Method for measuring noise parameters of microwave two-port

Me hod o measu ing noise pa ame e s o mic owa e wo-po A. Lhza o, L. P adell and J.M. O'Callaghan A new une -based me hod o measu ing he ou noise- pa ame e s o a wo-po is p oposed. I makes use o a no el measu emen a io ha includes noise powe s and misma ch ac o s simul aneously. In con as o p e ious wo ks, no es ic ions on he noise sou ce, une s a e empe a u es and cold empe a u es a e assumed. In oduc ion; The measu emen o he ou noise pa ame e s ("s) NPs o a wo-po in he mic owa e equency ange is usually pe o med by measu ing he wo-po de ice noise igu e F o a minimum o ou sou ce e lec ion-coe icien s ,, p oduced wi h a une connec ed a he wo-po inpu ( e lec ion- ype une ) [I ~ 61. The equa ion ela ing F and s, (i = 1, ..., N) is exp essed in lin- ea o m, and he esul ing o e de e mined linea equa ion sys em is sol ed o he NPs [I, 2, 51. A numbe o measu emen me hods ha e been p oposed. In 131, F( s ) is de e mined om he measu ed ,, and he co esponding noise powe s deli e ed by he wo-po o he ecei e , a oom empe a u e. The sys em gain is compu ed om he ho and cold noise powe s deli e ed by a wo-s a e noise-sou ce 13, 71. Equal ho and cold sou ce e lec ion-coe icien s sH = s,) mus be assumed. Typically, his assump ion does no a ec he measu e- men accu acy o he NPs, because he di e ences be ween ,, and s, a e e y small, bu some applica ions ( o example, c yo- genic measu emen s o adiome e calib a ion) may equi e di e - en ho and cold loads. In 141, a me hod is gi en ha a oids he o me es ic ion by using an al e na i e measu emen magni ude, i.e. he a io be ween he deli e ed noise powe s and a misma ch coe cien . Only he ho -sou ce measu emen is equi ed o de e - mine he sys em gain, bu i is implici ly assumed ha he cold ( oom) empe a u e, T,, equals he e e ence empe a u e, To (= 290K) [4]. This assump ion is a limi a ion in a eal labo a o y en i onmen , o whene e he une includes semiconduc o (PIN diode) swi ches, because he diodes add a non- he mal (sho ) con- ibu ion o he empe a u es o he une s a es, T,, (i = 1, ..., N). Al e na i e echniques o measu e he ou Nps o he pa icula case o a ansis o 181, make use o he ansis o equi alen ci - cui as addi ional in o ma ion. Howe e , a une mus be used o calib a e he ecei e noise. 10, , 120, 0.4 I I 200, I 0 10 20 30 ,GHz (34611j Fig. 1 Recei e noise pa ame e s measu ed using new me hod, me hod p oposed by Adamian [3] and me hod p oposed by Da idson [4] ~ new me hod 0 Da idson V Adamian While a une is equi ed o measu e he NPs o a gene al wo- po ando o calib a e he ecei e , a gene al case csH # Tsc, T, # To, T,, # To, and di e en T,, o e e y s a e i) is o en encoun- e ed. No accu acy deg ada ion should be expec ed in hese cases i a measu emen me hod wi h no es ic i e assump ions we e used. The pu pose o his Le e is o p opose a new me hod o measu ing he ou NPs o a wo-po , based on a e lec ion- ype une . I is a mo e gene al me hod han hose in [3, 41 because: (i) i does no equi e measu emen o he cold-sou ce; (ii) T, need no be To; (iii) c, (i = 1, ..., N) need no be ei he he same as o equal o To. Mo eo e , i demons a es an imp o ed accu acy in c i ical measu emen si ua ions (i.e. l opTl in he wo-po close o 1). Expe imen al e i ica ion is gi en up o 26GHz. ,GHz ~ Fig. 2 HEMT noise pa ame e s measu ed using new me hod, me hod p oposed by Adamian 131, me hod p oposed by Da idson [4] and F50 me hod [8] ~ new me hod 0 Da idson Adamian 0 F50 Measu emen me hod: To calib a e he ecei e , he une is con- nec ed o i s inpu and he noise powe deli e ed o he ecei e de ec o is measu ed o e e y une s a e , (i = 1, ..., N). This powe can be exp essed as: whe e k is he Bol zmann cons an , , is he ecei e inpu e lec- ion coe icien , Ts is he noise empe a u e o he sou ce imped- ance ,,, TJ ,) is i s co esponding ecei e noise empe a u e, (Cop) is he ecei e ansduce powe gain, Go is he ecei e ansduce powe gain o a ma ched sou ce ( , = 0), and p( R, ,) = (l-~~s~z)~l-~s~R~z is a misma ch ac o . Go is a cons an h oughou he measu emen , because i only depends on ecei e pa ame e s. To elimina e he gain cons an Go he noise powe PH deli e ed by a ho sou ce (whose ho empe a u e TH is known), is used as a e e ence o de ine a no el measu emen a io R,: The ecei e noise empe a u e T, is exp essed in a linea o m by using he Lane's pa ame e s A, B, C, D [I], whch a e unc ions o he ecei e NPs, T,,,,,, G,,, Bop, and R,,: whe e Y, = Gs + jBs is he sou ce admi ance. Subs i u ing eqn. 3 in o eqn. 2, he ollowing o e de e mined linea equa ion sys em is ob ained o A, B, C, D: [Sz] = [VI . [A B C D]' (i = 1, ..., N) (4) S, E R,TH - Ts, (5) The sys em in eqn. 4 is sol ed o A, B, C, D, by weigh ed leas - squa es using he concep o he pseudo-in e se ma ix, and he ecei e NPs a e eadily compu ed. This calcula ion comple es he ecei e calib a ion. Then he wo-po is inse ed, and by using he F iis's o mula, he ollowing equa ion is eadily de i ed: s; = TDUT( Sz) - R:T~~~(~~~) (i = 1, ..., N) (8) 1332 ELECTRONICS LETTERS 25 h June 1998 Vol. 34 No. 13 whe e R,‘ is de ined as in eqn. 2, bu wi h he e lec ion coe icien , e e ed o he wo-po inpu . In eqn. 9, he e lec ion coe i- cien s ,,’, s/ co espond o s, and ,,, espec i ely, bu a e e e ed o he wo-po ou pu . TDUT and Ga DuT a e he wo-po noise empe a u e and a ailable gain, espec i ely, and 72 is he ecei e noise empe a u e, compu ed om he ecei e NPs p e i- ously measu ed. The wo-po noise empe a u e in eqn. 8 is exp essed in linea o m, and a linea sys em simila o eqns. 4 - 7 is ob ained o [A B C DITDuT, wi h R, and S, eplaced by R,‘ and SE’, espec i ely. Expe imen al esul s: The me hod has been es ed on on-wa e ansis o s. The es se up includes a b oadband (2-26GHz), com- me cial une [6] wi h nine a ailable sou ce s a es. The une and ho sou ce e lec ion-coe icien s a e measu ed oge he wi h hei co esponding noise powe s and used in [2 - 91. Fig. 1 shows ha he measu ed ecei e NPs up o 26GHz o he me hod p oposed he e and o hose p oposed in [3, 41 a e almos iden ical, which is o be expec ed since he es condi ions needed in he o me me h- ods [3, 41 a e me (TsX = ,, o [3] and T,, = To o [4]). Fig. 2 compa es he measu ed NPs o an on-wa e HEMT up o 26GHz. The ag eemen be ween he ou me hods (Fs0 me hod [SI is also compa ed) is good excep a low equencies, o which l oPTl is e y high (close o 1). The new me hod is mo e obus o his c i - ical measu emen si ua ion han hose in [3, 41, which ha e non- physical pa ame e s. Conclusions; A no el une -based me hod o measu ing he ou NPs o a gene al wo-po wi h no es ic ions in he noise sou ce o une , has been p oposed and success ully applied o he ecei e calib a ion and o an HEMT. I has been compa ed o o he une -based me hods in he li e a u e, demons a ing accu- acy imp o emen s in he de e mina ion o he NPs o c i ical measu emen si ua ions, such as a de ice I & close o 1. Acknowledgmen : This wo k has been suppo ed by he esea ch p ojec s TIC93-672-C04-03 and TIC97-1129-C04-04 manced by he Spanish CICYT. 0 IEE 1998 Elec onics Le e s Online No: 19980942 A. Laza o, L. P adell and J.M. O’Callaghan (Poly echnic Uni e si y o Ca alunya (UPC), Dep . TSC, Campus No d UPC, 08034 Ba celona, Spain) 7 May I998 Re e ences LANE, R.Q.: ‘The de e mina ion o de ice noise pa ame e s’, P oc. CARUSO, G., and SANNINO, M.: ‘Compu e -aided de e mina ion o mic owa e wo-po noise pa ame e s’, ZEEE T ans. Mic ow. Theo y Tech., 1978, 26, (9), pp. 639-642 ADAMIAN, A., and UHLIR, A : ‘A no el p ocedu e o ecei e noise cha ac e isa ion’, IEEE T ans. Zns um. Meas., 1973, 22, (6), pp. 181-182 DA iDsoN, A.c., LEAKE, B.w., and STRID, E.: ‘Accu acy imp o emen s in mic owa e noise pa ame e measu emen s’, IEEE T ans. Mic ow. Theo y Tech., 1989, 37, (12), pp. 1973-1978 OCALLAGHAN, J.M., and MONDAL, J.P.: ‘A ec o app oach o noise pa ame e i ing and selec ion o sou ce admi ances’, ZEEE T ans. Mic ow. Theo y Tech., 1991, 37, (12), pp. 1376-1382 NPTS-26 Sys em, Cascade-Mic o ech, Inc., 14255 SW B igadoon, Bea e on, OR 97005 CROZAT, P.] DOUTLX, c., CTI*””ET, M , DANELON, V.) SYLVESTRE) a., and VERNET, G.: ‘SO 0 noise measu emen s wi h ull ecei e calib a ion wi hou une ’, Elec on. Le ., 1996, 3, pp. 261-262 LAZARO, A., PRADELL, L., BELTRAN, A., and O’CALLAGHAN, J.M.: ‘Di ec ex ac ion o all ou ansis o noise pa ame e s om Son noise igu e measu emen s’, Elec on. Le ., 1998, 32, (3), pp. 289- 291 ZEEE, 1969, 57, pp. 1461-1462 Nonlinea s abili y anallysis o mic owa e ci cui s using comme cial so wa e A. Sua ez, V. Iglesias, J.-M. Collan es, J. Jug0 and J.L. Ga cia A new echnique is p esen ed o he s abili y analysis o s eady nonlinea egimes in mic owa e ci cui s, using comme cial so wa e. The Nyquis s abili y c i e ion is applied o he open- loop ans e unc ions o he ci cui linea isa ion a ound he s eady s a e. Th ough a simple nonlinea op imisa ion echnique i is also possible o de e mine he p edic ed quasi-pe iodic o pe iod-doubled s eady solu ions. The s abili y analysis o wo a ac o -based ci cui s has p o ided excellen esul s when compa ed wi h ime domain simula ions and measu emen s. In oduc ion: Ha monic balance (HB) comme cial simula o s a e an in aluable ool o he analysis o he nonlinea s eady egimes o mic owa e ci cui s, such as powe ampli ie s, oscilla o s o e- quency double s. A nonlinea s abili y analysis is also necessa y in o de o ensu e he physical exis ence o he simula ed solulions [l, 21. This analysis p o ides in o ma ion abou he possible exis - ence o uns able na u al equencies ha would gi e ise o, o en undesi able, quasi-pe iodic o pe iod doubled egimes. Howe e , he s abili y analysis o hese egimes is no ye a ailable. Ins ead, comme cial simula o s only include s abili y analysis op ions o he DC solu ions o oscilla o ci cui s. In his Le e , a new echnique is p esen ed o he s abili y analysis o nonlinea s eady egimes, using comme cial so wa e. I is based on he Nyquis s abili y c i e ion, which is applied o he open-loop ans e unc ion o he ci cui linea isa ion a ound i s nonlinea s eady solu ion. To calcula e his ans e unc ion, a eal equency pe u ba ion is in oduced o e he s eady egime, in he o m o an auxilia y gene a o (AG) o neghgible ampli ude. This enables he e alua ion o he open-loop ans e unc ion a he AG loca ion. The Nyquis plo s a e hen di ec ly ob ained by sweeping he AG equency. Fo a igo ous analysis, a oiding unce ain y abou possible ze o-pole cancella ions, se e al obse - a ion po s should be conside ed sequen ially. A new echnique is also p esen ed o he s eady-s a e analysis o he p edic ed au onomous quasi-pe iodic and equency di ided egimes. This is based on nonlinea op imisa ion o he auxilia y gene a o a iables, imposing a non-pe u ba ion condi ion. The uns able na u al equency is es ima ed om he Nyquis plo , which p o ides a aluable s a ing poin o he op imisa ion. Since he new analysis echniques a e in ended o comme cial simula o s, hey a e eadily usable by any mic owa e-ci cui designe . Ad an age is also aken o he lexibili y o comme cial so wa e, which enables he analysis o complex opologies, which a e ypically di icul o in oduce in in-house so wa e. He e, he p oposed analysis me hod has been applied o he s abili y analysis o wo a ac o -based ci cui s: a simple ci cui o equency di ision and a equency double ha exhibi s an asynch onous ins abili y. The espec i e pe iod doubled and quasi- pe iodic solu ions we e p edic ed and de e mined by means o he new me hod, ob aining an excellen ag eemen wi h ime domain simula ions and measu emen s. Fo bo h he s abili y and s eady s a e analysis, HP-MDS comme cial so wa e has been used. Fig. 1 Block diag am o pe u bed ci cui , linea ised a ound nonlinea pe iodic solu ion XpO Analysis me hod: A nonlinea ci cui , exhibi ing a s eady egime o pe u ba ion will be supe imposed o e he s eady solu ion X,O. This is done by in oducing in o he ci cui an auxilia y gene a o (AG) o negligible ampli ude E and a iable equency ,, wi h a il e which elimina es i s in luence a all equencies di e en om i s own [3]. The inpu immi ance a ,, obse ed om he AG e - minals, may be spli in o wo con ibu ions. Whene e possible, -d-en al ;,, will he conside ed To analyse i s s abili y, a small ELECTRONICS LETTERS 25 h June 7998 Vol. 34 No. 13 1333