Design of bandstop filters by reactance transformation

a o cha ac e is ic, a ol age linea wi h equency o e a na ow band. The ne wo k can be designed o ha e an ou pu cha ac e is ic which has a ela i ely low de ia ion om linea - i y and a s eep g adien o e he disc imina o bandwid h. The ci cui was analysed using he elec ical equi alen ci - cui o he m.c. . (Fig. 2). To ob ain he heo e ical disc imina- o cha ac e is ic, i was necessa y o sub ac he absolu e magni udes o he wo ou pu ol ages, which could only be achie ed by nume ical echniques. We de ine i s a mode spac- ing, Aco, which is he di e ence be ween he an isymme ic- mode and symme ic-mode equencies o one m.c. . F om he equi alen ci cui o Fig. 2, he mode spacing is Aco = l/co0 LCC. Fo a gi en alue o maximum de ia ion om linea i y and mode spacing o each m.c. ., he maximum disc i- mina o bandwid h can be achie ed by op imising he il e design pa ame e s. 1737721 Fig. 2 Elec ical equi alen ci cui o one m.c. . su ace-acous ic-wa e-coupled esona o il e s4 which ha e he same equi alen ci cui . Acknowledgmen s: The au ho s hank Ca hodeon C ys als o p o iding he monoli hic c ys al il e s; S. J. Fos e acknow- ledges a Science Resea ch Council s uden ship. S. J. FOSTER N h Decembe 1979 M. REDWOOD Depa men o Elec ical & Elec onic Enginee ing Queen Ma y College, London El 4NS, England Re e ences 1 KEE-SIANG LU, s.: 'The applica ion o qua z c ys als o disc imina- o s, il e s and monoli hic il e s', Aus alian Elec onics Eng., 1971, pp. 21-24 2 SMITH, w. L.: 'The monoli hic FM disc imina o : a new piezo- elec ic de ice', IEEE T ans., 1968, CT-16-3, pp. 460-463 3 TRAVIS, c: 'Au oma ic equency con ol', P oc. IRE, 1935, 23, pp. 1125-1141 4 REDWOOD, M., TOPOLEVSKY, R. B., MITCHELL, R. F., and PALFREEMAN, J. s.: 'Coupled- esona o acous ic-su ace-wa e il e ', Elec on. Le ., 1975, 11, pp. 253-254 0013-5194/80/030104-02 $1.50/0 As an example, a disc imina o was designed o ha e a 6% maximum de ia ion om linea i y o e a 22 kHz bandwid h cen ed a 10-7 MHz. The heo e ical and expe imen al ou pu cha ac e is ics a e compa ed in Fig. 3. The m.c. .s had a mode spacing o 11-8 kHz and a esonan equency sepa a ion o 29-6 kHz. No spu ious modes we e obse ed a equencies ei he abo e o below he ange shown; as he ec i ied ou pu ol ages a e sub ac ed, il e s wi h a poo s opband can be ole a ed. 1-0 -25 -20 -15 -10 -5 0 5 10 15 20 25 equency de ia ion. kHz I737/3I Fig. 3 Disc imina o ou pu cha ac e is ic — heo e ical; + expe imen al. Cen e equency 10-7 MHz, inpu signal 1 V .m.s. Wi h disc imina o s designed in his way, smalle de ia ions om linea i y may be achie ed o e a na owe band, wi h he same m.c. . mode spacing, by educing he esonan equency sepa a ion. La ge bandwid hs may be ob ained by uning ou he s a ic capaci ance (Co in Fig. 2) o bo h m.c. .s. Wi hou uning, he disc imina o bandwid h is ypically 1-3 imes he mode spacing o a 2% maximum de ia ion and 2-2 imes he mode spacing o a 10% de ia ion. Wi h uning, he band- wid hs a e 1-7 and 2-6 imes he mode spacing o de ia ions o 2% and 10%. The maximum bandwid h, o a pa icula alue o de ia ion, is limi ed by he maximum mode spacing o he m.c. . ha can be achie ed ( ypically 30 kHz a 10-7 MHz). The disc imina o bandwid h and he mode spacing can bo h be equency scaled, i.e. inc easing he mode spacing by 10% inc eases he disc imina o bandwid h by 10%. A simila design echnique can be used o p oduce disc im- ina o s o highe equencies, using o e one mode m.c. .s o DESIGN OF BANDSTOP FILTERS BY REACTANCE TRANSFORMATION Indexing e ms: Fil e s, Reac ance The usual me hod o designing bands op il e s is he eac- ance ans o ma ion om a lowpass p o o ype. When he il e speci ica ions do no sa is y geome ical symme y, he choice o s opband cen al equency cons i u es an in e - es ing p oblem. This le e shows ha he mean squa e o he s opband edges is he s opband cen al equency ha leads o he lowes selec i i y pa ame e o he p o o ype. The speci ica ions o a bands op cha ac e is ic a e shown symbolically in Fig. la. This implies ha o (co| <<opl o | co | > op2, he passband loss should be less han ap. Fo o)al < | co | < coa2, he s opband loss should be g ea e han aa. The lowpass-bands op eac ance ans o ma ion is1 whe e <<Oa COp2 (1) I s applica ion o he speci ica ion in Fig. la de ines he p o o- ype shown in Fig. b, whe e ip = max (Clp , ilp2) i0 = min (QBl, Qa2) wi h o - P (0ol Wp2 - co£> 0)a2 (2a) (2b) (3a) (3b) being he ans o med equencies o iopX, cop2, coal and coa2, espec i ely. The p oblem ha a ises is he choice o coo,, he cen e ELECTRONICS LETTERS 31s Janua y 1980 Vol. 16 No. 3 105 equency o he ans o ma ion. I is e iden ha he mos con enien alue o co^ is ha which equi es he lowes -o de p o o ype. Conside ing ha he o de is an in ege , he e will be in gene al a ange o alues o co^, which p o ides such a minimum. This ange depends on he bands op il e speci ica ions and he app oxima ion used o he p o o ype. The e o e i s gene al cha ac e isa ion is di icul , i no impossible. a 77777777777777777, Theo em 2: I col, — <*>ai u>a2, he selec i i y pa ame e o he p o o ype ake he lowes possible alue. P oo : Le us assume ha coaXcoa2 < coPicop2 Acco ding o heo em 1, he alue o co^ ha p o ides he lowes K sa is ies 0)aiCOa2 < CO o < COpiCOp2 In his case, i is easy o p o e ha lpl > lp2 l2 > O.1 which, ollowing eqns. 2 and 3, leads o (6) [6907i] n Fig. 1 a Bands op il e speci ica ions b Lowpass p o o ype speci ica ions I is possible, hough, as is shown in his le e , o iden i y he alue o Woo ha equi es om he selec i i y pa ame e 1 o he p o o ype (4) he lowes possible alue. This in o ma ion is e y con enien , because i allows us o de e mine he lowes o de necessa y o he p o o ype and p o ides a e e ence o he ange o alues o a),*, ha such a minimum equi es. Theo em 1: The alue o co^ ha p o ides he lowes selec i i y pa ame e o he p o o ype sa is ies min {coplcop2, coal(oa2) < col, < max (copicop2, (oalo)a2) P oo : Le us assume ha col, < min {copicop2, (oaicoa2) I is easy o check in eqn. 3 ha The e o e, ollowing eqns. 2, 3 and 4, we ge (5) K = 0>a2 Fo co^ sa is ying eqns. 1 and 5, K will ake he lowes alue when col, is maximum, ha is col, = min {copicop2, coalcoa2) To comple e he p oo we ha e o p oceed in a simila way wi h he uppe limi . Co olla y: I <opicop2 = coalcoa2 (geome ical symme y), col, = copi coP2 = coai coa2 p o ides he lowes selec i i y pa a- me e o he p o o ype. Excep o col, = <Wpi, we ha e ha dK dcol >0 The e o e, o col, sa is ying eqn. 6, K is minimum o col, = coaicoa2. By a simila p ocedu e, we can show ha , i wai wa2 > wpi wp2, an iden ical esul holds. This comple es he p oo . I is in e es ing o men ion ha a simila esul can be ob- ained in he bandpass case. When iden ical minimum losses a e speci ied o bo h s opbands, he mean squa e o he pass- band edges is he cen al equency o he passband ha p o- ides he lowes alue o he selec i i y pa ame e o he lowpass p o o ype. 23 d No embe 1979 J. B. MARl O-ACEBAL C. NADEU-CAMPRUBI E. MASGRAU-GOMEZ ETSI Telecomunicacion Ap do. 2549, Ba celona, Spain Re e ence 1 TEMES, G. c, and MITRA, S. K.: 'Mode n il e heo y and design' (Wiley, 1973) 0013-5194/80/030105-02$!.50/0 OPTICAL DEMULTIPLEXER USING CONCAVE GRATING IN 0 7-0 9 u n WAVELENGTH REGION Indexing e m: Communica ions, In eg a ed op ics Expe imen al esul s o a demul iplexe using an abe a ion co ec ed conca e g a ing o an op ical sys em a e desc ibed. The demul iplexe has 10 channels and a wa eleng h spacing o 20 mm om 0-7 o 0-9 nm wa eleng hs. Inse ion losses and c oss alk we e less han 2-5 dB and — 30 dB, espec i ely, o all channels. In oduc ion: Op ical- ib e ansmission echnology has de eloped apidly owing o imp o emen s in op ical ib es, ligh sou ces and passi e de ices. Among hem, wa eleng h- di ision-mul iplexing (w.d.m.) ansmission is conside ed a p omising app oach o u u e sys ems—especially o sub- sc ibe loops and la ge-capaci y ansmission sys ems. The wa eleng h-di ision-mul iplexing (w.d.m) echnology, 106ELECTRONICS LETTERS 31s Janua y 1980 Vol. 16 No. 3