DC-coupled, single-to-differential design solutions using fully differential amplifiers (Part 1 of 2)

Transcription

1 DC-coupled, ingle-o-dierenial deign oluion uing ully dierenial ampliier (Par 1 o ) Michael See, Sr. Applicaion Manager, Ineril Corp. Since he emergence o he wideband ully dierenial ampliier (FDA) opology wih he inroducion o he AD8138 in 1999, a popular applicaion o hi ype o device ha been o conver a ingle-ended inpu o a dierenial ignal around ome common-mode volage. Thi i a ypical requiremen o drive all modern, high-peed ADC. A higher peed, where a doubly erminaed ranmiion line-ype environmen i deirable, a common applicaion would be o preen a deined, ingle-ended inpu impedance o mach ome ource impedance. Then, he FDA conver ha ingle-ended inpu ino a dierenial ignal wih ome gain cenered on he V cm o he ADC. Thu ar, a cloed-orm oluion or he reior value in hi applicaion o he FDA ha proven remarkably eluive, wih ieraive echnique he curren norm. While eecive, hee hunand-peck oluion mi ome o he more ueul inigh a cloed-orm oluion can provide. Building on previou work, an exac oluion or he required reior will be preened here along wih a deign example uing he 4-GHz ISL5510 FDA and he low-power, 10-bi, 500- MSPS ISLA110P50 ADC. DC-coupled, ingle-o-dierenial, wideband FDA applicaion circui The opology or conideraion i hown in Figure 1. Thi applicaion i inended o provide a deined inpu impedance mached o a known ource impedance ( ) and give he reuling inpu ignal a he node a gain o A v o he dierenial oupu cenered on a conrolled common mode volage e by he V cm conrol inpu. Figure 1. DC-coupled, ingle-o-dierenial circui wih inpu-impedance maching-analyi circui

2 Thi i one o hoe decepively imple-looking circui ha quickly ink ino an algebraic mora a layer aer layer o iue are conidered. A general analyi o hi circui wih unconrained reior value lead o mae o equaion ha provide only mode benei bu a rigorou oundaion or ome very ueul impliicaion (eerence 1 and eerence ). To move orward quickly wih hi dicuion, hoe impliicaion include uing equal eedback reior value and ha he eedback volage divider rom each oupu back oward he inpu node (+ & - in Figure 1) be e equal. One goal o hi circui i o have an oupu ignal ha i purely dierenial around he V cm DC bia volage. FDA applicaion circui will benei rom a mached volage divider back o he eedback poin o eliminae any inpu ignal o common mode oupu converion. In he circui o Figure 1, we would like he ignal a V i o only produce an oupu dierenial ignal ha i A v V i wih no modulaion o he V cm volage ha i ignal relaed paricularly a he requencie increae and he loop gain roll o. Maching he eedback divider raio i required o achieve hi. I he eedback reior are e equal, hen ha conrain can be decribed by Equaion 1. g g1 Eq. 1 The nex key inigh o move oward a reior-value oluion in Figure 1 i o recognize ha he impedance looking in oward g1 i no imply g1 a i normally would be in an invering op amp ype applicaion. While in ome applicaion o he FDA hi would be rue (ee eerence 3, or an example o an FDA applicaion where he FDA umming juncion volage have no inpu ignal componen oher han he dierenial loop gain error volage), in hi ingle-o-dierenial coniguraion, he inpu volage a he FDA umming juncion are moving wih he inpu ignal. I i criical o recognize ha wo loop are operaing in mo FDA device. The dierenial loop will orce he dierenial inpu volage acro V + and V - in Figure 1 o be ideally zero, bu he common-mode loop i moving he common-mode inpu volage wih he inpu ignal o hold he oupu V cm conan. So, imagine V i in Figure 1 moving up in volage wih a ixed oupu V cm. Thi will caue he common-mode volage a he FDA inpu o move up alo along wih he inpu ignal. Thi ha he eec o making he apparen inpu impedance looking ino g1 o be higher han imply g1 a he ampliier V + node i eenially a driven ource ha ha a V dependence in he direcion o reiing curren low ino he g1 reior increaing he apparen inpu impedance over ju g1.

3 I i hi acive inpu erminaion apec o Figure 1 ha ha led o he ieraive oluion mehodologie ued prior o he oluion preened here. Cloed-orm oluion or he reior in he ingle-o-dierenial FDA applicaion Drawing on ome recen ummary work by Jim Karki, where he recognize and deliver hi acive inpu impedance equaion and gain in Equaion 8 and 9 in eerence 4, we can ue hi perormance equaion o ar a oluion or ha will imulaneouly achieve he deired inpu mach and deliver he deired gain while holding he eedback divider raio mached. Boh eerence and 4 deine eedback divider expreion o impliy he equaion, repeaed a Equaion and Equaion 3 here. g1 g1 Eq. g g Eq. 3 The ull volage-divider equaion back o he V + inpu o Figure 1 will alo be conrained o equal β -. Thee wo β' will hereore be unequal or hi DC-coupled ingle-o-dierenial applicaion circui. The reuling circui will have a Noie Gain ha can be eaily recognized o be 1/β -. Thi can be ued wih volage eedback amplier (VFA)-baed FDA o eimae heir reuling cloed-loop ignal bandwidh. I he Gain Bandwidh Produc (GBP) i repored, hen a good eimae o cloed loop ignal bandwidh will be GBP β - Uing hee β, eerence 4 repor an apparen inpu impedance looking ino g1 a a Z A (acive impedance) erm given by Equaion 4. (Equaion 8 in eerence 4) Z A ( g1 ) ( 1 ) Eq. 4. Thi acive erminaion appear in parallel wih o e he oal apparen inpu impedance a V i in Figure 1. Auming hi condiion i achieved, hen he dierenial-gain expreion i given a Equaion 5 (Equaion 9, eerence 4). g1 ( ) Eq. 5

4 Everyhing i here o olve or, bu i i deiniely a non-rivial exercie o purue manually. Thee acive inpu-impedance oluion eem o generally reul in a quadraic oluion or he arge elemen. [See eerence 5 or a imilar example in he oluion or a complemenary DAC oupu o ingle ended uing he ingle op amp coniguraion legacy deign ailed o recognize here ha he invering node on he op amp i in ac dependen on he non-invering volage and hence dependen on he ignal o he invering pah o ha circui alo ha an acive erminaion piece and he oluion here i alo quadraic]. Here, he quadraic oluion or i hown a Equaion 6 (eerence 6) where he g elemen have been eliminaed and we are le wih only he arge gain, ource reior and eedback reior value o ge a oluion or ( ) ( ) (4 ) ( ) (4 ) 0 Eq. 6 Once we have he required o imulaneouly aiy he inpu impedance a V i ( Z A = ) and hi he deired gain, A v, he wo g reior are e uing Equaion 7 and Equaion 8. ` Eq. 7 g1 1 g 1 Eq. 8 The deign oluion delivered by Equaion 6 hrough 8 were iniially veriied hrough numerou example deign in ADS uing he Ineril ISL5510 wideband FDA ull ranior model (eerence 7). One oucome o having he cloed orm oluion or o Equaion 6 i ha buried in he oluion or i an expreion ha allow u o olve or he maximum achievable A v given

5 and. Looking a Equaion 6, where he denominaor par o he coeicien goe o zero, an ininie oluion or will reul. Solving or ha, give an expreion or max i an and have been choen. max ( ) ( 1 1 ( 4 ) ) Eq. 9. I i apparen rom Equaion 9 ha once you have picked an and are given an, here i a opological conrain on he maximum achievable gain in he circui o Figure 1. Mo deign do ar by picking an and hen lowing rom here conideraion on picking include 1. I he FDA i a Curren Feedback Ampliier (CFA) ype, e he bandwidh conrol.. appear a par o he oupu load in hi opology, very low value can ar o impair he oupu diorion 3. alo ener ino he oal oupu noie equaion. I ac a he gain or he inpu curren noie erm and add i own hermal noie. So very high value can ar o impac oupu noie exceively. Thi i paricularly rue or Curren Feedback baed FDA which will alo have higher umming juncion curren noie erm v. VFA baed FDA. 4. Very high value o or a Volage Feedback ype FDA can alo ar o inroduce an addiional eedback pole due o he paraiic inpu C' on he FDA umming juncion. Thi can omeime hur he phae margin,inroducing poible peaking or inabiliy depending on he device and gain eing. Normally, or Volage Feedback Ampliier (VFA)-baed FDA device, where he value ha coniderably more lexibiliy han Curren Feedback Ampliier (CFA) baed FDA device, an value in he 00Ω o 1500Ω i mo common. I i inereing o plo Equaion 9 or everal arge value over o e an upper bound on he achievable gain in he circui o Figure 1. Figure how hi in linear erm while Figure 3 how log gain and a log cale on.

6 Max. Achievable Gain (db) Max. Achievable Gain (V/V) Max. Volage gain v and Feedback eior value (Ω) =50 =75 =90 Figure. Maximum achievable gain v. parameric on. 40 Max. Volage Gain v and Feedback eior Value (Ω) =50 =75 =90 Figure 3. Maximum achievable db gain v. parameric on. An alernaive way o ue he denominaor expreion in Equaion 6 would be o ue a argeed and A v and olve or he value ha will orce he o ininiy giving only an g1 baed acive inpu erminaion. Doing hi give Equaion 10 or an max o orce o ininiy. max ( ( 4 ) ) Eq.10

7 unning an example deign uing Equaion 10, arge a gain o 10V/V wih = 50Ω. Equaion 10 give a required max = 9Ω and hen an g1 = 8.39Ω and g = 58.3Ω. Snapping hee value o cloe 1% give circui o Figure 4 where no elemen i ued, bu he inpu impedance will appear a 50Ω. Puing he elemen value o Figure 4 back ino he Z A (Equaion 4) give an inpu impedance o 50Ω. Figure 4. Gain o 10V/V wih no erminaion and 50Ω inpu mach. One poible oucome o a purely acive inpu-erminaion circui i a lower equivalen inpureerred noie. Figure 5 how an ADS imulaed oupu noie or he example o Figure 4 which will be including all he inernal noie elemen o he deign. Figure 5. Dierenial oupu po noie imulaion or he circui o Figure 4.

8 Thi oal oupu noie include he ource-reior noie o 0.89nV/ Hz divided down by he equivalen 50Ω inpu mach o 0.48nv/ Hz, hen gained up by 10 o be a 4.8nV/ Hz oupu po noie conribuion. The red curve below i he oal oupu noie wih he blue curve he oal inpu reerred noie. The 9.8nV/ Hz a he oupu mean he non-ource noie relaed erm are a approximaely 8.54nV/ Hz. Inpu reerred by he gain o 10 give approximaely 0.85nV/ Hz very cloe o he peciied dierenial volage noie or he ISL5510 by iel. So indeed, hi acive erminaion eem o be delivering an inpu reerred noie o ju he ampliier volage noie wih very lile added reior noie erm. The NF expreion rom hi inpu reerred po noie volage i given a Equaion 11. The e i here i he po noie a V i excluive o any noie delivered by he ource reior. NF 10 log ( 1 e i kt ) Eq. 11 Puing in number give a Noie Figure o 6.6dB or he circui o Figure 4. Thi i uing e i = 0.85nV/ Hz = 50Ω kt = Joule High-gain ampliier deign wih oher conideraion I i omewha urpriing how high he gain can be and ill achieve an inpu mach. Thi come rom he g1 olving or value <, which i an unuual (bu correc) reul. Figure 6 how an example deign or he ISL5510 aring wih a 499Ω eedback arge and hen Figure (or Equaion 9) indicae a maximum achievable gain o 18V/V i poible.

9 Figure 6. Gain o 1V/V, 50Ω inpu, ISL5510 Deign Tha would be where i headed oward ininiy and lipping over o a negaive number. Backing o a bi and argeing a gain o 1 rom a 50Ω ource give he elemen value hown in Figure 6 uing Equaion 6 o 8 o olve or he hree remaining reior, where again hee have been napped o andard 1% value. The reuling deign reior value o Figure 6 will give a gain rom V i o he dierenial oupu volage o Vo = 1V/V (or 1.6dB). While he 4.9Ω g1 reior look odd, going back o Equaion 4 and olving or he Z a give 74.5Ω. Thi acive inpu erminaion i coniderably higher han he phyical 4.9Ω elemen and combine in parallel wih he 150Ω o give an inpu impedance a V i o 50Ω. unning an ADS imulaion wih he ull ranior model o he ISL5510 in hi circui give he 58MHz a -3dB bandwidh o Figure 7. The noie gain o Figure 4 (1/β -, Equaion 3) i 9.06V/V which, wih he peciied 4-GHz gain bandwidh produc or he ISL5510, would predic a cloed loop bandwidh o 441MHz a reaonably cloe agreemen o imulaion.

10 Figure 7. Simulaed mall ignal AC repone rom Vi o dierenial Vo in Figure 4. Since a porion o he inpu mach i now e by he common mode eedback loop, i bandwidh become criical o mainaining a broadband mach. While no peciied in he ISL5510 daa hee, he mall-ignal repone bandwidh o he CM loop exceed 1GHz. There i a peciied BW rom he CM pin o he oupu common mode volage, bu ha i valy band-limied a he inpu pin on he ISL5510 o iler any noie on ha inpu. Pa hi inpu buer on he CM conrol inpu, he loop bandwidh i ar higher and criical o hi ype o applicaion. While i i cerainly poible o operae wih no and operae a he maximum gain o Equaion 9, geing all o he inpu mach hrough he Z A o Equaion 4 (ince ha i a loop-gaindependen acive erminaion), i i perhap more pruden o reain ome o bound he inpu impedance a he variou loop gain roll o. Having will alo provide a DC bia pah i he ignal pah rom i opened up or ome reaon keeping he FDA biaed correcly. Looking a a ew more o he deail in hi DC-coupled applicaion, he FDA inpu pin will be moving wih he inpu ignal a a volage ha i approximaely he divider rom he ource volage o he arge oupu V cm volage. I he ource were 0V cenered, and uing he argeed 0.535V oupu Vcm volage hown in he example o Figure 6, we would expec he CM volage a he FDA inpu pin (+ and -) o be approximaely a V ocm β - = +60mV wih a mall variaion around ha wih he inpu ignal V. The ISL5510, being a very-high-peed SiGe device, doe no provide a wing o negaive rail inpu age, nor a rail-o-rail oupu age, bu inead need approximaely 1.V headroom rom he negaive upply o he inpu common mode volage a V + and V -. The example o Figure 6 provide hi uing a -1.V power upply. Even a wing o negaive-rail-inpu FDA running on a ingle poiive upply and ground may have rouble wih a rue-ground-cenered bipolar inpu ignal wih high gain, a he common mode volage a he device inpu pin may exend below ground. One added iue o conider i ha wih V = 0V, he volage a V i i >0V. Thi will caue a DC curren o be delivered back oward he ource ha mu be conidered. So while i would normally be aumed ha V mu deliver curren o he V i poin, i i acually inking curren in mo cae. Thi curren i eenially providing he common mode level hi o he oupu o he FDA, which are mo oen a a poiive volage above ground o ge he dierenial volage wing maching up wih he inpu range o an ADC. eerence 1. Fully Dierenial Ampliier Applicaion epor, Jim Karki, Texa Inrumen applicaion noe SLOA054. hp://ocu.i.com.cn/cn/li/an/loa054d/loa054d.pd

11 . High Speed Dierenial ADC Driver Deign Conideraion, John Ardizzoni & Johnahan Pearon, Analog Device applicaion noe AN-106. hp:// 3. Deliver he lowe diorion and noie in a low-power, wideband, ADC inerace (Par 1 o 4), Michael See, Plane Analog, 4/5/011. hp:// and-noie-in-a-low-power--wideband--adc-inerace--par-1-o-4-4. Inpu impedance maching wih ully dierenial ampliier, Jim Karki, TI Analog Applicaion Journal 4Q 008, pp4-8. hp://ocu.i.com/li/an/ly310/ly310.pd 5. Wideband Complemenary Curren Oupu DAC o Single-Ended Inerace: Improved Maching or he Gain and Compliance Volage Swing, Michael See, Texa Inrumen applicaion noe, SBAA135, June 005. hp://ocu.i.com/li/an/baa135/baa135.pd 6. Conac he auhor or he deailed derivaion o hi equaion. 7 Wideband, Low Power, Ulra High Dynamic ange Dierenial Ampliier, Ineril ISL5510 hp:// Bi, 500MSPS, ADC Converer ISLA110P50, hp:// 9. Ineril ree power and pice imulaor download, isim PE hp://web.ranim.com/isim/download/isimpe.apx 10. Conac he auhor or he deign low o hee iler and/or example iler ile in isim PE Abou he auhor Michael See i Senior Applicaion Manager, Ineril Corp. wih more han 5 year o experience in high-peed ampliier deign, applicaion, and markeing. Previouly, he wa he Marke Developmen Manager or High-Speed Signal Condiioning, and a Diinguihed Member o he Technical Sa, a Texa Inrumen Inc. He currenly provide produc deiniion and cuomer deign-in uppor. Michael earned a BSEE rom he Univeriy o Kana and an MBA rom Colorado Sae Univeriy. He hare everal baic paen in high-peed op amp deign and ha wrien more han 85 produc daa hee, core o conribued aricle, applicaion noe and conerence paper.