Very wide range tunable CMOS/bipolar current mirrors with voltage clamped input

Oc obe 20, 1998 5:14 pm 1 Ve y Wide Range Tunable CMOS/Bipola Cu en Mi o s wi h Vol age Clamped Inpu Te esa Se ano-Go a edona1, Be nabé Lina es-Ba anco1, and And eas G. And eou2 1 Na ional Mic oelec onics Cen e (CNM), Ed. CICA, A . Reina Me cedes s/n, 41012 Se illa, SPAIN, Phone: 34-5-4239923, Fax: 34-5-4231832, E-mail: [email p o ec ed] 2 Dep . o Elec ical and Compu e Enginee ing, The Johns Hopkins Uni e si y, Bal imo e, Ma yland, USA Abs ac In low powe cu en mode signal p ocessing ci cui s i is many imes equi ed o use cu en mi o s o eplica e and ampli y/a enua e cu en signals, and o clamp he ol age o nodes wi h high pa asi ic capaci ances so ha he smalles cu en s do no in oduce unaccep able delays. The use o unable ac i e-inpu cu en mi o s would mee bo h equi emen s. In con en ional ac i e inpu cu en mi o s s abili y compensa ion is equi ed. Fu he mo e, once s abilized, inpu cu en canno be made a bi a ily small. In his pape we in oduce wo new ac i e-inpu cu en mi o s ha clamp hei inpu node o a gi en ol age. One o hem does no equi e compensa ion, while he o he may equi e unde some ci cums ances, bu o bo h inpu cu en may ake any alue. The mi o s can ope a e wi h hei ansis o s biased in s ong in e sion, weak in e sion o e en as CMOS compa ible la e al bipola de ices. I biased in weak in e sion o as la e al bipola s, he cu en mi o gain can be uned o e a e y wide ange. Acco ding o he expe imen al measu emen s p o ided in his pape , inpu cu en may spawn beyond nine decades, and cu en mi o gain can be uned o e 11 decades. As an applica ion example a sinusoidal gm-C based VCO has been ab ica ed whose oscilla ion equency could be uned o o e 7 decades be ween 74mHz and 1MHz. I. In oduc ion When using cu en mode signal p ocessing VLSI ci cui s i is no unusual ha a e y wide ange o cu en le els ha e o be handled. Fo example, when building low powe silicon e inas, ligh in ensi y is di ec ly and (app oxima ely) linea ly ans o med in o cu en [1]-[2]. Silicon e inas can sense up o six decades o ligh le els, which yields also six decades o cu en le els a he pho o ecep o s ou pu . I is imp ac ical o pe mi ha his cu en would con ol di ec ly he ime cons an o he comple e sys em. This would make a silicon e ina be as o high ambien ligh , bu six o de s o magni ude slowe o low ambien ligh . This is no ealis ic, and a way o speed up hese delays is by clamping he ol ages o hose nodes wi h high pa asi ic capaci ances. Since cu en mi o s a e necessa y elemen s o cu en mode signal p ocessing ci cui s, a e y compac solu ion is o use cu en mi o s ha clamp hei inpu ol ages. These cu en mi o s a e usually e e ed o as ac i e inpu cu en mi o s [3]-[4]. In he nex Sec ion he con en ional ac i e inpu cu en mi o is analyzed and i is shown why i needs compensa ion, why compensa ion depends on he mi o inpu cu en , and why his cu en canno be made a bi a ily small. In Sec ion III wo new sou ce d i en ac i e inpu cu en mi o opologies a e in oduced and s abili y is analyzed. One o he mi o s does no equi e compensa ion and he o he may equi e unde some ci cums ances. Howe e , o bo h s uc u es, inpu cu en can be made a bi a ily small wi hou ende ing uns able beha io . Sec ion IV p o ides some in ui ion Submi ed o IEEE T ansac ions on Ci cui s and Sys ems, Pa I on Ap il 24, 1998. Re ised e sion submi ed on July 31, 1998. Accep ed on Sep embe 4, 1998. Final e sion submi ed on Oc obe 20, 1998. Oc obe 20, 1998 5:14 pm 2 ega ding dynamic beha io o he mi o s. Sec ion V shows how o make he mi o s o ha e a con inuously adjus able gain unable o e a e y la ge ange. Sec ion VI s udies loading e ec s. In Sec ion VII i is shown how o ex end he mi o ing ope a ions o bipola ansis o s using he CMOS compa ible la e al bipola ansis o s, and inally in Sec ion VII expe imen al measu emen s a e p o ided ha show he inpu cu en s spawning beyond six decades and he cu en mi o gains being adjus ed o e 11 decades. As an applica ion example, he i s mi o is used o make a cons an linea inpu ange OTA whose ansconduc ance is unable o o e 7 decades. This OTA is hen used in a sinusoidal VCO whose oscilla ing equency could be uned om o . II. Con en ional Ac i e Inpu Cu en Mi o The con en ional ac i e-inpu cu en mi o [3] is shown in Fig. 1(a). By ed awing i s inpu s age as shown in Fig. 1(b), one ecognizes a s anda d (uncompensa ed) 2-s age CMOS ope a ional ampli ie [5], connec ed in a uni y-gain nega i e eedback con igu a ion. The i s s age o he opamp is he di e en ial inpu ampli ie o Fig. 1(a), and he second (in e ing) s age consis s o ansis o M1 and cu en sou ce . I is well known ha his s uc u e needs compensa ion [5], and ha he compensa ion ci cui y depends on he alue o he second s age bias cu en . Fu he mo e, i esul s imp ac ical o compensa e when has o be a ied o e many decades and eaches e y low alues. Fo he di e en ial inpu ol age ampli ie he OTA in Fig. 2(a) can be used. OTAs a e compensa ed by hei load capaci ance . An OTA connec ed in uni y gain eedback con igu a ion (as in Fig. 2(b)) has he small signal equi alen ci cui shown in Fig. 2(c), whe e elemen models he ansconduc ance gain o he OTA and i s ou pu conduc ance. T ansconduc ance gm-C 74mHz 1MHz Iin 1 2 Cp M1 V CLAMP V CLAMP Iin 1 2 M1M2 CpIo (a) 2 Cp M1 Iin 1 CA V CLAMP gm1 1go1 Cpa goa 2 (s) gm 1 2 gd1 C Cp (c) (b) (d) Fig. 1: Con en ional ac i e inpu cu en mi o , (a) ci cui schema ic ep esen a ion, (b) inpu s age d awn as a 2-s age opamp, (c) small signal equi alen ci cui o mi o inpu s age, (d) compensa ed ci cui . Iin Iin Iin Cpa gms( ) goa Oc obe 20, 1998 5:14 pm 3 is equency dependen because o he delay in oduced by he pa asi ic capaci ances o he OTA in e nal nodes. This delay can be modeled as [6] (1) whe e is he DC ansconduc ance gain o he OTA and models i s delay. This yields he ollowing s abili y condi ion o he ci cui in Fig. 2(c) (2) Using his model o he OTA wi h he s abili y condi ion o eq. (2), i is possible o analyze he s abili y o he ci cui in Fig. 1(b), whose small signal equi alen ci cui is shown in Fig. 1(c). T ansis o is modeled by elemen s , and , while he OTA is modeled by , and he node pa asi ic capaci ance . A e s aigh o wa d analysis i is easy o see ha , i eq. (2) is sa is ied, imposing he condi ion (3) gua an ees s abili y. Bu his equi es, a leas , ha which imposes a lowe bound on he alue o (and ) in Fig. 1(b). In p ac ice, he ci cui is usually compensa ed as shown in Fig. 1(d) [3], by adding a uni y gain ol age bu e and a compensa ion capaci o . Eq. (3) would change o (4) Bu again, canno be made a bi a ily small. in - in + bias V ou Cpa bias I (a) ou Cpa in (b) goa ou gm(s)( in- ou ) pa C (c) Fig. 2: (a) OTA s uc u e sui able o he di e en ial inpu ol age ampli ie .(b) Uni y gain eedback con igu a ion, and (c) small signal equi alen ci cui . gms( ) gms( ) gma 1s ωa ------–     = gma ωa Cpa gma ωa --------- > M1 gm1 go1 Cgd1 gms( ) gma 1s/ωa –( )= goa 1 Cpa Cgd1gm1gma –( ) gm1gma ωa ------------------ > gm1gma > gm1 Iin CA gm1Cgd1CA +( ) gm1gma ωa ------------------ gmaCgd1 +> gm1 Oc obe 20, 1998 5:14 pm 4 The wo new ac i e inpu cu en mi o opologies in oduced in his pape do no ha e his p oblem: (and consequen ly, ) can be made a bi a ily small. In he nex Sec ion hese mi o s a e in oduced and analyzed. III. Two New Ac i e Inpu Cu en Mi o s A. Fi s Topology The i s al e na i e ci cui o he one in Fig. 1(a) is shown in Fig. 3(a), whe e he OTA ou pu d i es he sou ce o ansis o ins ead o i s ga e. The OTA mus be able o sink wice he maximum expec ed alue o , which imposes an impo an design cons ain o he OTA: in Fig. 2(a) mus be, a leas , wice he maximum ope a ion cu en o he mi o 1. The mi o inpu s age can be ed awn as shown in Fig. 3(b), which can be conside ed o be a special wo s age opamp connec ed in uni y gain eedback con igu a ion. No e ha he second s age o his opamp is a posi i e gain ol age ampli ie , as opposed o he case o Fig. 1(b). Neglec ing body e ec o ansis o , he absolu e gain alue o his second s age would be iden ical o ha o Fig. 1(b). Also no e, ha he inpu node o his second s age is he sou ce o ansis o which is a low impedance node. This makes he ci cui o Fig. 1(b) o ha e a single dominan pole, and consequen ly i s beha io is quali a i ely simila o a single s age opamp in uni y gain eedback con igu a ion. To analyze he s abili y condi ions o his ci cui , le us eso o i s small signal equi alen ci cui , shown in Fig. 3(c). I s cha ac e is ics equa ion is 1. E en ually, special OTAs ha ope a e in a ype o class AB mode [7] could be used o op imize powe consump ion. gm1 Iin M1 Iin Ibias M1 M1 V CLAMP Iin 2 M1 1 M2 CpIo (d) gm 1 1 2 (s) m goa gpa Co1 gp C 1 2 (c) V CLAMP Iin 2 M1 1 M2 V G Io Cp (a) Iin 2 Cp M1 1 V G V CLAMP (b) Fig. 3: Fi s new ac i e inpu cu en mi o opology, (a) ci cui schema ic ep esen a ion, (b) inpu s age d awn as a 2-s age opamp, (c) small signal equi alen ci cui . (d) Second cu en mi o opology. Oc obe 20, 1998 5:14 pm 5 (5) Since he OTA is assumed o be compensa ed, eq. (2) is sa is ied, and he las e m o coe icien b in eq. (5) is posi i e. Howe e , b migh s ill become nega i e. The ollowing condi ion gua an ees a posi i e b coe icien (6) This can be achie ed by ei he adding an ex a capaci ance a node o by making he OTA o ha e a smalle delay (la ge ) o lowe . No e ha he igh hand side o eq. (6) is an inc easing unc ion o . Consequen ly, once eq. (6) is sa is ied o he maximum possible (maximum ) s abili y is gua an eed o any smalle alue o (and ). I eq. (6) canno be sa is ied, ano he way o achie e compensa ion o his opology is by adding a compensa ion capaci o be ween nodes and in Fig. 3. This yields he ollowing cha ac e is ics equa ion (7) I eq. (2) is sa is ied, coe icien a is posi i e as well as he second e m o coe icien b. Consequen ly, s abili y is gua an eed i (8) I he igh hand side o eq. (8) is nega i e, is no necessa y and eq. (6) esul s. I he igh hand side o eq. (8) is posi i e, hen should sa is y eq. (8) o he la ges alue o (o ). Once his is assu ed, eq. (8) emains alid o any smalle alue o (o ). B. Second Topology Ano he al e na i e ac i e inpu cu en mi o is he one shown in Fig. 3(d). No e ha in his case ansis o is connec ed as a diode a ound he nega i e eedback loop o he ampli ie , and ac s simply as a passi e de ice. The e o e, i he di e en ial ol age ampli ie is al eady compensa ed o uni y gain eedback, he ci cui should always be s able. This can be e i ied by pe o ming a simila analysis o ha o he i s opology. C. Discussion The s abili y analyses o bo h opologies a e alid whe he ansis o s and a e biased in hei weak o s ong in e sion egions o ope a ion. This allows he cu en mi o s o ope a e o a as2bs c+ + 0= a CpCpa = b goa gm1 +( ) Cp gm1gma ωa ------------------– go1Cpa gma ωa ---------–       += c gm1gma =        Cp gmagm1 ωagoa gm1 +( ) ------------------------------------- > 2 ωa gma gm1 gm1 Iin gm1 Iin CA 1 2 as2bs c+ + 0= a CpCpa CACpCpa gma ωa ---------–+       += b Cpgoa gm1 +( ) go1Cpa gma ωa ---------–       gma CA gm1 ωa ---------–       + += c gm1gma =        CAgm11 ωa ------ Cp gma ---------–       Cp goa gma --------- –> CA CA gm1 Iin gm1 Iin M1 M1 M2 Oc obe 20, 1998 5:14 pm 6 e y wide ange o cu en s: om alues equal o junc ion leakage cu en s up o he maximum cu en he OTA migh be able o sink. Also, ca e needs o be aken o a oid ha he OTA ou pu ol age eaches i s minimum (o maximum, o p- ype cu en mi o s) alue by adjus ing o a sa e enough le el. The s abili y ad an ages o hese wo new opologies wi h espec o he con en ional one o Sec ion II, come om he ac ha he di e en ial ol age ampli ie is loaded by a low impedance node, which makes he whole ci cui o beha e simila o a single pole (o one-dominan pole) sys em. Al hough he Topology 1 cu en mi o migh equi e s abili y compensa ion, i has ce ain ad an ages o e he Topology 2 one, as will be seen h oughou he pape : i is as e o e y low cu en s and i can be ope a ed in bipola mode by simply ebiasing cons an global ol ages. IV. T ansien Response A. Fi s Topology The ci cums ances unde which he cu en mi o will be slowes is when inpu cu en is smalles (in he o ange). In hese cases ansis o is ope a ing in weak in e sion and i is sa e o conside he OTA ac ing as an ins an aneous de ice ha does no in oduce any delay. I his is he case, he la ge signal ansien esponse o he ci cui in Fig. 3(b) can be compu ed by modeling he mi o inpu s age as shown in Fig. 4(a) bu wi h . I and model he OTA and is he cu en h ough ansis o , s aigh o wa d analysis yields he ollowing s a e equa ion (9) whe e is he OTA ol age gain. I changes in a s ep ashion om o , he solu ion o eq. (9) can be w i en as (10) whe e, (11) I we de ine as he delay ime i akes o o each , hen (12) No e ha i is su icien ly la ge can be easonably small, e en o low alues o . As inc eases he ci cui will espond as e and he delay in oduced by he OTA will s a o be app eciable. In his case, he ci cui shown in Fig. 4(a) wi h can be used o analyze i s ansien esponse. The esul ing s a e equa ion does no ha e an analy ical solu ion, hus in o de o ob ain an es ima ion o he delay in he cu en mi o one can eso o i s small signal equi alen ci cui , and conside makes a “li le” s ep. Neglec ing he OTA in e nal delay1 (cha ac e ized by VCLAMP nA pA M1 Cpa 0= gma goa IM1IS1VG1 1 –( ) /nUT { }exp= M1 Iin IM1 Cp goaA --------------I ˙M1Cp nUT A ----------I ˙M1 IM1 -------- + += A gma/goa = Iin Ic Ic IM1 ( ) IcIM1 ( )–[ ] 1ε+ ------------------------------------------- Ic Ic Ic –[ ] 1ε+ ---------------------------------e /τ1 = τ1 CpnUT A Ic ----------------- ,εIc goanUT ------------------= = d1 IM1 ( ) RIc d1τ1R --- 1 – 1R– ------------    1ε+ ln= A τ1 Ic Ic Cpa 0≠ Iin Oc obe 20, 1998 5:14 pm 7 ) he ollowing cha ac e is ics equa ion ( alid o weak and s ong in e sion) esul s o he ci cui d awn in Fig. 3(c), (13) The oo s o his equa ion a e gi en by (14) I wo complex poles esul and he ansien has an associa ed ime cons an o he o de o . I he poles a e eal, he dominan ime cons an may ange om ( o high alues o ) o ( o small alues o ). No e ha o e y small alues o ( and ) i ollows ha and , and he esul ing ime cons an is , as de i ed p e iously using he la ge signal i s o de model. On he o he hand, o e y la ge (and ) alues is also small and a dominan i s o de dynamics esul s wi h ime cons an . Consequen ly, o bo h e y small and e y la ge he e a e no complex poles and he dynamics is domina ed by a single eal pole. The maximum alue o is eached o (assuming ), and is . The e o e, i can be sa is ied, no complex poles (and no inging) will appea o he whole inpu cu en ange. I a compensa ion capaci o is used, he esul ing equa ion would be 1. The e ec o migh be included, al hough he main delay in oduced by he OTA is gi en by loaded by and o he loads. ωa gma Cpa oa gpa C 1 V G1 Iin 2 Cp M1 2CLAMP -V ma g( ) (a) oa g 1 pa C gs C1 M1 Iin 2 Cp 2CLAMP -V ma g( ) (b) Fig. 4: Equi alen ci cui s o compu ing ansien analysis i OTA delay canno be neglec ed, o (a) i s new opology and o (b) second new opology. ωa s2s τ3 ----- 1 τ1τa ----------+ + 0= 1 τ3 ----- goa gm1 + Cpa ----------------------- go1 Cp --------+= 1 τ1 ----- gm1A Cp --------------- = 1 τa ----- goa Cpa --------- =          so1 2τ3 --------– 1 1 4 τ3 2 τ1τa ---------- –±= τ3 2/τ1τa1/4> 2τ3 2τ3 τ3 2/τ1τa τ1τa/τ3 τ3 2/τ1τa Iin gm10≈ go10≈ τ3 2/τ1τa1« τaτ3 ≈ τ1 Iin gm1 τ3 2/τ1τa τ1τa/τ3Cp/gma ≈ Iin Iin τ3 2/τ1τa gm1goa = gm1/Cpa go1/Cp » A Cpa/4Cp A Cp/Cpa < CA Oc obe 20, 1998 5:14 pm 8 (15) whe e and wi h a, b and c gi en by eq. (7). Again, he associa ed dominan ime cons an would ake a alue be ween and . Fo e y small and e y la ge he e is a dominan eal pole o ime cons an ha p oduces a i s o de dynamics. Fo e y small i esul s , while o e y la ge i is . The maximum alue is eached o , o which wo eal poles esul bo h o simila ime cons an s a ound . B. Second Topology Fo he cu en mi o o Fig. 3(d) simila analyses can be done. Fo e y small inpu cu en s, such ha he OTA can be conside ed o espond ins an aneously, he ollowing s a e equa ion esul s (assuming and ) (16) Consequen ly, eqs. (10)-(12) would also be alid o his mi o as long as is subs i u ed by . I he OTA migh no longe be conside ed o espond ins an aneously, o i is no negligible wi h espec o , an es ima ion o he delays can be ob ained om he small signal equi alen ci cui o Fig. 3(d) wi h . Rou ine analysis yields he ollowing cha ac e is ics equa ion ( alid o weak and s ong in e sion) (17) Consequen ly, he se ling o he mi o has a dominan ime cons an ha can ange be ween alues o he o de o and . Fo e y small and e y la ge alues (and assuming ) i ollows ha and a dominan i s o de dynamics esul s wi h e ec i e ime cons an . Fo e y small his ime cons an is , while o e y la ge i is . The maximum alue o is eached o . The e o e, i can be sa is ied no complex poles will appea . C. Simula ions Ex ensi e Hspice ansien esponse simula ions ha e been pe o med on bo h opology cu en mi o s o con i m he p e ious analyses. Sizes o ansis o s and we e se o and he in e nal bias cu en o he OTA was . An inpu node capaci ance o was conside ed and inpu cu en was changed in a s ep ashion om o . The alue s2s τ3' ------ 1 τa' ------    2 + + 0= τ3'a/b= τa'( ) 2a/c= 2τ3' τ'a 2/τ3' Iin τ'a 2/τ3' Iin τ'a 2/τ3'τ1CA/gm1 +≈ Iin τ'a 2/τ3'Cp/gma ≈ 2τ3'/τa ( ) 2 gm1goa gmaCA/Cp +≈ 1/τ3' 2 goa/CAgma/Cp +( )= Cpa 0≈ Cgs10≈ Iin IM1 Cp goa A 1+( ) ------------------------------I ˙M1 CpnUT A 1+ -----------------I ˙M1 IM1 -------- + += A A 1+ Cgs1 Cp ωa0= s2s τ4 ----- 1 τ5 2 -----+ + 0= 1 τ4 ----- Cgs1Cp + Ce 2 -----------------------goa Cpa Cp + Ce 2 ---------------------gm1 Cgs1 Ce 2 -----------gma + += 1 τ5 2 ----- gmagm1 Ce 2 ------------------ = Ce 2CpCgs1CpCpa Cgs1Cpa + +=          2τ4 τ5 2/τ4 Iin CpCpa Cgs1 ,» 2τ4/τ5 ( ) 21« τ5 2/τ4 Iin τ1Cgs1/gm1 + Iin Cp/gma 2τ4/τ5 ( ) 2Cgs1Cpa +( ) /Cgs1Cp/A +( )= gm1goa gmaCgs1/Cp += A Cpa Cp < M1 M2 150µm5µm× 20µA Cp1pF= Ic 2Ic Oc obe 20, 1998 5:14 pm 9 o was swep loga i hmically om o . The ou pu o he cu en mi o was connec ed o a ol age sou ce equal o . The cu en h ough his ol age sou ce was ime-no malized o , whe e is he ime a which has eached 63.2% o i s o al excu sion alue (assuming a i s -o de -like esponse). Fig. 5(a) shows he simula ed ou pu wa e o ms, whe e he ampli ude has also been no malized wi h espec o , (18) In Fig. 5(b), o he ace wi h ci cles, he co esponding alues o as a unc ion o a e ep esen ed o Topology 1 wi h . As discussed p e iously in Sec ion IV.A, o e y small cu en s he ime cons an is in e sely p opo ional o cu en le el (see eq. (11)), while o la ge cu en s he ime cons an ends o se le o a cons an alue (see discussion a e eq. (14)). Fo be ween and he mi o ou pu cu en s ep esponse showed inging (p esence o complex conjuga e poles), while ou side his ange no inging is obse ed (absence o complex conjuga e poles). This was also p edic ed by he heo e ical discussion a e eq. (14). E en ually, inging could be educed o supp essed by imp o ing he ci cui phase ma gin by adding he compensa ion capaci ance men ioned in Sec ion III.A. Howe e , may inc ease he delays o he comple e ange o inpu cu en s. The same simula ions we e epea ed o he second opology. The esul ing alues o as a unc ion o a e ep esen ed in Fig. 5(b) using he ace wi h as e isks. Again o e y small cu en s he ime cons an is in e sely p opo ional o cu en and ends o se le o la ge cu en s (as p edic ed in Sec ion IV.B). P esence o complex conjuga e poles was obse ed o be ween and , as an icipa ed by he discussion a e eq. (17). No e ha o he lowe cu en s ange he esul ing alues o a e abou wice han hose o Topology 1. This is because o Topology 2 he inpu node capaci ance includes now also he sub h eshold ga e- o-bulk capaci ance o ansis o . Fo ga e oxide hickness and ga e a ea his capaci ance is [8]. The e o e, in his example, he e ec i e Fig. 5: T ansien Analyses Simula ion Resul s. (a) Time and Ampli ude No malized T ansien Responses o Topology 1 Cu en Mi o wi h Uni y Gain, (b) Ex ac ed alues o τn o bo h Topologies wi h Uni y Gain and Sweeping he Gain. (a) (b) 10−11 10−10 10−9 10−8 10−7 10−6 10−5 10−8 10−7 10−6 10−5 10−4 Iou τ n opology 1, gain=1 opology 2, gain=1 opology 1, Iin=10 nA opology 2, Iin=10 nA Ic 10pA 10µA VCLAMP 2.5V= Io ( ) Io /τn ( ) τn Io Ic Io /τn ( ) Ic – Ic ------------------------------- τn Ic CA0= Ic 2nA 100nA CA CA τn Ic Ic 10nA 100nA τn Cp Cgb M1 ox 10nm= A150 5µm2 ×= Cgb 0.4Aεox/ ox 1.05pF= = Cp Oc obe 20, 1998 5:14 pm 16 Fo he ab ica ed p o o ype VCO he capaci o alue is . When using con en ional CMOS OTAs o sinusoidal VCOs, hei equency uning ange is limi ed o li le mo e han one decade [6]. The eason is ha o uning he VCO equency, OTA ansconduc ances ha e o be changed. I he OTA ansconduc ance is adjus ed h ough i s di e en ial pai bias cu en hen he linea ange o he OTA is educed as i s ansconduc ance (and ) is lowe ed. I a linea ange abo e is desi ed, ansconduc ance uning is limi ed o li le mo e han one decade. The ansconduc ance o he OTA in Fig. 9 can be uned while main aining i s cu en (and linea ange) cons an . The wo op Topology-1 PMOS cu en mi o s a e uned simul aneously h ough con ol ol age and a e able o change he OTA ansconduc ance o o e 7 decades. Fig. 10(b) shows he expe imen ally ob ained ela ionship be ween oscilla ion equency and con ol ol age o he sinusoidal VCO. The minimum equency ha could be measu ed was , while he maximum was . Fig. 11 shows he measu ed sinusoidal wa e o ms o hese wo limi si ua ions. To show he e ec o OTA linea inpu ange deg ada ion, le us eso o Fig. 12. Classically, he OTA ansconduc ance is uned by changing i s di e en ial pai ail bias cu en . Fig. 12(a) shows he measu ed cu es o he OTA o Fig. 9 ( ) when using cu en o uning and lea ing cons an . Fig. 12(b) shows he cu es , which a e he i s de i a i es o hose in Fig. 12(a) no malized wi h espec o (de ined as he slopes a o Fig. 12(a)). The wides bell-shape cu e co esponds o he maximum and maximum . As is dec eased he bells become na owe (less inpu ange) un il he di e en ial pai ansis o s a e ully biased in weak in e sion and he linea inpu ange emains cons an (be ween one o wo ). In Fig. 12(a) and Fig. 12(b) he la ges measu ed ansconduc ance is , while he minimum is . I ins ead o using o une we use hen he cu es shown in Fig. 12(c) and Fig. 12(d) a e measu ed. Fig. 12(c) shows and Fig. 12(d) shows . In Fig. 12(c) and Fig. 12(d) he la ges measu ed ansconduc ance is , while he minimum is . No e ha now he OTA inpu ange is main ained cons an . As a esul , he OTA beha es almos linea ly om o which means ha low dis o ion sinusoids o peak- o-peak ampli ude can be ob ained wi h he VCO o Fig. 10 o he whole equency ange, as can be seen in Fig. 11. Fig. 11: Measu ed VCO ou pu s o minimum (73.94mHz) and maximum (1.015MHz) equencies. Ve ical scale is 50mV/di and ho izon al scales a e 2s/di o le ace and 200ns/di o igh ace. C10pF= gm-C Iss Iss 200mV Iss VG2 VG2 min 73.96mHz= max 1.015MHz= gm ISS Iou Vin ( ) /ISS Vin V+V- –= ISS VG2 I'ou Vin ( ) /gm gm Vin 0= ISS gm ISS nUT gm30.0µA/V= gm60.4pA/V= ISS gm VG2 Iou Vin ( ) /Iou max I'ou Vin ( ) /gm gm30.0µA/V= gm40.0pA/V= 100mV– 100mV+ 200mV Oc obe 20, 1998 5:14 pm 17 IX. Conclusions Two new ac i e-inpu cu en mi o s uc u es a e in oduced. The no el y esides in ha he ac i e ampli ie d i es ansis o sou ces ins ead o ga es. This allows he ampli ie o be connec ed in a nega i e eedback loop con igu a ion, ins ead o posi i e. The i s p oposed opology migh equi e compensa ion, while he second does no need i . Bo h opologies beha e much be e om a s abili y poin o iew han he con en ional ac i e inpu cu en mi o . This is because he ampli ie ou pu is connec ed o a low impedance node. The consequence is ha he mi o s emain s able o a bi a ily small ope a ion cu en s, hus allowing cu en anges o many decades. Expe imen al measu emen s e eal ha he cu en s in ol ed can a y o e 9 decades, and ha he gain o hese cu en mi o s can be con inuously uned o e 11 decades while main aining 1% linea i y e o in he mi o ing ope a ion. The mi o s can be used ei he wi h hei ansis o s biased as MOS o as CMOS compa ible la e al bipola de ices. Expe imen al esul s ha e been p o ided. As an applica ion example a sinusoidal VCO has been ab ica ed and es ed. I s equency could be con inuously uned o o e 7 decades h ough a single con ol ol age. To ou knowledge his has ne e been achie ed be o e o CMOS sinusoidal VCOs. −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vin (Vol s) gm (No malized) −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Vin (Vol s) Iou (No malized) −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Vin (Vol s) Iou (No malized) −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vin (Vol s) gm (No malized) (a) (b) (c) (d) Fig. 12: Expe imen ally measu ed dependence o OTA linea inpu ange on ansconduc ance uning. Fo di e en ial pai ail bias cu en (ISS) uning, linea ange dec eases as ansconduc ance dec eases: (a) no malized OTA ou pu cu en (Iou /ISS) as a unc ion o di e en ial inpu ol age, (b) no malized i s de i a i e o p e ious cu e. Fo uning h ough he op Topology-1 cu en mi o s: (c) no malized OTA ou pu cu en , (d) no malized i s de i a i e o p e ious cu e. gm-C Oc obe 20, 1998 5:14 pm 18 X. Acknowledgemen s This wo k was pa ially suppo ed by an ONR Mul idisciplina y Uni e si y Resea ch Ini ia i e (MURI) o Au oma ed Vision and Sensing Sys ems N00014-95-1-0409. XI. Re e ences [1] Ca e Mead, Analog VLSI and Neu al Sys ems, Addison-Wesley, 1989. [2] A. G. And eou, R. C. Mei zle , K. S ohbehn, and K. A. Boahen, “Analog VLSI Neu omo phic Image Acquisi ion and P e-p ocessing Sys ems,” Neu al Ne wo ks, ol. 8, No. 7/8, pp. 1323- 1347, 1995. [3] D. G. Nai n and A. T. Salama, “A Ra io-Independen Algo i hmic Analog- o-Digi al Con e e Combining Cu en Mode and Dynamic Techniques,” IEEE T ans. Ci c. & Sys ., ol. 37, No. 3, pp. 319-325, Ma ch 1990. [4] T. Se ano and B. Lina es-Ba anco, “The Ac i e-Inpu Regula ed-Cascode Cu en Mi o ,” IEEE T ans. Ci c. & Sys . Pa I, ol. 41, No. 6, pp. 464-467, June 1994. [5] P. E. Allen and D. 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