A large signal nonlinear MODFET model from small signal S-parameters

L-3 A LARGE SIGNAL NONLINEAR MDDFET DEL mon SMALL SIGNAL SPARMETERS* J. M. O'Callaghan and J. B. Beye Uni e si y o Wisconsin-Madison 1415 Johnson D i e, Madison, WI 53706-1691 Depa men o Elec ical and Compu e Enginee ing ABSTRACT A gene al echnique o p edic ing he FET la ge signal pe o mance has been de eloped. The echnique is based en i ely on expe imen al da a (small signal S-pa ame e s a di e en bias poin s) and he e o e is independen o he s uc u e o he FET. La ge signal measu emen s con i m he alidi y o he model. I. INTRODUCTION Modula ion doped FETs (MODFETS) ha e al eady been p o en o ha e good noise pe o mance o mic owa e applica ions (1). MODFETs a e also well sui ed o class B ampli ie s, since hei ans- e cha ac e is ic can be app oxima ed by a piecewise linea cu e and his leads o a la ge signal ansconduc ance independen o he signal le el. Howe e , he e a e ew la ge signal models a ailable and he de e mina ion o he pa ame e s o such models is di icul o equi es special equipmen . Fu he mo e, he models canno be used con enien ly in common CAD p og ams. The model and measu emen echniques p e- sen ed he e o e come hese p oblems. So wa e equi emen s include: a p og am (1 ike TOUCHSTONE'") o i an equi alen ci cui o S pa ame e da a; a simple leas squa e polynomial app oxima ion p og am; and he popula SPICE o nonlinea ime domain simula ions. Ha dwa e equi emen s a e basically limi ed o a ne wo k analyze o ca y ou he small signal S pa ame e measu emen s. 11. NONLINEAR MODFET CIRCUIT MODEL A. Ci cui Elemen s The nonlinea ci cui p oposed is an ex en- sion o a widely used small signal equi alen ci cui in which he nonlinea i y o Cgs( l) and IdS(Vl,Vds) is aken in o accoun (see Fig. 1). In his ci cui Ids( l, ds) models he nonlinea - i ies o he ansconduc ance (gm) and he ou pu conduc ance (Go) h ough Eqs. 1 and 2: *This wo k is suppo ed by Honeywell Inc., ONR and Caja de Pensiones (Ba celona, Spain). CH2725-0/89/0000-0347$01 .OO 0 1989 IEEE -Q Figu e 1 .A : MODFET model I Figu e 1 .B : Small signal equi alen o Ids B. De e mina ion o he Linea Elemen Values The alues o cds and he ex insic elemen s ha e been de e mined o a 300~m SONY MODFET by measu ing i s S pa ame e s a VDS,VGS = 0 and i ing i s equi alen ci cui a his bias poin (Fig. 2) (2), (3) (See Table 1). In ou model, only Cgs and Ids a e allowed o be ol age- dependen . To desc ibe his dependence we ha e o adjus gm, GO, C s, Ri, C d and cdc in Fig. 1 o ma ch he 2 pa ameae s a se e al bias poin s. Only he i s h ee pa ame e s a e used o cha ac e ize he nonlinea beha io o C s( l) and Ids(Vl,Vds)(4). The linea ized equi - agen s o ~i, Cgd, and cdc a e ound by a e aging hei alues a hese bias poin s. The ob ained alues a e: 347 1989 IEEE MTT-S Diges Ri = 1.22 0; C = 0.0438 pF; Cdc = 0.0518 pF gd (. .b. 70 KO Ps cF I" Ls - Figu e 2 Ze o-bias equi alen ci cui Table 1: Linea elemen s om ze o bias ci cui Ld = 0.0741 nH Lg = 0.0478 nH L, = 0.0588 nH Rd = 1.39 n Rg = 1.36 n Rs = 1.22 n cds = 0.0219 PF Cpg = 0.0267 PF Cpd = 0.0371 pF C. De e mina ion o Ids( l&d Ids *4. ) "m Figu e 3 Dis ibu ion o he bias poin s Figu e 3 shows he dis ibu ion o he bias poin s o which a small signal equi alen ci cui has been de e mined. I we assume ha Ids( l,yd,) can be exp essed as a p oduc o wo one- a iable unc ions; i.e.: pq( l) can be ound om he ans e unc ion a A his poin we can se pd(VDS ) 1; hen pg( l) is o ced o ake he a8uei o he ans e cha ac e is ic. F om Eq. 2 and knowing ha lds( TY DSQ) = (5) (VT being he pinch-o ol age), we can w i e Pg('1) = I gm(uSVDSQ)dU (6) T which allows us o e alua e he VI dependence o Ids om he measu ed g, a se e al bias poin s. Figu e 4 shows he alues o gm measu ed o VGS anging om -1.4V o 0.4V = 2V and hei co esponding alues o and pg D o = ""? Ids ~,VDSQ)) ound wi h Eq. 6. Simila s eps a e aken o de e mine he dependence o Ids wi h Vds: om Eqs. 1 and 3 we know ha GO( GSQY 'ds) = Pg( GCJ))Pi( ds) (7) 50 40 30 20 10 0 -1.5 -1 -0.5 0 0.5 Vl ( ol s) FIGURE 4: TRANSCONWCI'AKE AND TRANSFER CURVE FUR Vde=VLSQ=2V This equa ion, wi h he condi ion pd( DSQ) = 1 leads o pd o he nonze o alues o ds: Also, since Ids(V1,O) = 0, Pd has o be ze o o In Table 2, he p ac ical applica ion o Eq. 9 is shown: S a ing om he alues o G~(VG~Q,VDS! and pe o ming he nume ical in e- g a ion indica ed in Eq. 9, he alues o pd(VDS) a e ound o VDs anging om 0.5 o 4V. D. Polynomial i ing o p,( l), P,+(V~~) and Vds = 0. 3 o class B applica ions The app oach discussed so a has allowed us o desc ibe he ol age dependencies wi h one- a iable unc ions. Wha is needed now is o exp ess hese unc ions in a o m ha can be 348 Table 2 - De e mina ion o Pd(Vos) om O pu Conduc ance Da a (VGs = VGso - -0.N) VDS 0.5 1.0 2.0 3.0 4.0 GO (ms) 18.9751 8.2583 5.2548 3.7447 3.4330 VDS DsP I Go(mA) -13.5647 -6.1563 0 4.4445 8.0884 Pd(V0s) 0.4408 0.7215 1 1.1855 1.3934 handled by a CAD p og am. Ou wo k has been ocused owa ds ge ing a model o SPICE, whose use -de ined non1 inea i ies ha e o be exp essed in polynomial o m. The e a e se e al me hods o i a polynomial o a se o da a. Ou choice is he one desc ibed by Hayes (5) in which he sum o he squa es o he esidual e o is minimized by using a sum o o hogonal polynomials. O he algo i hms as well as comme icial so wa e can be used o his pu pose. Fo simula ing class A ope a ion we need o ge da a a VT < i < and ca y ou he i ing o pg( l) and C (??I? in his ange. How- e e , o class B and ?ope a ion i migh no be necessa y o ake measu emen s in he whole ange o alues o i. This is because we know be o ehand ha p (0) = 0 o i < VT and ha Cgs( l) beha es smoo&hly in his ange. Ad an age is aken o bo h ac s o limi he measu emen ange o VT < i < lmax. In ou case we a e in e es ed in class B ope a ion and ou de ice has VT = -lV and lmax = 0.4V which ou class B ange -2.4 5 l 5 0.4. Ex apola ion o pg below he pinch-o ol age consis s o adding ze os a disc e e alues o . Figu e 5 shows he p ocess o ou pa icula Ease (5.4uA ms e o wi h a 10 deg ee polynomi a1 ) . makes x:poin s o i 1ine: i iw polynomial 70 60 50 Ids(mA) 40 30 20 IO 0 -in -4 -3 -2 -1 0 0.5 l ( ol s) FIGURE 5: POLYNOMIAL FITTING OF THE TRANSFER CURVE No e ha o he lowe alues o i, pg( l) is qui e di e en om ze o. This is a ypical cha ac e is ic o polynomial i ing, i.e. he (absolu e) e o ends o be highe a he ex emes o he i ing in e al. The e o e, we can expec o ha e he highes ela i e e o s a he le mos ex eme o he ans e cha ac e is- ic whe e he cu en s a e small bu he i ing e o can be high. To a oid his e ec , a ew ze os we e added a alues o i less han -2.4V. Ex apola ion o Cgs( l) is mo e in ol ed. Fi s , a coe icien m has o be ound o i he measu ed alues o Cgs o he exp ession which can be la e used o ind Cgs o 1 < VT. Figu e 6 summa izes his p ocess o ou pa icula case (m = 0.474). A 3.8 F ms is ob ained wi h an 8 deg ee polynomial. 0 0.5 VI ( ol s) x : measu ed alues 0: ex apola ed alues line: i ing polynomial FIGURE 6: FOLYNOMIAL FITTING OF CgS(V1) AT VdS-VDSQ'2V ? o Finally, Pd(Vds) has o be in e pola ed o he alues shown in Table 2 and he poin pd(0) = 0. No e ha since in e pola ion is a pa icula case o polynomial i ing, he same so wa e ha has been used o i p ( i) and Cgs( l) can now be used o in e pola e pdq ds)- 111. EXPERIMENTAL RESULTS Measu emen s a 10 GHz on a SONY MODFET 2SK677H5 we e made o con i m he h ee basic nonlinea e ec s: 0 Nonlinea i y in Cgs o o Nonlinea dependence o Ids wi h Vds Nonlinea dependence o Ids wi h 1 The accu acy o he nonlinea beha io o Cps( l) was checked by measu ing he la ge signal 11 and compa ing i wi h simula ed da a. This is shown in Figu e 7, whe e he measu ed class A and class B S11 a e compa ed o he calcula ed ones o wo alues o inciden powe . 349 FIGURE 7: LARGE SIGNAL SI 1 Vas - -0.31V 0 Measu ed Class B Vos -3V as - -l Slmulaled Class B 1 PIN lnln - -5.86 dBm PIN - 9.14 dBm -The a ows lndlcale Ihe change In S11 wilh Inc easing PIN Simila ly, he la ge signal S22 is expec ed o be sensi i e o he nonlinea dependence o Ids wi h Vds. Figu e 8 shows compa i i e esul s o his pa ame e a wo bias le els. (This pa ame e showed low sensi i i y o he inciden powe ). FIGURE 8: LARGE SIGNAL S22 Measu ed) VoS - 3V ; VGs - -0.31V Simula ed -1ncldenl Powe : PI i - 4.14dBm -The a ow Indica es he change In S22 wilh lnc easlng Vos Finally, he accu acy in he modeled ans e cha ac e is ic was checked by compa ing he measu ed DC cu en gene a ed in class B ope a ion o he calcula ed alue. This is shown in Figu e 9 and again, good ag eemen is ound. IV. CONCLUSIONS x: measu ed solid 1im:calcula ed Cu en in mh -8 -4 0 4 Powe inciden in dBm P1GUQ.E 9: DC "T GENERATED IN CIASS 8 OPERATION V. REFERENCES K. Josin, T. Mimu a, Y. Yamashi a, K. Kosemu a and T.,, Sai o, "Noise Pe o mance o Mic owa e HEMT, IEEE MTT-S In . Symp. Dig. June 1983. W. Cu ice, "GaAs MESFET Modeling and Non1 inea CAD," IEEE T-MTT, Feb ua y 1988. F. Diamond and M. La i on, "Measu emen o Ex insic Se ies Elemen s o a !ic owa e FET Unde Ze o Cu en Condi ions, P oc. 12 h Eu opean Mic owa e Con e ence (Finland), Sep embe 1982. C. Raushe and H. A. Willing, "Simula ion o Nonlinea FET Pe o mance Using a Quasi- S a ic Model," IEEE T-MTT, Oc obe 1979. J. C. Hayes, Edi o , "Nume ical App oxima ion o Func ions and Da a," A hlone P ess, 1970. FET modeling can be done wi h li le ha dwa e and common so wa e. The p oposed model does no make any assump ion as o he physical s uc u e o he FET, and he CAD simula ions a e in good ag eemen wi h la ge signal measu emen s. 350