IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
43,
NO.
1,
JANUARY
1995
21
Analysis, Syn hesis, and Expe imen al Valida ion
o
a
New
Type
o
Mic os ip T ansi ion
F.
Maso ,
F.
Medina,
and
M.
Homo,
Membe ,
IEEE
Abs ac -This pape p esen s he heo e ical analysis, syn he-
sis, and expe imen al alida ion o a wideband ansi ion be ween
a con en ional mic os ip lie and a mic os ip line p in ed
on a double-laye subs a e. This ansi ion is use ul o link
con en ional mic os ip ci cui s o ce ain special con igu a ions
ab ica ed
on
double-laye subs a es.
A
pa icula case o gene ic
in e es is he ansi ion be ween mic os ip and suspended mi-
c os ip echnologies. The analysis is ca ied ou by using an
enhanced e sion o he spec al domain analysis
(SDA)
ha leads
o compu e codes quick enough o be used in an op imiza ion
design p og am.
I. INTRODUCTION
ICROWAVE ci cui s using mixed single- and double-
M
laye mic os ip echnologies equi e he use o ansi-
ions be ween mic os ips p in ed on wo di e en suppo ing
media. An example o his si ua ion can be ound
in
he
ansi ions be ween con en ional mic os ip and suspended
subs a e mic os ip echnologies. Ou in e es in his ansi ion
a ises om he s udy o he in e connec ion o a mic os ip
ci cui on a single-laye subs a e wi h a special di ec ional
couple sec ion ecen ly p oposed and s udied in
[l].
This
couple sec ion makes use o a double-laye con igu a ion.
In Fig.
1,
we show he ab up ansi ion be ween wo
504
mic os ip lines p in ed on wo di e en media. These lines
ob iously ha e di e en wid hs.
In
spi e o he ac ha
he cha ac e is ic impedance o he lines is he same a
bo h sides o he ansi ion, a big e lec ion coe icien is
expec ed as a consequence o he s ong misma ch be ween
he ans e se ield pa e ns a each side. F om a heu is ic
poin o iew, he pe o mance o he discon inui y should be
d as ically imp o ed by p o iding a smoo h ansi ion o he
a o emen ioned ield pa e n. Smoo hness could be achie ed
by means o a p og essi e change o he mic os ip wid h
om i s alue a he single-laye side,
w1,
o i s alue on he
double laye side,
w2.
Howe e , his g adual change has o
be ca ied ou in such a way ha he local cha ac e is ic
impedance,
Zc(z),
a any ans e se z-plane o he ansi ion
egion is s ill
50
R.
Thus, he ansi ion egion should be
made wi h a ansmission line whose geome ical pa ame e s
could be changed in a con inous way om he pa ame e s o
he line
on
he single-subs a e egion o he pa ame e s o
he line on he double-subs a e egion. A s uc u e use ul o
achie e his pu pose is he modi ied s ip con igu a ion whose
wo k was suppo ed by he DGICYT, Spain, P ojec No. TIC91-1018.
Facul ad de Fisica, Uni e sidad de Se illa, 41012 Se illa, Spain.
Manusc ip ecei ed Decembe
20,
1993; e ised Ma ch
17,
1994. This
The au ho s,a e wi h he Depa amen o de Elec hica y Elec omagne ismo,
IEEE
Log Numbe 9406791.
Y
x
Fig. 1. Di e en pe spec i es
o
an ab up ansi ion be ween single- and
double-laye mic os ips. (a) Top iew
o
he s ip pa e n
on
he uppe side
o
he uppe subs a e. (b)
G ound
me alliza ion
o
he bo om side
o
he uppe
subs a e.
(c)
Side iew o he ab up ansi ion. (d) Th ee-dimensional iew.
c oss-sec ion is shown in Fig.
2.
The s ip and slo wid hs
can be simul aneously modi ied as a unc ion o
z
(w(z)
and
s(z))
in such a way ha he cha ac e is ic impedance o he
s ip-slo s uc u e is
50
R
a any z-plane. The limi s
s
=
0
and
s
=
a
co espond o he geome y o he lines ac ually
p esen a each side o he ansi ion (i he alues o
w
a e
p ope ly chosen). This s uc u e has been al eady used o
he design o mic os ip/slo di ec ional couple s
[2]
(wi h
w
and
s
cons an along he z-di ec ion). Ob iously, he
z-p o ile o
W(Z)
is in some ex en a bi a y-while keeping
smoo hness-i
s(
z)
is p ope ly adjus ed. One possible
me alliza ion pa e n o he uppe side o he subs a e
implemen ing his concep is shown in Fig. 3(a)
(w
a ies
linea ly wi h
z
in his case), and Fig. 3(b) shows he ypical
me alliza ion shape o he bo om side.
I
he o al leng h o
he ansi ion egion is no oo sho , his s uc u e p o ides
a ela i ely low e lec ion ansi ion (when compa ed wi h
he ab up ansi ion in Fig.
1).
This pape also add esses he nume ically e icien analysis
and syn hesis o he p oposed ansi ion. An accu a e and
quick compu e code p o ides he cha ac e is ic p opaga ion
0018-9480/95$04.00
0
1995
IEEE
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22
IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
43,
NO.
1,
JANUARY
1995
Y
0
a
Fig.
2.
C oss-sec ion
o
he s uc u e used o designing he smoo h ansi ion
s udied in his pape .
x
x
e sion o he
SDA
unde quasi-TEM assump ions.
A
s uc u e
ha ing common ea u es wi h he one analyzed in his pape
was s udied in [3]. The guidelines epo ed in ha pape could
be also ollowed o analyze he s uc u e in Fig.
2.
Howe e ,
we ha e in oduced some modi ica ions in o de o speed up
he compu a ions. Ins ead o w i ing qn in eg al equa ion o
he su ace cha ge dis ibu ion on he s ip
(uz(2))
and he
slo ed g ound plane
(ul(x)),
we w i e he in eg al equa ion
o
U~(IC)
and he po en ial unc ion a he slo
(~(2)).
These
quan i ies a e linea ly ela ed o he su ace cha ge dis ibu ion
a he slo ed g ound plane
(u1
(x))
and he po en ial unc ion
a he s ip in e ace
(212(x))
as ollows:
The sine Fou ie ans o m o he p e ious in eg al equa ion
yields i s spec al domain e sion:
whe e
(I)
s ands o sine Fou ie ans o m and
a,
=
n /a
is he Fou ie a iable.
The
K2J(a,)
elemen s in (2) a e easily compu ed by ol-
lowing he spec al o mula ion in [4]. Thus, o he s uc u e
in Fig. 2 we can w i e
c)
(3.1)
(3.2)
9122(an)
man)
=
Gll(4
-
I
922(an)
912
(an)
K12(an)
=
-k21(an)
=
7
92dan)
ma,)
=
9;‘(an)
(3.3)
d)
whe e he spec al unc ions
ijZJ(an)
a e
[4]
Fig.
3.
Di e en pe spec i es
o
he smoo h ansi ion. (a) Top iew
o
he uppe me allized in e ace, (s ip in e ace).
(b)
Top iew
o
he lowe
in e ace (slo in e ace). (c) Longi udinal side iew
o
he smoo h in e ace.
(d) Th ee-dimensional iew.
pa ame e s o he s uc u e in Fig. 3. This p og am is used
in a simple
ad
hoc
op imiza ion scheme which compu es he
alue o
s
o a gi en alue o
w
in such a way ha he line
has
50
R.
Expe imen s ha e been ca ied ou o show ha he
pe o mance o he p oposed ansi ion is much be e han
o
he ab up ansi ion.
11.
ANALYSIS/SYNTHESIS
METHOD
I we wan o use he s uc u e in Fig. 2 as a ansi ion
geome y, we ha e o sol e o i s cha ac e is ic impedance as
a unc ion o
w
and
s.
This analysis can be easily ca ied ou
by means o he well-known
SDA
me hod. In o de o achie e
high nume ical e iciency, we ha e implemen ed an enhanced
No e ha he possible aniso opy o he subs a es can be ac-
coun ed o as well as, i necessa y,
mo e
complex mul ilaye
con igu a ions since he o mula ion in [4] is ully gene al.
As
is
well known, he pe uni leng h (p.u.1.) capaci ance
and induc ance o he ansmission s uc u e a e ob ained by
sol ing (1) o he s uc u e wi h and wi hou dielec ics. The
Gale kin me hod can
be
used o pe o m his ask. Due o
he physical na u e o he expec ed solu ion, he ollowing se
o basis and es unc ions a e used o app oxima e he slo
po en ial,
q(x),
and he s ip su ace cha ge densi y,
uz(x):
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MASOT
e
al.:
A
NEW
TYPE
OF
MICROSTRIP
TRANSITION
23
I
I
Fig.
4.
Scaled layou
o
he measu ed smoo h ansi ion-(a) slo in e ace,
(b) s ip in e ace-onnec ing a single laye
(E:
=
10;
hickness: 0.635
mm)
o
a double-laye (subs.
1:
E:
=
2.42;
hickness:
0.49
mm
&
subs.
2:
E',
=
10;
hickness:
hl
=
0.635
mm)
geome y. S ip wid hs:
wl
=
0.63
mm
(single
laye );
202
=
1.86
mm.
xm
I
0.m
200
4.m
6.00
Fig.
5.
P o ile
o
he s ip and
slo
me alliza ion pa e ns
o
he smoo h
ansi ion measu ed in
his
wo k.
p=l
whe e
Tn(cosO)
=
cos(n0)
and
Un(cosO)
=
sin(n0) (i.e.,
i s and second kind Chebyshe unc ions). This se o basis
unc ions accoun s o he symme y o he s uc u e and he
me al edge condi ion o bo h quan i ies.
As
a consequence o
his, ex emely good con e gence is achie ed as he numbe o
basis unc ions inc eases. No e ha o his se o unc ions he
p.u.1. capaci ance
is
he coe icien
a1
in
(5.2)
when he s ip
ol age
is
he uni y. The applica ion o he Gale kin echnique
yields a linea equa ion sys em o
{up;
p
=
1,
. .
.
,
n2)
and
{bq;
q
=
1,.
. .
,
nl}
whose coe icien s a e de ined ei he
in e ms o inne p oduc skon olu ion in eg als
o
simple
spec al se ies ( hanks o he use o Pa se al and con olu ion
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.2
0.0
0.2
0.4
0.6
0.8
'
1.0
1.2
1.4
(b)
Fig. 6. (a) Time-domain e u n
loss
(&I)
o he ab up ansi ion showing
he ga e used o de-embedding.
(b)
The
same
da a o he smoo h ansi ion.
heo ems).
The
la e ep esen a ion is used because he gene al
e m o he Fou ie se ies
is
known in closed o m in e ms
o
he Fou ie ans o ms o he basis unc ions (5)-which a e
gi en in e ms o Bessel unc ions-and he
kij(an)
unc ions
in
(2):
The spec al se ies in
(6)
ha in ol e
i
#
j
show good
exponen ial con e gence, bu he se ies in ol ing in e ac ions
be ween basis unc ions de ined
on
he same in e ace con e ge
e y slowly. Then, di ec summa ion is e y leng hy and is
no sui able o quick and accu a e design. Fo una ely, he
con e gence can
be
d as ically imp o ed by means
o
he
Kumme 's me hod (ex ac ion o he asymp o ic ails). No e
ha o la ge alues o he Fou ie a iable we ha e he
ollowing asymp o ic limi s:
(7.2)
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24
IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES, VOL.
43,
NO.
1,
JANUARY
1995
The asymp o ic se ies ob ained when we eplace
kii(an)
by
hei asymp o ic exp essions
(7)
and use he Fou ie ans-
o ms o he unc ions in
(5)
ha e he same o m han he
se ies conside ed in [5] in he con ex o he analysis o
he single boxed mic os ip line. Quasi-analy ical exp essions
a e epo ed he e o hose se ies ( he eade is e e ed o
ha pape o mo e de ails). The emaining se ies (o iginal
se ies minus asymp o ic se ies) con e ge exponen ially in a
ew Fou ie e ms. The applica ion o
his
echnique makes
he SDA ex emely e icien om he compu a ional poin o
iew: he a e age CPU ime o he analysis o ypical lines is
a ac ion o one second on a PCl386125 MHz pla o m wi h
80387
ma h cop ocesso .
The p e ious analysis has been ound use ul o imple-
men ing a simple
ad
hac
op imiza ion algo i hm
o
design
a g adual 50-R mic os ip-mic os ip ansi ion. The p og am
au oma ically compu es he slo wid h o a gi en s ip wid h
in o de o keep he line impedance as close o 50
R
as
speci ied. The e o unc ion
FZ(s)
=
2,
-
Zc(w,s)
(Z,
is he s anda d impedance alue,
50
Q
in he usual case) is
minimized o each alue o
w(z).
Fo he example epo ed
in his pape , we ha e chosen a linea a ia ion o he s ip
wid h, Le.
W(Z)
=
w1
+
(w2
-
wl)
.
(z/Z),
whe e
z
is he
coo dina e o he p opaga ion di ec ion,
w1
and
w2
a e
he
limi s o
w
on single
(w(z
=
0))
and double laye
(w(z
=
Z)),
and
Z
is he o al leng h occupied by he ansi ion a ea. Then,
s(z)
is compu ed wi h he op imiza ion p og am. The smoo h
beha iou o he e o unc ion,
FZ(s),
pe mi s one o employ
a simple op imiza ion me hod based on angen ou line, which
ypically con e ges wi hin wo o h ee i e a ions. The o e all
ansi ion design p ocess akes jus se e al seconds on he
a o emen ioned pe sonal compu e (in ou designs
s(z)
has
been compu ed o wen y in e media e alues o
w,
al hough
i e o en poin s
a e
enough om a p ac ical poin o iew i
hey a e p ope ly dis ibu ed along he ansi ion egion).
111. EXPERIMENTAL VALIDATION
In addi ion o he heo e ical analysis, we ha e ca ied
ou he expe imen al e i ica ion o ou conclusions. Thus,
we ha e ab ica ed a couple o ansi ions be ween a 50-R
mic os ip line ab ica ed on Epsilam-10 and ano he 5042
mic os ip line p in ed on a composi e Epsilam- 10/CuClad
subs a e. In ac , wo ansi ions o each ype ha e been
cascaded in o de o acili a e he measu emen p ocess. Figs.
4
and 5 show he dimensions and layou o he expe imen al
se up used o measu e he pe o mance o he ansi ion
p oposed in his wo k.
A
simila se up was buil using ab up
ansi ions such as hose shown in Fig.
1.
Time domain pos -
p ocessing o he measu ed da a pe mi s one o calcula e he
pa ame e s o he ansi ions unde s udy. The measu emen s
ha e been ca ied ou using he HP-8510
ANA.
The e ec o
coax-mic os ip ansi ions has been pa ially emo ed om
he measu ed esul s by using he me hod in [6], which exploi s
he ime domain capabili ies o he measu emen sys em.
The e lec ion
(S11)
ime domain esul s measu ed o
he ab up and he p oposed (smoo h) ansi ions a e shown
in Fig. 6(a) and (b), espec i ely. The po ion o he ime
0,
I
I
I
11
-5
-10
-15
-20
-25
-
30
-35
5
10
15 20
25
-40
Fig.
7.
ions. Compa ison o he S11- esponse o he ab up and smoo h ansi-
esponse co esponding o he ansi ion unde s udy has
been highligh ed in hose igu es ( he ime ga e has been
included). A e ga ing his pa o he measu ed esponse and
in e se Fou ie ans o ming, we ob ain he desi ed equency
domain pe o mance o bo h ansi ions
(see
Fig.
7).
The
e u n loss o he p oposed ansi ion is good enough o mos
p ac ical pu poses in he whole equency band conside ed
in he measu emen . Howe e , he pe o mance o he ab up
ansi ion is a he poo .
1V.
CONCLUSION
In he p esen -pape , we p opose a ansi ion geome y ha
could
be
use ul when connec ing double- and single-laye
layou s in plana mic os ip echnology. The basic wo king
p inciple o he p oposed s uc u e is ha
his
s uc u e p o-
ides smoo h change o he ans e se ield pa e n while
keeping unchanged he nominal cha ac e is ic impedance. The
con ol on he slo wid h allows us o ge a ansi ion as
smoo h as needed. The analysis o he ansi ion sec ion
has been ca ied ou using SDA echniques wi h a sui able
ma h p ep occesing. The analysis p og am gi es e y accu a e
esul s in ac ions o one second (PC/386/25 MHz pla o m).
So,
au oma ic design o he ansi ion can be achie ed in
a ew seconds on he abo emen ioned compu e pla o m.
Expe imen al e i ica ion o heo e ical p edic ion has been
included.
REFERENCES
[l]
F.
Maso , F. Medina, and
M.
Homo,
“Analysis and expe imen al
alida ion
o
a
ype
o
h ee
s ips mic os ip couple ,” ol. M’IT-42,
pp.1624-1635, Sep , 1994.
ZEEE T ans. Mic owa e
Theo y
Tech.
[2] M. Aikawa and
H.
Ogawa, “Double-sided
MICs
and hei applica ions,”
IEEE T ans. Mic owa e
Theo y
Tech,
ol. M’IT-37, pp.
406-413,
Feb.
1989.
[3]
F.
Maso , F. Medina, and M.
Homo,
“Accu a e quasi-”EM analysis
o
modi ied suspended mic os ip lines, and i s applica ion o di ec ional
couple design,”
Mic owa e
&
Op .
Tech.
Le ..
ol. 4, no.
2,
pp.
66-72,
Jan. 1991.
[4]
F.
Medina and M.
Homo,
“De e mina ion
o
G een’s unc ion ma ix
o mul iconduc o and aniso opic mul idielec ic plana ansmission
lines: a a ia ional app oach,”
IEEE T ans. Mic owa e
Theo y
Tech.,
VO~. MTT-33, pp. 933-940, OC . 1985.
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MASOT
e al.:
A
NEW TYPE
OF
MICROSTRIP TRANSITION
25
[5]
F.
Medina and M. Homo, “Quasi-analy ical s a ic solu ion o he boxed
mic os ip line embedded in
a
laye ed medium,’’
IEEE
T ans. Mic owa e
7’heo y
Tech.,
ol. MTl-40, pp. 1748-1756, Sep . 1992.
[6]
G.
G onau
and
I.
Wol ,
“A
simple b oad-band de ice de-embedding
me hod using
an
au oma ic ne wo k analyze wi h ime-domain op ion,”
IEE
T uns. Mic owa e Theo y Tech.,
ol. MTT-37, pp. 479483, Ma .
1989.
Fa ima Maso
was bo n in Badajoz, Spain, on
Janua y 29 h, 1964. She ecei ed he
Licenciada
deg ee
in physics om he Uni e si y o Se ille,
Spain, in 1987. She had a schola ship o he Spanish
Go e nmen and is cu en ly assis an p o esso
a he Applied Physics Depa men (Uni e si y o
Se ille). He esea ch in e es s ocus on he anal-
ysis o di ec ional couple s and il e s and o he
mul iconduc o line ci cui s.
F ancisco Medina
was bo n in
Pue o
Real, CBdiz,
Spain, on No embe , 1960 He ecei ed he Licen-
ciado deg ee in Sep embe 1983 and he Doc o
deg ee
in 1987, bo h in Physics, om he Uni-
e si y o Se ille, Spain.
He
spen he 198687
academic yea
a
he Labo a oue de Mic mndes de
I’ENSEEIHT (Toulouse, F ance) wi h a schola ~hip
o MEC-MRT.
He
was assis an p o esso a he Depa men
o Elec onics and Elec omagne ics, Uni e si y o
Se ille, dunng 1985-89 Since 1990, he has been
associa e p o esso o Elec ici y and Magne ism a he same ins i u ion
He
has been a membe
o
he Technical P og amme Commi ee
o
he 23 d
Eu opean Mic owa e Con e ence held in Mad id (Spain) on Sep embe , 1997
His esea ch deals mainly wi h analy ical and nume ical me hods o plana
s uc u es and applica ions o mul iconduc o lines
Manuel
Homo
(M’75) was bo n
in
To e del
Campo, Jack, Spain
He
ecei ed he Licenciado
deg ee in Physics in June 1969, and he Doc o
deg ee in Physics in Janua y 1972, bo h om he
Uni e si y o Se ille, Spain
Since Oc obe 1969 he has been wi h he
Depa men o Elec onics and Elec omagne wn
a he Uni e si y
o
Se ille, whe e he became an
assis an p o esso in 1970, associa e p o esso in
1975, and p o esso in 1986 He is a membe o
Elec omagne ism Academy o
M
I
T (Cambndge,
MA) His main ields o in e es include bounda y alue p oblems in
elec omagne x
heo y,
wa e p opaga ion h ough amso opic media, and
mc owa e in eg a ed ci cui s
He
is p esen ly engaged in he analysis o
plana ansmission lines embedded in complex ma enals, mul iconduc o
ansmission lines, and pnn ed an ennas.
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