Full-wave analysis of the excitation of magnetostatic-surface waves by a semi-infinite microstrip transducer - Theory and experiment

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- 0018-9480/03$17.00 © 2003 IEEE Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 01,2020 a 16:43:47 UTC om IEEE Xplo e. Res ic ions apply. 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 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 01,2020 a 16:43:47 UTC om IEEE Xplo e. Res ic ions apply. 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 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 01,2020 a 16:43:47 UTC om IEEE Xplo e. Res ic ions apply. 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 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 01,2020 a 16:43:47 UTC om IEEE Xplo e. Res ic ions apply. 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 [1] W. S. Ishak, “Magne os a ic wa e echnology: A e iew,” P oc. IEEE, ol. 76, pp. 171–187, Feb. 1988. [2] P. Kabos and V. S. S almacho , Magne os a ic Wa es and Thei Appli- ca ions. London, U.K.: Chapman & Hall, 1994. [3] A. K. Ganguly and D. C. Webb, “Mic os ip exci a ion o magne os a ic su acewa es:Theo yandexpe imen ,”IEEET ans.Mic owa eTheo y Tech., ol. MTT-23, pp. 998–1006, Dec. 1975. [4] A. K. Ganguly, D. C. Webb, and C. Banks, “Complex adia ion impedance o mic os ip-exci ed magne os a ic-su ace wa es,” IEEE T ans. Mic owa e Theo y Tech., ol. MTT-26, pp. 444–447, June 1978. [5] J. C. Se ha es, “Magne os a ic su ace-wa e ansduce s,” IEEE T ans. Mic owa e Theo y Tech., ol. MTT-27, pp. 902–909, No . 1979. [6] G. A. Vugal e and I. A. Gilinski, “Exci a ion and ecp ion o magne o- s a ic wa es by a mic os ip ansduce ,” So . Phys. Tech. Phys., ol. 30, no. 11, pp. 1332–1334, No . 1985. [7] E.-B. El-Sha awy and R. W. Jackson, “Full-wa e analysis o an in in- i ely long magne ic su ace wa e ansduce ,” IEEE T ans. Mic owa e Theo y Tech., ol. 38, pp. 730–738, June 1990. [8] J.-H. Lee and J.-W. Ra, “Full-wa e calcula ion o he adia ion impedance o mic os ip-exci ed magne ic su ace wa es,” Mic owa e Op . Technol. Le ., ol. 6, no. 7, pp. 441–444, June 1993. [9] C. Di Nallo, F. Mesa, and D. R. Jackson, “Exci a ion o leaky modes on mul ilaye s ipline s uc u es,” IEEE T ans. Mic owa e Theo y Tech., ol. 46, pp. 1062–1071, Aug. 1998. [10] D. R. Jackson, F. Mesa, M. J. F ei e, D. P. Nyquis , and C. Di Nallo, “An exci a ion heo y o bound modes, leaky modes, and esidual-wa e cu en sonas ipline s uc u es,” Radio Sci., ol. 35, no. 2,pp. 495–510, Ma . 2000. [11] F. Mesa and R. Ma qués, “In eg al ep esen a ion o spa ial G een’s unc ion and spec al domain analysis o leaky co e ed s ip-like lines,” IEEE T ans. Mic owa e Theo y Tech., ol. 43, pp. 828–837, Ap . 1995. [12] M. M ozowski, Guided Elec omagne ic Wa es. Some se , U.K.: Re- sea ch S udies P ess, 1997. [13] T. W. O’Kee e and R. W. Pa e son, “Magne os a ic su ace-wa e p op- aga ion in ini e samples,” J. Appl. Phys., ol. 49, no. 9, pp. 4886–4895, Sep . 1978. 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. Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 01,2020 a 16:43:47 UTC om IEEE Xplo e. Res ic ions apply.