Analysis and Experimental Characterization of Idle Tones in 2nd-Order Bandpass Sigma-Delta Modulators - A 0.8μm CMOS Switched-Current Case Study

ANALYSIS AND EXPERIMENTAL CHARACTERIZATION OF IDLE TONES IN 2nd-ORDER BANDPASS ZA MODULATORS - A 0.8Fm CMOS SWITCHED-CURRENT CASE STUDY Jose' M. de la Rosa, Bel& Pe' ez- Ve du, Fe nando Medei o, Rocio del Rio and Angel Rod iguez- Vazquez Ins i u o de Mic oelec hica de Se illa, IMSE (CNM-CSIC) Edi . CNM-CICA, A da. Reina Me cedes s/n, 41012 Se illa, SPAIN Phone: +34 95056666, FAX: +34 95056686, E-mail: [email p o ec ed] ABSTRACT Ths pape analyses he onal beha iou o he quan iza ion noise in 2nd-o de bandpass .U modula o s. The analysis p e i- ously pe o med o lowpass modula o s is ex ended o he band- pass case. As a esul . closed- o m exp essions o he equency o he idle ones a e de i ed o di e en loca ions o he signal cen e equency. The analy ical esul s a e alida ed h ough measu emen s om a silicon p o o ype ealized using ully di e - en ial swi ched-cu en ci cui s in a s anda d 0.8pm CMOS ech- nology' *'. 1. INTRODUCTION Among o he easons, &z zdpnss ZA Modula o s (BP-ZAMs) [l] a e o in e es due o hei sui abili y o ealize he Ana- log- o-Digi al (AD) con e sion o ei he In e media e F equency (IF) o Radio F equency (RF) signals in modem digi al adio e- cei e s. Such A/D con e sion pe mi s he implemen a ion o he IF s age in he digi al domain, hus allowing digi al con ol o he gain and he coe icien s o he IF il e . This has nume ous ad an- ages as compa ed o he adi ional (analog) adio ecei e s: e- duc ion o in e e ences, p og ammabili y, e c ... Mos epo ed BP-ZAMs ob ain hei a chi ec u e by applying a (LP-ZAM)[2][3]. Because o his ans o ma ion, a L h-o de LP-ZAM becomes a 2L h-o de BP-ZAM, keeping mos o he p ope ies o he o me . One o hese p ope ies is he p esence o idle ones in he ou pu spec um o he modula o . This phenome- non is caused by he co ela ion be ween he inpu signal and he quan iza ion e o [4]. The non-linea beha iou o he quan iza- ion e o is mo e signi ican as he numbe o in e nal le els o he quan ize and/o he o de o he modula o dec ease, he wo s case co esponding o a 1s -o de LP-ZAM wi h a I -bi quan ize . The onal beha iou o he quan iza ion e o in LPSAMs has been analysed elsewhe e [5][6][7]. Howe e , e y li le has been done cu en ly o BP-ZAMs. In [8] a non-linea analysis o a 2nd-o de BP-LAM is epo ed assuming ha he inpu is a sinus- oidal signal wi h equency equal o a qua e o he sampling e- quency - he ideal signal-band cen e equency. Howe e , as we demons a ed in [9], in p ac ical ci cui s his cen e equency be- comes shi ed due o he in luence o ci cui e o s, and such shi - ing needs o be conside ed o ealis ic onal beha io analysis. Asides wi h he analy ical conside a ions, his pape shows ex- pe imen al e idence o he onal beha io o a 2nd-o de BP-LAM silicon p o o ype. The demons a ion ehicle is a ully di e en ial swi ched-cu en (SI) ci cui , ealized in a 0.8pm, s anda d CMOS echnology. Measu emen s show ha he esul s ob ained o LP-ZaMs [5] can be ex ended o he bandpass case in o de o ex- plain he onal beha iou o he quan iza ion e o in BP-ZAMs. '"ais wo k has been suppo ed by he Spanish CICYT P ojec --I + ---1 ~ ans o ma ion o a Loowpnss EA Modula o TIC 97-0580 2. IDEAL ANALYSIS OF 2nd-ORDER BP-XAMs Fig.l(a) shows he block diag am o a 2nd-o de BP-UM. I has been ob ained by applying a :-I -- -:-? ans o ma ion o a 1s -o de LP-XAM. As a consequence o his ans o ma ion, he o iginal in eg a o becomes a esona o . Thus, he i s s ep o- wa ds he design o a BP-ZAM is choosing a sui able a chi ec u e o ealize he esona o ans e unc ion. This can be ealized U:;- ing di e en opologies [2]. In his pape we will adop a s uc u e consis ing o a eedback cascade o wo Lossless Disc e e ln eg c - o s (LDI), shown in Fig.l(b), whe e AF = 1 and AFB = 2. This s uc u e has been chosen because i keeps he poles inside he uni ci cle upon changes due o e o s o he eedback loop gain. Howe e , he use o his esona o equi es an addi ional de- lay block o be included in he digi al loop. see Fig.l(a), in o de o achie e he equi ed delay in he modula o eedback loop. 2.1 Linea analysis Assuming ha he quan iza ion e o is modelled as an addi i e whi e noise sou ce, he quan ize can be eplaced by he linea model shown in Fig.l(c) [6][7]. In such ;I case, he modula o in Fig. 1 (a) can be iewed as a wo-inpu , s and e , one ou pu , y . sys em. which in he 2-domain can be ep esen ed by: (11) whe e STF(:) and NTF(:) a e he signal ans e unc ion and he: noise ans e unc ion, espec i ely, Y(z) = STF(Z)X(Z) + NTF(~)E(C) -1 -7 STF(L) = : NTF(;) = I +c - (9) By making z = exp(j2n / S). whe e , is he sampling e- quency. i can be shown ha N,( ) has one ansmission ze o a J4, and ha he il e ing a ound his equency is ac ually o he band-s op ype. The inpu signal is allowed o pass while, a he same ime. mos o he quan iza ion noise powe is "shaped" so ha is pushed ou o he signal band. The in-band quan iza ion noise powe can be calcula ed by in eg a ing he ou pu powe Spec al .----_-. ._-_-_. (a) .----------~-------.-. I' .____. ll @ (C) ._-___-_-____ _-_____. Figu e 1. (a) Block diag am o he modula o in his pape . (b) LDI-loop esona o . (c) Linea model o he quan ize . 0-7803-6685-9/01/$10.0002001 IEEE IV-774 Densi y (PSD) wi hin he signal bandwid h, whe e Sp = A’/( 12 ,) is he PSD o he quan iza ion noise, A is he quan iza ion s ep, B,!, is he signal bandwid h and M = /(2B,,,) is he o e sampling a io. F om (3), and assuming ha he modula o inpu is a sinewa e o ampli ude A, 5 A/2 , he Signal- o-Noise & i0 ( SNR ) and he mnamic Range (DR ) a e gi en by: This ideal analysis shows ha he modula o esolu ion inc eases wi h M a a a e o abou l.S-bi /oc a e . This ideal ea u e is achie ed only i he esona o in Fig.l(b) is ealized wi hou e o s and he quan iza ion e o is modeled by a whi e noise sou ce. 2.2 Non-linea analysis In he linea model shown in Fig.l(c), he quan iza ion e o , e = y - . , , is assumed o be no co ela ed wi h he quan ize in- pu . .xl . Ac ually, his e o is a non-linea unc ion o sI , as il- lus a ed in Fig.2 o an N-bi quan ize i1. I x, a ies andomly om sample o sample in he in e al [.Y~,~~~~, . mas] (see Fig.2). e is la gely unco ela ed wi h sI [4] and he linea model p o ides good esul s. This is achie ed in LP-ZAMs o la ge modula o o de s and N > 1 [7]. The e o e, he wo s case o applying he linea model co esponds o a 1s -o de modula o wi h a 1-bi quan ize . Candy [6] demon- s a ed ha , o a dc inpu signal, he in-band quan iza ion e o powe a he modula o ou pu sha ply changes wi h he inpu am- pli ude. This is illus a ed in Fig.3(a) o M = 64 and A = 2. This p ope y o he quan iza ion e o , o en known as noise pa - em, is ansla ed o a 2nd-o de BP-XAM when he inpu signal is a single one placed a ,/4. This is illus a ed in Fig.3(b) by showing he simula ed in-band quan iza ion e o powe a he ou pu o Fig.l(a) as a unc ion o he inpu ampli ude. This be- ha iou can no be explained by he linea model (dashed line in Fig.3(b)) and hence, a non-linea analysis is equi ed. G ay [5] sol ed he non-linea di e ence equa ions o a 1 s -o de LP-ZAM, showing ha o dc inpu s, he quan iza ion e o spec um is disc e e, wi h ones (o en named idle ones) a --- (a) Figu e 2. Ideal quan ize . (a) Inpu -ou pu cha ac e is ics. (b) Quan iza ion e o . I. In he igu e, X,, s ands o he ull-scale ange o he quan ize . No e ha o N = 1 , X,, = A. Inpu le el e e ed o 32 Figu e 3. Noise pa e n o a (a) 1s -o de LP-EAM and (b) 2nd-o de BP-U. whe e A., is he ampli ude o . and (a) ep esen s he ac ional pa o a. The ampli ude o hese ones is 1 A lp,, = - (?XI?)- The abo e esul s can be ex ended o he bandpass case by ap- plying he equency ansla ion dc -- ,/4 o (5). This implies ha he quan iza ion e o spec um o a 2nd-o de BP-ZAM wi h a sinusoidal signal placed a ,/4 will ha e pai s o idle ones a No e ha he e a e ones placed a ound dc and ,/2 - simila o he case o 1s -o de LP-ZAMs. Howe e . in 2nd-o de BP-UMs he e a e also pai s o ones a bo h sides o ,/4 , he mos signi - ican being loca ed a ,/4 k A ,/(24) as will be demons a ed expe imen ally in Sec ion 4. 3. NON-IDEAL ANALYSIS - EFFECT OF SI ERRORS ON THE SIGNAL-BAND LOCATION In he p e ious sec ion he modula o was assumed o be ideal excep o he inhe en quan iza ion e o . In p ac ice, ci cui pa a- si ics modi y he ze oes o NT,(:), deg ading he noise-shaping and making he in-band quan iza ion noise o inc ease. As we demons a ed in [9], e o s in SI ci cui s cause he sig- nal-band cen e equency (o en named no ch equency, J1o ) o shi om i s nominal posi ion a ,/4 , causing an e o deno ed as 8 Io . which is app oxima ely gi en by: IV-775 whe e E, s ands o he se ling e o [lo], i l is he inpu esis - ance o he memo y cell, O 7 is he s ee ing swi ch-on esis ance, and goF, FB a e he ou pu conduc ances o he cu en mi o s used o ealize he gains, AF, FB , o he esona o in Fig.l(b). Conside ing ha he quan iza ion noise powe is minimum a ,,, , he signal should be cen e ed a ,,, in o de o ob ain a maximum DR. On he o he hand, placing a single one a a e- quency di e en om ,/4 in a BP-ZAM is equi alen o apply- ing a sinusoidal signal o low equency in a LP-CaM. As demon- s a ed in [5], he ou pu spec um o a 1s -o de LP-ZAM wi h a sinusoidal inpu signal o equency, i , is disc e e, wi h ones a : lp,, = s ii' o 17 = 1, 2, 3, ... (9) (14 - ?) , - This esul can be ex ended o he bandpass case by applying he equency ansla ion dc + ,/4 o (9). This implies ha he ou pu spec um o a 2nd-o de BP-EAM will ha e idle ones a : No e ha wo amilies o ones appea a bo h sides o J4, which can co up he signal in o ma ion as will be demons a ed by expe imen al measu emen s in he nex sec ion. 4. EXPERIMENTAL RESULTS The 2nd-o de BP-EAM o Fig.l(a) was ealized using ully di e en ial egula ed- olded cascode memo y cells. The I -bi quan ize was made up o a egene a i e la ch and an RS lip- lop and he I -bi DAC consis ed o a cu en sou ce con olled by he compa a o ou pu . These building blocks we e designed o a ain- ing he equi emen s o di ec A/D con e sion in AM digi al adio ecei e s, whose comme cial b oadcas band is om 5401cHz o 1.6MHz wi h s a ions occupying a lokHz wide band. This im- poses ha he sampling equency mus be unable o e he ange , = 2MHz o , = 6.4MHz. The ci cui was ab ica ed in a CMOS 0.8pm double-me al single-poly echnology. Fig. 4 shows he mic opho og aph o he chip. I also includes some isola e building blocks o es ing sepa- a ely. The ac i e a ea o he modula o is 0.35"' and he powe Figu e 4. Mic opho og aph o he modula o . consump ion is 42mW om a 5V powe supply. To e alua e ihe pe o mance o he modula o , i was a ached o a wo-laye 8:s. boa d, designed ollowing he indica ions in [ 1 11 o educe he swi ching noise. The ou pu bi s eams we e cap u ed wi h he HP82000 da a acqusi ion sys em and Kaise ( p = 20 )-windowed 32768-poin FFTs we e pe o med on each o hose bi s eams using MATLAB [ 121. 4.1 Measu emen s o an inpu one a ,/4 Fig.5 shows wo modula o ou pu spec a when clocked a , = 2MHz. No e ha , because o SI e o s, ,,, de ia es om he ideal posi ion a ,/4 . In his case, in = 2Q, oll = 472!3, acco ding o (8), yields ,,, z 0.246 s. As Fig.5 illus a es, he e a e ou g oups o idle ones whose equencies a e a unc ion o he inpu signal ampli ude. No e ha , as A, app oaches o A/2, wo o hese g oups (labelled as L, and RI in Fig.5) mo e away om ,/4 while he o he wo g oups (L2 and R2 ) app oach o J4. The ones wi h he la ges ampli ude ( E -30dB ) ;a e hose placed a : = 11jLA/V, goFB = 21pA/V and E, = 250ppm. which which ma ches wi h ha p edic ed by (7) o 11 = I, as demon- s a ed in Fig.6 by displaying L,. ? and RI, s. A,/A , show- ing a good ag eemen be ween heo y and measu emen s. In AM adio applica ions, ou -o -band idle ones a e c i ical be- cause, in he p esence o non-linea e o s, can mix wi h he inpu signal and all in o he signal band. Fo he special case o a single one a s/4, he mos signi ican in e modula ion componen s ( hose co esponding o A ~ app oaching o A ) will all app oxi- I I. I 0.1 0.2 0.3 0.4 OS Rela i e equency o , 01 . 1 -so0 . 0:1 . d.2 0.3 0.4 25 1. Relai e equency o , Figu e 5. Measu ed modula o ou pu spec a when clocked a , =, 2MHz o an inpu one o /4 and di e en ela i e ampli udes: (a) A,/A = 0.1 , (b) A, A = 0.14. IV-776 I 0.10 0.15 0.20 Figu e 6. Idle- one loca ion s.A,/A o an inpu one a J4 ma ely a ,/4, hus no deg ading he linea i y o he modula o . Howe e , in p ac ical applica ions he inpu signal will con ain spec al componen s a di e en equencies, and acco ding o ( IO). mul iple ones will appea inside he signal band. This is e - i ied by he ollowing measu emen s. 4.2 Measu emen s o an inpu one a ,,, Placing he inpu signal a ,,, o a BP-ZAM maximizes he esolu ion o such a modula o . Howe e , o he case o a 2nd-o - de BP-LAM, a la ge numbe o idle ones will appea , hus de- s oying he ope a ion o he modula o . Fig.7 illus a es his by plo ing a measu ed modula o ou pu spec um when clocked a , = 2MHz co esponding o a single one o -6dB inpu le el’ and app oxima ely loca ed a he no ch equency. Acco ding o (10). he equency o idle ones only depends on he ela i e loca ion o he inpu equency wi h espec o S/4. Howe e . as also shown in [5] o LP-CaMs. he ampli ude o such ones is s ongly dependen on he inpu signal ampli ude. Fig.8 illus a es his by plo ing he cen al pa o se e al meas- u ed ou pu spec a co esponding o di e en inpu ampli udes. The posi ion o he mos signi ican ones (see (10)) a e labelled. Obse e ha he ampli ude o said ones is no a mono onic unc- ion o he inpu le el. simila ly o wha happens o LP-LAMS. in which he ampli ude o idle ones is ela ed o he inpu le el h ough a linea combina ion o o dina y Bessel unc ions [5]. 5. CONCLUSIONS This pape demons a ed expe imen ally he s ong co ela ion be ween he quan iza ion noise and he inpu signal in 2nd-o de -1000 L 0.1 0.2 0.3 0.4 0.5 Rela i e equency <o Figu e 7. Measu ed modula o ou pu spec um o , = 2MHz and a -6dB inpu one a 491kHz ( ,,, = 0.246 , ). 1’2. Inpu le el is de ined as he inpu signal ampli ude e- e ed o he DAC ou pu le el ( = OdB in he igu e). %!; 0.33 0.15 0.28 b3 Relau e equency ojl . (a) 0 . -10 J -20 3 -30 2“ 1-50 2 -60 -70 %3 0.33 0.25 0.28 0.3C Rcl n c equency mjl (C) %: 0.23 0.25 0.18 0.3 Figu e 8. Measu ed modula o ou pu spec a (cen al pa ) o an inpu one a ,,, = 0.246 S (6 ,,, = 0.0045 , ) and di e en ela i e ampli udes: (a) A,/A = 0.03. (b)A, /A = 0.05. (c) A,/A = 0.1, (d) A,/A = 0.16. bandpass XA modula o s. This phenomenon has been s udied con- side ing ei he ha he noise shaping is ideal o i is deg aded by ci cui pa asi ics. As a esul o his s udy, closed- o m exp es- sions o he equency o idle ones ha e been de i ed ega ding di e en cases o he signal cen e equency. All esul s ha e been alida ed by measu emen s om a 0.8pm CMOS.p o o ype. REFERENCES R. Sch eie and M. Snelg o e. “Bandpass Sigma-Del a Modula ion”. Elec o iics Le e s. pp. 1560-1561. No embe 1989. F.W. Singo and W. M. Snelg o e. “Swi ched-Capaci o Bandpass Del a-Sigma A/D Modula ion a 10.7 MW. IEEE J. Solid-S o e Ci - A.K. Ong and B.A. Wooley. “A Two-Pa h Bandpass ZA Modula o o Digi al IF Ex ac ion a 20MHz”. I€€€ JOUIII~~ o Solid-S a e Ci cui s, pp. 1920-1933, Decembe 1997. W. Benne . “Spec a o Quan ized Signals”. Bell Sys . Tech. J.. R.M. G ay. “Quan iza ion noise spec a”. IEEE Tin scic ions on bi o - nm ioii Theoiy, pp. 1220- 1244. No embe 1990. J.C. Candy and G.C. Temes: “O e sanipling Del a-Sigma Da a Con- e e s , EEE P ess, 1992. S.R. No swo hy. R. Sch eie , G.C. Temes: “Del a-Sigma Coii e 7e s. Theo y. Design and Siinula io l”. New Yo k, IEEE P ess. 1997. T. Y. Chang and S. R. Ribyk. “Exac Analysis o Second-O de Band- pass Del a-Sigma Modula o wi h Sinusoidal Inpu s”. P oc. 1999 IEEE I i . Synip. Ci cui s and Sys ei?~ (ISCAS). Vol.?, pp. 372-375. J.M. de la Rosa. B. Pe ez-Ve du. F. Medei o, R. del Rio and A. Rod iguez-Vazquez, “Non-Ideal Quan iza ion Noise Shaping in Swi ched-Cu en Bandpass Sigma-Del a Modula o s ”. P oc. o 1999 Iii e~iin io inl Synposiu i on Ci cui s and Sys eiiis (ISCAS). Vo1.2. pp. 476-479. c i s, pp. 184-192. Ma ch 1995. pp.446-472. July 1948. [ 10lC.Toumazou. J.B.Hughes. and N.C. Ba e sby. S~~i ched-Cu pii s: An Aiinlogiie Technique o digi al ecliiiology. London. Pe e Pe e-ginus L d.. 1993. [ 11lJ.L. LaMay and H. T. Boga d. “How o Ob ain Maximum P ac ical Pe omlance om S a e-o - he-A Del a-Sigma Analog- o-Digi al Con e e s”. IEEE T ans. 011 bis unien a io i a id Meas i eiiien . pp. 861-867, Decembe 1992. [ 121MATWB: Use ’s Guide. The Ma hwo ks Inc.. 1991. IV-777