Concurrent Adaptive Cancellation of Quantization Noise and Harmonic Distortion in Sigma Delta Converter

Transcription

1 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: Cncurrent Adaptve Cancellatn f Quantzatn se and Harmnc Dstrtn n Sgma Delta Cnverter Hamd Mhsen Pur 1 and Ebrahm Farshd 2, 1 student, Dept f Electrcal Engneerng, Shahd Chamran Unversty f Ahvaz, Ahvaz, Iran, h-mhsen@mscstu.ac.r 2 Prfessr Asstant, Dept f Electrcal Engneerng, Shahd Chamran Unversty f Ahvaz, Ahvaz, Iran, farshd@scu.ac.r Abstract. Adaptve nse cancellatn (AC) technque can remves thermal and shaped wdeband quantzatn nse frm the utput f sgma-delta mdulatr and mprves SR and SFDR rats. AC flter mre than desred sgnal passes harmncs f nput sgnal caused by analg element such as peratnal amplfer f the ntegratr wthut any suppressn and ths ssue causes less ncrement n SR and SFDR f analg t dgtal cnverter. Ths paper presents a technque by addng an adaptve harmnc canceller flter n the frnt f AC flter addresses ths ssue and mprves cnsderably perfrmance f the ADC. The smulatn results demnstrate effectveness f ths cmbnatn technque n frst rder sgma-delta cnverter. Keywrds: Adaptve nse cancellatn, harmnc dstrtn, sgmadelta mdulatr, dgtal calbratn. 1 Intrductn Sgma-delta ADCs were dentfed n the md-1980s fr ther rbustness when mplemented n dgtal CMOS technlgy. They tradtnally use large ver- 29

2 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: samplng rats f 32x-128x t dgtze lw bandwdth sgnals wth 16t 20 bts reslutn. Mre recently, sgma-delta ADCs have been realzed wth lw versamplng rats f 4x-16x.A rule f thumb says t reduce the errrs ntrduced by fnte DC gan, DC gan has t be larger than OSR[l],[2]. In CMOS prcesses ne pssblty f mtgatn f effects f errrs caused by analg mperfectns s applyng dgtal calbratn [3]-[10]. Fr adaptve calbratn usually Least-Mean-Squared algrthm s used [3-5]. Calbratn wrks n sgmadelta ADCs are fcused mre n the DAC lnearty by usng dynamc element matchng technques [6], [7]. A few ther wrks address the prblems f nse transfer functn msmatch between the analg and dgtal dman [8]. Recently, a new apprach has calbrated nnlnear memry errr n dgtal dman [9]. A fully dgtal technque based n Adaptve se Cancellatn (AC) was reprted n [10] that remves wdeband nse frm the utput f sgma-delta mdulatr and mprves perfrmance f cnversn..the mst mprtant advantage f ths methd s fully mplementatn capablty n dgtal dman and ts lmtatn s passng harmnc dstrtn caused by analg mperfectns such as peratnal amplfer f dscrete tme ntegratr wthut any suppressn. In ths new apprach by addng an adaptve harmnc dstrtn canceller n the frnt f AC flter ths ssue wll be addressed and SR and SFDR f mdulatr wll be ncreased cnsderably. Ths paper s rganzed as fllws. In Sectn 2 analyss f harmnc dstrtn n sgma-delta mdulatr s dscussed. Sectn 3 revews emplyed Adaptve Dgtal Flters (ADF) n sgma- delta mdulatr. Sectn 4 presents basc prncples f prpsed technque. Sectn 5 presents the smulatn results t apply ths technque t frst rder sgma delta mdulatrs. Ths paper cncludes n Sectn 6. 2 Analyss f harmnc dstrtn Man surces f harmnc dstrtn n sgma-delta mdulatrs are sgnal-dependent clck feed thrugh, vltage ceffcent f capactrs, and nnlnear dc-gan 30

3 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: characterstc f peratnal amplfer [11]. In ths sectn frst the nnlnearty f peratnal amplfer wll be dscussed and then the errr caused by ths nnlnearty mdeled n frst rder sgma-delta mdulatr. Fg. 1. Amplfer dc-gan characterstc as a functn f the utput vltage [11]. 2.1 Amplfer dc-gan characterstc Fg. 1 shws the gan f amplfer as functn f utput vltage. Ths characterstc can be apprxmated by the fllwng -terms nterplatng plynmal: A(v ) α 0 α v 1 α 2 v 2... α 1 v 1 (1) y( n) A( n) 1 k y ( n) A (2) Where A s the mum gan, n ths paper A =27 and k 1 =1, and the hgher rder ceffcents are determned by the amplfer nnlnearty (Fg. 1). 31

4 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: harmnc dstrtn n frst rder mdulatr Fg. 2. (a) Shws a lssless SC ntegratr wth varable gan A(n) fr peratnal amplfer and equal Cs and C f. By usng charge cnservatn law n the end f 2 phase the fllwng equatn wll be fund: 2y (n) y (n 1) y (n) y (n) y (n 1) (3) A(n) A(n 1) The abve equatn ndcates a real ntegratr s cmpsed f tw parts: An deal ntegratr wth the tw left sde terms, and a perturbatn that s nversely prprtnal t the dstrtn plynmal f amplfer gan. Therefre, the dstrtn errr sgnal wll be: e ( n) a 1 a y ( n) a A 2k A 1 k b ( 1... ) b y ( n 1) (4) w the structure f frst rder sgma-delta wth cnsderng dstrtn f amplfer s shwn n Fg. 2(b). Fr recnstructn f dstrtn errr sgnal, the requre nfrmatn must be extracted frm the utput sgnal (d) f mdulatr. The errr sgnal cane be wrtten as: e a (n) a (d(n) e q (n)) b (d(n 1) e q (n 1)) 1 By drppng quantzatn nse frm abve equatn the dgtal versn f dstrtn errr sgnal wll be fund: 1 1 e ( n) a ( d( n)) b ( d( n 1)) (6) d 1 (5) 32

5 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: As t s clear, the recnstructed dstrtn errr sgnal ( e d (n) ) nt exactly equal wth e a (n) but the dfference s lttle and can be neglected. (a) (b) Fg. 2, (a) swtched-capactr realzatn f the ntegratr, and (b) the mdel wth cnsderng dstrtn sgnal [9]. 3 Revew f ADF emplyed n sgma-delta ADCs 3.1 adaptve nse cancellatn Adaptve nse cancellatn (AC) s ne f the nterestng technques used n vce prcessng fr separatng the perdc sgnal frm bradband sgnal [13], [14]. The frst tme n [10] the applcatn f AC s dscussed fr sgma- delta mdulatr. An AC blck s shwn n Fg. 3. In ths applcatn the nput f AC s utput f mdulatr that s cnsst f desred sgnal and bradband quantzatn nse, defned as: d(k) s(k) n(k) (7) 33

6 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: The ceffcents f the adaptve flter are tuned by Least-Mean-Squared (LMS) algrthm [3]. The delayed versn f nput sgnal s passed frm adaptve flter fr generatn f errr sgnal: e(k) d(k) (k) If t s assumed that nse s randm wdeband nse and delay lne s lng enugh, LMS fr btanng the mnmum Mean-Square-Errr f e (k) wll frces (k) t be a clse estmate f s (k), therefre wdeband shaped nse wll be attenuated and reslutn f cnverter wll be ncreased cnsderably [8]. (8) Fg. 3, Blck dagram f Adaptve nse cancellatn technque [10]. 3.2 Adaptve harmnc dstrtn canceller The harmnc errr sgnal wll be added t the utput f sgma- delta mdulatr and fr mtgatng the effect f t, the sgnal n (6) can be recnstructed and added wth negatve sgn t the utput f mdulatr. Fr estmatng f ceffcents n [9] a new apprach was reprted. In that the frst a tw level pseudrandm sgnal wll be added t the nput f sgma-delta mdulatr and then by usng Gradent-Descent Algrthm the ceffcents are estmated: 34

7 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: a b 1 1 a μ b μ a b e e 1 1 (n)t(n 1) e(n) (n)t(n 2) e(n) (9) The blck dagram f ths ADF s shwn n Fg. 4. Fg. 4, Blck dagram f harmnc dstrtn canceller [9]. 4 Basc prncples f prpsed technque The prblem f AC that reduces perfrmance f t, s passng harmncs caused by analg elements descrbed n prevus sectn wthut any suppressn. But f n any way the harmncs cancelled, the perfrmance f cnverter wll nt reduced. Fg. 5 shws the blck dagram f prpsed technque. In ths blck befre than AC anther ADF s used. Ths flter remves harmnc dstrtn 1 1 D(z) z X(z) E (z) (1 z )E (z) E (z) a q d (10) after that AC remves quantzatn nse: O( z) z 1 X ( z) (11) 35

8 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: Fg. 5. Blck dagram f prpsed technque 5 Smulatn results The behavral smulatn fr a frst-rder mdulatr wth 5 bt quantzer s dne. In ths smulatn OSR s 8 and the length f AC flter s 64. Fg. 6(a) and (b) shw utput frequency spectrum wth usng an AC flter n the back-end f an deal mdulatr and a real mdulatr. In Fg. 6(b) SDR s arund 17db decreased. In Fg. 6(c) the spectrum f mdulatr wth nly calbratn f harmnc dstrtn s shwn and fnally the results f usng cncurrently bth AC and harmnc dstrtn canceller are shwn n Fg. 6(d). In ths case the SFDR and SDR apprxmately 50% and 53% n cmparsn wth n calbratn ncreased. 6 Cnclusn In ths paper frst, harmnc dstrtn caused by a nnlnear amplfer n the frstrder sgma -delta mdulatr s analyzed and effect f ths dstrtn n AC technque s dscussed. In prpsed technque by usng an adaptve harmnc dstrtn canceller befre than AC the prblem f passng harmnc dstrtn frm AC s addressed. 36

9 Internatnal Jurnal f Cmputer Engneerng Scence (IJCES) Vlume 2 Issue 11 (vember 2012) ISS : 2250: (a) (b) (c) Fg. 6. Smulatn results f a 5-bt frst-rder mdulatr After calbratn :( a) AC wth A =1e8, (b) AC wth (d) A =20, (c) harmnc canceller, (d) cmbnatn f bth technque. References 1. Y.Tang, Dgtally-asssted Sgma-Delta ADCs fr Scaled CMOS Technlgy, Ph.D. dssertatn, F.Chen, Desgn f a Wdeband Lw-Pwer Cntnuus-Tme Sgma- Delta Analg-t-Dgtal cnverter (ADC) n 90nm CMOS Technlgy, Ph.D. dssertatn, Y. Chu, C. W. Tsang, B. klc, and P. R. Gray, Least mean square adaptve dgtal backgrund calbratn f ppelned analg-t-dgtal cnverters, IEEE Trans. Crcuts Syst. I, Reg. Papers, vl. 51, n. 1, pp.38 46, Jan

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