Multirate cascaded discrete-time low-pass ΔΣ modulator for GSM/Bluetooth/UMTS

1198 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 6, JUNE 2010 Mul i a e Cascaded Disc e e-Time Low-Pass 16 Modula o o GSM/Blue oo h/UMTS Lynn Bos, S uden Membe , IEEE, Ge d Vande s een, Senio Membe , IEEE, Pie e Rombou s, Membe , IEEE, A nd Geis, S uden Membe , IEEE, Alonso Mo gado, Y es Rolain, Fellow, IEEE, Gee Van de Plas, Membe , IEEE, and Julien Ryckae , Membe , IEEE Abs ac —This pape shows ha mul i a e p ocessing in a cas- caded disc e e- ime 16 modula o allows o educe he powe consump ion by up o 35%. Mul i a e p ocessing is possible in a disc e e- ime 16 modula o by i s adap ibili y wi h he sampling equency. The powe educ ion can be achie ed by elaxing he sampling speed o he i s s age and inc easing i app op ia ely in he second s age. Fu he mo e, a cascaded 16 modula o en- ables he powe e icien implemen a ion o mul iple communica- ion s anda ds. The ad an ages o mul i a e cascaded 16 modula o s a e demons a ed by compa ing he pe o mance o single- a e and mul i a e implemen a ions using beha io al-le el and ci cui -le el simula ions. This analysis has been u he alida ed wi h he design o a mul- i a e cascaded iple-mode disc e e- ime 16 modula o . A 2-1 mul i a e low-pass cascade, wi h a sampling equency o 80 MHz in he i s s age and 320 MHz in he second s age, mee s he e- qui emen s o UMTS. The i s s age alone is sui able o digi izing Blue oo h and GSM wi h a sampling equency o 90 and 50 MHz espec i ely. This mul imode 16 modula o is implemen ed in a 1.2 V 90 nm CMOS echnology wi h a co e a ea o 0.076 mm 2 . Mea- su emen esul s show a dynamic ange o 66/77/85 dB o UMTS/ Blue oo h/GSM wi h a powe consump ion o 6.8/3.7/3.4 mW. This esul s in an ene gy pe con e sion s ep o 1.2/0.74/2.86 pJ. Index Te ms—Cascade, CMOS, del a sigma modula ion, mul i- mode, mul i a e, sigma del a modula ion. I. INTRODUCTION BY exploi ing o e sampling, a modula o can digi ize a na ow equency band wi h a high esolu ion. Mo e- o e , such a modula o is less sensi i e o he non-ideali ies o i s in insic building blocks compa ed o o he analog o dig- i al con e e s. This is pa ly due o he sp ead in equency o he non-ideal e ec s by he o e sampling and pa ly by he shaping ob ained by he eedback ac ion. This ad an age will be inc easingly impo an as he indus y is d i en by echnology Manusc ip ecei ed Sep embe 15, 2009; e ised Feb ua y 05, 2010; ac- cep ed Feb ua y 21, 2010. Cu en e sion published June 09, 2010. This pape was app o ed by Associa e Edi o Michael Flynn. This wo k was suppo ed by he Ins i u e o he P omo ion o Inno a ion h ough Science and Technology in Flande s (IWT-Vlaande en), he Fund o Scien i ic Resea ch (FWO-Vlaan- de en), he Flemish Go e nmen (Me husalem 1), and he Belgian Fede al Go - e nmen (IUAP VI/4). L. Bos and A. Geis a e wi h IMEC, B-3001 Leu en, Belgium, and also wi h he V ije Uni e si ei B ussel, B ussels, Belgium (e-mail: L[email p o ec ed]). G. Vande s een and Y. Rolain a e wi h he V ije Uni e si ei B ussel, B us- sels, Belgium. P. Rombou s is wi h Ghen Uni e si y, Gen , Belgium. A. Mo gado is wi h he Ins i u e o Mic oelec onics o Se ille (IMSE), CNM-CSIC, Se ille, Spain. G. Van de Plas and J. Ryckae a e wi h IMEC, B-3001 Leu en, Belgium. Digi al Objec Iden i ie 10.1109/JSSC.2010.2046240 scaling, ha con inuously challenges he design o analog ci - cui s wi h he e e inc easing p ocess a ia ions and educed supply ol ages. Al hough con inuous- ime (CT) modula o s a e some- imes a o ed o e disc e e- ime (DT) modula o s o hei low-powe consump ion and wide-bandwid h pe o mance, in case a high esolu ion is equi ed, DT modula o s a e p e e ed o hei easie implemen a ion as cascaded s uc- u es. Indeed, highe esolu ion can be achie ed by inc easing he o de o noise shaping. Howe e , high-o de single-loop modula o s equi e ca e ul design o p e en ins abili y [1] and his can be a oided by cascading se e al inhe en ly s able i s - and second-o de s ages (known as Mul i-s Age noise SHaping, MASH [2]–[4]). The cancella ion o he quan iza ion noise o he i s s age in cascaded a chi ec u es is based on he pe ec ma ch be ween he ans e unc ions in he modula o and he digi al il e ing in he digi al cancella ion il e s. This pe ec ma ch is mo e di icul o ealize in CT modula o s [5]. Mo eo e , CT modula o s a e highly sensi i e o ji e and p ocess a ia ions [5]–[7], while DT modula o s a e app ecia ed o hei obus ness as hei ans e unc ions ely on capaci o a ios. This ad an age will become e en mo e p onounced as echnology will scale u he . Finally, DT modula o s o e a s aigh o wa d econ igu abili y o he sys em by adjus ing he sampling equency. Ne e he- less, since ope a ional ampli ie s (opamps) a e equi ed, he applica ion o hese modula o s emains limi ed, so a , o sampling equencies up o 300 MHz [8]–[11] and signal bandwid hs up o 10 MHz [8], [9]. In his wo k, we exploi he dis ibu ion o he sampling e- quency h oughou DT modula o s as an ex a deg ee o eedom by adding a mul i a e dimension o he sys em [12]. This allows o each a be e powe op imum o he o e all sys em. The bene i s o a mul i a e app oach in a DT de- sign can easily be seen when conside ing he i s in eg a o in he modula o : he i s in eg a o is usually he la ges con ib- u o in he o e all powe consump ion. E o s in he i s s age a e no il e ed by he loop and hus ha e he s onges impac on he ’s esolu ion [13]. Hence, he i s in eg a o mus be designed acco ding o he o e all dynamic ange o he modu- la o . This esul s in highe speci ica ions on i s building blocks and consequen ly, la ge powe consump ion. By educing he sampling speed in he inpu s age, he powe o he i s in e- g a o can be educed while he esul ing loss in esolu ion can be eco e ed by inc easing he clock speed in he la e s ages o he sys em. This inc eased clock speed in he la e s ages o he modula o will ha dly in luence he equi ed speci ica ions 0018-9200/$26.00 © 2010 IEEE BOS e al.: MULTIRATE CASCADED DISCRETE-TIME LOW-PASS MODULATOR FOR GSM/BLUETOOTH/UMTS 1199 Fig. 1. A chi ec u e o he iple-mode mul i a e 2-1 cascaded 16 modula o wi h digi al cancella ion il e s o UMTS, GSM and Blue oo h. o i s building blocks since hei non-ideali ies (noise and dis- o ion) a e a enua ed by he i s s age. In his way, mul i a e p ocessing can be exploi ed o ade pe o mance o powe and lexibili y. Mul i a e p ocessing inside a single-loop modula o e- qui es a decima o in he eedback pa h [12]. This decima ion is c i ical since all i s non-ideali ies a e no supp essed by he loop. This complexi y can be a oided when implemen ing a cascaded a chi ec u e in which he sampling equency is modi ied be- ween he cascaded s ages, since he e is no eedback om he second o he i s s age. A cascaded a chi ec u e also o e s ano he ad an age: a powe e icien implemen a ion in a mul imode con ex by swi ching o he app op ia e las s ages when needed [9]. Each communica ion s anda d (in his wo k GSM, Blue oo h and UMTS) equi es a ce ain esolu ion speci ica ion and hence a di e en o de o he noise shaping [14], [15]. In a cascaded a chi ec u e, he modula o o de is no ixed by he mos demanding communica ion s anda d. Ins ead, he modula o can wo k o example as a second-o de single-loop o as a 2-1 cascade depending on he s anda d speci ica ions. The mul i a e p ocessing echnique was al eady p oposed in [12] in which beha io al-le el simula ions we e used o show ha he esolu ion o a cascaded wi h he i s loop ope - a ing a a sampling equency and he second loop a is equi alen o he esolu ion o a cascade wi h bo h loops ope a ing a . Tha pape [12] concluded ha he e idence o he powe educ ion o he i s s uc u e could only be quan- i ied by ansis o -le el simula ions. No in eg a ed mul i a e cascaded disc e e- ime modula o has been epo ed o he au ho ’s knowledge. To da e, wo mul i a e modula o de- signs can be ound in he li e a u e: a single-loop disc e e- ime [16] and a mul i a e cascaded con inuous- ime [17] mod- ula o . Howe e , bo h hese designs epo simula ion esul s only. Fi s , his wo k p o es wi h beha io al-le el and ci cui -le el simula ions ha mul i a e p ocessing in DT cascaded modula o s enables o educe he powe consump ion. Second, his wo k p esen s he i s implemen ed iple-mode DT mul i a e cascade modula o . The design was ealized in 90 nm CMOS echnology and achie es s a e-o - he-a pe o mance [11]. The measu emen esul s show a dynamic ange o 66/77/85 dB o UMTS/Blue oo h/GSM wi h a powe consump ion o 6.8/3.7/3.4 mW. This esul s in an ene gy pe con e sion s ep o 1.2/0.74/2.86 pJ. The pape is s uc u ed as ollows. Sec ion II desc ibes he sys em-le el a chi ec u e o he iple-mode mul i a e cascaded modula o . Sec ion III p esen s a pe o mance analysis, suppo ed by ci cui simula ions, in which bo h single- a e and mul i a e app oaches a e compa ed in e ms o esolu ion and powe consump ion. This analysis p o ides he speci ica ions o he building blocks o he elec ical design o he modula o . In Sec ion IV, he sys em a chi ec u e and he ci cui opologies o i s a ious building blocks (opamps, swi ched-capaci o in eg a o s, quan ize s) a e speci ied. Also he limi a ions and non-ideal e ec s on he design a e discussed and ad ice o u u e implemen a ions is gi en. Sec ion V epo s he measu emen esul s and emphasizes he imp o emen s ha a e ob ained o e a single- a e app oach. Finally, Sec ion VI concludes he wo k. II. SYSTEM-LEVEL ARCHITECTURE The sys em-le el a chi ec u e o he mul i a e cascaded modula o is shown in Fig. 1 oge he wi h he digi al cancel- la ion il e s. The cascaded s uc u e consis s o a second-o de i s s age ope a ing a a sampling equency o , an upsam- ple wi h an in ege upsampling ac o N and a i s -o de second s age ope a ing a a sampling equency o . The digi al ou pu s eams o bo h s ages a e ecombined wi hin he digi al cancella ion logic ha , ideally, elimina es he quan iza- ion noise o he i s s age. This ecombina ion can be done a wo di e en a es: ei he he ou pu o he i s s age is upsam- pled o he ou pu o he second s age is downsampled, he la e being shown in he schema ic o Fig. 1. The i s second-o de s age alone achie es a su icien pe o mance o he Blue oo h and GSM s anda ds while he ull 2-1 cascade is necessa y o mee he UMTS speci ica ion. A de ailed block diag am o he modula o , wi hou digi al cancella ion il e s, is shown in Fig. 2. The i s s age uses a eed- back opology wi h an ex a eed o wa d b anch om he inpu o he second in eg a o inpu o educe he ou pu swing o he i s in eg a o . In bo h s ages, 1.5-bi quan ize s a e employed o u he educe he ou pu swing o he in eg a o s and imp o e he dynamic ange o he modula o . This can be done easily be- cause a 1.5-bi ( h ee-le el) digi al analog con e e (DAC) can eadily be implemen ed using a ully di e en ial swi ched-ca- paci o ci cui [18]. To calcula e he ans e unc ion o a modula o , he quan ize is eplaced by a linea model ( wi h 1200 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 6, JUNE 2010 Fig. 2. Ci cui implemen a ion o he mul i a e 2-1 cascaded 16 modula o . he quan ize gain and he quan iza ion noise). The dig- i al ou pu s eams o he i s and second s ages and op- e a ing wi h a sampling equency o and espec i ely can be exp essed as (1) (2) wi h (3) and he upsampling il e (4) while , a e espec i ely he quan ize gain o he i s and second s age, , and , s and o he inpu signal and quan iza ion noise o he i s and second s age, espec i ely. The ela ionship be ween he loop coe icien s and he quan ize gain a e de i ed by ensu ing a second-o de noise shaping in he i s s age: (5) (6) and a i s -o de shaping in he second s age [13]: (7) A e upsampling he digi al ou pu o he i s s age and p o- cessing he wo digi al s eams in he cancella ion il e , he ou pu o he ull cascade becomes (8) In o de o cancel he quan iza ion noise o he i s s age , he digi al cancella ion il e s mus be chosen equal o (9) (10) wi h (11) (12) The ou pu o he cascade gi es a e pe ec cancella ion o (13) III. PERFORMANCE ANALYSIS This sec ion ex ac s he pe o mance in e ms o esolu ion and powe consump ion o he 2-1 cascaded modula o (shown in Fig. 2) o di e en se ings o he upsampling ac o and he sampling equency used in he i s s age. Fi s , he esolu ion is es ima ed using beha io al-le el simula ions wi h an ideal model. Nex , o compa e he powe consump ion o each con igu a ion, simula ions o ansis o -le el opamps a e pe o med. Since he global powe consump ion is domina ed by he opamps, he equi ed speci ica ions on hese ampli ie s, BOS e al.: MULTIRATE CASCADED DISCRETE-TIME LOW-PASS MODULATOR FOR GSM/BLUETOOTH/UMTS 1201 TABLE I RESOLUTION OF THE DIFFERENT CONFIGURATIONS OF 2-1 CASCADE 16 MODULATOR OBTAINED BY BEHAVIORAL-LEVEL SIMULATIONS GBW and SR, a e de e mined o es ima e he global powe con- sump ion. A. Ex ac ion o he Resolu ion In his sec ion he esolu ion is de e mined o an ideal cas- caded modula o o di e en upsampling ac o s and sam- pling equencies. The 2-1 cascade modula o desc ibed in Sec ion II has been modeled by using unc ional blocks in Simulink [19]. The i e di e en es cases in he beha io al-le el simula- ions a e shown in Table I. Among hese es cases, h ee upsam- pling ac o s we e conside ed: o he single- a e case, and o he mul i a e case. The mul i a e se ing is chosen as a e e ence o compa ison. In his e e ence design, he o e sampling a io o he i s s age is chosen o achie e an o e all ENOB o he cascade highe han 10 bi s in a signal bandwid h o 1.92 MHz ( he speci ica ion o UMTS). This leads o a sampling equency in he i s s age o 80 MHz. In he single- a e as well as in he mul i a e case, sam- pling equencies o 80 MHz and 160 MHz ha e been consid- e ed o he i s s age o s udy he e ec o he sampling e- quency and he upsampling ac o on he esolu ion and powe consump ion. The ollowing se ings we e used in he beha io al-le el model: • All he loop coe icien s, shown in Fig. 2, a e equal o 1/2. Thei alue was maximized, in o de o minimize he ca- paci i e load, un il he ou pu swing o he in eg a o s hi s hal he supply ol age . In hese condi- ions, is equal o 3 [using (11)] and equal o 2 [using (12)]. • The e e ence ol age o he DAC is ixed o 0.8 V. In- c easing he e e ence ol age inc eases he dynamic ange o he modula o . Howe e , he ou pu s o he opamps e- qui e a ce ain head oom o unc ion p ope ly. This head- oom is de e mined by he sa u a ion equi emen o he ou pu s age o he opamp. • The inpu sine wa e ampli ude is se o . The esul ing ENOB a e gi en in Table I. We obse e ha he single- a e se ing wi h MHz (second ow in Table I), he mul i a e se ing wi h and MHz ( ou h ow in Table I) as well as he mul i a e se ing wi h and MHz ( i h ow in Table I) achie e he highes ENOBs. Hence, hey a e he p e e ed con igu a ions o p o- ide a su icien SNDR ma gin o he ansis o -le el design. As p edic ed by [12], he esolu ion o he single- a e cascade Fig. 3. Implemen a ion o he disc e e- ime swi ched-capaci o in eg a o wi h a h ee-le el DAC. a 160 MHz (second ow in Table I) and he mul i a e cascade, wi h he i s s age a 80 MHz and he second s age a 320 MHz ( i h ow in Table I), achie e simila pe o mance. B. Ex ac ion o he Powe Consump ion In his sec ion, he powe consump ion is analyzed o h ee ou o he i e es cases abo e [(1), (2), and (5)] om Table I. The o al powe consump ion o he sys em is mainly de e - mined by he GBW and SR me ics o he opamps and hese ampli ie s a e assumed o be he dominan con ibu o s in he global powe consump ion. This assump ion will be con i med by he ansis o -le el simula ions o he global sys em as de- sc ibed in Sec ion IV-E. The modula o in Fig. 2 has been im- plemen ed in Spec e wi h all he opamps blocks mapped o a ansis o -le el design in a 90 nm CMOS echnology. All he o he building blocks we e modeled using a Ve ilog-A model. The powe consump ion es ima ion was ealized by ex ac ing he equi ed cu en speci ica ions o he opamps in he di - e en con igu a ions. The ci cui -le el model was buil as ollows: • Each swi ched-capaci o in eg a o (SCI) was imple- men ed as shown in Fig. 3 (mo e explana ion can be ound in Sec ion IV-A). The capaci i e loading o each opamp was added in he ci cui -le el model. • The main design c i e ia o he opamp in he SCI a e su - icien DC gain and ou pu swing, la ge GBW and SR. A wo-s age opamp opology was chosen o p o ide DC gain up o 55 dB [20]. The ampli ie consis s o a olded-cascode inpu s age ollowed by a Mille compensa ed common- sou ce s age [Fig. 4(a)]. As can be seen, one cascode an- sis o in he i s s age was emo ed o ensu e he sa u a ion o he h ee s acked ansis o s ed wi h a supply ol age o 1.2 V. The second s age was added o inc ease he ou pu swing o he opamp. The speci ica ions on he GBW and 1202 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 6, JUNE 2010 TABLE II SPECIFICATIONS ON THE OPAMPS AND RESOLUTION FOR DIFFERENT CONFIGURATIONS OF THE 2-1 CASCADE 16 MODULATOR OBTAINED BY OPAMP TRANSISTOR-LEVEL SIMULATIONS Fig. 4. Topology o (a) he opamp and (b) i s common-mode eedback ci cui . he in e nal SR (de e mined by he bias cu en o he inpu s age and he Mille capaci o ) de e mine . The ex e nal SR (de e mined by he ou pu s age cu en and he load capaci ance) o he ampli ie s can be adjus ed acco ding o he equi ed sampling equency by a ying . The Mille capaci o is chosen o be abou a ac o o 2 smalle han he load capaci o . To educe he powe consump ion, he ou pu cu en is educed as much as pos- sible (which dec eases he ex e nal SR). The e o e, in his case, he ex e nal SR is simila o he in e nal SR. The con inuous- ime common-mode eedback ci cui is gi en in Fig. 4(b). A small capaci o was added in pa allel wi h he common-mode sensing esis o s o p o ide su icien common-mode phase ma gin. • The inpu sampling capaci o s a e se o 450 F and 300 F o he i s and second SCI o he i s s age and 200 F in he SCI o he second s age. These capaci o alues esul om a comp omise be ween noise, ma ching sensi- i i y and capaci i e loading o he opamps. • The swi ches a e modeled in Ve ilog-A wi h an on/o - e- sis ance. • The quan ize s in Ve ilog-A ha e a delay, ise and all ime. • The upsample is modeled by an ideal sample and hold con olled by he clock o he i s s age. The samples held a e hen ans e ed o he second s age a a a e imes highe depending on he es case. The minimum equi emen s (shown in Table II) o he h ee opamps in he 2-1 cascade in he h ee con igu a ions ha e been ound by i e a i ely dec easing hei alue un il he modula o esolu ion s a s o deg ade. The ex e nal SR and he ela ed , beha e as expec ed; doubling he sampling equency in he i s s age equi es dou- bling he o he i s s age ampli ie s [ om case (1) o (2) o Opamp 1 and Opamp 2]. The ex e nal SR equi emen on he second s age ampli ie (Opamp 3) is ela i ely lowe han ha o he i s s age (Opamp 1 and 2) in he single- a e cases [(1) and (2)]. This can be explained by he ac ha he i s s age has he highes impac on he o e all esolu ion and hus he speci- ica ions on i s building blocks a e he mos demanding. Conside ing he GBW, he in e nal SR and he ela ed ,i can be seen ha he equi emen s in he second-s age ampli ie (Opamp 3) a e also ela i ely lowe han hose o he i s s age (Opamp 1 and 2) in he single- a e cases [(1) and (2)]. The equi emen s o he i s s age a e hal ed when compa ing he single- a e case a 160 MHz and he mul i a e case [case (2) o (5)]. The equi emen s o he single- a e case a 80 MHz and he one a 160 MHz canno be compa ed since he esolu ion o he i s es -case is lowe . These obse a ions lead o he conclusion ha , in o de o achie e low powe consump ion, he sampling equency o he i s in eg a o needs o be kep as low as possible. Mo eo e , inc easing he sampling equency in he second s age can be done wi hou subs an ially a ec ing he powe consump ion. To ob ain he o al cu en consump ion o each opamp o each con igu a ion, he cu en o he inpu s age, he ou pu s age, he cascode and he CMFB ci cui o each opamp a e summed. Consequen ly, he mul i a e se ing wi h a minimal and a maximal appea s o be he op imal in e ms o powe consump ion o a ixed esolu ion. The o al ou pu cu en consump ion o his se ing (5) is 35% lowe han ha o he single- a e case, sampling a 160 MHz (2). BOS e al.: MULTIRATE CASCADED DISCRETE-TIME LOW-PASS MODULATOR FOR GSM/BLUETOOTH/UMTS 1203 The esolu ion o he di e en ci cui -le el con igu a ions (Table II) is compa able wi h he esul s ound by beha - io al-le el simula ions in Simulink (Table I). IV. CIRCUIT IMPLEMENTATION To alida e he concep a he ansis o -le el and e i y he esul s ob ained in Sec ion III, he mul i a e 2-1 cascade modula o o Fig. 2 has been implemen ed in a 90 nm digi al CMOS p ocess. The ci cui was designed o ope a e a an up- sampling ac o o 4 and a sampling equency MHz. A single- a e se ing o 80 MHz was also implemen ed o com- pa ison pu poses. To demons a e he mul imode pe o mance o he cascaded modula o s, he i s s age alone was designed o digi ize GSM and Blue oo h a a sampling equency o 50 MHz and 90 MHz, espec i ely. The wo-s age cascade was a ge ed o he UMTS s anda d wi h a sampling equency o 80 MHz and 320 MHz in he i s and he second s age, espec i ely. This sec ion desc ibes he o e all chip implemen a ion and he opology o he building blocks in he modula o . The di e en building blocks used in he sys em a e he swi ched- capaci o in eg a o s, he quan ize s and he upsample . A. Swi ched-Capaci o In eg a o The opology o he SCI is shown in Fig. 3. This ci cui em- ploys bo om-pla e sampling o educe he sensi i i y o pa a- si ic capaci ances and cha ge injec ion. The swi ches a e imple- men ed as MOS ansmission ga es, which comp ise he pa - allel connec ion o an nMOS and a pMOS swi ch o educe he dependency o he on- esis ance wi h he d ain sou ce ol age. The bias cu en o he inpu s age o he opamp shown in Fig. 4, is de e mined by he speci ica ions on he GBW and he in e nal SR. I is se o app oxima ely 350 A. As his cu - en has a negligible con ibu ion o he o al powe consump- ion, i is ixed o he h ee ampli ie s. The wid h o he ou pu ansis o o he ampli ie o he hi d in eg a o was doubled wi h espec o he i s and second one, in o de o p o ide he necessa y double ou pu cu en in he mul i a e case wi h . The bias cu en and ou pu s age cu en can be adjus ed o achie e he equi ed GBW, he in e nal SR and he ex e nal SR o all opamps du ing measu emen s. The con inuous- ime common-mode eedback only consumes abou 300 A o cu en . MOM-capaci o s we e used o enable he ab ica ion in a digi al 90 nm CMOS p ocess. B. Quan ize The 1.5-bi quan ize needs o pe o m a h ee-le el quan iza- ion o he inpu . I consis s o wo iden ical blocks, comp ising a compa a o p eceded by a swi ched-capaci o (SC) ne wo k [Fig. 5(a)]. This SC ne wo k gene a es wo ol age h esholds a a le el o and by shi ing he posi i e o he nega i e inpu signal by depending on he h eshold. The used sampling capaci o is 200 F. The 1.5-bi ou pu da a, is ex ac ed by sub ac ing bo h ou pu s. The compa a o [Fig. 5(b), le ] is based on a egene a i e la ch d i ing a Se -Rese (SR) la ch [Fig. 5(b), igh ]. Fig. 5. Implemen a ion o (a) he 1.5-bi quan ize and (b) he compa a o . C. Upsample The upsample in e pola es he quan iza ion e o signal o he i s s age by a ac o o 4. The quan iza ion e o is equal o he sub ac ion o he ou pu o he loop il e and he digi al ou pu o he ADC. The upsampling ope a ion o he ou pu o he loop il e is implemen ed by eplacing he swi ched-capac- i o sampling ne wo k o SCI by he s uc u e in Fig. 6. Du ing , he ou pu o SCI is sampled on ou equal sampling ca- paci o s, each wi h a alue o 200 F. The samples a e hen suc- cessi ely p ocessed in ou clock phases by SCI , using he 4 imes as e clock o he second s age. Since he ou pu o he 1.5-bi quan ize is held cons an du ing he en i e sampling pe iod o he i s s age, i s ol age can be sampled di ec ly wi h he sampling clock o he second s age. In addi ion o his mul i a e mode, a single- a e mode o he cascade is o eseen by p ocessing only one o he ou upsam- pling capaci o s. D. Non-Ideali ies and Limi a ions o he Modula o This sec ion p o ides some conside a ions abou he non-ide- ali ies in his mul i a e cascade modula o . I also gi es some hin s o u u e implemen a ions. Finally, he limi a ions o he applica ion o his mul i a e cascade modula o a e discussed. • In he cu en implemen a ion, he upsample loads he second SCI by i s ou pa allel sampling capaci o s, which inc eases he capaci i e load o his SCI. Mo eo e , he sho sampling ime o he upsample equi es he second SCI o se le in a 4 imes sho e ime ame. This cons ain he e o e inc eases he equi ed GBW and SR speci ica ions and his esul s in simila equi emen s o he second opamp as o he i s one. This e ec was also 1204 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 6, JUNE 2010 Fig. 6. Implemen a ion o he upsample . TABLE III PERFORMANCE FOR THE 2-1 CASCADE 16 MODULATOR OBTAINED BY TRANSISTOR-LEVEL SIMULATIONS obse ed in he ci cui -le el simula ions in Sec ion III-B. In addi ion, he quan ize o he i s s age needs o se le 2 o 4 imes as e , because i s decision is al eady needed in . Fo una ely, he powe consump ion o his as e quan ize is negligible wi h espec o he one o he am- pli ie s. The wo discussed issues could be alle ia ed by se e al echniques, e.g., he ime-in e lea ing o he sam- pling capaci o o he second s age and allowing a clock cycle delay in he a chi ec u e. • In a u u e design, ex a a en ion will be de o ed o isola ing he sampling o he ou pu o he second in eg a o by he upsample om he sampling by he quan ize o he i s s age. I bo h sampling e en s occu a he same ins an , he load o he second in eg a o is inc eased and sampling spikes a e p oduced. To coun e ac his, he quan ize o he i s s age was sligh ly skewed, bu in a u u e design a mo e elegan solu ion should be ound. An al e na i e solu ion is o use a eed o wa d s uc u e in he i s s age. Indeed, in a eed o wa d s uc u e, he inpu o he second s age is aken di ec ly a e he second in eg a o , so be o e he eed o wa d addi ion. This ensu es a p ope isola ion be ween he quan ize sampling and he upsample by he adde . Un o una ely, his a chi ec u e equi es an adde , which esul s in ex a powe consump ion. • As men ioned in he in oduc ion, cascaded modula- o s in gene al a e sensi i e o capaci o misma ches. To e i y his sensi i i y, he sampling capaci o s we e modi- ied by 1% and he pe o mance, esul ing om his an- sis o -le el simula ion, showed ha he e is no impac . This was con i med by he measu emen s, which p o ed ha an op imiza ion o he digi al coe icien s in he digi al can- cella ion il e s did no inc ease he pe o mance. A sim- ula ion o he ansis o -le el implemen a ion in he ou p ocess co ne s showed a maximum loss o 1 bi in he case o slow–slow. TABLE IV CURRENT BREAKDOWN FOR THE MULTIRATE 2-1 CASCADE 16 MODULATOR AS OBTAINED BY TRANSISTOR-LEVEL SIMULATIONS Fig. 7. Chip mic opho og aph. • The p oposed mul i a e cascade equi es a 4 imes highe sampling equency in he second s age. The a ainable bandwid h in he design o ope a ional ampli ie s limi s he maximum sampling equency o abou 320 MHz nowa- days. The simula ions o he implemen ed swi ched-ca- paci o in eg a o in he second s age show, howe e , ha he ou pu only has o se le o abou 70% o he heo- e ical p edic ed ou pu , wi hou de e io a ing he pe o - mance. Ne e heless, o communica ions s anda ds wi h signal bandwid hs la ge han 10 MHz, he applica ion o his mul i a e cascading can be limi ed by he achie able sampling equency o he opamps. In his case, i will be necessa y o limi he upsampling ac o o maximally 2. E. Simula ed T ansis o -Le el Pe o mance To ex ac he nominal esolu ion o he mul i a e cascade, ansis o -le el simula ions o he ull chip o each s anda d BOS e al.: MULTIRATE CASCADED DISCRETE-TIME LOW-PASS MODULATOR FOR GSM/BLUETOOTH/UMTS 1205 Fig. 8. (a) Measu ed spec a a peak SNDR o UMTS; (b) he compa ison o he mul i a e and single- a e cascade o UMTS zoomed in om 0.8 MHz un il 10 MHz, (c) Blue oo h and (d) GSM. ha e been pe o med. The esolu ion and powe consump ion a e summa ized in Table III. The UMTS s anda d was simu- la ed wi h a sine wa e inpu wi h an ampli ude o 0.8 V and a equency o 0.5 MHz. The cascade is also simula ed in a single- a e mode a 80 MHz. The cascade could no be simu- la ed wi h a sampling equency o 160 MHz since he i s s age is no designed o his highe sampling equency. A simula ed cu en consump ion b eakdown o he ull mul i a e cascade is also shown in Table IV. These powe igu es show ha , al hough he second s age wo ks a ou imes he sampling equency o he i s s age, i s consump ion emains compa able o he i s s age SCIs. This is achie ed by elaxing i s speci ica ions and he e o e demons a es he po en ial o a mul i a e app oach in cascaded modula o s. I also con i ms he assump ion ha he powe consump ion is de e mined by he ope a ional ampli ie s. The ansis o -le el simula ions o bo h he esolu ion and he powe consump ion a e in good ag eemen s wi h he mixed-le el simula ions o Sec ion III-B. The modula o has been ab ica ed in a digi al 90 nm CMOS p ocess [11], which means ha no analog op ions we e p o- ided. The chip mic opho og aph is shown in Fig. 7. The ac i e a ea o he modula o including swi ched-capaci o in eg a o s, quan ize s, clock gene a ion and DAC is only 0.076 mm . The p ocessing by he digi al cancella ion il e s is done in Ma lab. V. EXPERIMENTAL RESULTS This sec ion discusses he measu emen esul s: esolu ion, powe consump ion, dis o ion, compa ison o mul i a e and single- a e mode and he compa ison wi h o he mul imode disc e e- ime modula o s. A. Resolu ion and Powe Consump ion The measu emen o he UMTS mode spec um gene a ed by he mul i a e cascaded echnique is shown o he peak SNDR in Fig. 8(a), whe e he no ch a esul s om he upsampling in he digi al cancella ion logic. Wi h a o al powe consump ion o 6.83 mW d awn om 1.2 V supply, a peak SNDR o 65.5 dB is achie ed. This esul s in an ENOB o 10.5-bi and a igu e o me i o 1.2 pJ pe con e sion s ep o he mul i a e cascade. The ou pu spec um o he modula o in he GSM and Blue- oo h modes a e shown o peak SNDR in Fig. 8(c) and (d). Wi h a powe consump ion o 3.43 mW and 3.7 mW, a peak SNDR o 77 dB and 76 dB is achie ed o GSM and Blue oo h, espec- i ely. This esul s in a FoM o 2.86 pJ/con and 0.74 pJ/con . The esolu ion as well as he powe consump ion a e in good co ela ion wi h he ansis o -le el es ima ions. Fig. 9 shows he SNDR e sus he inpu ampli ude o he di - e en modes. A dynamic ange (DR) o 66/77/85 dB is achie ed o UMTS/Blue oo h/GSM, espec i ely. 1206 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 6, JUNE 2010 TABLE V MEASURED PERFORMANCE OF THE 2-1 CASCADE 16 MODULATOR FOR 3S TANDARDS Fig. 9. Measu ed SNR e sus inpu ampli ude o he 16 modula o o h ee s anda ds: UMTS, Blue oo h and GSM. B. Dis o ion The spec um esul ing om a 2- one es wi h 175 and 200 kHz in he UMTS mode is shown in Fig. 10. The hi d-o de in e modula ion dis o ion (IM3) is 76 dB wi h each one a 10.9 dBFS ( he powe whe e he peak SNDR has been eached). Simila pe o mance is ob ained o he o he modes. A o al ha monic dis o ion (THD) o 75/81/80.5 dB and a spu ious- ee dynamic ange (SFDR) o 79/83/83 dB is eached a he peak SNDR o UMTS/Blue oo h/GSM. C. Compa ison o Single-Ra e and Mul i a e Pe o mance The mul i a e pe o mance was also compa ed o a single- a e pe o mance a a sampling equency o 80 MHz ( he slew- a e equi emen s o he ampli ie s a e educed acco dingly). The single- a e se ing p o ides a ma ginal educ ion o he powe consump ion (6.43 mW). Howe e , he SNDR d opped by 7 dB. The esul ing FOM is 2.38 pJ/con , which is he double o he mul i a e se ing. This clea ly shows ha mul i a e ope a ion o e s a pe o mance imp o emen . The op igh o Fig. 8(b) Fig. 10. Measu ed hi d o de in e modula ion dis o ion o he mul i a e 2-1 16 modula o o UMTS. shows he shaping imp o emen o he mul i a e app oach on he ou pu spec um. The single- a e se ing has a THD o 68.3 dB a a peak SNDR and a SFDR o 70.5 dB. D. Conclusion Table V summa izes he measu ed pe o mance o he design. Fig. 11 compa es he FoM (compu ed wi h DR) o di e en mul imode disc e e- ime modula o s [9], [21]–[25]. Re s. [21], [22], [24] use a single-loop a chi ec u e o ealize a mul- imode modula o , while [9], [23], [25] employ a cascaded a chi ec u e. The ou s a s on he igu e ep esen he achie ed pe o mance o GSM, Blue oo h, he non-op imized single- a e al e na i e o UMTS and he p oposed mul i a e solu ion o UMTS. I can be obse ed ha he p oposed chip demons a es s a e-o - he-a pe o mance. Re s. [21], [24] use 0.18- m ech- nology, he es 0.13- m echnology and hei a ea is a leas 2.5 imes as la ge as his wo k [11].