IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 2003 903
Full-Wa e Analysis o he Exci a ion o
Magne os a ic-Su ace Wa es by a
Semi-In ini e Mic os ip
T ansduce —Theo y
and Expe imen
Manuel J. F ei e, Rica do Ma qués, Membe , IEEE, and F ancisco Medina, Senio Membe , IEEE
Abs ac —This pape p esen s a new me hod o he comple e
cha ac e iza ion o he adia ion o magne os a ic-su ace wa es
in mic os ip ansmission lines wi h longi udinal magne iza ion.
This me hod is based on he analysis o he exci a ion o leaky
modes in mic os ip lines and p o ides bo h he p opaga ion con-
s an and he complex impedance o he mic os ip. F om hese
quan i ies, he adia ion esis ance and o he ele an cha ac e is-
ics o he line can be di ec ly ob ained.
Index Te ms—Cha ac e is ic impedance, leaky mode,
magne os a ic-su ace wa e (MSSW).
I. INTRODUCTION
MICROSTRIP MAGNETOSTATIC-SURFACE-WAVE
(MSSW) ansduce s a e use ul in he design o delay
lines, il e s, and o he de ices [1], [2]. Al hough p ac ical
ansduce s ha e ini e leng h, he analysis o he adia ion o
MSSW in mic os ip lines o in ini e leng h is usually consid-
e ed as a easonable app oach o p ac ical de ices [3]–[8].
One o he main p oblems in he design o mic os ip-exci ed
MSSW ansduce s is he cha ac e iza ion o he adia ion e i-
ciency, i.e., he calcula ion o he inpu o adia ion impedance.
This p oblem has been sol ed in he pas by calcula ing he
a e age powe ca ied away by he MSSW exci ed by he mi-
c os ip h ough he Poyn ing ec o associa ed wi h he MSSW
[3]–[5], [8]. The calcula ion o he Poyn ing ec o equi es he
compu a iono heMSSW ields.To each hisgoal,bo hamag-
ne os a icapp oach[3],[4] anda ull-wa eanalysis[5],[8]ha e
been epo ed in he li e a u e. In [3] and [4], a uni o m su ace
cu en densi y is assumed on he s ip and analy ical exp es-
sions a e ob ained o he MSSW ields. In [8], he ields a e
analy ically calcula ed a e he su ace cu en densi y is nu-
me ically compu ed by means o a ull-wa e analysis using he
Gale kin me hod.
In his pape , we de elop a me hod o ob ain he complex
p opaga ion cons an and he complex cha ac e is ic impedance
Manusc ip ecei ed Ap il 23, 2002; e ised Sep embe 20, 2002. This wo k
was suppo ed by CICYT and FEDER unds unde P ojec TIC2001-3163.
The au ho s a e wi h he Mic owa e G oup, Depa men o Elec onics and
Elec omagne ism, Uni e si y o Se ille, 41012 Se ille, Spain.
Digi al Objec Iden i ie 10.1109/TMTT.2003.808633
Fig. 1. (a) Two semi-in ini e mic os ip lines ed by a 1-V del a-gap sou ce
applied a
z
=
0
. (b) C oss sec ion o he mic os ip line. (c) Equi alen ci cui .
o an in ini ely long mic os ip MSSW ansduce . F om hese
pa ame e s, he adia ion e iciency and o he ele an quan i-
ies o he in ini e and/o he ini e leng h ansduce s a e hen
ob ained. No di ec compu a ion o he MSSW ields is equi ed
in his analysis, which is a signi ican ad an age o he p oposed
me hod.
The ollowing sec ions desc ibe he guidelines o he me hod
o analysis. Then, some nume ical and expe imen al esul s a e
shown. Finally, concluding ema ks a e p esen ed.
II. METHOD OF ANALYSIS
The me hod epo ed in [9] and [10] o analyze he exci a ion
o leakymodesinp in ed-ci cui linesisappliedhe e o heanal-
ysis o he mode p opaga ing along a YIG-loaded longi udinally
magne izedmic os ip line adia ingMSSWs. Thisme hod con-
sis s o he ull-wa e analysis o he cu en exci ed in a pai
o semi-in ini e mic os ip lines ed by a 1-V del a-gap sou ce.
Fig.1(a)and(b)shows hes uc u eunde s udy.Fig.1(c)shows
he equi alen ci cui o he s uc u e.
Assuming ha is he elec ic ield imposed by he
del a-gap ol age sou ce, he su ace cu en densi y on he con-
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904 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 2003
duc o s ip can be ob ained a e sol ing he ollowing elec-
ic ield in eg al equa ion (EFIE) [10]:
(1)
whe e is he spa ial dyadic G een’s unc ion,
wi h he a iables ex ended om o ( s ands
o he s ip wid h) and om o . The elec ic ield
in he gap is modeled as
(2)
whe e is he Di ac del a unc ion. The EFIE (1) is sol ed
using he Gale kinme hodbyexpandingbo h he ans e se and
longi udinal componen s o he su ace cu en densi y, and
, in o a gene al se o comple e domain basis unc ions as
ollows:
(3)
(4)
The unc ions a e he unknown coe icien s in he
Gale kin p oblem and he unc ions a e he basis
unc ions, which a e gi en by
(5)
(6)
ha is, i s and second kind no malized Chebyshe
polynomials weigh ed by he p ope edge condi ion [7], [8]. I
mus be no ed ha he in eg a ion o he unc ions u ns
ou o be
(7)
whe e is he K onecke del a. Taking his in o accoun , he
cu en on he s ip is gi en by he coe icien ela ed o he
ze o h-o de basis unc ions o , ha is, . The EFIE
(1) is ans o med in o he Fou ie domain and, a e applying
he Gale kin me hod, he ollowing ma ix equa ion is ob ained
[10]:
(8)
The unc ion in (8) accoun s o he Fou ie ans-
o m o he unknown coe icien s in (4), a e he
K onecke del as ha cons i u e he independen elemen s, and
a e he ma ix elemen s gi en by
(9)
Fig. 2. Typical in eg a ion pa h in he complex
k
plane. The c osses indica e
he loca ion o he poles o he SDGF.
whe e and a e he Fou ie ans o m o he
basis unc ions, is he -componen o he spec-
al dyadic G een’s unc ion (SDGF), and is a p ope in e-
g a ion pa h in he complex -plane. The SDGF has poles in
he complex -plane and he in eg a ion pa h has o sui -
ably de ou a ound hese poles [7]–[11]. The ma ix equa ion in
(8) is sol ed ollowing he K ame ’s ule, and he Fou ie ans-
o m o he cu en is inally exp essed as
(10)
whe e is hede e minan o he Gale kinma ix
(9) and is he de e minan o he ma ix ob ained a e
subs i u ing he column o he ma ix (9) by he
column o independen e ms in (8).
A. Compu a ion o he P opaga ion Cons an
The unc ion has poles in he complex -plane which
co espond o he p opaga ion cons an s o he modes p opa-
ga ing along he mic os ip [10]. These poles a e calcula ed by
sea ching o he ze os o he denomina o in (10). Sea ching
o he ze os in a s uc u e as ha shown in Fig. 1 a equen-
cies inside he MSSW egion p o ides a pai o complex alues,
being he phase cons an o
he mode p opaga ing along he s ip and being he a enua-
ioncons an .Thesemodalsolu ionsco espond oaquasi-TEM
mode on he mic os ip line, which adia es MSSWs in o he
YIG slab [6], and he e a e ob ained using he in eg a ion pa h,
, as depic ed in Fig. 2.
The poles in he complex plane a e loca ed in he second
and ou h quad an s, e y close o he eal axis. The pa h
is de o med a ound his axis a om he poles o accele a e
he con e gence o he in eg a ion. Leaky modes in iso opic
p in ed-ci cui lines ha e modal solu ions associa ed wi h poles
ha a e loca ed in he i s and hi d quad an s in he complex
plane ( his means ha leaky mode ields g ow exponen ially
along he di ec ion [11]). Since he poles in he plane
associa edwi h hemodep opaga ingalong heYIG-loadedline
a e loca ed in he second and ou h quad an s, he ields o his
mode decay exponen ially along he di ec ion, he imagina y
pa o hese poles accoun ing o he a enua ion cons an in
his di ec ion. This beha io is ypical o complex modes [12].
Howe e , he SDGF poles a e so close o he eal axis ha he
exponen ial decay in he di ec ion is e y slow. The e o e,
he epo ed modes would be be e cha ac e ized as backwa d
leaky modes, ha is, leaky modes which adia e la e ally and
backwa d wi h espec o he di ec ion o p opaga ion o he
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FREIRE e al.: FULL-WAVE ANALYSIS OF EXCITATION OF MSSWs BY SEMI-INFINITE MICROSTRIP TRANSDUCER 905
Fig. 3. Equi alen ci cui in he ansmission-line model o he semi-in ini e
YIG-loaded mic os ip line.
L
: induc ance;
C
: capaci ance;
R
: adia ion
esis ance.
mode. This ac was al eady epo ed in [8], whe e i is shown
ha he powe lux associa ed wi h he MSSW o ms an angle
wi h he s ip di ec ion g ea e han 90 .
B. Compu a ion o he Cha ac e is ic Impedance and
Radia ion Resis ance
As shown in [9] and [10], he esidue con ibu ion o a
he pole loca ion gi en by in he complex plane
p o ides he complex ampli ude o he cu en associa ed wi h
he mode o p opaga ion cons an . Following his idea, he
cha ac e is ic impedance o he conside ed mic os ip mode can
be eadily compu ed. The a o emen ioned esidue con ibu ion
is exp essed as
(11)
The esidue is compu ed wi h a low nume ical e o by in e-
g a ing (10) a ound using a Gauss–Chebyshe
quad a u e, he ob ained cu en being a complex numbe in
gene al. In Fig. 1(a), he ol age imposed by he sou ce is ap-
plied be ween poin s and being his ol age V.
The impedance seen be ween he wo e minals and o he
del a-gap sou ce is de ined as he a io o he ol age be-
ween hese poin s and he cu en a , i.e.,
(12)
Fig. 1(c) shows a ci cui model o he s uc u e o Fig. 1(a). In
hisci cui model, woloadsco esponding o hecomplex cha -
ac e is ic impedance o he wo semi-in ini e lines a e se ies
connec ed be ween e minals and o he sou ce. The e o e,
he cha ac e is ic impedance is hen gi en by one hal o he
impedance be ween and as
(13)
Thus, once he p opaga ion cons an is ob ained,
he compu a ion o he esidue o p o ides he
cha ac e is ic impedance o he line.
The adia ion esis ance pe uni leng h o he line is ob-
ained om and , using he ansmission line model shown
in Fig. 3, he inal esul being
(14)
Fig. 4. Radia ion esis ance
R
e sus equency. The s uc u e is as shown
in Fig. 1 wi h he ollowing s uc u al pa ame e s:
w
=
178

m,
l
=2
:
28
mm,
h
= 254

m,
h
=6
:
25

m,
h
!1
;
"
=10
";"
=10
";"
=
15
"
;
H
= 650
Oe,
4
M
= 1750
G,
1
H
=0
Oe.
Fig. 5. P opaga ion cons an e sus equency o he s uc u e o Fig. 4.
Resul s a e shown o bo h uni o m and nonuni o m (Chebyshe polynomials)
cu en dis ibu ion.
III. NUMERICAL RESULTS
A. Theo e ical Resul s
In Fig. 4, ou esul s o he adia ion esis ance o an in i-
ni emic os ip MSSW ansduce a e shownandcompa ed wi h
hose ob ained in [3]. The compu a ion o he cu en has been
ca ied ou using wo di e en choices o he basis unc ions.
The i s one consis s o aking he basis unc ions as shown in
(5) and (6), including bo h e en and odd Chebyshe polyno-
mials ( in (4) leads o he con e gence o he esul s).
The second choice consis s o aking
(15)
(16)
i.e., a uni o m cu en is imposed on he s ip, as is assumed in
[3]. The cu es in Fig. 4 show ha ou compu a ions o he a-
dia ion esis ance a e in ag eemen wi h hose ob ained in
[3] ollowing a qui e di e en me hod when he same hypo h-
esis abou he dis ibu ion o he cu en on he s ip is made.
Figs. 5 and 6 show ou esul s o he p opaga ion cons an and
hecomplexcha ac e is icimpedance, espec i ely, o hesame
mic os ip MSSW ansduce o Fig. 4.
A e y impo an conclusion conce ning he modeling
o p ac ical MSSW ansduce s mus be highligh ed om
hese igu es. P ac ical ansduce s ha e ini e leng h and a e
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906 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 3, MARCH 2003
Fig. 6. Real and imagina y pa s o he cha ac e is ic impedance o he
s uc u e o Fig. 4. Resul s a e shown o bo h uni o m and nonuni o m
(Chebyshe polynomials) cu en dis ibu ion.
Fig. 7. Ske ch o he mic os ip-ci cui line and pic u e o he expe imen al
se up. Dimensions o he YIG sample:
d
=
5
cm,
l
=4
mm. S ip wid h:
w
=1
:
43
mm.
sho -ci cui ed a he end [2]. Following he con en ional ci cui
heo y, he inpu impedance o hese de ices is hus gi en by
(17)
whe e is he leng h o he ansduce . A usual app oxima-
ion [3]–[5], [8] consis s o assuming ha , so ha
. The cu es in Figs. 5 and 6 show ha his
assump ion can be ha dly jus i ied excep o e y sho ans-
duce s ( mm). Simila esul s leading o his conclusion
we e sys ema ically ob ained by he au ho s o he p esen pape
o many o he YIG-loaded mic os ip con igu a ions and s a ic
bias magne ic ields. A simila conclusion was also p e iously
epo ed in [6].
B. Compa ison Wi h Expe imen al Resul s
Fo he pu pose o e i ying inpu impedance compu a ions
using exp ession (13) [and (17)], measu emen s ha e been
ca ied ou wi h he expe imen al se up shown in Fig. 7.
In p ac ical de ices, he inpu mic os ip ansduce mus be
accompanied by an ou pu mic os ip ecei e . Howe e , he
simple mic os ip-ci cui line shown in Fig. 7 ha ing a single-
inpu mic os ip ansduce ills ou pu pose. Inpu impedances
o a YIG-loaded sho -ci cui ed line o ini e leng h equal
o 4 mm has been measu ed using he HP 8510 B au oma ic
ne wo k analyze . The inpu line is a 50- line buil on a
0.49-mm- hick dielec ic subs a e, which imposes a s ip wid h
o mm o ge a - cha ac e is ic impedance. The
same s ip wid h is chosen o he YIG-loaded line sec ion
( ansduce ) in o de o minimize ansi ion e ec s. Figs. 8 and
9 shows inpu esis ance and inpu eac ance e sus equency.
The heo e ical esul s ha e been ob ained om (13) and (17).
Fig. 8. Inpu esis ance e sus equency. The s uc u e is as shown in Fig. 1
wi h he ollowing s uc u al pa ame e s:
w
=1
:
43
mm,
l
=4
mm,
h
=
0
:
49
mm,
h
=40

m,
h
=0
:
5
mm;
"
=2
:
43
;"
=10
;"
=15;
H
=
1000
Oe,
4
M
= 1880
G,
1
H
=0
:
6
Oe.
Fig. 9. Inpu eac ance e sus equency o he s uc u e o Fig. 8.
Fig. 10. Re u n loss in decibels. The s uc u e is as shown in Fig. 1 wi h he
ollowing s uc u al pa ame e s:
w
=1
:
43
mm,
l
=4
mm,
h
=0
:
49
mm,
h
=40

m,
h
=0
:
5
mm;
"
=2
:
43
;"
=10
;"
= 15;
H
= 500
Oe,
4
M
= 1880
G.
The compu a ion o he cu en has been ca ied ou using wo
choices o he basis unc ions in he same way as in Fig. 4, ha
is, imposing a uni o m cu en on he s ip by means o (15) and
(16) and using he basis unc ions gi en in (5) and (6) including
bo h e en and odd Chebyshe polynomials [wi h in
(4)]. The heo e ical esul s co esponding o he expansion
in o Chebyshe polynomials show a good ag eemen wi h he
expe imen al esul s, which indica es ha he expansion in o
Chebyshe polynomials seems a mo e ealis ic hypo hesis han
assuming a uni o m cu en densi y on he s ip.
Finally, Fig. 10 shows he e u n loss o he s uc u e ana-
lyzed in Figs. 8 and 9 o a di e en bias magne ic ield. A good
ag eemen is ound again be ween heo e ical and expe imen al
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FREIRE e al.: FULL-WAVE ANALYSIS OF EXCITATION OF MSSWs BY SEMI-INFINITE MICROSTRIP TRANSDUCER 907
esul s. Small di e ences can be a ibu ed o he ini e dimen-
sions o he YIG slab [13] and highe o de modes gene a ed a
he ansi ion be ween he YIG-loaded sec ion and he dielec-
ic-loaded sec ion.
IV. CONCLUSION
A new me hod o he comple e cha ac e iza ion o in ini ely
long mic os ip MSSW ansduce s is p esen ed. This me hod
is based on he analysis o he exci a ion o leaky modes in mi-
c os ip lines. A signi ican ad an age o his me hod is ha no
explici compu a ion o ields and Poyn ing ec o a e equi ed
o ob ain he line impedance and/o he adia ion esis ance o
he ansduce .Theme hodcanbeapplied oob ain he adia ion
e iciency o p ac ical ansduce s o ini e leng h by using con-
en ional ansmission-line heo y. A good ag eemen wi h p e-
ious heo e ical esul s and wi h expe imen s has been ound.
REFERENCES
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[12] M. M ozowski, Guided Elec omagne ic Wa es. Some se , U.K.: Re-
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Manuel J. F ei e was bo n in Cádiz, Spain, in
1972. He ecei ed he Licenciado and Ph.D. deg ees
in physics om he Uni e si y o Se ille, Se ille,
Spain, in 1995 and 2000, espec i ely.
F om 1995 o 1996, he se ed in he Royal Na al
Obse a o y, Spanish Na y, San Fe nando, Cádiz,
Spain. In 1996, he joined he Mic owa e G oup,
Depa men o Elec onics and Elec omagne ics,
Uni e si y o Se ille. In 1998, he was a Visi ing
Resea che wi h he Depa men o Elec ical and
Compu e Enginee ing, Uni e si y o Hous on,
Hous on, TX. He is cu en ly an Assis an P o esso wi h he Depa men o
Elec onics and Elec omagne ics, Uni e si y o Se ille. His esea ch in e es s
include leakage in mic owa e in eg a ed ci cui s, mic owa e p opaga ion in
e i e de ices, and pe iodic s uc u es.
Rica doMa qués(M’95)wasbo ninSanFe nando,
Cádiz, Spain. He ecei ed he Licenciado and Doc o
deg ees om he Uni e si yo Se ille,Se ille,Spain,
in 1983 and 1987, espec i ely, bo h in physics.
Since 1984, he has been wi h he Depa men o
Elec onics and Elec omagne ism, Uni e si y o
Se ille, whe e he is cu en ly an Associa e P o esso .
His main ields o in e es include compu e -aided
design (CAD) o mic owa e in eg a ed-ci cui
(MIC) de ices, wa e p opaga ion in e i es, and
o he complex aniso opic and/o bi-iso opic media
and ield heo y.
F ancisco Medina (M’90–SM’01) was bo n in
Pue o Real, Cádiz, Spain, in No embe 1960. He
ecei ed he Licenciado and Doc o deg ees om
he Uni e si y o Se ille, Se ille, Spain, in 1983 and
1987, espec i ely, bo h in physics.
F om 1986 o 1987, he spen he academic yea
wi h he Labo a oi e de Mic oondes de l’ENSEEIHT,
Toulouse, F ance. F om 1985 o 1989, he was a
P o eso Ayudan e (Assis an P o esso ) wi h he
Depa men o Elec onics and Elec omagne ism,
Uni e si y o Se ille, and since 1990, he has been
a P o eso Ti ula (Associa e P o esso ) o elec omagne ism. He is also
cu en ly Head o he Mic owa es G oup, Uni e si y o Se ille. His esea ch
in e es includes analy ical and nume ical me hods o guidance, esonan
and adia ing s uc u es, passi e plana ci cui s, and he in luence on hese
ci cui s o aniso opic ma e ials.
D . Medina was a membe o bo h he Technical P og am Commi ee (TPC)
o he 23 d Eu opean Mic owa e Con e ence, Mad id, Spain, 1993, and he
TPC o ISRAMT’99, Malaga, Spain. He is on he Edi o ial Boa d o he IEEE
TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. He has been a e-
iewe o o he IEEE and Ins i u ion o Elec ical Enginee s (IEE), U.K., pub-
lica ions.
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