Design of a band-pass sigma-delta modulator with reduced number of opamps

Design o a band-pass sigma-del a modula o wi h educed numbe o opamps A. P. VegaLea~ F. Munoz, R. G. Ca ajal, A. To alba, J. Tombs and L.G. F anquelo Dp o. de lng. Elee/ oniea, Escuela Supe io de Ingenie os, Uni e sidad de Se illa, Se illa, Spain Abs ac This pape is in ended o compa e he pe o mance o a Band-Pass con e e s uc u e and i s Low-Pass p o o ype 2nd o de Sigma-Del a Analog o Digi al con e e . Fo his pu pose Ma lab simula ions o he 4 h o de Band-Pass con e e ha e been pe o med and i s powe consump ion calc~la ed when using he equi alen Op-Amp used m he Low-Pass modula o . Fi s o all will be desc ihed he me hod used o calcula e he ans e unc ion and, hus he s uc u e o he Band-Pass s uc u e o be es ed. A e a band-pass ans e unc ion has been ob ained i is implemen ed using educed numbe o opamps. This opology is compa ed o he exis ing ones and a sys em le el simula ion and cha ac e isa ion is pe o med. Finally, ji e limi a ions a e s udied. T ansis o le el simula ions using Spec e ha e been done in o de o alida e MA TLAB simula ions p io o layou design. 1. In oduc ion In applica ions whe e an IF signal bas o, be demodula ed and con e ed o digi al, wo solu IOns may be used. The i s one consis s in do,:",- con e ing he signal o base-band and con e mg o. Two con e e s would be needed. This solu ion is sensible o he misma ch be ween he eal and imagina y b anches o he demodula o . O he p oblems as o se and II noise sensi i i ies a ec he pe o mance o he low-pass con e sion, An al e na i e solu ion is o pe o m a band-pass AID con e sion o he IF signal and demodula e in he digi al domain. This can be accomplished using a band-pass sigma-del a modula o . ThIS me hod IS ee om he wo-pa h misma ch beCliuse i uses only one con e e . The low equency disables he e ec s o he II noise. The main disad an age o hese s uc u es is he e ec o ji e on he SNDR. This makes necessa y o build a low ji e y clock ha ensu es ha he inpu sampled signal SNR is euough no o deg ade hc modula o 's pe o mance. , Two me hods a e a ailable o ind an app opna e ans e unc ion o he band-pass modula o , 'The simples way is o s a wi h an exis ing low-pass s uc u e and pe o m a low-pass- o-band-pass ans o ma ion [I]. The second mc hod is o design he ans e unc ion ia a Gene alised Fil e App oxima o [2]. These a e ou ines ha adjus he poles and ze os o H(z) o accomplish wi h he ampli ude speci ica ions demanded by he designe . A e ha design, a s abili y s udy mus be pe o med o gua an ee he co ec beha iou . T ans o ming an exis ing low-pass in o a band-pass s uc u e is mo e used because low-pass s uc u es a e be e known and widely used. The p esen design will be buil om an exis ing 2 nd o de Low- Pass con e e and a Low-pass- o-band-pass ans o ma ion will be applied. 2. Ioow-Pass p o o ype A good app oach in designing band-pass modula o s is s a ing wi h a sui able low-pass s uc u e. The s a egy o building a low-pass p o o ype enables us o ake ad an age . o he s abili y pe o mance and he nOIse p ope ies ha a e well s udied o low-pass sys ems. Once a e ensu ed hese p ope ies in he low-pass modula o , we can a on he ask o uns o ming o a band- pass modula o p ese ing bo h s abili y and noise pe o mance. The inal band-pass s uc u e mus i he needed equi emen s o signal band and o e - sampling a io. Once he low pass s uc u. e ~s designed, a low-pass- o-band-pass ans o ma IOn IS applied, This ans o ma ion mus map he poles and ze os a ound he wo=O equency o hei inal wo=w, equency. The e a e wo app oaches o go ahead wi h his ans o ma ion. Each o hem has ad an ages ha mus be s udied in o de o choose he one ha i s ou needs, a) Gene alised N-pa h ans o ma ion is achie ed doing z,," +1- ZN. This ans o ma ion p ese es modula o dynamics bu inc ease he modula o o de unnecessa ily (N)2) o esul in a band-pass cen ed a ,/2 o z+ (aliasing p oblems). b) Seeond o de Low-Pass-To-Band-Pass ans o ma ions gi e ull con ul o e he pass-band loca ion bu do no p ese e modula o dynamics. Fo his s a egy, he l ans onna ion: z,,"-z'(z+aY(a'z+I), whe e-I<a<l (I) .<0 gi es sys ems close o DC. 0>0 gi es sys ems close o ,/2. When a=O (I) Z7-Z' and he esul is a Band-Pass s uc u e wi h ,l4 cen al equency. This way. s abili y is gua an eed as well as he modula o dynamics. This will hen be he app oach o be ollowed in o de o build he p oposed s uc u e. In igu e I is ep esen ed he 2"" o de Low-Pass p o o ype. I has been widely s udicd and, hUB. is a good s a ing poin o build ha band pass modula o . Once SUbs i u ing Z by -- . he s uc u e is he one depic ed in igu e 2. I is clea ly seen ha in eg a o s ( igu e I) a e ans o med in o esona o s, bu he o e all s uc u e is unchanged. In igu e 2 is ep esen ed he esul o his ans o ma ion. 3. Cha ac e isa ion o a low-pass p o o ype The i s s ep in he desigu o a band-pass modula o using he low-pass o band-pass ans o ma ion me hod is o desigu i s low-pass p o o ype. This low-pass p o o ype is he one depic ed in igu e I. Mul iple simula ions ha e been pe o med o ully eha ac e ise i s dynamic beha iou . The esul s o hese simula ions, using bo h MIDAS [12] and MATLAB [II], a e shown in igu es 3, 4. To accomplish an op imum beha iou we look in o he esul s o build ou sys em using he bes coe icien s o imp o e SNDR and i s sensi i i y o a ia ions o hese eoe icien s, as well as he pe o mance ha will be needed in he desigu o he ci cui 's building blocks [I, 10]. AI his poin ( unc ional sys em simula ion) alues o bandwid h, maximum inpu ampli ude, op-amp dynamic speci ica ions a e all ela ed o a no malised equency ,. Once a alue o , is de ined, all he o he pa ame e s can be known as absolu e alues. Once is de ined ou low-pass p o o ype, he <: by _Z·2 ans o ma ion is pe o med. In igu e 4 a e ep esen ed he alues ha can be aken o design he opamp. On he x axis is ep esen ed he a io; Tsl(2·TAU). E e y cu e has been calcula ed o a SRn, being SR=SRn·2· ,V_ 4. Band-Pass s uc u e Se e al op ions a e a ailable o implemen he ans o med pass-band modula o . The di ec ans onna ion consis s in eplacing in he low-pass s uc u e he in eg a ocs by esona o s ( igu e 2) modi ying he second adde o main ain he desi ed ans e unc ion. Resona o s a e usually buil using wo opamps. This is a d awback in he design o low-powe ci cui s. A i s al e na i e is o design a single opamp esona o . This s uc u e, 157 depic ed in ib'll e 5, is desc ibed in [2). The use o his s uc u e complica es he clocking scheme, adding 6 ex a clocks a hal he sampling equency. In his kind o s uc u es i is ex emely impo an o kccp a s ic con ol on clock phases o a oid sigual dependen clock eedlh ough ha will appea inband as an image o he inpu equency a ound /4. Ano he solu ion o ob ain a band-pass modula o is eplacing he esona o s by Two-Delay In eg a o s as d awn in igu e 6. In his s uc u e in eg a o s only use addi ion, he is why bo h inpu and ou pu pola i ies need o be in e ed e e y wo delays. This e ec is modelled mUl iplying hose siguals by he sequence: {I, I, -I, -I, I, I, -I, -I, ... }. As in he case o esona o s. wo in eg a o s a e needed o pe o m be wo-delay in eg a ion. In [3] a di e en solu ion is ob ained o build an equi alen band- pass sys em as be one in igu e 6. The in e es ing poin o his is he possibili y o implemen ing an N'" o de s uc u e using N opamps. In igu e 6 is d awn be block diag am o a one bi modula o (p oposed in [3]) ha sol es he p oblem using a minimum numbe o opamps. This consis s in down-con e ing he inpu sigual o i s base-band I and Q componen s. Once he signal is down- con e ed, i is p ocessed in he base-band egion and inally up-con e ed o i s o iginal IF. Looking close we scc ba while one b anch is in eg a ing a a iable inpu , he olbe one is in eg a ing a "0", ha is, Iba b anch emains wi h a ixed ou pu du ing Iba cycle. We can ob ain he wo-delay in eg a o wi h only one opamp ha has wo in eg a ing capaci o s connec ed. Du ing odd cycles, he i s capaci o is in eg a ing while he o he is idling (disconnec ed). Do ing e en cycles, he second capaci o is in eg a ing while he i s one is idle. This solu ion has he disad an age o Ibe deg ada ion o he signal because o pa h misma ch be ween he I and Q b anches. A solu ion o ob ain a good ma ching is also p oposed in [3]. The solu ion p esen ed he e depa s om igu e 6 and implemen s he wo-delay in eg a o blocks using a single opamp, leading o he s uc u e p oposed in igu e 7. This s uc u e does no down- con e o p ocess I and Q b anehes ( liS p oposed in [3]) a oiding he p oblems ha a e de i ed om I and Q b anches misma ch. This opology is implemen ed wi h he single opsmp SC ei eui! d awn in igu e 8. To accomplish he wo-<lelay in eg a ion, he opamp is p o ided wi h 2 capaci o s ha hold bo h, I and Q. b anches. A e e y cycle one o he b anches is in eg a ing while he o he is idle. The p oblem o gain sensi i i y can be neglec ed due o he low SNDR sensi i i y o in eg a ion gain o his s uc u e ( ig. 9,10). Powe consump ion will be iden ical han o he Band-Wid h equi alen Base-Band Sigma-Del a Modula o and opamp pe o mance emains simila o hose needed o Base-Band modula o (Fig. 10). The e only emains he disad an age o he eme o ji e in band-pass s uc u es ha equi es a e y good clock. 5. Band-Pass simula ion The band-pass s uc u e based upon he ci eui o igu e 7 bas been simula ed using MA TLAB, aod i s SC e sion using CADENCE (Fig. 8). In igu es 9,10 is shown he pe onnance expec ed h ough simula ion. In igu e 10 is depic ed he SNDR loss o di e en alues o he Slew-Ra e and he BandWid h o he ope a ional ampli ie s used o implemen he wo- delay in eg a o s. The x -axis is no malised o Ts and he SR is no malised o Del a/Ts. These esul s a e simila o hose ob ained o he opamps used wi h a low-pass sigma-del a modula o , hus ha ing simila powe consump ion. Because o his and ha we use same numbe o opamps o band- equi alen low-pass and band-pass modula o s, band-pass modula o s can accomplish he same powe consump ion as he la e . 6. Simula ions using CADENCE and MATLAB Once is he band-pass modula o cha ac e ised, he s uc u e o igu e 7 has been implemen ed in a SC ci cui ( igu e 8) and simula ed wi h CADENCE (Spec e). In igu e II is ep esen ed he equency esponse o bo h (MA TLAB and Spec e) simula ions. Di e en ial Opamps ha e been emula ed wi h an Analog HDL as well as he compa a o and ol age double s. In he mal e sion o his pape ully ansis o -le el esul s using Spec e will be included. Simila pa ame e s we e used in bo h cases: GI=O.25 G2=0.5 Inpu sigual ampli ude=o 0.35·Del a Inpu sigual equency: 0.6·Sigual-Band/2 OSR=256 Ideal condi ions we e supposed o ji e , compa a o and opamp pe o mance. 7. Ji e in iuence in Band-Pass modula o s In band-pass modula o s, whe e siguals a e no hea ily o e -sampled, ji e is a majo p oblem o he equency esponse o ou sys em. Clock ji e esul s in non-uni o m sampling and inc eases he o al eno powe in he quan ize ou pu . An es ima ion o his e o is calcula ed in [8]. Once he inpu analog sigual is sampled, he ji e has no in luencc on he sys em as i beha es as an analog sampled-da a compu e [IJ. I he inpu da a is sampled wi hou ji e , he sys em will ha e a 158 co ec beha iou e en i i s in e nal clocking is a ec ed by ji e . Then, ji e - ela ed p oblems will appea a he inpu sample and hold s age. I is p o en ha unde an unco ela ed gaussian andom ji e wi h s anda d de ia ion dT, he powe o he e o signal is: Sj'."= A2·(2·pi- xdT)'/2 Whe e A is he signal ampli ude and , is i s equency. This e o will be o in e es inside he signal hand. Since he ji e is conside ed whi e, he powe e o is educed by he o e sampling a io (M), which is 4 in he p oposed band-~ass s uc u e. Sin.""",<Del a'·(2·pi·dT) /(8 'M) To e alua e he ole a ed ji e , one mus calcula ed he maximum SNR desi ed a he sys em's ou pu and limi he SNR o a sampled inpu sigual (wi h ji e ) o ha alue. I we expec o ha e a maximum ou pu SNDR o 100dB, he jille mus be limi ed as o ob ain a sampled inpu sigual SNR o mo e han dB's when ji e is p esen . In o de o compa e he e ec s o clock ji e in ou sys em some MA TLAB simula ions ha e heen pe o med. The ji e ha a ec s he clock has di e en simula ed magui udes: a) NULL ji e . b) 100 ppm. An inpu sinusoid signal is sampled using an OSR (O e -sampling Ra io) o 256 o a low-pass modula o and OSR~ o a /4 cen al pass equency modula o . F equency esponses a e sampling o each case a e shown in igu es 12, 13. F equency is ela ed o FI, whe e , is he sampling equency. I is clea ly seen ha he e ec o ji e on he spec a is wo sened when dee easing he OSR. This makes band-pass modula o s much mo e sensi i e o clock ji e han low-pass modula o s. This is he majo d awback ha p esen band-pass modula o s. The nex se o simula ions shows he dependency o OSR in he e ec o ji e . A ji e o 50ppm has heen applied o di e en equency pu e sinusoidal signals. The e ec o ji e makes he spec a o loose a ound 30dB in SNR when mo ing he wo king equency om base-hand o /4. These simula ions a e summa ised in igu e 16. They show he e ec o ji e in bo h low-pass and band-pass modula o s. As expec ed, he e ec on he band-pass modula o is much highe . 8. Conclusions A wo-delay in eg a o using a single opamp is used o build a band-pass sigma-del a modula o . Only wo opamps whe e needed o implemen a 4'" o de s uc u e wi h a simila powe consump ion as equi alen low-pass modula o s. [I) [2) [3) [4] [5J [6] Re e ences "DELTA-SIGMA DATA CONVERTERS, heo y, design and simula ion". S e en R. No swo hy, Richa d Sch eie and Gabo C. Te nes. IEEE P ess. "ANALOG CIRCUIT DESIGN ... " Willy Sansen, Rudy J. Van de Plasshe and Johan H. Huijsing. Kluwe Academic Publishe s. "A FOURTH-ORDER BANDPASS DELTA- SIGMA MODULATOR WITH REDUCED NUMBER OF OP-AMPS". Bang·Sup Song. IEEE Jou nal o solid-s a e ci cui s. Vol 30, No. 12, Decembe 1995. "DESIGN OF LOW·VOLTAGE LOW. POWER CMOS DELTA-SIGMA AID CONVERTERS". Vicenzo Peluso, Michiel S eyae . Winy Sansen. Kluwe Academic Publishe s. "THE DESIGN OF LOW-VOLTAGE, LOW- POWER SIGMA-DELTA MODULATORS". Shah ia Robii, B uce A. Wooley Kluwe Academic PublisheIll. "TOP-DOWN DESIGN OF HIGH· PERFORMANCE SIGMA·DELTA MODULATORS". Fe nando Medei o, Angel Pe ez-Ve du, Angel Rod iguez-Vazquez. KJuwe Academic Publishe s. [7] [8] [9] [IOJ [Ill [12] Figu es ''MODELING AND HIGH-RESOWTION SIGMA·DELTA MODULATORS". Louis Albe Williams Ill, Augus 1993, S an o d Uni e si y. ICL93-022 "THE DESIGN OF SIGMA-DELTA MODULATION ANALOG-TO·DIGITAL CONVERTERS". Be nha d E. Bose , B uce A. Wooley. IEEE Jou nal o solid-s a e ci cui s. Vol SC·23, pp.l298-1308. Decembe 1995. "SWITCHE!)'cAPACITOR BANDPASS DELTA-SIGMA AID MODULATION AT 10.7 MHz". F ank W. Singo , W. Ma in Snelg o e. IEEE Jou nal o solid-s a e ci cui s. Vol 30, No.3, Ma ch 1995. "A 9()O..mV LOW-POWER DS AID CONVERTER WITH 77-dB DYNAMIC RANGE". Vicenzo Peluso, Pe e Vanco enland Augus o M. Ma ques, Miehiel Sley.e , Will; Sansen. IDEE Jou nal o solid-s ale ci cui s. Vol 33, No. 12, Decembe 1998. "SIGNAL PROCESSING ALGORITHMS IN MATLAB". Samuel D. S eams, Ru h A. Da id "MIDAS USER MANUAL". Shah ia Rabii, Louis A. Williams Ill, Be nha d E. Bose , B uce A. Wooley S an o d Uni e si y, Oc . 1997 Figu e 1. 2" o de Low-pass p o o ype. Figu e 2. 4 h o de Band-Pass modula o using esona o s. }o~jgu e 3. SNDR oc a 2 nd o de LP S uc u e Figu e 4. Opamp Spui icaiions o a lnd o de LP s uc u e 159 FIgu e 5. Swi ched Capaci o implemen a ion o a esona o Figu e 6. 4'" o de Band-Pass modula o 0: . ,. INP .,. INN •• :.-y' 0> . ,. '0 C., C, V eul ~OUT 0 C, Figu e 7. Swi ched capaci o implemen a ion o a Band-Pass Sigman-Del a modula o using a educed numbe o opamps LP s uc u e 160 Figu e 10, 11. Band-pass F equeucy esponse a) NULL b) 100 ppm Figu e 12. Ji e y signals o OSR=256 Figu e 14. E ec o ji e when Sampling~a~p~u~ ~e~!!~ , .. lM)sl.HIhlW a) Low-po.s modula o a) NULL ji e b) 100 ppm Figu e 13. Ji e y signals o OSR=4 Figu e 15 E ec o ji e on a) low-pass modula o and b) band-pass modula o . 161