An Overview of Feed-forward Design Techniques for High-Gain Wideband Operational

Transcription

1 An Overview of Feed-forward Dein Technique for Hih-Gain Wideband Operational Tranconductance Amplifier Bharath Kumar Thandri and Joe Silva-Martinez Department of Electrical Enineerin Analo and Mixed Sinal enter Texa A&M Univerity ollee Station, TX ABSTRAT: In thi paper, feed-forward technique are revied and ued for the dein of hih-frequency Operational Tranconductance Amplifier (OTA). For the ame power conumption and imilar tranitor dimenion the two-path and three-path folded-cacode OTA preent both maller ettlin error and fater repone a compared with the typical folded-cacode topoloy. Alo, a No-apacitor FeedForward (NFF) compenation, which ue a hih-frequency pole-zero doublet to obtain hih ain, hih GBW and a ood phae marin, i dicued. The ettlin-time of the NFF topoloy can be fater than that of hiher miller baed OTA, even if the lat topoloy ue larer tranconductance value. Experimental reult for the multi-trajectory OTA fabricated in the AMI 0.5 µm MOS proce demontrate the feaibility of the feed-forward cheme. Key word: Operational Tranconductance Amplifier, Broadband amplifier, Feedforward technique, hae ompenation technique, Multipath amplifier, Folded-acode Amplifier. I. Introduction The increain need for fater and more accurate I poe challenin dein pecification for amplifier which are the baic buildin block for many application uch a precie analo filter, A/D and D/A converter. IF witched-capacitor filter and hih-reolution data converter with amplin frequencie above 00 MHz are demandin very fat OTA with ettlin time below 3-4 nec [-24]. It i very difficult to dein an amplifier with both hih ain and hih bandwidth. Hih ain amplifier ue cacode tructure or multi-tae dein with lon channel lenth tranitor biaed at low current level. Hih bandwidth amplifier ue inle-tae dein with hort channel lenth tranitor biaed at hih current level. Since the folded-cacode OTA preent a inle paraitic pole and relatively lare D ain, it i commonly ued for hih-frequency application [5, 7-8]. For uch application, the typical folded-cacode tructure preent ome limitation becaue -type cacode tranitor determine the paraitic pole if N-driver are ued; the phae marin of the reultin tructure i limited. Reulated telecopic tructure are becomin more popular due to the power avin, at the expene of limited inal win [3-5]. In order to extend the folded cacode frequency bandwidth, everal phae compenation cheme have been reported in the literature [8-2]; thee technique are - -

2 briefly decribed in the next ection. It i hown that multi-path folded-cacode OTA i fater and more accurate than the conventional folded-cacode OTA due to the action of the feed-forward path. acadin of individual ain tae ive a hih ain amplifier, but each tae introduce a low frequency pole, which produce a neative phae hift and derade the phae marin. Many phae compenation cheme for multi-tae amplifier have been reported in literature [6, 7, 9-24]. All the reported cheme are a variation of the baic Miller compenation cheme for a two-tae amplifier. The dominant pole i puhed to lower frequencie due to Miller effect, reultin in lower bandwidth tructure. Alo, a RH zero i created; hence a nullin reitor i uually ued to cancel it effect. Other reported compenation cheme ue the poitive phae hift of a LH zero created by a feedforward path to improve amplifier phae repone [22-23]. The feed-forward compenation cheme employ a feedforward path to create LH zero, but doe not ue any miller capacitor. The dominant pole i not puhed to lower frequencie and reult in a hiher ain-bandwidth product with a fat tep repone. The theoretical apect of feedforward technique are dicued in ection II. Section III deal with folded-cacode OTA with feed-forward path. Hih ain two-tae amplifier without miller compenation are conidered in ection IV; it i hown that the NFF technique i robut even if the interatin and load capacitor are varied in a very lare fahion. Section V decribe the circuit imulation and experimental reult; the concluion are drawn in the lat ection. II. Settlin-time in preence of a pole-zero pair In thi ection, the peed of a witched-capacitor amplifier in preence of a pole-zero pair i conidered. A macromodel of the typical circuit capacitive amplifier ued in witched-capacitor circuit i hown in fiure a. By uin conventional circuit analyi technique it can be found it mall inal tranfer function a 2 m r 0 Open-loop ain v in v x v o 3 m v x 0 4 / 2 loed-loop ain /r 0 L eff Fiure. Typical OTA baed capacitor amplifier: a) chematic and b) typical open and cloed loop manitude repone. v v 0 i ( ) m ( ) ( β ( )) 4 β 2 m 3 2 βa V () - 2 -

3 where A v = m / 0 and β= 2 /( 2 3 ) are the amplifier open-loop D ain and the feedback factor, repectively. A typical open and cloed loop manitude repone i depicted in fiure b. The ideal cloed-loop amplifier ain i iven by - / 2 ; it can be noticed in eqn. that when the teady tate i reached, the error in the final value i determined by the factor /(βa V ). The cloed-loop bandwidth i determined by the riht-hand ide zero and paraitic pole. The location of the pole i β β β = m m m eff = = 2 ( 3 ) 4 β ( 3 ) (2) L where L (= 4 β( 3 )) i the effective loadin capacitor. It i important to reduce the paraitic capacitor 3 to increae β, epecially for hih frequency application. The typical tep repone of the underdamped capacitive amplifier i hown in fiure 2. It conit of two phae, initial lew phae (aumed to be linear) and a non-linear ettlin to a final value. -v o V in GBW limitation D-ain limitation Slew rate Fiure 2. Step repone of a unity ain amplifier with enouh phae marin. Sinle-tae OTA lew-rate i determined by the amount of current that can be delivered or extracted from the output and the effective load capacitor (SR = I/ L ); uually cla AB amplifier increae SR [2]. The non-linear phae i determined by both the effective pole frequency eff and phae marin, and in many practical lowvoltae cae dominate the overall ettlin time. If the lew-rate phae and the RH zero are inored, the cloedloop pule repone of the amplifier i iven by the followin equation v o (t) = v o (t 0 e ) βa eff v t αv i (t) (3) - 3 -

4 - 4 - where α= / 2 i the ideal amplifier ain. A hih performance amplifier hould have hih eff for fat ettlin and hih D ain A V for accurate final value. The analyi of the amplifier impule repone in the preence of a pole-zero doublet i more complex; in [25-27] it wa hown that the preence of low-frequency pole-zero pair may enerate low component that reduce inificantly the amplifier' peed; thi i not the cae if hihfrequency pole-zero doublet are preent. In order to conider the effect of hih-frequency pole-zero pair let u aume that the overall open-loop tranconductance of the amplifier i characterized a m Z m () G = (4) If the riht-hand ide zero m / 2 i inored, uin equation and 4, the cloed-loop tranfer function i obtained a ( ) ( ) V 2 2 eff m 0 eff Z Z i 0 A v v β β (5) where eff (=β m L ) i defined by equation 2. It can be eaily found that the cloed-loop pole are real if the followin condition i atified 0.5 / L 0 Z eff eff < (6) Due to the preence of the zero and the finite OTA output reitance, the pole miht be real even if < eff. Accordin to equation 5, the cloed-loop pole are located at ± 2 L 0 Z eff eff L 0 Z eff,2 4 2 (7)

5 For real pole, both pole are located above and below to ( ( eff / Z ) 0 / L )/2, repectively. If the pole are complex conjuate, the real part increae above due to the effect of both zero and OTA output reitance. Alo, both zero and amplifier output reitance reduce the imainary part of the pole. Fiure 3 how the typical root locu of a two-pole and zero ytem. In both cae, the lowet frequency pole i cloe to the frequency of the zero if enouh feedback i ued. A common cae for the feed-forward amplifier to be dicued in the followin ection i hown below in fi. 4; it correpond to the root-locu hown in fi. 3a. Both open loop and cloed-loop ain are depicted. Notice in thi fiure that cloed-loop pole-zero doublet appear cloe to the open-loop zero frequency if enouh feedback factor i preent. S-plane Im S-plane Im z X p2 X p Re X p2 z X p Re (a) (b) Fi. 3. Typical root locu for a ytem with two pole and zero; a) zero i located at hih frequencie, and b) zero located between the pole. In both cae the dominant pole i terminated by the zero. Open-Loop Gain 2 loed-loop Gain z p2 p Fi. 4. Open and cloed loop tranfer function of a econd order ytem in preence of a zero. The zero i located after the open-loop pole. Shown in equation 8 i the cloed-loop amplifier impule repone (aumin that 2 ). 2 h(t) = βa V ( ) ( ) ( ) t t ( ) ( ) 2 2 Z e Z 2 e 2 Z (8) - 5 -

6 Slow output component are avoided if both cloed-loop pole and 2 are placed at hih frequencie; thi however i poible if and only if the zero i located at hih frequencie. An important obervation here i that if the dominant pole i cloe to the location of the zero, it coefficient (proportional to - Z ) i reduced then reducin the effect of poible low component. III. Feed-forward technique for folded-cacode OTA The typical folded-cacode OTA i hown in fiure 5a [7]; it mall-inal tranconductance ain i approximately iven by the followin expreion G m m (9) m VDD VDD V MFB M3 M3 (4/3)I B V MFB M2 (4/3)I B M2 V MFB (4/3)I B 2I B 2I B M M M i 0 V B V B i 02 i 0 V B v i M V B v i2 M i 02 (4/3)I B MN V BN v i M M v i2 V BN (4/3)I B I B 2I B I B (4/3)I B VSS VSS (a) Fi. 5. a) Typical folded-cacode OTA and b) Folded-cacode OTA uin complementary differential pair. (b) where m i the mall-inal tranconductance of M, and i the capacitance aociated with the ource of M. The tranconductance of the cacode tranitor (-tranitor) and the equivalent paraitic capacitor at that node determine the open-loop pole frequency. For wide-band application lare unity ain frequency i needed, therefore the frequency of the paraitic pole (= mp / ) mut be placed at very hih frequencie. If we conider the ame ate dimenion and ame bia current for tranitor M and M then m > m becaue the mobility of the N-tranitor i hiher than the mobility of the -tranitor (3 time for the technoloy ued). If econd order effect uch a mobility deradation, it can be found that 2µ m = I 3 B (0) Θ OX WL - 6 -

7 In thi expreion, W and L are the width and lenth of the ate of M, repectively, and I B i the tranitor bia current. OX and µ are the oxide capacitance and the mobility of the carrier in the channel, repectively. The parameter Θ i a reult of the paraitic capacitor at the cacode node, and can be expreed a apacitor@ ource of M Θ = > () GS where GS i the ate-ource capacitance of M; for practical circuit 2.5>Θ>. In accordance with eqn. 0 and, the larer Θ the lower the frequency of the non-dominant pole i; hence it i deirable to reduce a much a poible the drain and ource area of critical tranitor. Increain the bia current increae the frequency of the paraitic pole; unfortunately, the dc ain reduce and the power conumption increae. Limitin the width of the cacode tranitor miht increae the frequency of the paraitic pole but thi benefit i limited becaue the aturation voltae mut be maintained within the limit dictated by the upply voltae and inal win, mobility deradation due to vertical electrical field become more critical in that cae a well. On the other hand, a reduction in the lenth of the cacode tranitor reduce V DSAT and increae ; the drawback i the reduction of the OTA dc ain, and tranveral electric field may reduce the effective mobility of the carrier. The frequency of the paraitic pole can be increaed by a factor 3 /2 if the dual of the circuit hown in fiure 5a i employed; the N-type and -type tranitor are replaced by -type and N-type tranitor, repectively. The drawback i that the overall amplifier tranconductance i reduced due to the reduced mobility of the carrier in the -driver. The ideal OTA hould ue N-type tranitor for both differential pair and cacode, uch that their hiher mobility increae both the mall inal tranconductance and phae marin. Thi i the major advantae of the telecopic tructure [3-4] but unfortunately it output win i limited, epecially for low-voltae application and if low V T tranitor are not available. To overcome ome of thee tradeoff, a number of feedforward compenation technique have been reported [5, 8-2]. The technique propoed in [9] ue R network connected to the ate of the cacode tranitor, hence a zero i introduced uch that the paraitic pole i partially compenated. In the technique propoed in reference [0], the low-frequency inal flow throuhout the -type cacode tranitor and, by uin R network, the hihfrequency inal flow throuhout the N-type cacode tranitor. Due to the hiher mobility of the N-tranitor, better performance can theoretically be achieved. The additional network increae the capacitance of the paraitic node reducin the frequency of the pole and additional ilicon area i needed; a low-frequency polezero may increae amplifier ettlin time. In reference [], the ate of the cacode tranitor i directly connected to the input inal; by uin that feed-forward cheme, further improvement in the OTA phae marin are obtained due to the preence of a hih frequency zero. A major drawback of thi technique i that the atedrain capacitor of the cacode tranitor affect the preciion of the ytem, epecially for witched-capacitor circuit. Thi drawback ha been partially olved by uin cro-coupled capacitor [2]

8 omplementary differential pair have bein ued for lon time for the dein of rail to rail amplifier [6]. They can alo be ued for fat amplifier [7], where all cacode tranitor can be exploited a hown in fiure 5b. It can be hown that he mall-inal tranconductance of the compoed OTA i iven by m N m2 m mn m m m2 G m () ( m m2 ) (2) N m mn where and N are the paraitic capacitor lumped to the ource of tranitor M and MN, repectively. The overall current conumption i 4 I B, ame a the folded-cacode OTA previouly dicued. The low-frequency mall-inal tranconductance i iven by m m2. For ame overall current and ame input capacitance, it mall inal tranconductance i around 5 % le than the one for the typical folded-cacode OTA. For ame tranconductance and ame power, the width of the driver mut be caled up by 30 %; the input capacitance increae by the ame factor, thi i a major drawback of thi topoloy. The lew-rate, on the other hand, i 33% hiher becaue the ourced/inked current can be a hih a (4/3)I B. Since the -tranitor at the output tae are handlin leer dc current their dimenion can be relaxed, then the paraitic pole can be placed at hiher frequencie. From Fi. 5b, the pole lumped at the ource of M i located at lower frequency than thi at the ource of MN; the phantom zero lie in between. Since the pole lumped to the cacode node and the zero are located at hih frequencie, the ettlin time i not deraded accordin to the dicuion of the previou ection. The current-mirror cacode OTA hown in Fi. 6a ha a non-dominant pole at ate of M6 in addition to the pole of the cacode tranitor. The overall mall inal tranconductance i iven a: N m = N G m (3) N2 and m6 m3 N ; (4) GS6 N2 ( N) GS3 SB3 where m3(6) i the tranconductance of tranitor M3 (M6), and N= m2 / m6. The current-mirror cacode OTA uffer from a imilar limitation a the tandard folded-cacode OTA; durin neative lewin, only half of the drain current of M2 i employed in dicharin the load capacitance becaue the dc current provided by M5-8 -

9 cancel the other half. However, a larer fraction of the overall current ued can be tranferred to the load if N>. With a current ain reater than in the current mirror, the ize of the input tranitor can be reduced for ame GBW a the folded-cacode OTA. Althouh thi decreae the input capacitance, the paraitic capacitance at the ate of M6 increae, then puhin the non-dominant pole to lower frequencie. For ame power conumption, N> increae the current level at the output tae, lowerin the OTA dc ain. It hould be pointed out that if the phae marin i enouh, thi tructure may ettle fater than the folded-cacode OTA becaue of it enhanced SR and maller input capacitance (larer β). VDD 4I TAIL N M4 M5 V MFB V B V MFB 4 TAIL I N V B M5 M4 2 TAIL I N V in V in- V out M M V out- M3 V BN V BN M3 M2 M6 M6 M2 N : : N VSS (a) VDD ( M N ) 2 TAIL I M N M5 V MFB 8I TAIL M N V MFB M5 ( M N ) 2 TAIL I M N M4 V B V B M4 V in V in- V out M M M M V out- M3 V BN V BN M3 M2 M7 M : N : M6 M6 VSS : M M7 : N (b) Fi. 6. a) 2-current mirror OTA with cacode output tae, and b) three-path operational tranconductance amplifier. M2 A three-path OTA built by the combination of the three different OTA i depicted in Fi. 6b [8]. A foldedcacode OTA i implemented due to the action of M, M2 and M3, and a current-mirror cacode OTA i - 9 -

10 compoed by tranitor M-M3 and M6. Alo, a current-mirror folded-cacode OTA i embedded due to M, M4, M6 and M7. The OTA input conit of a plit differential pair; half of the ac current enerated by the input tae i injected to the ource of the N-type cacode tranitor, providin a fat path for the current. The other part of the current i delivered to the current mirror. M6 i the baic tranitor of the current mirror: one of it copie, M2, i mirrored to the output tae with a ain of N. M7 provide a current ain factor M. The OTA dominant pole i determined by the equivalent reitor and capacitor at the OTA output, while the two non-dominant pole are lumped to the cacode tranitor M3 and M4, and the ate of M6, repectively. The mall-inal tranconductance i iven a follow: M N 2 M N N N2 ( M N) N2 G m = N N2 (( M N) ) m (5) m3 m6 m4 N ; N2 ; (6) GS3 SB3 GS6 ( M N) GS4 SB4 N2 i the mot important non-dominant pole and limit the frequency repone of the overall amplifier. Tranitor M2, M6 and M7 mut be optimized for maximum frequency repone. Since the frequency of one of the zero i below the frequency of N and, in an areive dein N2 can be elected cloe to the OTA unity ain frequency. A compared with the reular folded-cacode OTA, N2 i below the frequency of the nondominant pole of the folded-cacode tructure; it can be hown that for ame V DSAT and ame L, the ratio of the non-dominant pole of the two trcture, non-dominant F- / non-dominant-3-path, i rouhly 2/(MN). The 3-path OTA ha maller input tranitor ize, leadin to reduced input capacitance; a a reult, it cloed-loop feedback factor increae and the cloed-loop repone i fater if the phae marin i ood enouh. For lew, the 3-path OTA output current i a reater portion of the total current, a all tranitor except M5 adjut dynamically their current durin lewin. On the other hand, thi topoloy i a bit noiier than the folded-cacode OTA and the one uin the complementary differential pair due to the maller tranconductance of the input tae. Thi i, however, not critical for many S application wherein the mot important noie contribution are due to the witch reitance. The four OTA dicued in thi ection were compared in a S fully-differential amplifier with input, feedback and loadin capacitor of pf each. The OTA were deined for the ame tranconductance, ame current conumption and ame output voltae win. The three-path OTA wa deined with N=4 and M=; for the current mirror cacode OTA we ued a current mirror factor of N=4. The pule repone for thee topoloie i hown in Fi. 7. Wherea the other OTA ue maller fraction of the total bia current durin the lewin phae, the three-path OTA outperform the other topoloie in thi apect. Althouh the multi-path OTA uffer from relatively poor phae marin it ettlin time i comparable with other topoloie. The multiple-path dein achieve a ubtantial improvement in both SR and accuracy a compared with the reular folded-cacode OTA

11 The three-path dein achieve the bet ettlin accuracy (ettlin error < 0.42 %). Thi tudy uet that the imple current-mirror cacode OTA, uually not preferred for hih-peed application becaue of poor phae marin, perform better than the tandard folded-cacode OTA. The reult are ummarized in table I path 0.4 urrent mirror omplementary Output voltae (V) urrent-mirror omplementary Folded-cacode 3-path Folded-cacode Time (nec) Fi. 7. OTA ranient repone for a differential input tep of 500 mv. The pule i applied at t=0.25 nec. Table I. omparion of imulation reult for 4 different OTA. The OTA mall inal tranconductance i around 4.2 ms for all tructure. arameter Foldedcacode urrent-mirror omplementary 3-path OTA cacade diff pair SR [V/µ] D ain [db] T[%] [n] T[0.%] [n] Settlin error [%] Input noie [0-9 V/Hz /2 ] * Between bracket i the number of input tranitor. IV. Feedforward cheme for multi-tae OTA with no Miller apacitor acade of amplifier i becomin very popular for witched-capacitor application a well [6, 9-24]. Several compenation cheme have been reported in literature for multi-tae amplifier [22-23]; two of them are hown - -

12 in Fi. 8. The invertin amplifier are not needed if differential tae are ued. The dc ain for thee tructure i iven by the multiplication of the 3 ain tae; hence dc ain of db can eaily be achieved. m - m2 v i m m3 m2 v 0 (a) m - m2 v i m m3 m2 v 0 m4 (b) Fi 8. Three-tae amplifier with a) neted Miller compenation, and b) Neted Miller compenation with a feedforward path. Due to the 3 hih impedance node, double miller compenation i required for proper phae marin. The multipath miller tructure hown in fiure 8b incorporate a feedforward path ( m4 ); thi trajectory improve the hih frequency repone of the tructure cancelin the riht-hand zero due to the miller capacitor, but till double miller compenation i needed. The claic two-tae miller compenation cheme i hown in Fi 9. The openloop dominant pole, pd = 0 /A V2 m, i puhed to lower frequency becaue of the increae in the effective capacitance caued by the compenation capacitor ( m ) and the ain of the econd tae. Thi decreae the open loop unity ain frequency u (~ m / m ) and reult in lower ettlin time. The non-dominant pole i mainly iven by m2 /( 0 02 ); unfortunately the load capacitor 02 depend on the application and miht be lare, hence the peed of the ytem i limited. For ood tability, the condition m2 /( 0 02 ) > m / m mut be atified; unfortunately hih-frequency S circuit may require lare load capacitor that force u to ue lare m2 further increain the power conumption and paraitic capacitance. Riht half plane (RH) zero at z = m2 / m i enerated then a nullin reitor mut be ued to compenate thi effect. In ome other circuit uch a that hown in fi. 8b a feed-forward path ( m4 ) i ued for thi purpoe

13 m R z m m v i 02 v 0 Fi. 9. Two tae Miller compenation. Feedforward compenation technique have been ued to boot the dc ain of OTA, epecially for low-frequency application [28]. Here we ue feed-forward path for the phae compenation of a multi-path OTA [29]; fiure 0 how the implified chematic. The NFF compenation cheme doe not employ any compenation capacitor, but ue a Left plane (LH) zero for obtainin ood phae repone. LH zero caue poitive phae hift in the phae and it i ued to cancel part of the neative phae hift caued by the pole. The concept can be explained if the tructure i analyzed. - m m2 v i v 0 m3 Fi 0. No capacitor Feed forward (NFF) compenated two-tae amplifier. It can be eaily found that the overall open-loop mall inal tranconductance ain i G m () m2 ( A ) Z ( A m2 m3 ) = m m3 (7) where A i the dc ain of the firt tae (= m / 0 ), and the dominant pole of the firt tae i located at = 0 / 0. The dc tranconductance i approximately iven by m= m m2 / 0. By uin thi OTA in the amplifier confiuration hown in Fi., and accordin to eqn., 2, 4-5, 7 and 7, it can be found that the cloed-loop zero and pole are located at the followin frequencie - 3 -

14 z m2 m3 m 0 (8) m3 02 ± m m2 L,2 4 2 ( ) (9) 2L 0 m3 02 Notice that the real pole can alway be obtained if m3 i further increaed, but the frequency of the cloed-loop dominant pole and zero decreae, and low component miht appear, ee equation 8. The dominant pole and zero are cloe enouh (mimatch leer than 0 %) if 4 ( ) m3 m m2 0 2 L 0 < 0.25 (20) Additional computation how that under thi condition, the pole are located at β m m2 (2) 0( β m3 0 ) β β m3 m3 2 = (22) L 4 β( 3 ) Notice that under thee condition z and p (enouh feedback) are very cloe to each other reardle the abolute value of the load capacitor ued; the root-locu i imilar to the one depicted in Fiure 3. The frequency of both p and z increae, increain the peed, if the paraitic capacitor at the output of the firt tae, 0, are reduced; thi i a quite important dein conideration. If 0 i reduced, then complex pole miht appear, but thee can be tolerated. Althouh ome rinin appear in the tranient repone, fat repone reult if the real part of the pole i lare enouh. A witched-capacitor amplifier ha been imulated with = 3 = 4 =0.5pF, and 2 =pf, ee fiure. The tranconductance m, m2 and m3 were et at ma/v, 4 ma/v and 0 ma/v, repectively; the paraitic capacitor at the output of the firt tae, 0, wa etimated to be around 0.25 pf, ee fiure 0. The amplifier dc ain i around 90 db, becaue a telecopic amplifier i ued for the firt tae; the dein detail of the amplifier are dicued in the next ection. Shown in fiure a i the tranient repone for the NFF amplifier under the followin cae ( 3 =0.25pF and 4 =0.5pF): ) =0.5pF, 2 =pf and 0 = 0.25 pf (nominal cae) 2) =0.5pF, 2 =pf and 0 = 0.5 pf (lare capacitance at the output of firt tae) - 4 -

15 3) =0.5pF, 2 =pf and 0 = 0.75 pf (laret capacitance at the output of firt tae) 4) = pf, 2 =2pF and 0 = 0.25 pf (bier input and interatin capacitor) A expected, cae 3 i the mot critical one; larer 0 (= 0.75 pf) lead to a zero located around 70 MHz only; the cloed-loop dominant pole will be located around thi frequency leadin to low component. Thi effect i evident in curve 3. Althouh the variation in the parameter are lare, the 0. % ettlin time i around 3.2 nec for cae and 4. The pule repone can be very low if 0 increae, cae 2 and 3, where % ettlin i 3.3 and 7 nec, repectively. 0.6 Vout (Volt) ae ae 2 ae E-9 4E-9 5E-9 6E-9 0E0 2E-9 4E-9 6E-9 8E-9 E-8 Time (Sec) (a) 0.6 Vout (Volt) ae ae2 ae NFF E-9 4.0E-9 5.0E-9 6.0E E0 2E-9 4E-9 6E-9 8E-9 E-8 Time (Sec) (b) Fi.. a) ule repone for the NF two-tae amplifier and b) the miller amplifier

16 For comparion, a two-tae miller amplifier with lare tranconductance tae wa deined; the tranconductance ued are m = m2 =0 ma/v and a nominal miller compenatin capacitor of 2 pf; a nullin reitor optimized for RH zero cancellation i ued. The amplifier dc ain i et at 90 db. Three cae are imulated for the miller amplifier: ) Input and interatin capacitor of 0.5 pf, pf and miller=2pf 2) Input and interatin capacitor of pf, 2 pf and miller=3pf 3) Input and interatin capacitor of pf, 2 pf and miller=4pf Notice that the NFF approach (nominal cae, 0 =0.25 pf) can be fater than the miller amplifier, even if the lat tructure ue larer tranconductance. V. EXERIMENTAL AND SIMULATED RESULTS A witched-capacitor amplifier uin the 3-path OTA ha been fabricated in a tandard 0.5 µm proce throuh the educational ervice of MOSIS; a microphotoraph of the chip i hown in Fi. 2. Input, interatin and load capacitor of 0.5 pf were ued. A ource follower i ued a buffer to drive the lare capacitor of the external device and pad. The amplifier pule repone i depicted in fiure 3. The % ettlin-time i 2 nec; the tandalone buffer, board impedance, connector, rie and fallin time of the inal enerator (around nec), and witch delay are reponible for more than 7 nec. Simulation reult, dicued in the previou ection, how that the amplifier ettlin time i le than 4 nec. Thi cheme ha been uccefully ued for the dein of a hih-order 64-MHz witched capacitor filter [8]. Fiure 2. hip microphotoraph of the witched-capacitor 3-path amplifier

17 Fiure 3. ule repone for the witched-capacitor amplifier uin the 3-path OTA. A two-tae OTA uin NFF compenation cheme wa implemented in AMI 0.5µm MOS technoloy with upply voltae of ±.25 V; the chematic i hown in fiure 4. The active area for the amplifier i around 0.6 µm 2. The bia current for the firt tae i only I B =50 µa, and the one ued in the econd tae i I B2 =2 ma. For the feedforward tae the tail current i I B3 =5mA. The tranitor apect ratio are 960µm/0.6µm for the firt differential pair, 600µm/0.9µm for the econd tae and 20µm/0.9µm for the feedforward path. The oal were to have hih dc ain in the firt tae with relatively hih unity ain frequency, and m3 >> m, m2 ; accordin to eqn. 8 and 2 the pole-zero matchin hould be fairly ood. ot-layout imulation how that for a load capacitance of 8pF and an tep of 300mV, the % ettlin time of the OTA wa 5. nec. Neither overhoot nor low frequency component were oberved. The pot-layout imulation reult for a inle ended OTA how a D ain of 9 db, ain-bandwidth product of 325 MHz and lew-rate of 40 V/µec. An invertin amplifier, imilar to the one hown in fiure, wa experimentally teted. For the tet etup, external capacitor of 5 pf were employed; the load capacitance ued wa 2 pf (etimated capacitance of meaurement equipment probe capacitance and packae bond-pad capacitance). The chip wa meaured; the % ettlin time for an input tep of 0.8 V wa 6-7 nec; around 2 nec correpond to lew-rate (due to the lare inal win) and 4-5 nec are lumped to the non-linear ettlin. The amplifier pule repone for lare input inal (up to 2 Volt pk-pk) i hown in fiure 5; notice that mot of the ettlin time i due to lew-rate limitation. For thee reult, the input ede had a fall time of around 3 nec due to B, bond-pad paraitic (DI-40 packae wa ued), and equipment loadin effect. The output tep repone ha no rinin, which how a ood phae marin. ot-layout imulation reult for the amplifier with a 4 nec fall time input tep, and paraitic capacitor at the OTA input of 3 pf, and load capacitor of 2 pf how a % ettlin time of around 3.5 nec, which i in conformance with the meaured reult

18 VDD M6 M6 M7 M7 V B M5 M5 v 0 V BN M4 M4 M M M2 M2 VSS I B I B2 VSS M3 M3 I B3 v i VSS Fi. 4. Sinle-ended amplifier with NFF compenation cheme. ONLUSIONS Feed-forward technique can improve the peed of cloed loop witched-capacitor network. It ha been hown that the fully-differential OTA baed on multi-trajectorie preent hiher lew-rate and uperior ettlin performance than the conventional folded-cacode OTA. The pole-zero pair preent in feed-forward topoloie mut be placed at hih frequencie to avoid low ettlin component. Another important advantae of feedforward cheme i that due to the maller paraitic capacitor preent at the input, the error after ettlin i more than 3 time maller than that obtained with the reular folded-cacode OTA. The NFF compenation cheme allow u to have both hih ain and fat ettlin time, reultin in accurate and fat tep repone. The increae in GBW a compared to other compenation cheme i due to the fact that the pole are not plit. LH zero are ued to cancel the phae hift of pole to obtain a ood phae marin. The effect of pole-zero mimatche on feed-forward amplifier performance wa tudied and it wa hown that the pole-zero cancellation hould occur at hih frequencie for bet ettlin time performance. Experimental reult for the OTA how fat ettlin time and ood tability. Simulation and experimental reult for the amplifier are in accordance with the theoretical derivation

19 (a) (b) Fiure 5. Experimental reult for the inle-ended amplifier; b) loed look of the tep repone. REFERENES [] S.I. Liu,.H. Kuo, R.Y. Tai and J. Wu, A double-amplin peudo-two-path bandpa modulator, IEEE Journal of Solid-State ircuit, vol. 35, pp , Feb [2]. uinato, D. Tonietto, F. Stefani and A. Bachirotto, A 3.3-V MOS 0.7-MHz ixth-order bandpa modulator with 74-dB dynamic rane, IEEE Journal of Solid-State ircuit, vol. 36, pp , Apr 200. [3] T. Salo, T. Hollman, S. Lindfor and K. Halonen, An 80-MHz 8 th order bandpa modulator with 75dB - 9 -

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