Nonlinear time-domain macromodeling of OTA circuits

NONLINEAR TIME-DOMAIN MACROMODELING OF OTA CIKCUITS B. Pe ez-Ve du , J. C uz 7, B. Lina es-Ba anco S, A. Rod iguez-Vazquez , J.L. Hue as and E. Sanchez-Sinencio $ D o. Elec 6nica y Elec omagne ismo, Uni e sidad de Se illa. 41012-Se illa. SPAIN #Texas A&M Uni em y, Dep . o Elec ical Enginee ing, College S a ion, TX 77843, USA ABSTRACT ape we p esen an accu a e nonlinea mac omode: o he OTA which is sui able o he ansien simula ion o OTA-based CMOS analog in eg a ed ci cui s. As compa ed o de ice-le el OTA models, he p oposed mac omodel is ad an a eous in e ms o CPU ime. Besides, in ci cui s wi % many OTAs, i does no ha e he p oblems o con e gence ha he de ice-le el has. All he mac omodel pa ame e s can be calcula ed om measu emen s made a he OTA e minals. Expe imen al esul s om a 3pm CMOS OTA p o o ype as well as simula ion esul s om de ice-le el models a e included and compa ed o simula ion esul s om he mac omodel. In his INTRODUCTION Fo many yea s he con en ional ol age Val Ampli ie (opamp) has been he wo kho se o analog ci cui design. Recen ly, he 0 e a ional T ansconduc ance Ampli ie (0TA)jas been aemons a ed o be posn ially ad an ageous o he syn hesis o high- equency analog building blocks [l- 41. One eason o his is ha ansconduc ance am li ie s do no ha e any high in e nal impedance no e, hence no equi ing in e nal compensa ion capaci o s and he eby yielding la ge bandwid hs ha he opamp. Ano he appealing ea u e o he OTA is ha i s ansconduc ance gain can be ex e nally con olled, he eby allowing p og ammable applica ions. These p e ious ea u es ha e mo i a ed an in e es in he applica ion o he OTA o he syn hesis o con inuous- ime analog ci cui s, ei he o linea [5,61 o o nonlinea [7,81 a plica ions. These e o s un pa allel o he p oposal o new CMOS OTA implemen a ions ha a e capable o linea ope a ion in la ge inpu ol age anges [1,3,4,9]. The ul ima e goal is he implemen a ion o high- e uency con inuous- ime analog ci cui s in ully monoli%ic o m. The design o in eg a ed ci cui s ely on he e icien use o an app op ia e se o CAD ools. In pa icula , elec ical simula ion ools (like SPICE21 a e essen ial o he design o analog in eg a ed ci cui s. Al hough elec ical simula ion can be done using de ice-le el models, eso ing o mac omodels is a common s a egy o educe he CPU- ime e ui ed in simula ing complex analog sys ems. Se e al opamp mac omodels ha e been epo ed in he pas (see e e ences in [lo]). Howe e , li le ha e been s ill done abou OTA mac omodeling, he ew con ibu inns 1441 ISCAS '89 exis ing [11,121 no being speci ically ocused on he inclusion o he mac omodel in a elec ical simula ion ool. I es ic s ou abili y o p ope ly analyze complex OTA-based analog in eg a ed ci cui s. In his pape we o e come his d awback by p esen ing an OTA mac omodel which is sui able o he ime-domain simula ion o OTA-based CMOS analog ci cui s. OTA MACROMODEL OTA speci ica ions and pa ame e s Figu e 1 shows a gene ic CMOS OTA a chi ec u e consis ing o an inpu ansconduc ance s age ollowed by cu en mi o s 121. The inpu s age pe o ms he co e ope a ion o di e en ial- ol age o cu en con e sion while he cu en mi o s a e used o s ee he ou pu cu en s o he di e en ial ampli ie o a high impedance ou pu node. Se e al ypes o cu en mi o s [131 and ansconduc ance s a es [1,3,4,91 can be used in Fig.1, he eby esul ing in a oad ca alog o p ac ical OTA implemen a ions. I ESPEJOS P I Figu e 1: Gene ic CMOS OTA block diag am The ideal model o Fig.1 is a linea di e en ial- ol age-con olled cu en -sou ce, he only pa ame e equi ed o desc ibe his ideal model being he DC ansconduc ance gain o he OTA, g,. The beha io o p ac ical OTAs de ia e om wha is expec ed using he ideal model in di e en ways. In he ollowing he e is a lis o he pa ame e s and speci ica ions o be conside ed in he p oposed mac omodel. DC small-signal OTA ansconduc ance gain e Inpu ca aci ance V,, Inpu eg ed o se ol age CH2692-2/89/0000-1441 $1.00 0 1989 IEEE u iic im na i n can ~e m aineu mo n u -. w. henne n JenKins. -~ (217) 333-4789 Linea egion (less han 1% de ia ion) o he ol age o cu en con e sion Nonsa u a ed egion o he ol age o cu en con e sion Maximum ou pu cu en Minimum ou pu cu en High- equency pole Maximum ou pu ol age Minimum ou pu ol age Delay o he op ol age-sa u a ion s a e Delay o he bo om ol age-sa u a ion s a e Minimum ou pu cu en in he op ol age- sa u a ion s a e Maximum ou pu cu en in he bo om ol age-sa u a ion s a e Ou pu Resis ance Ou pu Capaci ance Each pa ame e abo e is di ec ly ela ed o he co esponding OTA speci ica ion and can be calcula ed om ex e nal measu emen s a he OTA e minals. Mac omodel a chi ec u e Figu e 2 shows he block diag am o he p oposed mac omodel consis ing o ou s ages. The di e en s ages a e connec ed by ol age-con olled sou ces. ,A~ A s age ln e media s age Figu e 2: Mac omodel a chi ec u e All he nonlinea i ies in he mac omodel a e implemen ed using analog swi ches, as i is done in [ 101 o he opamp. The con ol s age in Fig.2 gene a es he h eshold signals equi ed o con olling he analog swi ches. The inpu s age includes he inpu impedance, o se ol age and CMRR. I s implemen a ion is simila o he co esponding s age in [lo]. Figu e 3a shows he implemen a ion o he in e media e s age. The condi ions o each analog swi ch o be a he posi ion 0 a e gi en in he i s ow o Table 1; he co espondin condi ions o he posi ion 0 a e included in he seconi ow. The in e media e s age is d i en by he ou pu ol age o he inpu s age,V,, and de elops an ou pu ol age Vb. Analysis gi es he ollowing dynamic equa ion o desc ibe he inpu -ou pu ope a ion o Fig.3a: dVb 'b c - +- =I(V ) I d H, whe e I(VJ is he nonlinea unc ion depic ed in Fig.3b. When pa icula ized o small-signal, his equa ion accoun s o he DC ansconduc ance gain (pa ame e gml in he lis abo e) also p o iding a sin le ole app oach [2] o he hi h equenc beha io o &e 'BTA (pa ame e o1 =I/R, !,i The nonsnea i ies in he OTA ol age o cu en con e sion a e modeled by he ans e cha ac e is ics o Fig.3b ( ia he pa ame e s IH+, 18-, 8, -, Sl+,82-, &+). I(",) 3a 3b Figu e 3: a)In e media e s age, b)DC OTA ans e cha ac e is ic Table 1: Swi ching condi ions o Pig.3a (Zb= VdR,) The ou u s age is shown in Fig.4. The swi ching condi ions & he analog swi ches used in his s age a e gi en in Table 2. As o Table 1, he i s ow co esponds o he posi ion 0. Besides, he swi ches LS and LIZ exhibi a con olable delay in he 0 o 0 ansi ion. +- Figu e 4: Ou pu s age The ou pu s age is d i en by he ou pu ol age o he in e media e s age, b, and models he ou pu impedance and he ou pu ol age sa u a ion 1442 cha ac e is ics, including he limi a ions on he a ailable cu en when he ou pu ol age is a sa u a ion, and he ime delays appea ing when he OTA is d i en ou o he ol age sa u a ion s a es (pa ame e s Is-, Is+,TD- and TD+). V,>Eg+ V.,>Es+ Vu<&- V,,<Is- lb<Io ls-<Io 1b>I0 Is+>Io Table 2 Swi ching condi ions o Fig.4 (I*& VdRI) Mos o he elemen alues o he mac omodel can be di ec ly calcula ed om measu emen s. RP is included o a oid he cu en sou ces om being in open ci cui a any ime and mus be selec ed la ge enough. MACROMODEL PERFORMANCE Figu e 5 is a mic opho og a h o a CMOS 3pm double me al p o o ype o he &'A a chi ec u e o Fig.1, whe e we ha e used enhanced Wilson cu en mi o s [ 131 and he ex ended- ange di e en ial ampli ie o Fig.6 [l]. Figu e 5 CMOS 3pm O A p o o ype 1 1 Figu e 6: Linea ized di e en ial pai I1 I Di e en measu emen s ha e been made on he es ci cui o Fig.'la, whe e he o o ype o Fig.5 is connec ed o se e al ancilla y ogchip com Figu es 8a,c show wo osciloscope dispczE m he es ci cui s o Fig.7a. Figu es 8b,d show he co esponding wa e o ms ob ained by simula ion using DIANA [14] and he OTA mac omodel. Figu es 8a.b a e o C,, = 33pF, GI. = 1lR~ = 0, he signal d i ing he es ci cui being a 5Khz sinusoidal wa e o m.On he 1443 o he hand, Figs.8c,d a e o CL = 200pF, RL = 212KQ and a squa e inpu signal. 7a 7b Figu e 7: Tes s ci cui s Ru = 50KQ) 8a n E a - !4 s- 0 5 E 4 P - 0 5 In .. 1....1....1....1 8d ' ' 7~10-~ 8~10'~ 9~10'~ lo5 Figu e 8: Expe imen al e sus simula ed wa es ~ ~__~ ~ u iic im na i n can ~e m aineu mo n u -. w. henne n JenKins. -~ (217) 333-4789 P e ious igu es shows a e y close ag eemen be ween expe imen al and simula ion esul s. The o e shoo s in he expe imen al wa e o ms a e due o he eac i e beha io o he expe imen al se up. The pe o mance o he new mac omodel has been also compa ed o ha o de ice-le el models. B he way o example, Fig.9a shows se e al wa e& ms ob ained when simula ing he es ci cui o Fig.7b by using SPICE2 and de ice-le el models. The co esponding esul s when using ou mac omodel in DIANA a e shown in Fig.9b. The OTAs o his example used a con en ional noncompensa ed di e en ial ampli ie and enhanced Wilson cu en mi o s. As i can be seen, he ag eemen be ween he mac omodel and he de ice-le el model is e y good. Howe e , he o me is much mo e e icien in e ms o CPU- ime han he la e . Conce ning his poin , ou expe ience o his and many o he examples and simula ion uns gi es a a io n=TdT which anges be ween 4 and 30, whe e TD is he CPU- ime o he de ice-le el model and T, is he co esponding ime o he mac omodel. n 9b Figu e 9 Simula ion esul s o Pig.7b a) De ice-le el model, b) Mac omodel ol ages:O.l ol sld ; cu en s 10pA/d 1)lSCUSSION OF HESULTS A mac omodel o he OTA has been p esen ed whose ea u es can be summa ized in he ollowing poin s: 1) I is a la ge signal nonlinea mac omodel. 2) I models he inpu -ou pu beha io o he OTA, hus being adequa e o di e en OTA implemen a ions ( o ins ance, wo di e en OTAs a e conside ed in he sec ion on mac omodel pe o mance). 3) All he nonlinea i ies in he new mac omodel a e simula ed using h eshold unc ions [lo]. 4) The mac omodel pa ame e s can be calcula ed om measu emen s made a he OTA e minals. 5) I yields easonably accu a e simula ions, p o iding impo an ad an ages in e ms o CPU- ime sa ing. 6) Besides he educed CPU- ime, he mac omodel in ci cui s wi h many OTAs does no ha e he se ious p oblem o con e gence (in SPICES) ha he de ice-le el model has. 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