r m it t iv it y o f 7.1, and w ith thickness o f 160 fj.m.
T h e to p and
th e b o tto m b o u n d a rie s are g ro u n d co n d u cto rs. T h e th re e c o n d u c to rs are placed
between th e fo u r d ie le c tric layers.
T h e le n g th o f th e lin e s is 1.2 m m , and th e
w id th is 0.2 m m . F ig .5 .6 shows the exam ple.
C onductor 4
(G round)
P ort 6
C on d u cto r 3
Port 5
Port 4
C o n d u cto r 2
Port 3
C on d u cto r I
Port 2
Port 1
C onductor 4
(G round)
F ig u re 5.6: A n e x a m p le o f th re e -c o n d u c to r tra n s m is s io n lin e m o d e l
T h e capacitances betw een th e co n d u cto rs are o b ta in e d b y the 2 -D F E M p e r­
fo rm e d on several c o n d itio n s w h ich im pose some c o n d u c to rs to be one %-o lt and
th e o th e rs to be zero v o lt.
L e t the g ro u n d c o n d u c to rs be the fo u rth c o n d u c to r. T h e n , th e ca pa cita nce s to
o b ta in are C 1 2 , C 1 3 , C m , C 2 3 , C 2 4 , C 3 4 . N o te th a t th e e xa m p le co rre sp on d s to th e
case o f m = 4 in th e p re v io u s section. T h e re fo re , th e n u m b e r o f th e co n d u c to rs
o f one v o lt is n o t necessary to be two.
69
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1
11 0 [ V ]
I
I 0[V ]
1
— i
0[V )
1
j
l(V ]
1
— 1
0[V ]
I
I
0 [V]
1
—
1
□
1M
1
J1 0 [ V ]
im
I
Mode (1,0,0)
I 0[V ]
Mode (1.0,1)
— I 0[V ]
\
I 0[V ]
0 [V]
I
I
I [V]
1 [V]
I-
J
I [V]
I (V]
1
J
I [V]
------------------------------------1 0 [ V )
1______________________________ I 0 [ V |
Mode (1,1,0)
Mode (1,1,1)
F ig u re 5.7: E x c itin g voltages fo r each system
L e t th e vo lta g e o f th e g ro u n d be zero v o lt w ith o u t lo sin g g e n e ra lity, and le t the
c o n d itio n w ith x v o lt a t th e firs t c o n d u c to r, y v o lt a t th e second c o n d u c to r and z
v o lt a t th e th ir d c o n d u c to r, be “ m o d c ( r , y, z )’’ fo r convenience, even th o u g h these
are n o t in d e p e n d e n t modes. N o te t h a t th e m ode( 1,0,0) and m o d e ( 0 , l, l) is n o t
th e same, because th e g ro u n d is alw ays zero v o lt im p lic itly . B u t the s y m m e try o f
th e s tru c tu re reduces th e n u m b e r o f th e c o n d itio n s to be p e rfo rm e d . E q u a litie s o f
C
12
= C -2 3 and C 1 4 = C 3 4 in d ic a te th a t m o d e ( l, 0 ,0 ) is e qu a l to m o d e ( 0 ,0 , l ) and
th a t m o d e (l.l.O ) is equal M o d e ( 0 , l, l) .
F ig .5 .7 shows fo u r c o n d itio n s to o b ta in
a ll th e capacitances between th e co n d u cto rs.
T h e s y m m e try d erives th a t th e ca pa cita nce o f th e m o d e ( 1,0,0) is C 7 2 + C
C 1 4 as w ell as C j j + C 2 3 + C ^ .
73
+
A lso , th e ca p a cita nce o f th e m ode( 1,0,0) is
70
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C i j + C jx + C 2 3 + C 2 4 as w ell as C y j + C
m o d e ( l,0 ,l) is
C14 +
+ C -^ + C 2 4 . T h e ca pa cita nce o f the
4- C y j + C 3 4 , and th e capa cita nce o f th e m o d e ( l, l, l) is
+ C34.
T h e capacitance o f the m ode( 1,0,0) is 0 .268nF b y the 2-D F E M . A lso , the
oth e rs are o b ta in e d as 0.338nF fo r th e m o d e ( l, l, 0 ) , 0.521nF fo r th e m o d e ( l,0 ,l)
and 0 .4 0 1n F fo r the m o d e ( l, l, l) . T h e n th e capacitances between co n d u cto rs are
o b ta in e d as follow s.
(
\
C 12
1 1 1 0 0 0
C \z
Cm
V
/
>
(
\
0.263
0.095
0 1 0 1 0 1
0.263
0.0075
0 1 1 1 1 0
0.338
0.165
(5.21)
\
C 23
1 1 0 0 1 1
0.338
0.095
C24
1
0
1
0
1
1
0.521
0.253
0
0
1
0
1
1
0.401
0.165
C 34
J
V
T h e capa cita nce m a trix is d e rive d as,
/
\
0.268
- 0 .0 9 5
-0 .0 0 7 5
- 0 .0 9 5
0.260
-0 .0 9 5
-0 .0 0 7 5
-0 .0 9 5
0.268
71
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(5.22)
T h e eigenvectors o f th e m a tr ix is,
/
\
/
0.5
0.5
- 0 .7 0 7
0.707
0.5
\
0.707
(5.23)
0.5
/ V
0.707
/
\
/
L e t th e in trin s ic m odes c o rre s p o n d in g to th e eigenvectors ‘m o d e A " , “ m ode
B ” and “ m o d e C” . T h e in tr in s ic im pedances c o rre sp o n d in g to th e m odes are
o b ta in e d by 2 -D F E M w ith th e e x c itin g voltages p ro p o rtio n a l to th e co m p o n e n ts
o f th e co rre sp on d ing e ig en ve cto r. A t th a t tim e , the voltages are m u ltip lie d by
3
v/3 , since
i= 1
V£ =
1
in th is case.
T h e m ode im pedances o b ta in e d th is w ay were 7.50Q fo r m ode A , 2 5 .5 IQ fo r
m o d e B and 16.11Q fo r m o d e C.
F ro m F ig .5 .8 to F ig .5 .1 2 show co m p arison s o f th e s c a tte rin g p a ra m e te rs o f
o u r p ro p o s in g m odels (dashed lin e ) and o f fu ll-w a v e e le c tro m a g n e tic s im u la tio n
re su lts (s o lid lin e ).
72
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S ll
0
Re(Sll)
Re(Sll) Model
-0 .0 5
-0 .0 5
0.1
Im (Sll)
-0 .1 5
-
-0 .1 5
Im(Sll) Model
0.2
-
0
1
2
3
4
5
6
7
Freq [GHz]
F ig u re 5.8: S l l responses o f th e exam ple
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
0.2
i m ( S ll)
-
S21
0.3
Im (S 2 1 )
Im ( S 2 1 )
M odel
0 .2 5
0.2
(T Z S )u il
cn
0 .1 5
0 .1 5
0u6
0.1
0.1
R e (S 2 1 )
R e (S 2 1 )
M odel
0 .0 5
F r e q [G H z ]
F ig u re 5.9: S2
1
responses o f th e e xam ple
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S41
1
R e (S 4 1 )
0 .9
-0.2
R e (S 4 1 ) M odel
0.8
(TfrS)uiI
- 0 .4
v
OS
0 .7
Im(S41)
Im ( S 4 1 )
-
0.6
-
0.8
M odel
0.6
0 .5
- 1
0
1
2
4
3
c
6
7
8
F r e q [G H z ]
F ig u re 5.10: S41 responses o f th e exam ple
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S 21
0.2
0.3
Im (S 1 2 )
Im(S12) Model
0.25
0.2
(ZTS)uil
0.15
(N
cn
0.15
iu
at
0. 1
0.1
Re(S12)
Re(Sl2) Model
0.05
0.05
0
1
2
3
4
5
6
7
8
Freq [GHz]
F ig u re 5.11: S12 responses o f th e exam ple
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S22
Im ( S 2 2 )
Im ( S 2 2 )
M odel
-0 .0 5
CN
-
0.1
-
R e (S 2 2 )
<D
0.1
a.
R e (S 2 2 ) M odel
-0 .1 5
-
-0 .1 5
0.2
-
0
1
2
3
4
5
6
7
8
F r e q [G H z ]
F ig u re 5.12: S22 responses o f the exam ple
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.2
(Z ZS )u il
-0 .0 5
5.4
Design Examples of Microwave Circuits
In th is section, tw o kin d s o f m icrow ave c irc u its are design and ve rifie d .
The
m a te ria l is supposed to be low te m p e ra tu re co -fire d ceram ics (L T C C ), w hich
w o u ld be th e m a jo r m a te ria l fo r m u lti-c h ip -m o d u le s (M C M s ) in m o b ile te rm in a l
e q u ip m e n ts these days. The c irc u its have th re e -la y e r s tru c tu re w ith re la tiv e p e r­
m it t iv it y is 7.1 whose wave le n g th a t 5 G H z is 22.5 m m . Each la ye r has thickness
o f 160 fim , and lin e w id th is
5 .4 .1
2 0 0
/xm.
B a n d - P a s s F ilte r
T h e fir s t design e xa m p le is a band-pass filte r. Its pass-band is 4.9 to 5.1 G H z w ith
th e in s e rtio n loss less th a n 0.5 d B , and s to p -b a n d s are fro m 4.4 to 4.5 G H z and
fro m 5.5 to 5.6 G H z w ith the re je ctio n m o re th a n 15 d B . F ig .5 .1 3 (a ) shows th e
o b ta in e d c irc u it, and F ig .5 .1 3 (b ) shows th e co m p a riso n between th e G A m odel
(so lid lines) and the e le ctro m a g n e tic s im u la tio n 1 (dashed lines).
T h e o b ta in e d
size o f th e o u te rm o s t p a tte rn was 3.67 m m b y 3.05 m m . T h e c o m p u ta tio n tim e
o f th e e le ctro m a g n e tic s im u la tio n was a b o u t 30 seconds p e r one frequency on P C
w ith P e n tiu m I I I 700 M H z. T h e c o m p u ta tio n tim e o f the G A process was a b o u t
40 h o u rs on th e same P C , w ith 200 c irc u its tested a t
8
frequencies th ro u g h
2 0 0
generations. These results agree w ell, and th is fa c t verifies the m o d e l v a lid ity .
‘ E M sight w ith A W R Microwave office 2001 Ver.4.01
78
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(a)
BPF356HZ
-10
CQ
'D
-2 0
Cfl
-30
-40
-50
3
3.5
4
4.5
5
5.5
6
6.5
7
F re q [G H z ]
(b )
F ig u re 5.13: B and-pass filte r whose pass-band is 4.9 to 5.1 G H z , a n d sto p -b a n d s
are fro m 4.4 to 4.5 G H z and fro m 5.5 to 5.6 G H z.
(a) C ir c u it p a tte rn s in
th re e -la ye r s tru c tu re , (b ) Responses o f th e band-pass filte r
79
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5 .4 .2
B a n d -S to p F ilte r
T h e second design exam ple is a b a n d -s to p filte r . Its sto p -b a n d is 5.0 to 5.1 G H z
w it h th e re je c tio n m ore th a n 12 d B . a n d pass-bands are fro m 4.6 to 4.8 G H z
and fro m 5.3 to 5.5 G H z w ith th e in s e rtio n loss less th a n 0.7 d B . F ig .5 .1 4 (a )
shows th e o b ta in e d c irc u it, and F ig .5 .1 4 (b ) show s th e com parison betw een th e
G A m o d e l (s o lid lin e s) and the e le c tro m a g n e tic s im u la tio n (dashed lin e s). T h e
size o f th e o u te rm o s t p a tte rn was 3.93 m m b y 3.57 m m . T h e c o m p u ta tio n tim e
o f th e e le c tro m a g n e tic s im u la tio n was a b o u t 40 seconds per one frequency on P C
w ith P e n tiu m I I I 700 M H z . T h e c o m p u ta tio n tim e o f the G A process was a b o u t
2 0
hours on th e same P C , w ith
2 0 0
c irc u its te ste d a t
8
frequencies th ro u g h
1 0 0
g en e ra tion s. These results agree w e ll, and th is fa c t verifies the m odel v a lid ity .
80
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BuOum Layer
(a)
B E F@ 5 GH z
-1 0
CQ
•O - 2 0
Sll
S21
Sll (EM)
521 IEM!
-50
3
3.5
4
4.5
5
F re q
5.5
6
6.5
[G H z]
(b )
F ig u re 5.14: B a n d -s to p filte r whose s to p -b a n d is 5.0 to 5.1 G H z, and pass-bands
are fro m 4.6 to 4.8 G H z and fro m 5.3 to 5.5 G H z.
(a) C irc u it p a tte rn s in
th re e -la y e r s tru c tu re , (b ) Responses o f th e b a n d -s to p filte r
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5.5
Conclusions
E v o lu tio n a ry g e n e ra tio n o f 3 -D m icrow ave line-segm ent c irc u its em bedded in m u l­
tila y e r s tru c tu re u s in g G A was proposed. T h e developed p ro ce d u re o p tim iz e d a
line-segm ent c irc u it w ith a v a rie ty o f to p o lo g y, a nd ended u p w ith a c ir c u it th a t
exceeded e xp e cta tio n s.
O u r d e ve lo p in g m u ltic o n d u c to r tra n sm issio n lin e m o d el enabled c o m p u ta tio n
tim e to be p ra c tic a l. T ra d itio n a l approach to o b ta in the s c a tte rin g p a ra m e te rs
o f a m u ltic o n d u c to r tra n sm issio n lin e had depended on fu ll-w a v e e le c tro m a g n e tic
s im u la tio n s , o r s o lu tio n s o f sp ecific tra n sm issio n lin e d iffe re n tia l e q u a tio n s w h ich
becam e ve ry c o m p lic a te d form s w hen th e n u m b e r o f co n d u cto rs was la rg e. T h e
m o d el developed in th is ch a p te r was d erive d b y ve ry sim p le p ro ce d u re .
is easy to be em bedded in C A D p ro gram s.
T h is
E ven i f th e n u m b e r o f c o n d u c to rs
become large, the G A do n o t care a b o u t the d e riv a tio n o f m odels.
T w o exam ples o f filte r have been p e rfo rm e d . T h e sizes o f these filte rs were
a b o u t seventh to e ig h th o f wave le n g th . T h e fa c t v e rifie d th a t c o m b in a tio n o f the
G A o p tim iz a tio n and the proposed tra n sm issio n lin e m o d el has a s tro n g design
c a p a b ility fo r the co m p a ct 3 -D m icrow ave line-segm ent c irc u its .
82
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CHAPTER 6
Conclusions
W e have in tro d u c e d an e v o lu tio n a ry g e n e ra tio n o f m icro w a ve line-segm ent c ir­
c u its u sin g G A . T h e d e ve lo p e d p ro ced u re o p tim iz e s a lin e -se g m e n t c ir c u it w ith a
v a rie ty o f to p o lo g y, a n d ends u p w ith a c irc u it th a t exceeds e xp e cta tio n s. A lso,
th e p ro ced u re g u a ra n tie s th e c ir c u it n o t to be la rg e r th a n th e size specified in
advance.
P a tte rn s o f c irc u its are expressed by sets o f param ete rs. G e n e tic a lg o rith m s
are used to change th e p a ra m e te rs fo r the c irc u its to s a tis fy s p e cifica tio n s . T h e
p a ra m e te rize d expression o f th e c irc u it was devised so th a t a n y k in d o f set o f the
p a ra m e te rs corresponds to a c e rta in feasible p a tte rn s w it h in th e g ive n space.
F o r tw o -d im e n s io n a l c ir c u it design, re d u c tio n o f th e c o m p u ta tio n tim e to eval­
u a te fre qu e ncy responses o f m a n y c irc u its is realized by d e co m p o sin g each c irc u it
in to sim p le elem ents such as T -ju n c tio n s , corners and open-ends, a nd syn th e sizin g
th e ir S p aram ete rs a g a in to o b ta in th e responses o f th e c ir c u it.
F o r tw 'o -d im e n sio na l c ir c u it w ith c o u p lin g effects, a c ir c u it is decom posed in to
e q u a l-le n g th coupled lin e s p a ir as w e ll as T -ju n c tio n s , corners a nd open-ends, and
b e in g synthesized a ga in in t o th e w h o le c irc u it.
A d d in g a ttr ib u te o f th e s h u n t capacitance to a lin e , c irc u its w ith lu m p e d
elem ents are p u t in to th e s o lu tio n s .
T h is enables to solve th e p ro b le m w ith
s m a lle r c irc u its so lu tio n s.
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F o r th re e -d im e n sio n a l c ir c u it design, re d u c tio n o f th e c o m p u ta tio n tim e is
re a liz e d b y d eco m p o sing each c ir c u it in to v ia m odels w h ic h in c lu d e c h a ra cte ris tic s
o f la y e r-c o n n e c tin g vias as w e ll as T -ju n c tio n s , corners a n d open-ends. A lso , the
n e w ly developed m u ltic o n d u c to r tra n s m is s io n lin e m o d e l w ith b ro ad -sid e c o u p lin g
effects is used. These v ia m o d e ls and tra n s m is s io n lin e m o d els are synthesized
in to th re e -d im e n s io n a l c irc u its to be o p tim iz e d .
Som e e xam ples were designed and teste d to v a lid a te th e proposed G A o p ti­
m iz a tio n techniques. Several low -pass filte rs (L P F ) a n d several band-pass filte rs
(B P F ) were designed b y the proposed 2 -D lin e -se gm en t te ch n iq u e and were fab­
ric a te d in a s trip lin e s tru c tu re . A ls o , a p ow er d iv id e r a n d a m a tc h in g c ir c u it fo r
a F E T were designed a n d fa b ric a te d to be tested. T h e responses showed good
agree m e n t e xcep t th a t s lig h t s h ift o f th e responses to h ig h e r fre q u e n cy were m ea­
su re d in some filte rs . A L P F was designed b y u sin g th e c o u p le d -lin e m o d el. T h e
c a lc u la te d re s u lt showed reasonable responses th o u g h , th e G A c o u ld n o t u tiliz e
th e c o u p lin g effect e ffe c tiv e ly to design co m p a c t filte rs .
B u t th e co n s id e ra tio n
o f th e c o u p lin g effect seemed to be in d isp e n sa b le fo r fre q u e n cy se nsitive s p e cifi­
c a tio n s . O n th e o th e r hand, a n o th e r e xa m p le o f co up le d lin e w ith th e lu m p e d
e le m en ts showed c a p a b ility to reduce f ilt e r size.
A B P F a nd a B E F were de­
sig n e d by 3 -D line-segm ent te ch n iq u e a n d v e rifie d by fu ll-w a v e e le c tro m a g n e tic
s im u la tio n . T h e re su lts showed goo d agreem ent.
T h e proposed e v o lu tio n a ry design o f m icro w a ve c irc u its w it h line-segm ents is
v e ry p o w e rfu l te ch n iq u e for co m p a c t m icrow ave co m p o n e n ts as w e ll as special
fre q u e n c y sp e cifica tio n s such as h a rm o n ic filte rs w ith som e a tte n u a tio n poles.
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F u tu re w orks
T h e G A has a weak p o in t o f slow convergence a ro u n d th e o p tim a l p o in t. C o m b i­
n a tio n o f th e G A and th e c o n ve n tio n a l m in im iz a tio n tech n iq ue was tested. B u t
d e riva tive s o f th e s c a tte rin g m a tr ix respect to p aram ete rs w h ich co rre sp on d to
co ntin u o u s va ria bles were d e rive d b y num erical d e riv a tio n s . T h e n th e convergence
o f the to ta l design to o k huge c o m p u ta tio n tim e. I f th e a n a ly tic a l d e riv a tio n co u ld
be p e rfo rm e d , fast convergence m ig h t be obta in ed .
T h e y ie ld a nalysis is also im p o rta n t in the n e x t s tu d y because m a k in g com ­
p onent s m a ll m eans increase o f th e re la tive e rro r o f its dim ensions. I f the co m p o ­
nents w ill be fa b ric a te d in dense m o d u le like a m u lti-c h ip -m o d u le (M C M ) m ade
by lo w te m p e ra tu re co -fire d ceram ics (L T C C ) o r in a m icro m a ch in e d S i m o d u le ,
tech n ica l lim it o f fa b ric a tio n m u s t be included in th e m odels.
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APPENDIX A
The S parameters of the circuit
T h e d e riv a tio n o f th e S p aram ete rs o f th e c ir c u it is d escribed b rie fly in th is
a p p e n d ix.
L e t th e S m a tr ix fo r th e elem ent n, th a t is p o s s ib ly a T - ju n c tio n , a rig h t angle
co rn er , a open end, a v ia o r a m u ltic o n d u c to r tra n s m is s io n lin e fo r e xam ple, be
S (n), the n
b (») = S (">a(n) + c (n)
a (n),b (n) and
( A .l)
are c o lu m n ve ctors re p re se n tin g th e in p u t, o u tp u t and e x c ita tio n
a m p litu d e s co rre s p o n d in g ly .
U sually,
/
\
1
c (0 =
( A . 2)
V ° /
i f elem ent
1
is fo u r - p o r t elem ent and th e firs t p o rt is connected to th e in p u t
86
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te rm in a l. T h e c o n d itio n th a t a ll th e o th e r p o r t are te rm in a te d corresponds to
(
\
0
c ( 0
=
fo r i ^
1
.
(A -3 )
V ° /
L e t T be the c o n n e c tin g re la tio n m a trix o f the c ir c u it.
Then
and b^n)
sa tisfy
b = Ta
(A .4 )
where
(
(
\
\
ad)
bd)
,( 2 )
b (2)
a =
(
\
42)
c =
b =
a -
(A .5)
C(N )
b (N )
\
/
V
J
\
)
We o b ta in a fro m
a = (T - S )_1c ,
(A . 6 )
b= r(r —s)_1c ,
( A .7)
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where
(
\
S (1>
0
0
S<2>
•••
0
•••
0
0
S =
(A .8 )
s(n)
0
0
\
/
T h is in d ica te s th e elem ent 7V, o f th e m a tr ix T th a t is defined as
T = T {T - S )
-i
( A .9)
is th e response a t node i w ith in c id e n t node j, w h ich is the d e fin itio n o f S ij.
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APPENDIX B
Parameters of the implemented program
T h e im p le m e n te d p ro g ra m has in p u t param eters as described in T a b le .B .l. T h e
va lu es we use a lm o s t a ll th e tim e in th is d is s e rta tio n are d escribed w ith a w o rd
“ u s u a lly " .
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Table B .l: Param eters o f the program
G A p a rt
p o p u la tion
max. generation
m u ta tio n p ro b a b ility
cross over p ro b a b ility
parameters
C ir c u i t p a r t
S tructure
flags (switches)
node interval
coupling distance
shunt C values
S p e c ific a tio n p a r t
frequencies
spec, type
goal values
satisfaction values
T h e num ber o f genes in G A is set 100 to 500 usually.
M a x im u m ite ra tio n num ber o f generations is
set 100 to 500 usually.
P ro b a b ility o f m u ta tio n is set 0.05 usually.
P ro b a b ility o f cross over is set 0.04 usually.
Each param eter has values as
X max is set 8 usually
Xmax-Ymax are set according to the problem
o th e r parameters has a value between 0 to 1
2-D filte rs (2 ports), 2 -D dividers (3 p o rts),
2-D m atching c irc u it (2 p o rt), 3-D filte rs (2 ports)
P rogram runs to (design by G A / sim u la tio n ).
S param eters o f elements are
( ideal sym m etric ones / pre-calculated ones).
Lines cross (perpendicular / w ith a rb itra ry angle).
O p tim iz a tio n is done by
(o n ly G A / com bination w ith the least square method).
T e rm in a tio n has (frequency dependency
for F E T b fch in g c irc u it / 50 fi) .
W eather a d d itio n o f shunt Cs
are allowed in some lines o r not.
W eather some lines w ill be removed or n ot.
Each node has interval from
other nodes at least 0.3 m m usually.
Lines are considered coupled i f the space is
less th a n 1 . 0 m m usually.
The values and probabilities o f shunt Cs are defined.
Frequencies o f spec.s has u n it o f GHz
Spec.s can be set as more than, less th a n or
close to certain value
G A perform s o p tim iza tio n to meet th is values.
I f a ll spec.s meet the satisfaction values, the G A w ill end.
90
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R
efer en c es
[1] J .H .H o lla n d , A d a p ta tio n in n a tu ra l a n d a r t if ic ia l system s, T h e U n iv e rs ity
o f M ic h ig a n press, 1975
[2] R .L .H a u p t, J .J .M e n o z z i, C .J .M c C o rm a c k , T h in n e d a rra ys u sin g genetic a l­
g o rith m s , A n te n n a s a n d P ro p a g a tio n S o cie ty In te rn a tio n a l S ym p osium ,
1993. A P -S . D ig e st V o l. 2 , pp712 -715, 1993
[3] R .L .H a u p t, T h in n e d a rra y s using g e n e tic a lg o rith m s , A n te n n a s and P ro p ­
a g a tio n , IE E E T ra n s a c tio n s on , V o l.42, pp993 -999, J u ly, 1994
[4] R .L .H a u p t, O p tim u m qua n tised lo w sidelobe phase tapers f o r a rra ys , E lec­
tro n ic s L e tte rs , V o l.31, p p l l l 7 -1118, J u ly 1995
[5] R .L .H a u p t, O p tim iz a tio n o f su b a rra y a m p litu d e tapers , A n te n n a s and P ro p ­
a g a tio n S ocie ty In te rn a tio n a l S y m p o s iu m 1995. D ig e st , V o l.4 , p p l8 3 0 -1833,
1995
[6 ] R .L .H a u p t, P ha se -o n ly a d a p tive n u llin g w ith a g e n e tic a lg o rith m , A nte n na s
a nd P ro p a g a tio n , IE E E T ra n s a c tio n s on , V o l.45, p p l0 0 9 -1015, June 1997
[7] R .L .H a u p t, J .M .J o h n s o n ,
a g e n e tic a lg o rith m ,
D y n a m ic p h a se -o n ly a rra y beam c o n tro l u sing
E v o lv a b le H a rd w a re 1999 P roceedings o f the F ir s t
N A S A /D o D W o rk s h o p o n, pp217 -224, 1999
[8 ] R .L .H a u p t,
O p tim u m p o p u la tio n size a n d m u ta tio n rate f o r a sim ple real
g e n e tic a lg o rith m th a t o p tim iz e s a rra y fa c to rs , A n te n n a s a nd P ro p a g a tio n
S ocie ty In te rn a tio n a l S y m p o s iu m 2000. IE E E , V o l.2 , p p l0 3 4 -1037, 2000
[9] Y ou C h u n g C hung; R .L .H a u p t, O p tim u m a m p litu d e a nd phase c o n tro l f o r an
a da p tive lin e a r a rra y u sin g a g e n e tic a lg o rith m , A n te n n a s and P ro p a g a tio n
S ociety IE E E In te rn a tio n a l S y m p o s iu m 1999 , V o l.2 , 1999 p p l4 2 4 -1427 ,
1999
[10] Y ou C h u n g C hung; R .L .H a u p t, A d a p tiv e n u llin g w ith s p h e rica l arrays using
a g e n e tic a lg o rith m , A n te n n a s a nd P ro p a g a tio n S o cie ty IE E E In te rn a tio n a l
S y m p o s iu m 1999 , V o l.3 , pp2000 -2003 , 1999
[11] Y ou C h u n g C hung; R .L .H a u p t, G A s u s in g va rie d a nd fixe d b in a ry chrom o­
some lengths a nd real chrom osom es f o r lo w sidelobe s p h e ric a l-c irc u la r a rra y
p a tte rn synthesis , A n te n n a s a nd P ro p a g a tio n S o cie ty IE E E In te rn a tio n a l
S y m p o s iu m 2000 , V o l.2 , p p l0 3 0 -1033 , 2000
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[12] D .M a rca n o, M ..Jimenez, F .D u ra n , O .C hang,
S ynthesis o f ante nn a a rra ys
using genetic a lg o rith m s , Devices, C irc u its and S ystem s, 1995., Proceedings
o f th e 1995 F irs t IE E E In te rn a tio n a l Caracas Conference on , pp328 -332,
1995
[13] D .M a rca n o, F .D u ra n , O .C ha n g, Synthesis o f m u ltip le beam lin e a r antenna
arra ys using g enetic a lg o rith m s , A n te n n a s and P ro p a g a tio n S ociety In te r­
n a tio n a l S ym p osium 1995. D ig e st , V ol.2 , pp938 -941, 1995
[14] D .M a rca n o,
M .Jim en e z,
O .C h a n g ,
Synthesis
o f lin e a r
a rra y
using
S c h e lk u n o ff’s m ethod and g e n e tic a lg o rith m s , A n te n n a s and P ro p a g a tio n
S ociety In te rn a tio n a l S ym p o siu m 1996. D igest , V o l.l, pp584 -587, 1996
[15] D .M a rca n o, L.G om ez, O.Sosa,
P la n a r a rra y a n te n n a synthesis using ge­
n e tic a lg orithm s w ith a p e n a lty fu n c tio n , M icrow ave and O p to e le ctro n ic s
Conference 1997, S B M O /IE E E M T T -S In te rn a tio n a l , V o l.l , pp285 -290,
1997
[16] D .M a rca n o,
Synthesis o f lin e a r and p la n a r a n te n n a a rra ys using genetic
alg orith m s , A n te n n a s and P ro p a g a tio n S ociety In te rn a tio n a l S ym p o siu m
1997 D igest , V ol.3, p p l 6
8 8
-1691, 1997
[17] D .M a rca n o, F .D u ra n , Synthesis o f a nte nn a a rra ys u sin g genetic a lg o rith m s
, IE E E A ntennas and P ro p a g a tio n M agazine , V ol.42, p p l2 -20,. June 2000
[18] A .T e n n a n t, M .M .D a w o u d , A .P .A n d e rs o n ,
A rra y p a tte rn n u llin g by ele­
m e n t p o sitio n p e rtu rb a tio n s u sin g a genetic a lg o rith m , E le ctro n ics L e tte rs ,
V ol.3 0 , p p l7 4 -176, Feb. 1994
[19] B .C ham bers, A .P .A n d e rso n , R .J .M itc h e ll, A p p lic a tio n o f genetic a lg o rith m s
to the o p tim is a tio n o f adaptive a n te n n a arrays and ra d a r absorbers , G en e tic
A lg o rith m s in E ng in e ering S ystem s:
G A L E S IA . pp94 -99, 1995
In n o v a tio n s a n d A p p lic a tio n s 1995.
[20] B .P .K u m a r, G .R .B ra n n e r, A new technique o f a na lysis o f unequally spaced
lin e a r arrays , A nte n na s and P ro p a g a tio n S ociety In te rn a tio n a l S ym p o siu m
1995. Digest , V o l.4, pp2014 -2018, 1995
[21] B .P .K u m a r, G .R .B ra n n e r,
D esign o f lo w sidelobe c irc u la r rin g a rra ys by
elem ent radius o p tim iz a tio n , A n te n n a s and P ro p a g a tio n S ociety 1999 IE E E
In te rn a tio n a l S ym p o siu m 1999 , V o l.3 , pp2032 -2035, 1999
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[22] R .J .M itc h e ll. B .C h a m b e rs, A .P .A n d e rso n ,
A r r a y p a tte rn synthesis in the
com plex p la n e o p tim is e d by a gen e tic a lg o rith m . E le c tro n ic s L e tte rs , V o l.32,
p p l8 4 3 -1845, S ep t. 1996
[23] R .J .M itc h e ll, B .C h a m b e rs, A .P .A n d e rso n , A r r a y p a tte rn c o n tro l in the com ­
p le x p la n e o p tim is e d by a genetic a lg o rith m , A n te n n a s a n d P ro p a g a tio n ,
T e n th In te rn a tio n a l Conference on, V o l. l , pp330 -333, 1997
[24] F .A re s , S .R .R e n g a ra ja n , E .V illa n e u v a , E .S k o c h in s k i, E .M o re n o ,
A p p lic a ­
tio n o f g en e tic a lg o rith m s and sim u la te d a n n e a lin g technique in o p tim is in g
the a pe rtu re d is trib u tio n s o f a nte nn a a rra y p a tte rn s , E le c tro n ic s L e tte rs ,
V o l.32, p p l4 8 -1 4 9 , Feb. 1996
[25] L u Y ilo n g , Y an K een Keong, Fu Jeffrey a nd C h in L e o n a rd , A n o ve l approach
f o r p a tte rn syn th e sis o f a rb itra ry a rra y ,
R a d a r 1996. P roceedings., C IE
In te rn a tio n a l C onference o f , pp457 -460, 1996
[26] K e e n -K e o n g Y a n , Y ilo n g Lu , Sidelobe re d u c tio n in a rra y -p a tte m synthesis
u sin g g en e tic a lg o rith m , A ntennas and P ro p a g a tio n , IE E E T ra n sa ctio n s on
, V ol.4 5 , p p l l l 7 -1 122, J u ly 1997
[27] B c n g -K io n g Yeo, Y ilo n g L u , A rra y fa ilu re c o rre c tio n w ith a gen e tic algo­
r ith m , A n te n n a s a nd P ro p a g a tio n , IE E E T ra n s a c tio n s on , V o l.47, pp823
-828, M a y 1999
[28] K .F .S a b e t, K .F ., D .P .Jones, J u i-C h in g C heng, L .P .B .K a te h i, K .S a ra b a u d i,
J.F .H a rv e y , E ffic ie n t p rin te d a n te n n a a rra y syn th e sis in c lu d in g coupling ef­
fe cts u sin g e v o lu tio n a ry genetic a lg o rith m s , A n te n n a s a n d P ro p a g a tio n So­
c ie ty IE E E In te rn a tio n a l S ym posium 1999 , V o l.3 , 1999 pp2084 -2087, 1999
[29] K .N .S h e rm a n , Phased a rra y shaped m u lti-b e a m o p tim iz a tio n f o r L E O satel­
lite c o m m u n ic a tio n s u sin g a genetic a lg o rith m , Phased A r r a y S ystem s and
T e ch n o lo g y 2000 Proceedings. IE E E In te rn a tio n a l C onference on, ppSOl 504, 2000
[30] A .P e to sa , S .T h ira k o u n e ,
L in e a r a rra y o f d ie le c tric re s o n a to r antennas op­
tim iz e d u sin g a g e n e tic a lg o rith m f o r low -sidelobe a p p lic a tio n s , M icrow ave
C onference 2000 A sia -P a cific, pp21 -24, 2000
[31] M .S h im iz u , D e te rm in in g the e x c ita tio n co efficie n ts o f an a rra y using genetic
a lg o rith m s , A n te n n a s and P ro p a g a tio n S o cie ty In te rn a tio n a l S ym p o siu m
1994. A P -S . D ig e s t , V o l.l, pp530 -533, 1994
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[32] F .J.A re sPena, J .A .R o d rig u c z -G o n z a le z , E .V illa n u e v a -L o p e z and S .R .R e n g a ra ja n ,
G enetic a lg o rith m o p tim iz a tio n o f a n te n n a a rra ys w ith va ria b le in te re le m e n t
spacings , A nte n na s a n d P ro p a g a tio n , IE E E T ra n sa ctio n s on , V o l.4 7 , pp506
-510, M arch 1999
[33] K .M a rk u s , L .V a ske la in e n , O p tim is a tio n o f synthesised a rra y e xcita tio n s ris­
in g a rra y polynom e co m p lex ro o t sw apping and g e n e tic a lg o rith m s ,
M i­
crowaves, A nte n na s a n d P ro p a g a tio n , IE E P roceedings - . V o l.145 , pp460
-464, Dec. 1998
[34] P .K ozakow ski,
M .M ro z o w s k i,
W .Z ie n iu ty c z ,
S ynthesis o f n o n u n ifo rm ly
spaced arrays using g e n e tic a lg o rith m , M icrow aves a nd R a d a r 1998 M IK O N
’98., 12th In te rn a tio n a l C onference on , V ol.2 , pp340 -344, 1998
[35] G .P .Junker, S .S .K uo, C .H .C h e n , G e n e tic a lg o rith m o p tim iz a tio n o f antenna
a rra ys w ith va ria ble in te re le m e n t spacings , A nte n na s a n d P ro p a g a tio n So­
c ie ty In te rn a tio n a l S y m p o s iu m 1998, V o l.l, pp50 -53, 1998
[36] W .-C .L iu , B .A .A u s tin ,
a lg o rith m ,
O p tim is e d shaped p a ra s itic a rra y u sin g the genetic
M icrow aves, A n te n n a s and P ro p a g a tio n , IE E P roceedings - ,
V o l. 146, pp339 -341, O c t. 1999
[37] A .U d in a , N .M .M a rtin , L .C .J a in , L in e a r antenna a rra y o p tim is a tio n by ge­
n e tic means , K no w le d ge -B a se d In te llig e n t In fo rm a tio n E n g in e e rin g Systems
1999. T h ird In te rn a tio n a l C onference, pp505 -508, 1999
[38] J .M . Johnson,
G en e tic a lg o rith m design o f a sw itchable shaped beam lin e a r
a rra y w ith p hase-only c o n tro l ,
Aerospace C onference 1999 Proceedings,
V o l.3 , pp297 -303. 1999
[39] P.Lopez, J .A .R o d rig u e z , F .A re a , E .M o re n o ,
Low sidelobe level in alm ost
u n ifo rm ly excited a rra y , E le c tro n ic s L e tte rs , V o l.36, p p l9 9 1 -1993, Nov.
2000
[40] P.Lopez, J .A .R o d rig u e z , F .A re a , E .M o re n o , Low -sidelobe p a tte rn s fro m lin ­
ea r and p la n a r a rra ys w ith u n ifo r m e x c ita tio n s except f o r phases o f a s m a ll
num ber o f elements , E le c tro n ic s L e tte rs , V o l.37, p p l4 9 5 -1 4 9 7 , Dec. 2001
[41] J .A .R o d rig u e z, F .A re s, E .M o re n o , G .F ra n ce sch e tti, G e n e tic a lg o rith m p ro ­
cedure f o r lin e a r a rra y fa ilu r e c o rre c tio n , E le ctro n ics L e tte rs , V o l.36, p p l9 6
-198, Feb. 2000
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[42] A .B o a g , E .M ich ie lssen , R . M it t r a , D esign o f e le c tric a lly loaded w ire antennas
usin g g en e tic a lg o rith m s , A n te n n a s and P ro p a g a tio n , IE E E T ra n sa ctio n s
on , V o l.44, pp687, M a y 1996
[43] Z .A ltm a n , R .M it t r a , A .B o a g ,
N ew designs o f u ltra w ide-band com m u n ica ­
tio n a ntennas using a g e n e tic a lg o rith m , A nte n na s and P ro p a g a tio n , IE E E
T ra n sa ctio n s on , V o l.45, p p l4 9 4 -1501, O ct. 1997
[44] Z .A ltm a n , J .W ia r t, R . M it t r a ,
the gen e tic a lg o rith m ,
D esign o f high g a in dipole a nte nn a s using
A n te n n a s and P ro p a g a tio n S ociety In te rn a tio n a l
S ym p o siu m 1998, V o l.l, pp3 0 -33, 1998
[45] E .E .A lts h u le r, D .S .L in d e n , W ire -a n te n n a designs usin g g e n e tic a lg o rith m s ,
IE E E A n te n n a s and P ro p a g a tio n M agazine , V o l.39, pp33 -43, A p r il 1997
[46] P .L .W e rn e r, Z .A ltm a n , R . M it t r a , D .H .W c rn c r, A .J .F e rra ro ,
G en e tic algo­
r ith m o p tim iz a tio n o f stacked v e rtic a l dipoles above a g ro u n d p la ne , A n te n ­
nas and P ro p a g a tio n S ociety In te rn a tio n a l S ym p o siu m 1997 D ig e st , Vol.3,
p p l9 7 6 -1979, 1997
[47] D .S .L in d e n ,
U sing a real chrom osom e in a genetic a lg o rith m f o r w ire an­
te n n a o p tim iz a tio n , A n te n n a s and P ro p a g a tio n S o cie ty In te rn a tio n a l S ym ­
p o siu m 1997 D ig e s t , V ol.3, p p l7 0 4 -1707, 1997
[48] L in d e n , D.S, W ire antennas o p tim ize d in the presence o f s a te llite stru cture s
usin g genetic a lg o rith m s , A erospace Conference P roceedings, 2000 IE E E ,
V o l.5, pp91 -99, 2000
[49] B .S .S a n d lin , A .J .T e rz u o li, S e n s itiv ity o f a genetic a lg o rith m s o lu tio n f o r a
w ire ante nn a geom etry , A n te n n a s and P ro p a g a tio n S o cie ty In te rn a tio n a l
S ym p o siu m 1998, V o l.l, pp5 4 -57,1998
[50] B .A .A u s tin , W e n -C h un g L iu ,
G en e tic a lg o rith m o p tim is a tio n o f vehicle-
m o u nte d loop a n te n n a f o r N V IS a pp lica tio n s , E le c tro n ic s L e tte rs . V o l.35,
pp252 -253, Feb. 1999
[51] B .A .A u s tin , W e n -C h u n g L iu , A n o ptim ized shaped Y agi-U da a rra y using
the g enetic a lg o rith m , A n te n n a s and P ro p a g a tio n 1999. IE E N a tio n a l C on­
ference on., pp245 -248, 1999
[52] D .C o rre ia , A .M .J.S o ares, M .A .B .T e ra d a ,
O p tim iz a tio n o f g a in , impedance
and bandw idth in Yagi-U da a nte n n a s using genetic a lg o rith m , M icrow ave
a nd O p to e le c tro n ic s Conference 1999. S B M O /IE E E M T T - S , A P S and LE O S
- IM O C ’99. In te rn a tio n a l , V o l. l, pp41 -44 , 1999
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[53] E .A .Jones, W .T . Jo ines,
G e n e tic design o f lin e a r antenna a rra ys , IE E E
A n te n n a s a nd P ro p a g a tio n M a g a zin e , V ol.42, pp92 -100, June 2000
[54] B .G .P o rte r, G .B .N o a kes, S .S .G e a rh a rt,
D esign o f dual-band d ua l-p o la rize d
tvire antennas u sin g a g e n e tic a lg o rith m , A nte n na s and P ro p a g a tio n S ociety
1999 IE E E In te rn a tio n a l S y m p o s iu m 1999 , V o l.4, pp2706 -2709, 1999
[55] R .S chlub, D .V .T h ie l, J .W .L u , S .G .O ’ Keefe, D u a l-b a n d six-elem ent sw itched
p a ra s itic a rra y f o r s m a rt a n te n n a c e llu la r co m m u n ica tio n s system s , Elec­
tro n ic s L e tte rs , V o l.36, p p l3 4 2 -1343, A u g . 2000
[56] R .S chlub, D .V .T h ie l, J .W .L u , S .G .O ’Keefe,
D u a l band sw itch e d -p a ra sitic
w ire antennas f o r c o m m u n ic a tio n s and d ire c tio n fin d in g , M icrow ave C on­
ference 2000 A s ia -P a c ific , pp74 -78, 2000
[57] A .D .C h u p rin , J .C .B a tc h e lo r, E .A .P a rk e r, D esign o f convoluted w ire a n te n ­
nas using a gen e tic a lg o rith m , M icrow aves, A n te n n a s and P ro p a g a tio n , IE E
Proceedings, V o l.148, pp323 -326, O c t. 2001
[58] E .M ic h ie ls s e n ,J .M .S a je r,a n d R .M it t r a , Design o f m u ltila ye re d FSS and wave
guide f ilt e r using G e n e tic A lg o rith m s , IE E E A n te n n a s and P ro p a g a tio n So­
c ie ty In te rn a tio n a l S y m p o s iu m d igest, 1993, pp 1936-39
[59] E . M ichielssen, J. - M . S ajer, S. R a n jith a n , R. M it t r a , D esign o f lig h tw e ig h t,
broad-band m icro w a ve absorbers u sing genetic a lg o rith m s , M icrow ave T h e ­
o ry and Techniques, IE E E T ra n s a c tio n s on , V o l.41, p p 1024 -1031, J u n e -J u ly
1993
[60] E . M ichielssen, J. - M . S a je r, R. M it t r a ,
P a re to -o p tim a l design o f broad­
band m icrow ave absorbers u sin g g en e tic a lg o rith m s , IE E E A n te n n a s and
P ro p a g a tio n S ocie ty In te rn a tio n a l S ym p osium d igest, 1993, p p 1167-1170
[61] D .S .W eile, E .M ich ie lsse n , D .E .G o ld b e rg , M u ltio b je c tiv e synthesis o f electro­
m a g ne tic devices u sin g n o n d o m in a te d s o rtin g gen e tic a lg o rith m s , A n te n n a s
and P ro p a g a tio n S o c ie ty In te rn a tio n a l S ym p o siu m , 1996. A P -S . D ig e st ,
V o l.l pp592 -595, 1996
[62] D .S .W e ile , E .M ich ie lsse n , E v o lu tio n a ry o p tim iz a tio n o f e le ctrom agnetic de­
vices using advanced o pe ra tors a n d p o p u la tio n stru ctu re s ,
A n te n n a s and
P ro p a g a tio n S o cie ty In te rn a tio n a l S ym p osium , 1997. A P -S . D ig e st , V o l.3
p p l6
6 8
-1671, 1997
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[63] A .R .F o ro o ze sh , A .C h e ld a v i, F .H o d ja t, D esign o f J a u m a n n absorbers using
a d a p tive g e n e tic a lg o rith m , A n te n n a s, P ro p a g a tio n and E M T h e o ry, 2000.
P ro cee d in gs. IS A P E 2000. 5 th In te rn a tio n a l S y m p o s iu m on, pp227 -230,
2000
[64] S .C h a k ra v a rty , R .M ittr a , D e sig n o f m icro w a ve f ilt e r s using a b in a ry coded
g e n e tic a lg o rith m , A n te n n a s a n d P ro p a g a tio n S o c ie ty In te rn a tio n a l S ym ­
p o s iu m , 2000. IE E E , V o l.l. p p l4 4 -147, 2000
[65] S .C h a k ra v a rty , R .M ittr a , N .R .W illia m s , A p p lic a tio n o f m ic ro -g e n e tic algo­
r ith m ( M G A ) to the synthesis o f broadband m ic ro w a v e absorbers co m p ris­
in g m u ltip le fre q u e n cy selective surfaces embedded in d ie le c tric a n d m agnetic
m edia , A n te n n a s and P ro p a g a tio n Society, 2001 IE E E In te rn a tio n a l S ym ,
V o l.4, pp6 9 2 -695. 2001
[6 6 ] S .C h a k ra v a rty , R .M ittr a , N .R .W illia m s ,
O n the a p p lic a tio n o f the m ic ro -
g e n e tic a lg o rith m to the design o f broad-band m ic ro w a v e absorbers co m p ris­
in g fre q u e n cy-se le ctive surfaces embedded in m u ltila y e re d d ie le c tric m edia ,
M ic ro w a v e T h e o ry a n d Techniques, IE E E T ra n s a c tio n s on , V o l.4 9 , p p l0 5 0 1059, Ju n e 2001
[67] Ju n o K im , H o n g -B a e Lee, C h a n g y u l Cheon, H yeong-S eok K im , H y u n K y o
Ju n g , a n d S ong-Y op H a h n,
N u m e ric a l design tech n iq ue f o r waveguide T-
ju n c tio n in H -p la n e , A n te n n a s and P ro p a g a tio n S o c ie ty In te rn a tio n a l S ym ­
p o s iu m 1995 D ig e st , V ol.3, p p l5 6 2 -1565, 1995
[6 8 ] J .M . Jo h n so n and Y .R a h m a t-S a m ii, G en e tic a lg o rith m s and m ethod o f m o­
m ents ( G A / M o M ) : A novel in te g ra tio n f o r a n te n n a design , A n te n n a s and
P ro p a g a tio n S ociety In te rn a tio n a l S ym p o siu m 1997 D ig e st , V o l.3 , p p l6 6 4
-1667, 1997
[69] J .M .J o h n s o n and Y .R a h m a t-S a m ii, G enetic a lg o rith m s and m ethod o f m o­
m e n ts ( G A / M O M ) f o r the design o f in teg ra ted a n te n n a s ,
A n te n n a s and
P ro p a g a tio n , IE E E T ra n s a c tio n s on , V o l.47, p p l6 0 6 -1614, O c t. 1999
[70] R .M .E d w a rd s , G .G .C o o k , S .K .K h a m a s , R .J .A id le v , B .C h a m b e rs,
Design
o f c irc u la rly p o la rise d p rin te d s p ira l a n te n n a u s in g d u a l objective genetic
a lg o rith m , E le c tro n ic s L e tte rs , V ol.3 4 , pp608 -609, 2 A p r il 1998
[71] R .M .E d w a rd s , S .K .K h a m a s , G .G .C o o k ,
D e sig n o f p rin te d e ccen tric s p ira l
a n te n n a s u sin g g en e tic a lg o rith m o p tim is a tio n , A n te n n a s and P ro p a g a tio n
1999. IE E N a tio n a l Conference on., pp375 -379, 1999
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[72] Y ilo n g L u , Y .R a h m a t-S a m ii,
O p tim a l design o f the generalized three-
p a ra m e te r aperture d is trib u tio n by the E m p e ro r-se le ctive g en e tic a lg o rith m
, A n te n n a s and P ro p a g a tio n S o c ie ty 1999 IE E E In te rn a tio n a l S ym p osium
1999 , V o l. l, pp422 -425, 1999
[73] H .M o s a lla e i, Y .R a h m a t-S a m ii, N o n -u n ifo rm L u n e b u rg lens a nte nn a s: a de­
sig n approach based on genetic a lg o rith m s , A n te n n a s and P ro p a g a tio n So­
c ie ty 1999 IE E E In te rn a tio n a l S y m p o s iu m 1999 , V o l.l, pp434 -437, 1999
[74] H .M o s a lla e i, Y .R a h m a t-S a m ii, N o n u n ifo rm L u n e b u rg a n d tw o -s h e ll lens a n ­
ten n as: ra d ia tio n ch a ra c te ris tic s a n d design o p tim iz a tio n , A n te n n a s and
P ro p a g a tio n , IE E E T ra n sa ctio n s on , V o l.49, pp6 0 -69, Jan 2001
[75] H .C h o o , A .H u ta n i, L .C .T rin tin a lia , H .L in g , Shape o p tim is a tio n o f broadband
m ic ro s trip antennas using g en e tic a lg o rith m , E le c tro n ic s L e tte rs , V o l.36,
pp2057 -2058, Dec. 2000
[76] L i-C h u n g , T .C h a n g , W .D .B u rn s id e ,
A n u ltra w id e -b a n d w id th tapered resis­
tiv e T E M h o rn antenna , A n te n n a s and P ro p a g a tio n . IE E E T ransactions
on , V o l.4 8 , Dec. 2000 p p l8 4 8 -1857, D ec. 2000
[77] B .A ljib o u r i, E .G .L im , H .E vans, A .S a m b e ll, M u ltio b je c tiv e g en e tic a lg o rith m
approach f o r a dual-feed c irc u la r p o la ris e d p a tch a n te n n a design , E le ctron ics
L e tte rs , V o l.36, p p l0 0 5 -1006, Ju ne 2000
[78] Y o u C h u n g C hung.
R .H a u p t,
L o g -p e rio d dipole a rra y o p tim iz a tio n ,
A erospace Conference Proceedings, 2000, V o l.4, pp449 -455. 2000
[79] B .V .S e s tro re ts k y , S .A .Iva n o v, M .A .D riz e . K .N .K lim o v , The g e n e tic concept
o f top o lo gical synthesis o f waveguide p o la riz a to r w ith e llip tic a l fa c to r 0.95 f o r
a nte nn a s o f s a te llite c o m m u n ic a tio n o f a C -band 3 .7 /6 .5 G H z , M icrow ave
C onference 2000. M icrow ave and T e le c o m m u n ic a tio n Technology. 2000 10th
In te rn a tio n a l C rim e a n , pp388 -390, 2000
[80] D .H .W e rn e r, P .I.'W erner, K .H .C h u rc h ,
G e n e tic a lly engineered m u ltib an d
fr a c ta l a n te n n a s , E le ctro n ics L e tte rs , V o l.37, p p llS O -1151, S ept. 2001
[81] A .J o h n a nd R .H .Jansen,
E v o lu tio n a ry g e n e ra tio n o f ( M ) M I C com ponent
shapes u sin g 2 .5 D E M s im u la tio n a n d d iscrete g e n e tic o p tim iz a tio n ,
M i­
crowave S ym p o siu m D igest 1996. IE E E M T T - S In te rn a tio n a l , V o l. 2 , pp745
-748, 1996
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[82] J.M .Jo h n so n , Y .R a h m a t-S a m ii, G enetic a lg o rith m s in e ng in e ering electro­
m agnetics,
IE E E A n te n n a s and P ro p a g a tio n M a g azin e , V o l.39, pp7 -21,
1997
[83] Y .R a h m a t-S a m ii, J.M .Jo h n so n , E le ctrom agnetic o p tim iz a tio n by g en e tic al­
gorithm s, J o h n W ile y and sons, Inc., 1999
[84] J .R .K o z a ,F .H .B e n n e tt,D .A n d re ,M .A .K e a n e ,a n d F .D u n la p , A u to m a te d syn­
thesis o f analog e le ctrica l c irc u its by mean o f g en e tic p ro g ra m m in g , IE E E
Trans. E v o lu tio n a ry c o m p u ta tio n , v o l.l, N o .2, p p l0 9 -1 2 8 , 1997
[85] D .P a v Iid is e t.a l.,
The design and p erform ance o f th re e -lin e m ic ro s trip cou­
plers, IE E E T ra n s. M T T , vol.24, No.10, pp631-640, 1976
[86] S .Y a m a m o to, e t.a l.,
Coupled s trip tra n sm issio n lin e w ith three ce n te r con­
ductors, IE E E Trans. M T T , vol. 14, No. 10, pp446-461, 1966
[87] C .R .P au l,
A n a ly s is o f m u ltic o n d u c to r tra n s m is s io n lin e s, John W ile y and
Son’s In c ., 1994
[88] N.Fache, F .O ly s la g e r and D .D e .Z u tte r, E le ctro m a g n e tic and c irc u it m odeling
o f m u ltic o n d u c to r tra n s m is s io n lines, O x fo rd science p u b lic a tio n , 1992
[89] W .H .P ress,
S .A .T e uko lsky,
W .T .V e tte rlin g ,
B .P .F la n n e ry ,
N u m e ric a l
Recipes in F o rtra n , 2 n d E d., C am bridge U n iv e rs ity Press, C h a p te r 11, 1992
[90] R .E .C o llin , F o u n d a tio n s f o r m icrow ave engineering, 2 n d E d., M e G ra w H ill,
pp427-432, 1992
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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