Multi-bit cascade ΣΔ modulator for high-speed A/D conversion with reduced sensitivity to DAC errors

1 o 9 Mul i-bi Cascade ΣΔ Modula o o High-Speed A/D Con e sion wi h Reduced Sensi i i y o DAC E o s Indexing e ms: Mul i-bi ΣΔ Modula o s, High-speed, high- esolu ion A/D con e sion. This pape p esen s a ΣΔ modula o (ΣΔM) which combines single-bi and mul i-bi quan iza ion in a cascade a chi ec u e o ob ain high esolu ion wi h low o e sampling a io. I is less sensi i e o he non-linea i y o he DAC han hose p e iously epo ed, hus enabling he use o e y simple analog ci cui y wi h nei he calib a ion no im- ming equi ed. In oduc ion: A p esen , he e is an inc eased in e es in he use o ΣΔ con e sion in mixed-signal CMOS elecom chips [1]. New a chi ec u es a e equi ed o achie e high esolu ion wi h low o e sampling a io M. Two non-exclusi e s a egies can be adop ed o his end [2]: high-o de il e ing o he quan iza ion noise, and mul i- bi (MB) quan iza ion. They make he in-band quan iza ion noise powe in e sely p opo ional o, espec i ely, ( = il e o de ) and ( =numbe o bi s in he in e nal quan ize ). Examples o low-o e sampling a io ΣΔM's using bo h s a egies a e epo ed elsewhe e [2]-[7]. These ad anced a chi ec u es a e g ouped acco ding o he echniques used o: a) gua an ee s able ope a ion o he high-o de il e ; b) a enua e he e o s due o he MB DAC non-linea i y. A common s a egy o he la e case in ol es using calib a ion [2][3][5], while he o me equi emen can be sol ed h ough he p ope choice o scaling ac o s o ese ing ci cui y [2][3]. Howe e , some a chi ec u es o e come hese p oblems wi h nei he calib a ion no ese ing equi ed. The basic idea consis s o : i s , pe o ming he high-o de il e ing h ough a cascade s uc u e o gua an ee uncondi ional s abili y o any inpu le el and ini ial condi ion [4][6][7]; secondly, using MB quan iza ion only a he las s age o he cascade o a enua e he in luence o he MB DAC non-linea i y [6][7]. P e ious MB cascade ΣΔM's [6][7] a e in ended o a enua e he DAC e o powe by a ac o . The a chi ec u e in his Le e ob ains a a enua ion PQ M2L1+ L 2b1–() 2 b M5 M7 © IET (The Ins i u ion o Enginee ing and Technology). This ma e ial is p esen ed o ensu e imely dissemina ion o schola ly and echnical wo k. Copy igh and all igh s he ein a e e ained by au ho s o by o he copy igh holde s. All pe sons copying his in o ma ion a e expec ed o adhe e o he e ms and cons ain s in oked by each au ho 's copy igh . In mos cases, hese wo ks may no be epos ed wi hou he explici pe mission o he copy igh holde . 2 o 9 ac o . We show ha his can be achie ed h ough p ope choice o he a chi ec u e coe icien s and ha he deg ada ion due o misma ch is ole able o up o . Hence, his modula o is easible o ob aining up o 13-bi esolu ion wi h o e sampling a ios as low as 16. Modula o a chi ec u e: Fig. 1 shows a gene ic dual-quan iza ion N-s age cascade ΣΔM [8]. I includes single-bi quan iza ion in all he s ages excep in he las one which inco po a es a MB quan ize . A e digi al cancella ion o he quan iza ion e o o he o me , he ollowing is ob ained o he Z-domain ou pu : (1) whe e is he Z- ans o m o he modula o inpu , is an scala la ge han uni y (needed o p e en o e loading in he cascade), is he las s age quan iza ion e o , is he e o induced in he las s age DAC, and . No e ha is -o de shaped, which may signi ican ly educe he linea i y equi emen o he DAC. Based on his idea, wo MB ΣΔM a chi ec u es ha e been p oposed. The one in [6] uses a 2-s age 2-1 cascade ( ), while he one in [7] uses a 2- s age 2-2 cascade ( ). In bo h cases, ollowing (1), is 2nd- o de shaped. Wi h he same p inciple, Fig. 2 shows a no el MB cascade ΣΔM a chi ec u e ha be e exploi s he dual-quan iza ion echnique. I is a 3-s age 2-1- 1 cascade ( ) wi h single-bi quan iza ion in he i s wo s ages and MB quan iza ion in he las one. Table 1 shows he ans e unc ions o he digi al blocks in Fig. 2 and he ela ionships be ween analog and digi al coe icien ha cancel he quan iza ion noise in he i s wo s ages. The analog coe icien s (in eg a o weigh s) mus be p ope ly chosen o a oid p ema u e o e loading o he s ages in he loop and maximize he dynamic ange (DR). We p opose he ollowing: , so ha , . Such a choice can be ealized by using b3= Yz() Xz()zLT –d1z1– –() LTENz() d1z1– –() LTLN –() EDz()++= Xz() d ENz() EDz() LTL1…LN ++= EDz() LTLN –() h L12= L2 ,1= L12= L2 ,2= EDz() L12= L2 ,1= L3 ,1= g1g1' 0,25,== g2g3 =g4'g4'' 1 g2',g3'g3'' 0,5,== = == = g42= d01–= d12d2 ,0d3 ,2=== 3 o 9 only 2-b anch SC in eg a o s wi h educed ou pu swing and dynamic equi emen s. A e digi al cancella ion, he Z-domain modula o ou pu esul s: (2) No e ha he DAC e o s a e 3 d-o de shaped. Thus, he in-band noise powe a he modula o ou pu esul s: (3) whe e and ep esen he powe o he las s age quan iza ion and DAC e o , espec i ely. The la e con ibu ion is a enua ed by (ins ead o as in [6][7]). In luence o O he Non-Ideali ies: In p ac ice, in eg a o weigh misma ch and ini e DC-gain p oduce incomple e cancella ion o he quan iza ion noise in he i s s ages o he cascade, hus deg ading he signal- o-(noise+dis o ion) a io (SNDR). This imposes an uppe limi on he use ul esolu ion o he las s age quan ize . Abo e his limi , he bene i s o ine quan iza ion in he las s age may be masked by he un-cancelled po ion o he quan iza ion noise o he p e ious s ages. Fig. 3 shows he hal -scale SNDR ob ained by beha iou al simula ion o he new modula o as a unc ion o he las quan ize esolu ion. These simula ions include in eg a o weigh misma ch (sigma = 0.1%) and ini e DC-gain (1000); acco ding o hem, using quan ize s wi h mo e han 3-bi esolu ion does no make sense. Howe e , his is enough o signi ican ly educe he equi ed o e sampling a io espec o he single-bi case. Fig. 4 compa es he wo s -case SNDR (sigma = 0.1%) as a unc ion o he inpu le el o he 2-1-1 3bi ΣΔM wi h ha o hose in [6][7], always using op imized in eg a o weigh s; o comple eness, we also make a compa ison wi h he 2-1-1 single-bi . Compa ed o he 4 h-o de a chi ec u es, he new one ea u es he la ges DR wi h he lowes o e sampling a io. Pa icula ly, o each simila pe o mance wi h he single-bi app oach, M mus be a leas 24. In summa y, because he new a chi ec u e ole a es he analog non-ideali ies o 3-bi quan iza ion (wi h no calib a ion needed), i is easible o high- equency ΣΔ Yz() z4– Xz() 21 z1– –() 4E3z() 21 z1– –() 3EDz()++= P2-1-1MB 4σQ 2π8 9M9 ---------- σD 2π6 7M7 ----------+ ⎝⎠ ⎛⎞ = σQ 2 σD 2 M7 M5 4 o 9 ADC's wi h low o e sampling a io and, hence, low-powe consump ion. Acknowledgmen : This wo k has been suppo ed by Spanish C.I.C.Y.T. unde con ac TIC97-0580. F. Medei o B. Pé ez-Ve dú J.M. de la Rosa A. Rod íguez-Vázquez Ins i u o de Mic oelec ónica de Se illa - C.S.I.C Edi icio CICA-CNM A da. Reina Me cedes s/n 41012-Se illa, SPAIN Re e ences 1 CHAN, Z-Y, MACQ, D., HASPESLAGH, D., SPRUYT, P. and GOFFART, B.: “A CMOS analog on -end ci cui o an FDM-based ADSL sys em”, IEEE Jou nal o Solid-S a e Ci cui s, 1995, SC-30, (4), pp. 1449-1456 2 NORSWORTHY, S.R., SCHREIER, R. and TEMES G.C. (Edi o s): Del a-Sigma Da a Con e e s: Theo y, Design and Simula ion, IEEE P ess, New Yo k, 1997 3 BAIRD, R.T., and FIEZ, T.S.: “A Low O e sampling Ra io 14-b 500-kHz ΔΣ ADC wi h a Sel -Calib a ed Mul ibi DAC”, IEEE Jou nal o Solid-S a e Ci cui s, 1996, SC-31, (3), pp. 312-320 4 MARQUES, A., PELUSO, V., STEYAERT, M. and SANSEN, W.: “A 15-bi 2 MHz Nyquis Ra e ΔΣ ADC in a 1μm CMOS Technology”, P oc. ESSCIRC'97, 1997, pp. 68-71 5 CHEN, F., and LEUNG, B.H.: “A High esolu ion Mul ibi Sigma-Del a Modula o wi h Indi idual Le el A e aging”, IEEE Jou nal o Solid-S a e Ci cui s, 1995, SC- 30, (4), pp. 453-460 6 BRANDT, F., and WOOLEY, B. A.: “A 50-MHz mul ibi ΣΔ modula o o 12-b 2- MHz A/D con e sion”, IEEE Jou nal o Solid-S a e Ci cui s, 1991, SC-26, pp. 1746- 1756 7 TAN, N., and ERIKSSON, S.: “4 h-o de 2-s age Δ−Σ modula o using bo h 1 bi and mul ibi quan ize s”, Elec onics Le e s., 1993, 29, pp. 937-938 8 DIAS, V.F., and LIBERALI, V.: “Cascade Pseudomul ibi Noise Shaping 5 o 9 LIST OF CAPTIONS: Figu es: Fig. 1 Gene ic dual-quan iza ion N-s age cascade ΣΔM Fig. 2 Block diag am o he 2-1-1 cascade MB ΣΔM Fig. 3 SNDR s. las quan ize esolu ion in p esence o non-ideali ies Fig. 4 Wo s -case SNDR s. inpu le el in p esence o capaci o misma ch and ini e in eg a o DC-gain Tables: Table 1: Coe icien ela ionships in Fig. 2 6 o 9 Modula o s', IEE P oceedings.-G, 1993, 140, pp. 237-246 ΣΔ1 ΣΔ2 ΣΔN L1 L2 LN Y1 Y2 YN X2 X3 XN X Y CANCELATION LOGIC E1 E2 EN Q 1-Bi Q b-Bi Q 1-Bi Fig. 1 Gene ic dual-quan iza ion N-s age cascade ΣΔM 7 o 9 Y1 XE1 g2 −g2' g1 −g1' D/A g3 g3' g3'' − −Y2 E2 D/A H1(z) + + d1 d0 − g4 g4' g4'' − −Y3 E3 d3+ Y + d2 A/D b-Bi D/A b-Bi b b ED H2(z) H3(z) H4(z) Fig. 2 Block diag am o he 2-1-1 cascade MB ΣΔM − Cancella ion Logic 8 o 9 Las quan ize esolu ion (bi ) Hal -scale SNDR (dB) Fig. 3 SNDR s. las quan ize esolu ion in p esence o non-ideali ies 123456 65 70 75 80 85 90 Ideal Wi h e o s Fig. 4 Wo s -case SNDR s. inpu le el in p esence o capaci o misma ch and ini e in eg a o DC-gain -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Inpu / Re e ence (dB) 0 10 20 30 40 50 60 70 80 90 SNDR (dB) 2-1-1, 3bi , M = 16 2-1-1, M = 24 2-1, 3bi , M = 24 2-2, 3bi , M = 16 INL = 1%FS Weigh misma ch = 0.1% DC-gain = 1000 9 o 9 Table 1: Coe icien ela ionships in Fig. 2 Digi al Digi al/Analog Analog H1z() z1– = d01g3'g1g2g3 ()⁄–= g1'g1 = H2z() 1z1– –() 2 = d1g3'' g1g2g3 ()⁄= g2'2g1'g2 = H3z() z1– = d20= g4'g3''g4 = H4z() 1z1– –() 4 = d3g4'' g1g2g3g4 ()⁄=