Thermometer-to-binary Encoder with Bubble Error Correction (BEC) Circuit for Flash Analog-to-Digital Converter (FADC)

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1 Thermometer-to-bary Ecoder wth Bubble Error Correcto (BEC) Crcut for Flash Aalog-to-Dgtal Coverter (FADC) Bu Va Heu, Seughyu Beak, Seughwa Cho +, Jogkook Seo ±, Takyeog Ted. Jeog,* Dept. of Electroc Egeerg, Myogj Uversty + Gree Growth Team, Korea Electrcty Power Research Isttute ± R&D Dvso, LS Idustral Systems { bvheu, shbeak, ttjeog }@mju.ac.kr, kepcho@kepr.re.kr, jkseo@chol.com Abstract Thermometer-to-bary (TM2B) ecoder s a mportat compoet of a Flash Aalog-to-Dgtal Coverter (FADC). Bubble error, extremely ofte, effects the correcto of TM2B as well as hgh speed samplg rate. I ths paper, we propose a MUX-based TM2B crcut that ca correct bubble errors. Error correcto ablty of our proposed crcut s compatble wth prevous methods. The smulato results show that the proposed crcut requres a small umber of trasstors ad cosumes low power. Keywords; Thermomete-to-bary Ecoder, Bubble Error Correcto Crcut (BEC), Flash ADC A revew shows that MUX-base crcut has may advatages such as chp area, power cosumpto [0]. I. INTRODUCTION As a result of developmet of storage system, optcal commucato, ad ultra-wdebad commucato, the demad for hgh-speed aalog to dgtal coverter (ADC) has beg creased []. Amog dfferet ADC archtectures, flash ADC offers the hghest samplg rate wth low resoluto [2]. Utl ow, flash ADC s the oly archtecture satsfyg the hgh samplg rate requremet of those areas. May researches are tryg to crease samplg rate ad reduce power cosumpto of flash ADC [], [3], [4]. Despte of dfferet specfc desg, geeral structure of a flash ADC cludes three compoets as show Fgure. The frst compoet s a resstor ladder that provdes 2 voltage refereces, whch are dvded to equally space values, for a output flash ADC. The secod compoet s a set of 2 comparators. Each comparator compares put voltage ad refereced voltage. Output of a comparator s dgtal value f put voltage s hgher tha refereced voltage. The 2 outputs of comparators always have the form of a thermometer code. The last compoet s a TM2B dgtal crcut covertg 2 put thermometer code to output bary code. The straghtforward method to mplemet TM2B crcut s to use a bary-ecoded ROM [5], [6]. Aother method couts the umber of bt thermometer code by a Wallace tree couter [7]. Later, a method use a logc gate based o fat-tree s proposed [8]. Recetly, E. Sal ad M. Vesterbacka proposed a method based o multplexer [9]. Fgure. Structure of Flash ADCs Because flash ADC operates at very hgh speed, bubble error there are oe or some logcal above sequece of logcal 0 thermometer code wll happe. Bubble error s result of may sources, for example, clock jtter, devce msmatch, offset voltage. The put thermometer code of a TM2B crcut s vald code. Cosequetly, f there s o correcto crcut, the output of the TM2B crcut or the output of the ADC ths case s correct. Wallace-tree method ca reduce all bubble errors. Ufortuately, ths method s ot sutable for practcal ADC due to the complexty of the crcut, hgh power cosumpto, ad relatvely low speed. ROM-based ad fat-tree TM2B crcuts use 3-put AND gate to correct bubble error [5], [8]. N. Agrawal ad R. Paly propose a mprovemet for bubble error correcto of ROM-base TM2B ecoder []. Although MUX-based ecoder has may advatages, o research proposes a bubble error correcto (BEC) crcut for t /0/$ IEEE

2 I ths paper, we propose a MUX-based TM2B ecodg wth BEC crcut. Aalyss shows that the proposed crcut has the same error correcto ablty as ROM-based ad fat-tree crcut. Crcut desg ad smulato wth Cadece s tool shows that the proposed crcut ot oly requres a small umber of trasstors but also cosumes low power. The rest of the paper s orgazed as follow. Secto II ad Secto III dscuss the ROM-based ad fat-tree TM2B ecoder. Secto IV presets our proposed crcut. Secto V dscusses the equvalet fuctoalty of crcuts, descrbes smulato setup ad preset smulato results. The last secto s the cocluso. II. ROM-BASED TM2B ENCODER The structure of a ROM-based ecoder s show Fgure 2. The ecoder cludes two sub-crcuts, a thermometer-tooe-hot (TM2OH) sub-crcut ad a ROM-based ecodg subcrcut. The TM2OH sub-crcut coverts thermometer code to oe-hot code. The ROM-based ecodg sub-crcut s a ROM crcut that covert put oe-hot code to output bary code. TABLE I. llustrates the operato of a 7-to-3 ROM-based TM2B ecoder. Each row of the table s a vald put code ad ts correspodg output at each sub-crcut outputs. As llustrated the table, the 7-to-3 ROM-based TM2B ecoder has 7 puts ad 3 outputs. There are total 8 dfferet vald put codes ad 8 correspodg output codes. OUT IN.( IN )' =,2,,2 2 () = + where OUT s the output at the posto ad IN are the put at the posto, +, respectvely. + Fgure 3. TM2OH Sub-crcut of a 7-to-3 ROM-based TM2B Ecoder IN Fgure 2. Structure of ROM-based TM2B Ecoder TABLE I. CONVERTING OPERATION OF A 7-TO-3 ROM-BASED TM2B ENCODER Thermometer code Oe-hot code Bary code The TM2OH sub-crcut s mplemeted by 2-put AND gate whch oe put s verted. Fgure 3. s the TM2OH subcrcut of a 7-to-3 ROM-based TM2B ecoder. Except the hghest sgfcat output, other outputs are determed by below formula Fgure 4. TM2OH Sub-crcut wth BEC of a 7-to-3 ROM-based TM2B Ecoder ROM-based ecodg sub-crcut s a ROM-structure crcut wthout address decodg crcut. The cotet of ROM

3 s the bary value output of the TM2B crcut. It does ot eed the address decodg crcut because ts put s oe-hot code whch ca be used to access ROM structure drectly. The crcut structure preseted above paragraphs caot hadle bubble error. Wheever bubble error happes, the output of the ecoder becomes correctly. Ths reduces the effcet of the crcut. Therefore, a bubble error correcto crcut s ofte used ROM-based TM2B ecoder. The BEC crcut ROM-based ecoder s a modfed TM2OH sub-crcut. Istead of 2-put AND gate, the BEC crcut uses 3-put AND gate. The ew crcut performs the covertg ad correctg processes smultaeously. The output ca be determed by below equato. OUT = IN.( IN+ )'( IN+ 2)' =,2,,2 3 (2) Fgure 4. s the BEC crcut for a 7-to-3 ROM-based TM2B ecoder. As show the fgure, every output s a AND operato of three puts where all puts except lowest put are verted. III. FAT-TREE TM2B ENCODER The structure of a fat-tree TM2B ecoder s show Fgure 5. Smlarly wth ROM-based ecoder, fat-tree ecode also has two sub-crcuts. The frst sub-crcut coverts thermometer code to oe-hot code. The frst sub-crcut has the same structure as the TH2OH sub-crcut of ROM-based ecoder. The secod sub-crcut coverts oe-hot code to bary code. However, the secod sub-crcut has a dfferet structure wth ROM-based ecodg sub-crcut. where b 0, b, b2 are bary code outputs ad h to h 7 are thermometer code puts. Reusg some sub-crcuts, the umber of OR gates are reduced. Fgure 6. s the fat-tree ecodg sub-crcut of a 7-to- 3 fat-tree TM2B ecoder. The OR result of put h 6 ad put h 7 s reused to geerate output b. Ths structure ca be easy to exted to hgher umber of puts. H07 H06 H05 H04 H03 H02 H07 H05 H03 H0 t7:6 t7:6 B02 B0 B00 Fgure 6. Fat-tree Ecodg Sub-crcut of a 7-to-3 Fat-tree TM2B Ecoder Because fat-tree TM2B ecoder uses TM2OH sub-crcut as ROM-based TM2B ecoder, BEC crcut of fat-tree TM2B ecoder s detcal wth the oe of ROM-based TM2B ecoder. IV. PROPOSED CIRCUIT MUX-BASED TM2B ENCODING WITH BEC CIRCUIT MUX-based TM2B ecoder coverts thermometer code to bary code drectly. The ecoder uses multplexers as prmtve gate to mplemet covertg fucto. A 7-to-3 MUX-based TM2B ecoder s show Fgure 7. As show the fgure, the crcut has a hgh structure. Hece, the crcut ca exted to hgher put ecoder easly. Fgure 5. Structure of Fat-tree TM2B Ecoders Fat-tree ecodg sub-crcut s a logc crcut. Wth a 2 puts crcut, each output s a OR operato of 2 puts. Equatos (3), (4), ad (5) are the formulas that covert oe-hot code to bary code. 0 h + h3 + h5 h2 + h3 + h6 2 h4 + h5 + h6 = (3) = (4) = (5) Fgure 7. A 7-to-3 MUX-based TM2B Ecoder

4 MUX-based TM2B ecoder has may advatages such as low power cosumpto, low crcut complexty, etc [9], [0]. I prevous researches, however, t lacks the BEC ablty. I ths research, we propose a MUX-based TM2B ecoder that ca correct bubble error. The structure of our proposed crcut s show Fgure 8. The MUX-based TM2B ecoder prevous researches becomes the MUX-based ecodg subcrcut our proposed crcut. A ew sub-crcut s added before the MUX-based ecodg sub-crcut. The ew crcut removes bubble error thermometer code. V. DISCUSSION AND SIMULATION RESULTS Comparg wth BEC crcut for ROM-based TM2B ecoder, the proposed BEC crcut has the same correcto ablty. Both crcuts ca correct sgle bubble error,.e. oly oe put s vald betwee two vald puts. If there are more tha oe bubble errors, the output of both crcuts are stll correct. TABLE II. llustrates the outputs of both crcuts. There are three cases, case A s a sgle bubble error, case B s a double bubble errors, ad case C s a trple bubble errors. As show the table, both crcuts ca correct the bubble error case A, sgle bubble error. The bold umbers the table show the correcto of crcuts. Also the table, both crcuts caot correct the bubble errors case B ad case C. The outputs of both crcuts are dfferet but all of them are vald code. TABLE II. OUTPUT OF BEC CIRCUITS Fgure 8. Structure of the Proposed MUX-based TM2B Ecoder wth BEC Sub-crcut Thermometer-to-thermometer wth BEC sub-crcut s a set of 2-put gate. Except the most sgfcat bt, outputs of the crcut are determed by equato (6). OUT IN + IN =, 2, 2 2 (6) = + Fgure 9. s the proposed BEC sub-crcut of a 7-to-3 TM2B puts 2-tput OR gates. ecoder. As show the fgure, a crcut wth 2 requres 2 2 Iput wth bubble error TM2OH wth BEC Proposed BEC crcut A B C A B C A B C Wth the same fuctos, the proposed crcut has advatages crcut complexty ad power cosumpto. To compare the complexty, three dfferet 63-to-6 TM2B wth BEC ecoders are desged three methods, ROM-based ecoder, fat-tree ecoder, ad MUX-based ecoder. Crcuts are desged wth Cadece tool. The lbrary was used s TSMC25. The umber of trasstor requremet of three methods s show TABLE III. As show the table, fat-tree ecoder requres the hghest umber of trasstors. The proposed crcut requres fewer trasstors tha fat-tree crcut but lttle more trasstors tha ROM-based crcut. TABLE III. CIRCUIT COMPLEXITY OF 63-TO-6 TM2B ENCODER CIRCUITS Crcuts Trasstor requremet ROM-based + BEC crcut 74 Fat-tree + BEC crcut 832 MUX-based + proposed BEC crcut 722 To compare the power cosumpto, three TM2B crcuts are smulated wth Cadece tool. The crcut cofgurato s show Fgure 0. Iput geerator geerates value for 63 puts of tested 63-to-6 TM2B crcuts. The put values are chage from the maxmum value to the mmum value. Bary value outputs of TM2B crcuts are measured to verfy the correcto of crcuts. Power cosumpto s motored smulatg process ad reported at the ed of the smulatg process. Fgure 9. Proposed BEC sub-crcut of a 7-to-3 MUX-based TM2B Ecoder

5 Fgure 0. Crcut Cofgurato for Power Cosumpto Average power cosumpto of three crcuts operatg at 500 MHz s show TABLE IV. As show the table, ROM-base ecoder crcut cosumes most power, whereas fattree crcut cosumes least power. The proposed crcut requres oly a lttle more power tha fat-tree crcut. [6] K. Uyttehove, A. Marques, M. Steyaert, A 6-bt GHz acqusto speed CMOS flash ADC wth dgtal error correcto, Proc. of CICC 2000, pp , 2000 [7] R. Kaa, F. Kaess, M. Declercq, A 640 mw hgh accuracy 8-bt GHz flash ADC ecoder, Proc. of ISCAS 99, vol. 2, pp , 999 [8] D. Lee, J. Yoo, K. Cho, J. Ghazav, Fat Tree Ecoder Desg for Ultra-hgh Speed Flash A/D Coverters, Proc. Of MWSCAS-2002, vol. 2, pp. II-87 - II-90, 2002 [9] E. Sal, M. Vesterbacka, A Multplexer Based Decoder for Flash Aalog-to-dgtal Coverters, Proc. Of TENCON 2004, vol. 4, pp , 2004 [0] E. Sal, M. Vesterbacka, Thermometer-to-bary Decoders for Flash Aalog-to-dgtal Coverters, Proc. Of ECCTD 2007, pp , 2007 [] N. Agrawal, R. Paly, A Improved ROM Archtecture for Bubble Error Suppresso Hgh Speed Flash ADCs, Proc. Of AISPC 2008, pp. -5, 2008 TABLE IV. AVERAGE POWER CONSUMPTION OF 6-BIT TM2B ENCODER CIRCUITS AT 500MHZ Crcuts Average power cosumpto (mw) ROM-based + BEC crcut.83 Fat tree + BEC crcut MUX-based + proposed BEC crcut.2 TABLE III. ad TABLE IV. show that the proposed crcut has a balace betwee crcut complexty ad power cosumpto. VI. CONCLUSION I ths paper, we proposed a MUX-based TM2B ecoder wth BEC crcut. The proposed crcut ca correct sgle bubble error. Crcut smulato shows that the proposed crcut has low crcut complexty ad low power cosumpto. Proposed crcut wll be prototyped ad tested to verfy smulato results ext research. ACKNOWLEDGEMNTS Ths work s also supported by KESRI, whch s fuded by Korea Wester Power Compay. Ths work s supported by Korea Scece ad Eg. Foudato (KOSEF) grat fuded by the Korea gov. (MEST) (No ). Ths work s supported by the Korea gov. Mstry of Kowledge ad Ecoomcs(MKE) uder the grat No. I of the Electrc Power Idustry Tech. Evaluato ad Plag Ceter (ETEP). REFERENCES [] K. Deguch, N. Suwa, M. Ito, T. Kumamoto, T. Mk, A 6-bt 3.5-GS/s 0.9V 98-mW Flash ADC 90-m CMOS, IEEE J. of Sold State Crcuts, vol. 43, pp , 2008 [2] R.V.D. Plassche, CMOS tegrated aalog-to-dgtal ad dgtal-toaalog coverter, Kluwer Academc Pulshers, Secod edto, 2003 [3] M. Cho, A.A. Abd, A 6-b.3-Gsample/s A/D Coverter 0.35-µm CMOS, IEEE J. of Sold-state Crcuts, vol. 36, pp , 200 [4] C. Sader, M. Clara, A. Sater, T. Hartg, F. Kutter, A 6-bt.2- GS/s low-power flash-adc 0.3-μm dgtal CMOS, IEEE J. of Sold-state Crcuts, vol. 40, pp , 2005 [5] F. Kaess, R. Kaa, B. Hochet, M. Declercq, New Ecodg Scheme for Hgh-speed Flash ADC s, Proc. Of ISCAS 97, vol., pp. 5-8, 997

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