High-order cascade multibit /spl Sigma//spl Delta/ modulators for xDSL applications

ISCAS 2000 - IEEE In e na ional Symposium on Ci cui s and Sys ems, May 28-31, 2000, Gene a, Swi ze land HIGH-ORDER CASCADE MULTIBIT CA MODULATORS FOR xDSL APPLICATIONS R. del Rio, E Medei o, B. Pe' ez-Ve dLi, and A. Rod iguez-V izquez Ins i u o de Mic oelec dnica de Se illa - CNM-CSIC Edi icio CICA-CNM, C/Ta ia s/n, 41012- Se illa, SPAIN Phone: +34 95 5056666. Fax: +34 95 5056686, E-mail: [email p o ec ed] ABSTRACT This pape explo es he use o CA modula o s o AD con e - sion in xDSL applica ions. Two high-o de mul ibi a chi ec u es, he 2-I-lm0 modula o [7] and ano el2-1-1-lmb cascade (MASH), a e p oposed o achie e 14bi dynamic ange @ 4.4MSls using low o e sampling a io. They show e y low sensi i i y o he in emal DAC linea i y e o , wi h no calib a ion equi ed. Simula ions show his pe o mance can be achie ed in p esence o ci cui impe ec- ions, using submic on digi al CMOS p ocesses. 1. INTRODUCTION CAModula o s (CAMs) ha e been success ully employed in he pas o IOW-, medium- equency AD con e sion [l]. The use o o e sampling and noise-shaping echniques in hese con e e s a oids he need o ex emely accu a e analog building blocks, wha makes hem e y sui able in he con ex o poo -analog-pe o mance submic on CMOS p ocesses. Such ad an ages ha e encou aged designe s o widen he bandwid h o EA con e e s up o he da a acquisi ion and communica ion anges [2]-[SI, demanding high- es- olu ion and high-speed ope a ion. Conside ing only quan iza ion noise, he dynamic ange DR o a CAM can be oughly es ima ed as ollows: L IC J whe e L s ands o he modula o o de , M o i s o e sampling a io, and B o he in e nal quan ize esolu ion in bi s. In high-speed applica ions, inc easing he signal bandwid h , while main aining an achie able sampling equency , implies he use o a mode a e M, since M = s/(2 x). In his scena io, he na u al way o inc ease DR in o de o cope wi h high- esolu ion speci ica ions is o eso o high-o de (inc easing L), mul ibi (inc easing B) CAMs. Howe e , wo impo an d awbacks a ise: On he one hand, unlike 1s - and 2nd-o de loops, high-o de loops a e no uncondi ionally s able. On he o he , he linea i y o he mul ibi CAM is ul ima ely lim- i ed by ha o he mul ibi DAC in he eedback pa h. Bo h p oblems ha e been pa ially o e come; ac ually, high-o de ZAMs ha e been s abilized h ough se e al echniques [I]: i.e., p ope choice o he scaling ac o s, use o mul ipa h eed- o wa d s uc u es, o ese ing o he in e nal a iables i uns able ope a ion is de ec ed. On he o he hand, a common s a egy o pal- lia e he s ong dependence on he in e nal DAC linea i y is using calib a ion ei he in he analog o in he digi al domain [I]. Ne e heless, cascade mul ibi a chi ec u es o e come hese pe o ming he high-o de il e ing by cascading low-o de (1 s - and 2nd-) CAMs o gua an ee uncondi ional s abili y, and using mul ibi quan iza ion only a he las s age o he cascade o a enua e he in luence o he DAC non-linea i y [2]. This pape explo es he use o such a chi ec u es o ob ain [email p o ec ed]/s - speci ica ions in he ange o xDSL equi emen s. In Sec ion 2, wo cascade mul ibi a chi ec u es a e conside ed: a 4 h-o de 3-s age cascade (wi h he s uc u e 2-1-1) and a 5 h-o de 4-s age cascade (2-1 -1 -l), bo h including mul ibi quan iza ion. Sec- ion 3 is dedica ed o analyze he impac o ci cui impe ec ions deg ading he modula o s pe o mance. p oblems wi h nei he calib a ion no ese ing equi ed by: 2. CASCADE MULTIBIT XAMs Fig.1 shows a gene ic L h-o de N-s age cascade mul ibi CAM. I includes single-bi quan ize s in all s ages excep he las one which has a mul ibi quan ize . In cascade CAMs, he quan iza ion e o induced in each s age is emodula ed by he ollowing one in he cascade. Once in he digi al domain, by p ope ly combining he ou pu s o he s ages, i is possible o cancel ou he quan iza ion e o in all s ages excep ha in he las one, which appea s a he modula o ou pu a enua ed by a shaping unc ion o o de equal o he summa ion o he o de o all s ages. Thus, ideally, he ollowing is ob ained o he Z-domain ou pu : IL -1 W-L,) Y(z)=z-LX(z)+d(l -z- ) EN(Z)--d(l --z ) E,(z) (2) whe e X(z) is he Z- ans o m o he modula o inpu , d is an scala la ge han uni y esul ing om p ope scaling o he ans e ed sig- nal o p e en o e loading o he s ages, E$z) is he las -s age quan iza ion e o , E,(z) is he e o induced in he las -s age DAC, Fig. 1: Gene ic L h-o de N-s age cascade mul ibi CAM. (*) This wo k has been pa ially suppo ed by he ESPRIT P ojec 29261 MIXMODEST, and he CICYT P ojec TIC 97-0580 0-7803-5482-6/99/$10.00 02000 IEEE 11-37 and L = L, + . . . + L,. No e ha ED(z) is (L - L,) h -o de shaped, wha signi ican ly elaxes he DAC linea i y speci ica ions, wi h nei he co ec ion no calib a ion equi ed. Se e al cascade mul ibi CAMS ha e been epo ed: a 3 d-o de 2-1 cascade (2-lmb) [2], a 4 h-o de 2-2 cascade (2-2mb) [3], and a 4 h-o de 2-1-1 cascade (2-12mb) [7]. Acco ding o eq.(2), DAC-induced e o is 2nd-o de shaped in he i s wo modula o s and 3 d-o de shaped in he las one. Thus, while in he 2-lmb and 2-2mb a chi ec u es he in-band powe o such e o is a enua ed by M5, i is a enua ed by M7 in he 2-12mb. This conside ably educes he sensi i i y o he la e o he DAC ZNL, simpli ying he e o e i s design. Fig.2 illus a es he 2-12mb cascade CAM. A 5 h-o de 4-s age 2-1-1-1 cascade using mul ibi quan iza ion in he las s age (2-13mb), Fig.3, has been de eloped as an ex ension o he o me o one mo e o de , while p ese ing i s p ope ies. Ide- ally, he ollowing Z-domain ou pu is ob ained o bo h modula o s: Digi al HI(?) = z-' whe e i has been assumed ha he ela ionships among digi al and analog coe icien s and he alues o he digi al il e s H&z), k = 1, ,.., 6 a e hose in Table 1 and 2, espec i ely. The e o e, he in-band e o powe a bo h modula o ou pu s is Digi al/Analog Analog _I d - 1 -- &?I' = g, 831 O- s,g,g, (4) whe e c i = [A/(28- 1)12/12 is he powe o he las -s age quan iza ion e o (A s ands o he las -s age quan ize ull+ale) and c i ep esen s he DAC-induced e o powe . No e ha his e o is a enua ed by M9 in he 2-13mb. 2.1 In eg a o weigh op imiza ion Wha e e se o coe icien s (in eg a o weigh s in Fig.2 and 3) ul illing he ela ionships in Table 1 and 2 leads o he exp essions in eq.(3). Ne e heless, he ollowing conside a ions mus be aken in o accoun in ac ual implemen a ions: The le el o he signal ans e ed om one s age o he nex in he cascade mus be low enough o a oid o e loading he la e . I * Cancella ion Logic Fig. 2: 4 h-o de 2-1-1 cascade mul ibi CAM (2-12mb). ' Cancella ion Logic Fig. 3: 5 h-o de 2-1-1-1 cascade mul ibi ZAM (2-13mb). TABLE 1: Digi al ans e unc ions and ela ionships o he 2-1' ZAM. I Digi al I Digi al/Analog I Analog I H2(z) =(1 -z-1)2 d, = - g,' =2g,'g2 s,gzg3 U d2 = 0 g,' = s3"g4 H3(Z) = 2-1 TABLE 2: Digi al ans e unc ions and ela ionships o he 2-1'' CAM. . I~_ , I 82' = 2g,'g, H,(z) = z-1 d, = 0 I The ou pu swing equi ed o he in eg a o s, which depends on hei weigh s as well as on he inpu le el, mus be physically achie able. In SC implemen a ions his limi is de e mined by he supply ol ages. Digi al coe icien s d, and d, , which ampli y he las -s age quan iza ion e o in eq.(3), should be as small as possible. Addi ional conside a ions in o de o simpli y he design a e: Digi al coe icien s should be 0, 1 o mul iple o 2. Mul ibi quan ize gain mus be such ha he loop gain o he las s age equals uni y. Mo eo e , i should no be oo la ge in o de 11-38 o simpli y he design o he mul ibi quan ize . Table 3 p esen s good selec ions o he in eg a o weigh s o he 2-I2mb and 2-13mb, o which he ou pu swing equi emen is educed o only he e e ence ol ages. In addi ion, in bo h cases he las -s age quan iza ion e o is ampli ied only by 2, d, = d, = 2 in eq.(3). This means a sys ema ic loss o esolu ion o 6dB (Ibi ) espec o he ideal case gi en in eq.(l). Howe e , his loss is small when compa ed o ha caused by s abiliza ion and non-linea i y co - ec ion mechanisms used in o he app oaches [ 13. Ano he 5 h-o de mul ibi cascade we ini ially conside ed, a 2-2-lmb CAM, was dis- ca ded a his poin because he se o coe icien s equi ed o a oid o e loading lead o d, = 8 (3bi sys ema ic loss). TABLE 3: Analog and digi al coe icien s in Fig.2 and 3. Shaded cells co espond o he 2-13,nb modula o These coe icien s p esen wo addi ional ad an ages: Because he la ges weigh in all h ee-weigh in eg a o s can be easily ob ained as a combina ion o he o he s, an SC implemen- a ion will only equi e wo-b anch in eg a o s. No e ha only one b anch is needed o he i s in eg a o . The o al numbe o uni a y capaci o s is only 16 o he 2-12mb and 19 o he 2-13mb modula o , smalle han in o he cascade ZAMs - 29 uni a ies in [5] and [8], and 44 in [6]. 3. CIRCUIT NON-IDEALITIES Excep o he DAC-induced e o s, he a chi ec u al s udy in Sec ion 2 assumes ideal condi ions. Ne e heless, ci cui impe ec- ions deg ading he CAM pe o mance mus be aken in o accoun in p ac ice. These non-ideali ies can be g ouped in wo ca ego ies: hose a ec ing he quan iza ion noise ans e unc ion, whose e ec s ongly depends on he a chi ec u e conside ed, o ins ance in eg a o leakage and weigh misma ching, and hose ha can be modeled as an e o sou ce a he i s in eg a- o ; such app oxima ion is jus i ied by he ac ha he con ibu- ion o emaining in eg a o s is a enua ed by inc easing powe s o he o e sampling a io. This is he case o he mal noise, de ec i e se ling in in eg a o s, e c. 3.1 In eg a o leakage and weigh misma ching The ideal s udy de eloped in Sec ion 2 assumes ha he ela ion- ships o Table 1 and 2 a e ul illed and ha he ans e unc ion o he in eg a o s is exac ly z-'/( 1 - -l) . Howe e , hese assump- ions a e no alid in p ac ice: On he one hand, ac ual alues o in eg a o weigh s di e om nominal ones due o misma ch in capaci o s a ios. On he o he , he in eg a o ans e unc ion abo e is modi ied by he ini e DC-gain o he ampli ie s. 0 1 2 3 4 5 81 s (a) B (bi ) 2 3 4 5 B (bi ) Fig. 4: Modula o esolu ion s. las -quan ize esolu ion o : (a) 2-1 ,mb CAM and (b) 2- 1 3mb CAM. (A, = 2500, weigh misma ch ( = 0.1 %, and DAC INL = 0.4% FS) Bo h non-ideali ies esul in an incomple e cancella ion o he quan iza ion e o o he o me s ages and deg ade he modula o DR [9]. Analysis shows ha he ex a in-band e o powe due o hese non-ideali ies is: whe e A, s ands o he opamp DC-gain, e e s o misma ching in weigh s g,, g,, g3and g,", and c : = A2/12 is he quan iza ion e o powe o a single-bi quan ize . No e ha hese ex a e o con ibu ions can in p ac ice mask hose in eq.(4), since hey a e only a enua ed by M3 and M5 . Fig.4 shows simula ion esul s o he e ec i e esolu ion o he 2-12mb and 2-1 3mb modula o s when a ying he las -s age quan ize eso- lu ion B, wi h M ac ing as a pa ame e (depic ed o e each cu e). No e ha cu es sa u a e in he p esence o hese non-ideali ies, leading o a p ac ical limi o he use o mul ibi quan iza ion - g ossly es ima ed by he hick solid line. Inc easing B o e his limi would no u he imp o e he modula o DR. Ne e heless, esolu- ions below his limi a c enough o signi ican ly elax he ci cui equi emen s wi h espec o single-bi app oaches. 3.2 O he ci cui s impe ec ions Di e en [M, B] pai s can be a p io i selec ed om Fig.4 o he 2-I2mb and he 2-13mb modula o s, in o de o ul il speci ica ions o [email p o ec ed]/s. Ne e heless, as ope a ion equencies inc ease 11-39 in ZAMs, he de ec i e se ling o SC in eg a o s becomes one o he dominan e o s limi ing he modula o s pe o mance. Thus, he inal choice among possible [M, B] pai s mus be done in p ac ice conside ing he opamp dynamic equi emen s in ol ed. Table 4 shows an es ima ion o he equi ed opamp bandwid h (GBW) o he di e en [M, B] pai s ob aining >13bi o bo h modula o s. M = 16, B = 4 o he 2-I2m6 modula o and M = 14, B = 3 o he 2-13mb a e he less demanding pai s o 14bi esolu ion. No e ha mul ibi quan iza ion signi ican ly elaxes he dynamic equi emen s wi h espec o a single-bi app oach. Fo ins ance, a 2-12 modula o wi h single-bi quan iza ion would equi e M = 22 o ob ain 14bi esolu ion. This highe M would lead o an inc ease o -35% on he powe consump ion pe opamp. TABLE 4: Es ima ed opamp GBW o ope a ion a 4.4MS/s. 2-1~~0 14 61.6 +I 0.5 0.5 0.1 25 20 0.2 68 20% 2.25 0.9 +1/%2’ 20 3 0.4%FS 86.4dB (14.1 bi ) -91.5dB -95.5dB 102.4dB .IOl.ldB / The o e all in luence o ci cui impe ec ions on he modula o pe o mance has been e alua ed using SDOF’T [9], a sizing ool o SC CAMS. This ool combines accu a e analy ical exp essions o each e o con ibu ion and s a is ical op imiza ion, wha allows us o ind op imized, non-o e sized speci ica ions o he building blocks. Table 5 summa izes he ci cui equi emen s p o iding [email p o ec ed]/s o bo h a chi ec u es, aking in o accoun he di - e en e o con ibu ions (e.g., quan iza ion and he mal noise, se - ling e o , capaci o misma ching, ini e opamp DC-gain). Fig.5 shows beha io al simula ion esul s using ASIDES [9] o he signal- o-(noise+dis o ion) a io SNDR o bo h modula o s in he p esence o he ci cui s impe ec ions in Table 5. The maximum SNDR, ob ained o a -5dB inpu le el, is 80.5dB o he 2-I2m6 and 79dB o he 2-13mb. The DR is 86dB and 84.5dB, espec i ely. These esul s p esen bo h a chi ec u es as good candida es o ob ain high- esolu ion, high-speed ope a ion in xDSL applica ions, wi h a mode a e powe consump ion. In ac , wi h he explo ed mod- ula o s, DAC non-linea i ies up o 0.4%FS can be ole a ed wi h mode a e equi emen s o he building blocks. - Uni - Mllz ‘ pF pF 9’0 pp n/L 46 kQ dB -2 mA/ nL4 niV bi - - - - - 80 70 - 60 s 50 M e 9 40 ‘ 30 20 10 CONVERTER (Non-linea i y (INL) 5 Iynamic ange Inpu le el (dB) Fig. 5: SNDR as a unc ion o he inpu le el. 0.4%FS 87.7dB TABLE 5: Modula o sizing esul s Uni a y capaci o 0.5 Capaci o non-linea i y _i Sigma [NTEGRATORS DC-gain 2 DC-gain non-linea i y 5 Maximum ou pu cu en Di e en ial ou pu swing :OMPARATORslHys e esiS 5 I 20 A/D/A ]Resolu ion I4 ’henna1 noise -95.9dB ncomple e se ling noise -102.3dB *. Only hi d in eg a o needs +2V ou pu swing 4. REFERENCES [I] S. R. No swo hy, R. Sche eie and G. C. Temes (Edi o s):: “Del a-Sigma Da a Con e e s: Theo y, Design and Simula- ion”, IEEE P ess, 1996. [2] B. B and and B. A. Wooley: “A 50-MHz Mul ibi CA Modula- o o 12-b 2-MHz AD Con e sion”, IEEE J. o Soli -S a e, Ci cui s, ol. 26, pp. 1746-1756, Dec. 1991. [3] N. Tan and S. E iksson: “Fou h-O de Two-S age Del a-Sigma Modula o Using Bo h 1 Bi and Mul ibi Quan ize s”, Eleci onics Le e s, ol. 29, pp. 937-938, May 1993. [4] G. M. Yin and W. Sansen: “A High-F equency and High-Reso- lu ion Fou h-O de CA A/D Con e e in BICMOS Technol- ogy”, in P oc. o Eu opean Solid-S a e Ci cui Con , pp. 1-4, Sep . 1993. [5] A. Ma ques, e al.: “A 15-b Resolu ion 2-MHz Nyquis Ra e AZ ADC in a 1 -pm CMOS Technology”. IEEE J. o Soli&S a e Ci cui s, ol. 33, n. 7, pp. 1065-1075, July 1998. [6] A. Feldman, e al.: “A 13-Bi , 1.4-MSIs Sigma-Del a Modula o o RF Baseband Channel Applica ions”. IEEE J. o Solid-S a e Ci cui s, ol. 33, n. 10, pp. 1462-1469, Oc . 1998. [7] E Medei o, e al.: “A 13-bi , 2.2-MS/s, 55-mW Mul ibi Cas: cade CA Modula o in CMOS 0.7-pm Single-Poly Techno$- ogy”. IEEE J. o Solid-S a e Ci cui s, ol. 34, n. 6, pp. 748-760, June 1999. [8] Y. Gee s, e al.: “A 3.3-V, 15-bi , Del a-Sigma ADC wi h aSig- nal Bandwid h o 1.1 MHz o ADSL Applica ions”. IEEE J. $ Solid-S a e Ci cui s, ol. 34, n. 7, pp. 927-936, July 1999. [9] .F. Medei o, B. PC ez-Ve dli and A. Rod iguez-Vizquez: “Top-Down Design o High-Pe o mance Sigma-Del a Modu- la o s”, Kluwe Academic Publishe s, Bos on, 1998. 11-40