COMPARATIVE STUDY OF ENCODERS FOR PARALLEL-TYPE ADCS

Transcription

1 OMPAATIVE TUDY OF ENODE FO PAALLEL-TYPE AD Pul Pereir (,3), Jorge. Fernndes (2,3) () Deptº Engª Eletroténi, Esol uperior de Tenologi, I.P..B., Av. Empresário, stelo Brno, Portugl Phone (35) Fx (35) e-mil: (2) Instituto uperior Ténio / (3) INE-ID Liso,. Alves edol, 9, Liso, Portugl Phone (35) Fx (35) e-mil: jorge.fernndes@ines-id.pt Astrt - Anlog-to-digitl onverters (ADs) for high smpling frequenies hve prllel-type rhitetures, where the output of the omprtors is the so-lled thermometer ode. The digitl prt of suh ADs n e just n enoder from the thermometer ode to inry ode; however, different types of error n e implemented to enhne the AD overll performne. In this pper we ompre three different types of enoders: without error ; with error ; with n th order error. These enoders re ompred with respet to the yield of the AD with the different enoders, ssuming the use of n identil nlog prt. The yield is defined y four different riteri: monotoniity, sene of missing odes, nd either integrl or differentil nonlinerity elow speified vlue. Keywords - Anlogue-to-digitl onverters, Prllel ADs, Thermometer ode-to-inry s, Digitl error.. INTODUTION High-speed ADs with smpling frequenies in the tens (or hundreds) of MHz hve prllel-type rhitetures. The fullprllel rhiteture is the most used rhiteture when speed is the most importnt requirement, lthough this rhiteture requires lrge numer of omprtors (2 N - for N its), whih leds to lrge re nd power onsumption []. Due to this onstrint nd lso to the omprtors offset voltge, the resolution is usully limited to 8 it. Alterntives to the fullprllel rhiteture re the two-step nd the pipeline rhitetures [], where full-prllel ADs with redued numer of its re used s su-iruits. The omprtors offset voltge (V O ) is of prtiulr importne euse it is responsile for the stti nonidel This work ws supported y Fundção pr iêni e Tenologi (Portugl) through projets PAXI 2/2./TIT/66/95, PAXI 3300/99 nd POI (Qudro omunitário de Apoio III). The uthors re with INE-ID-Liso ( reserh enter of Instituto uperior Ténio). performne: it imposes limits on the integrl nd differentil nonlinerity nd my originte missing odes or even e responsile for non-monotoni ehviour []. V O, due to mismthes, is rndom vrile whih is ssumed to hve norml distriution []. Although, V O n e redued y iruit design tehniques, this usully leds to n inrese of power onsumption nd re. The lthed omprtors output is the so-lled thermometer ode ( 000 ) nd the offset voltge of the omprtors n use ules (e.g., 00 ) in this thermometer ode originting errors in the output ode. The enoders n e designed to orret lrge errors, tht pper s non-monotoniity of the trnsfer hrteristi of the AD or s missing odes, or even to redue lrge nonlinerity errors, using digitl shemes. We hve divided the enoders into three different lsses: without error ; with error, where simple ules n e orreted with minor modifition to the si enoder; nd with n th order error, where ules n e orreted. The n th order error enoders onsidered re the Mngelsdorf [2], the it swpping [3], nd the Wlle tree [4] enoders. The first two use thermometer ode orretor, etween the omprtors nd the enoder input to mke the of the thermometer ode. A different pproh is used y the Wlle tree method: insted of orreting the thermometer ode the numer of s is evluted. These different lsses of enoders re ompred for the ses N=8 its nd N=4 its. These re prtil vlues, respetively, for full-prllel ADs nd for su-onverters in two-step rhiteture. The expeted yields of n AD re ompred, for different enoders, using s riteri the requirement of monotoniity, sene of missing odes, nd either integrl or differentil nonlinerity elow speifi vlue. 2. PAALLEL-TYPE AD In full-prllel AD (Fig. ) the input voltge v I is pplied to nk of lthed omprtors, where it is ompred with

2 the eqully sped referene voltge levels otined from the resistor ldder. The referene voltge levels re the trnsition voltge levels in the trnsfer hrteristi of n idel AD (Fig. ). All the omprtors with referene voltge elow v I exhiit logi level nd ll the omprtors with referene voltge ove v I exhiit the omplementry logi level resulting in the so lled thermometer ode ( 000 ). This ode is enoded to inry form y n enoder lok. The full-prllel AD uses 2 N - omprtors (hene lrge re nd high power onsumption); lterntive rhitetures like two-step prllel (Fig.2), re used to redue the numer of omprtors. Two-step or multi-step rhitetures usully use full-prllel AD su-iruits. The sujet of AD hrteriztion is still under disussion. In this pper we will onsider tht the idel AD trnsfer hrteristi hs equl ode in widths, nd the stti prmeters used re defined s follows [5]: V V 3 V 2 V v I Lth Lth Lth E N O D E (MB) 2 (LB) ode V V 2 V 3 v I 3. DIFFEENT TYPE OF ENODE () Bsi The simplest iruit to onvert the thermometer ode to inry ode uses deoder with XO gtes to detet the 0J trnsition in the thermometer ode nd then ddress OM for the proper inry enoding (Fig. 3). The OM n e implemented with NMO trnsistors nd pull-up devies (pull-up resistors re represented in Fig. 4). This enoder does not perform ny error, so ule in the thermometer ode will use tht t lest three lines re ddressed in the OM, resulting in the AND of the orresponding three output odes. This will use nonmonoti trnsfer hrteristi for the AD nd the existene of missing ode. (2) with st Order Error orretion By using 3-input XO gtes, insted of the 2-input XO gtes in the simple enoder just presented, errors (ules) in the thermometer ode n e prtilly orreted, thus voiding the ddressing of severl lines in the OM: non-monotoni trnsfer hrteristi is voided ut missing ode my our. ENODE T7 T6 B2 Fig. - Full-prllel AD nd trnsfer hrteristi. v in T5 omprtor Bnk T4 OM B B0 T3 v IN /H AD M it M it (MB) T DA M it T AD L it L it (LB) Fig. 3 - Bsi. Fig. 2- Two-step prllel AD. Monotoni AD: the output odes do not derese (inrese) for uniformly inresing (deresing) input signl, disregrding rndom noise. Missing ode (M): ode tht does not our for ny vlue of the input signl. Integrl nonlinerity (INL): Mximum differene etween the idel nd the tul ode trnsition levels fter orreting for gin nd offset. Differentil nonlinerity (DNL): Mximum differene etween the idel nd the rel ode in width. Fig. 4 - NMO OM with pull-up resistors.

3 (3) with n th Order Error orretion A higher order error enoder using the Mngelsdorf [2], the it swpping [3] or the Wlle tree [4] methods n improve the, with respet to the previous sheme, nd n perform of higher order ules, depending on the method hosen. () Mngelsdorf method The Mngelsdorf method orrets the thermometer ode efore enoding. The output of eh omprtor is ompred with the outputs of the two djent omprtors nd hnged if it is different from oth. Eh omprtor orreted output is T N : previous; insted of orreting the thermometer ode nd then using si enoder, it uses single lok where oth opertions re performed. An exmple for three it enoder is presented in Fig.6 where the si ell is summing iruit of s. The truth tle of this si ell is presented in Tle where, nd, re the its to e summed, is the sum result nd is the rry. If the result is presented with the formt then it represents the numer of ones t the input in inry form. T7 T6 T5 T4 B 0 (LB) T N = TN TN + TN TN + + TN TN+ where T N : is omprtor output without. This method orrets one digit ule in ny position (e.g., ) ut not ules tht re more thn one digit long (e.g., ). T3 T2 T B B 2 (MB) Fig.6: Wlle Tree (exmple for 3 it). () Bit swpping method The it swpping method lso orrets the thermometer ode nd then uses si enoder. The logi opertion represented in Fig.5 is performed etween eh two onseutive omprtors nd ules in the thermometer ode desend if they re s or send if they re 0s. Tle I - umming lok truth tle A2 A Q2 Q A A2 Q Q Fig. 5 - Bit swpping lthing element nd truth tle. In order to perform of ules it is neessry to use n olumns of it swpping lthes, nd therefore the order of error to e performed should e refully evluted. () Wlle tree method If the it swpping method is implemented with its mximum order (2 N ) the lgorithm is equivlent to ounting the numer of s. The Wlle tree method implements the sme lgorithm diretly, without moving the s through the thermometer ode (this method is used to implement high speed multipliers in omputer rithmeti units). The Wlle tree method is different from the The tree struture mens tht there is n inrese in the numer of stges with the numer of its; however the internl nodes re ll low pitne node ensuring fst response. 4. OMPAATIVE TUDY To ompre the three lsses of enoders we hve simulted two full-prllel ADs (with N= 8 it nd N= 4 it) imposing n offset t eh trnsition point of the trnsfer hrteristi. This offset is rndom vrile with norml distriution [], nd models the offset voltge of the lthed omprtor whih is ssumed to hve zero men nd to e independent for different omprtors. The most signifint results re presented in Fig. 7, where the yield is the perentge of ADs tht meet the speifi riteri. The results for the monotoniity riterion re otined from 2000 smples; for the missing ode nd INL.5 LB riteri the results re otined fter disrding the smples tht hve filed the monotoniity riteri.

4 The results plotted for n th order error enoder orrespond to the highest order (2 N ) level. Our omprtive study leds to the following generl onlusions: I. The non-monotoni ehviour n e totlly eliminted y the use of n n th order error enoder. For the si nd the error enoders the yield redution due to non-monotoniity is signifint, even for very low vlues of the offset voltge. II. The missing ode riteri shows tht the n th order error enoder n gin e very effetive in improving the yield. The si enoder n e pprently etter thn the enoder with error, ut it should e noted tht we hve only onsidered the yield due to sene of missing odes fter exluding the nonmonotoni ADs. III. The results onerning INL nd DNL led to the sme generl onlusions. For nonlinerity lower thn the n th order error enoder shows slight improvement over the other enoders, ut it should e noted tht these results re sed on the smples tht hve pssed the monotoniity riterion; for nonlinerity greter thn, the n th order error enoder shows signifint improvement over the other enoders, nd this improvement is more importnt for higher resolution or () () () 0.00 (d) (e) (f) Fig.7 - ADs for () N=8 it, Monotoniity; () N=4 it, Monotoniity; () N=8 it, Missing odes; (d) N=4 it, Missing odes; (e) N=8 it, INL.5 LB; nd (f) N=4 it, INL.5 LB

5 higher σ(v O )/V LB. These onlusions show tht is desirle to use error enoder, Mngelsdorf enoder, or low order it swpping enoder, euse the yield is signifintly enhned without high ost with respet to the simple enoder. The Wlle tree enoder or higher order it swpping enoder improve the AD for ll the riteri nd n e justifile when the resolution inreses (lower V LB nd higher numer of trnsition levels), or when the offset voltge inreses. The hoie etween these two enoders depend on the order of error. If higher order error is needed the Wlle tree enoder is the most suitle, ut it my e too ostly for high resolutions. In this se, medium (3 rd or 4 th order) order error using the it swpping enoder n e the est solution, sine it is good ompromise etween effiieny nd dded iruitry. 5. ONLUION In this pper we onsider three types of thermometer-toinry ode enoders: without error ; with error nd with n th order error. These enoders re studied nd ompred with respet to the expeted yield of the AD, with the different enoders, defined y four different riteri: monotoniity, sene of missing odes, nd either integrl or differentil nonlinerity elow speifi vlue. The results show tht low order error produes signifint inrese in yield with smll inrese in iruitry. For medium resolution ADs, the Wlle tree is the most effetive euse it leds to n inrese of performne (not only of the yield) with eptle dded iruitry. For higher resolution ADs the Wlle tree enoder n eome too ostly nd the use of medium order error using it swpping n e ompromise etween improved performne without to muh dded iruitry. AKNOWLEDGEMENT The uthors re grteful to Prof. M. Medeiros ilv nd Eng. Edgr Aluquerque for helpful disussions onerning the work reported here. EFEENE [] J. Fernndes, onversores A/D om Arquiteturs de Tipo Prlelo, PhD Thesis, IT, [2]. Mngelsdorf A 400-MHz Input Flsh onverter with Error orretion, IEEE J. olid-tte ir., vol. 25, pp. 84-9, Fe [3] V.E. Gruts, Y..Yu, E.O.Tr nd T.Ymguhi, A Dul 4-it 2-Gs/s Full Nyquist Anlog-to-Digitl onverter Using 70-ps ilion Bipolr Tehnology with Boroseni-Poly Proess nd oupling-bse Implnt, IEEE J. olid-tte ir., vol.24, pp , Apr [4] F.Kess,.Knn, B.Hohet nd M.Delerq New Enoding heme for High-peed Flsh ADs, in Pro. IEEE Int. ymp. iruits yst., June 997. [5] IEEE tndrd 057, IEEE tndrd for Digitizing Wveforms eorders, De. 994.