Current-mode Biquadratic Universal Filter Design with Two Terminal Unity Gain Cells

Transcription

1 0 H. ALPASLAN, E. YUCE, CURRENT-MODE UNVERSAL FLTER DESGN WTH DUAL PORT UNTY GAN CELLS Current-mode Biqudrtic Universl Filter Design with Two Terml Unit G Cells Hlil ALPASLAN, Erkn YUCE Dept. of Electricl nd Electronics Engeerg, Pmukkle Universit, Kikli, 0070 Denizli, Turke lpslnster@gmil.com, erknuce@hoo.com Abstrct. A grounded prllel loss ctive ductor nd two current-mode (CM) universl filters re presented this pper. All the circuits use two voltge followers ( nd current follower (CF). The prllel loss ctive ductor cludes grounded cpcitor which is ttrctive tegrted circuit (C) technolog. The CM universl filters hve one put nd stndrd three outputs such s bnd-pss (BP), low-pss (LP) nd high-pss (HP) responses. All-pss nd notch outputs cn be obted b ddg etr one CF. Suggested structures this pper cn be constructed with commercill vilble ctive devices such s AD8s. Non-idel g nd trsic X-terml prsitic resistor effects re emed. Severl computer simultions with SPCE progrm nd eperimentl results b emplog AD8s re drwn to verif theoreticl ones. Kewords. Loss ductor simultor, current-mode filter, unit g cell, current follower, voltge follower.. ntroduction Active filters cn be esil relized tegrted circuits (C sted of stndrd pssive filters. Therefore, the hve been used mn nlog pplictions from pst to present [-]. Besides, the cn be clssifiction such s current-mode (CM) filters nd voltge-mode (VM) filters. CM signl processg cuse higher frequenc of opertion due to smll lod resistor nd wide dnmic rnge of CM ctive devices []. Second genertion current conveors (CC re well known ctive devices [5]. Non-idel voltge nd current gs restr the CC performnces. Current followers (CF nd voltge followers ( known s unit g cells (UGC hve quite smll ctive sensitivities [6], [7]. UGCs re widel used for voidg double non-idel current nd voltge g effects of the CCs designg ctive filters the open literture [6-]. CM biqudrtic universl filter [6] uses two CFs, one of which is plus tpe while the other one is mus tpe, one nd four dmittnces. Furthermore, the LP output is obted from resistor between nd mus tpe CF. CM universl biqud [7] uses CF nd nd five dmittnces. CM filter of [7] hs bnd-pss g which is less thn unit. Proposed CM biqudrtic filter [8] uses si UGCs, three of which re used s CFs wheres the others re emploed s s, nd ne dmittnces. One of the CM universl filters [9] uses four CFs, three s nd eight dmittnces for three puts nd one output current. Other circuit [9] conts three CFs nd three s nd eight pssive components for one put three output currents. CM filter [0] is composed of three CFs, two s nd si dmittnces where used technolog is.μm CMOS process. Moreover, the used CFs hve two outputs. n [], two universl CM filters, designed b BJT technolog, one of which is multi put multi output filter which hs three dul output CFs, one nd four pssive components. The other one is multi put sgle output filter which hs one dul output CF, one sgle output CF, one nd four pssive components. Proposed filter circuit [] which is VM/ CM cludes four s, four dul output CFs nd seven pssive components which power suppl voltges re ±5 V nd used technolog is.μm CMOS process. Also, it hs comple ternl structure. The universl filter [] need to revise of some element connections nd/or used elements. n [], the proposed first nd third filter configurtions use nno-frds level cpcitors. The other current-mode filter circuit [5] is one put one output bsed on current mirror rrs. Besides, its power suppl voltges re ±5 V nd used technolog is 0.8μm CMOS process. n [6], the proposed modified CM universl filter hs more ctive components which re four digitll controlled CF, two dul-output CF, two buffers. On the other hnd, the universl filters cn be used some pplictions for emple, termedite frequenc stges of trnsmitters nd receivers, some telephone decoder nd crossover networks [7]. n this stud, two second-order universl filters which re derived from n electronicll tunble loss grounded ductor simultor re composed of two s nd one CF nd smller number of pssive components. The suggested prllel grounded loss ductor cludes grounded cpcitor, which is dvntgeous C technolog [8, 9]. The first filter cn provide gs for lowpss nd bnd-pss responses while the second (reorgn-

2 RADOENGNEERNG, VOL., NO., APRL 0 05 ized) one cn relize g for onl low-pss response. The developed filters from the prllel grounded loss ductor cn simultneousl provide ll the stndrd filter responses such s low-pss (LP), bnd-pss (BP) nd highpss (HP) responses. Also, notch nd ll-pss responses cn be esil obted b ddg n etr CF to the troduced filters. All proposed circuits cn be constructed with commercill vilble ctive devices such s AD8s [0]. Some simultion nd eperimentl results re cluded to confirm the theor. Content of this stud is orgnized s follows: fter description of the UGCs section two, identifiction of the proposed universl filters section three is given. Designtion of the simultion nd eperimentl results re respectivel given sections four nd five. Conclusion is given the lst section, section si.. Unit G Cells A CF+ cn be obted from CC+ b groundg -terml of the CC+ nd cn be obted from CC+ b groundg z-terml of the CC+ [5]. Electricl smbols of the CF+ nd re shown Fig.. The CF+ nd re idell defed () nd (), respectivel. V 0 CF z z Vz z scz R z V 0 sc R V ( ( V z, () Z ( 0 V. () Z s ( ) Frequenc dependent non-idel current g of the CF+ is α( = α 0 / (+s/w α ) s well s frequenc dependent non-idel voltge g of the is β( = β 0 / (+s/w β ). The DC non-idel gs re α 0 = + α nd β 0 = + β which re idell equl to unit. Their bndwidths, w α nd w β, re idell equl to fit. n ddition to this knowledge, - << α << nd - << β << re known s current trckg error nd voltge trckg error, respectivel. Fortuntel, the pole frequencies f α nd f β re effective t high frequencies; therefore, their effects cn be ignored t low nd medium frequencies. However, CFs hve no voltge g effects becuse of the virtul ground t their put termls nd lso s hve no current g effects. Prsitic resistors R z nd R nd prsitic cpcitnces C z nd C re the prsitics of z nd termls of the CF+ nd, respectivel. The X-terml hs prsitic impednce Z ( = (/sc ) // (R + sl ) which is idell equl to zero. n this stud, the CMOS CC structure of [] Fig. is used for the CF+ nd. V C M M M V DD ( ) z 0 M M 5 M 6 V V M 7 M 8 M 9 M 0 V SS Fig.. CMOS CC ternl structure of [6]. ( b ) Fig.. Smbolic representtion of () CF+, (b). V 0,, () z 0, V V. () ncludg non-idel current g of the CF+ nd nonidel voltge g of the together with their prsitic impednce effects, the CF+ nd cn be chrcterized () nd (), respectivel.. Proposed Universl Filters A simple pssive filter cn be obted b usg prllel R-L-C nd/or series R-L-C circuits. n ddition, n ctive ductor circuit cn be used sted of pssive ductor filter circuit. As result, n ctive filter cn be constituted b mkg some modifictions such s ddg some pssive circuit elements on ctive ductor circuits [], []. A grounded ctive ductor topolog nd its equivlent circuit re given Fig. nd, respectivel.

3 06 H. ALPASLAN, E. YUCE, CURRENT-MODE UNVERSAL FLTER DESGN WTH DUAL PORT UNTY GAN CELLS V Z CF R R R ( ) ( ) z ( ) Fig.. Proposed ctive ductor circuit. Z eq V L eq Req Fig.. Smbolic equivlent circuit of the proposed ductor. nput impednce eqution of the proposed ductor is given (5). Zeq ( Req sleq (5) Z( R sc( R R R ) Equivlent resistnce is equl to R nd equivlent ductnce is equl to C(R + R )R / β α β, which cn be seen from (5). Chrcteristic equtions (D ( with onl prsitic resistors nd D ( with onl non-idel g of the filter trnsfer functions (TF Fig. 5 re given (6), where R = R + R. Besides, X-terml prsitic resistors of the UGCs (R, R nd R ) nd non-idel gs ffect the filter TFs s seen from (7) nd (8), respectivel. R C HP BP BP LP s CC ( R R D ( s CC RR scr (6.b) R ( R R ))( RR D ( R ( R R)) (7.) scr ( RR R ( R R)) (7.b) D ( scr ( RR R ( R R)) (7.c) D ( scr( RR R ( R R ) RR R (7.d) D ( HP s CC RR (8.) D( BP BP LP R scr (8.b) R D( scr (8.c) D ( R (8.d) R D( When cluded both non-idel gs nd prsitic resistors, equtions for the filter TFs re much more comple. Thus, the proposed universl filter circuit is reorgnized s seen from Fig. 6, the second suggested filter. Chrcteristic eqution, D (, for the filter Fig. 6 is given (9) where R b = R + R + R. Current TFs, ngulr resonnce frequenc (w 0 ) nd qulit fctor (Q) cludg non-idel g nd prsitic resistor effects for the reorgnized second-order universl filter circuit re given (0) nd (). R CF R R R R z CF R R R R z C HP BP C R LP C HP R R C BP LP BP Fig. 5. The first proposed biqudrtic universl filter. Fig. 6. The second proposed second-order universl filter. D ( s C C R ( R R sc R ( R b b R R R R ) R ) R (9) Here, C C ( R ( R R ( R R C ( R R R ( R R 0 R R R )( R R D ( s s (6.) R ( R R ( R R ( R R R ( R R )) R R R ) 0 )) R ) )) R ) HP BP LP s CC Rb ( RR RR RR) (0.) D ( sc( RR RR RR) (0.b) D ( scrb R R (0.c) D(

4 RADOENGNEERNG, VOL., NO., APRL 0 07 w 0 R C C R ( R R R R R R ) b b (.) C( RR RR RR) R Q (.b) R R C R del form equtions for the two universl filters re given from () to (). D s C C R R sc R () ( HP s CC RR (.) D( BP R scr (.b) R D( BP BP scr (.c) D( LP R (.d) R D( w0 (.) C C R R All the simultions re performed b mens of SPCE which smmetricl power suppl voltges re selected s V DD = -V SS =.5 V nd V c = 0. V is chosen. The proposed grounded prllel loss ductor with pssive element C = 0 pf nd R = R = R = 6.66 Ω ieldg L eq = 8.0 nh nd R eq = 6.66 Ω re simulted, the results re shown Fig. 7. The first proposed filter nd its reorgnized form hve R = R = kω, R =. kω, (R = kω which is used onl for the first filter), C = 00 pf nd C = 0 pf. This pssive component vlues result Q.08 nd f o.8 MHz. The CMOS CC structure given Fig. is sized with stndrd 0.5μm technolog. All the MOS trnsistors re worked sturtion region for ll simultions. Also, spect rtios of the MOS trnsistors re given Tb.. MOS trnsistors W(μm) L(μm) M, M, M M, M M M 7, M 8, M 9, M Tb.. Dimensions of the used CMOS trnsistors Fig.. CR Q (.b) C R Sensitivit nlsis is ccomplished order to eme the performnce of the proposed universl filters. Pssive sensitivit vlues of the proposed filter with respect to w 0 nd Q for the idel equtions () re found (5). w0 Q Q S R, R, C, C S R, C S R, C (5) f previous stge of the proposed filters is not high output impednce, etr one CF is used for ech of the filters. Similrl, if the net stge of the proposed filters is not low put impednce, etr one CF is used for ech response. n ddition to these, if one of the cpcitor of the proposed filters is removed from ground nd connected to the X terml of the dditionl CF to obt high output impednce current, the high frequenc of the proposed filters cn be ffected []. Therefore, the prsitic resistor of the X terml of the dditionl CF should be chosen s smll s possible to improve high frequenc performnce of the suggested filter.. Simultion Results Fig. 7. AC nlsis results for the loss ductor. db cutoff frequenc of C is restricted b the X-terml resistors. However, when the resistor R is used, this restriction cn be more effective, which is shown Fig. 8. Fig. 8. Effects of the resistor R on the proposed CM universl filters. n this stud, MC nlsis for hundred simultion runs is mde b pplg 0% devition on cpcitor C for the first nd second developed universl filters. Simultion results relted with MC nlsis re given Fig. 9 nd 0, respectivel. As seen from the MC nlsis, the cpcitor C nd resistor R ffect the filter performnce. Moreover, both cpcitor C nd resistor R effects on the proposed filter re given Fig..

5 08 H. ALPASLAN, E. YUCE, CURRENT-MODE UNVERSAL FLTER DESGN WTH DUAL PORT UNTY GAN CELLS Fig. 9. MC nlsis for the first proposed filter. Fig.. The first proposed filter TFs AC nlsis. Fig. 0. MC nlsis for the second proposed filter. Fig.. mpct on the db cutoff frequenc of C b chngg C nd R. AC nlsis of the first proposed universl filter outputs such s BP, HP nd LP responses is given Fig.. AC nlsis of the reorgnized universl filter TFs such s BP, HP nd LP responses is given Fig.. Fig.. AC nlsis results for the reorgnized filter. While C is chngg from 0 pf to 00 pf with 0 pf steps nd put current mgnitude is 50 μa, step response of the HP output current on C nd BP output current on C for the reorgnized universl filter re given Fig.. Q nd step response re terrelted s seen

6 RADOENGNEERNG, VOL., NO., APRL 0 09 from Fig.. n theor, impendg ζ is dmpg fctor nd σ is ttenution. Q, ccordg to these prmeters, is given (6) [5]. The unit step signl with 50 μa current mplitude nd 0. μs rise time is pplied to the proposed filter. Moreover, the result of the filter current outputs on C nd C re given Fig.. w Q 0 (6) power dissiption for the second filter circuit is evluted s 6.87 mw. Fig. 6. FFT simultion results. Fig.. The responses to the put unit step signl of the second universl filter. Totl hrmonic distortion (THD) results for HP nd BP TFs of the reorgnized filter circuit re shown Fig. 5. Fig. 7. NOSE simultion results. Fig. 5. THD results s chngg put current mgnitude. Fst Fourier trnsform (FFT) simultion for the second filter circuit is mde where 5 μa nd 50 μa put susoidl signls re seprtel pplied nd results re given Fig. 6. Besides, noise effects for the second filter circuit re given Fig. 7. For the second filter, the NOSE vlues re quite smll nd THD vlue is under % even put current mgnitude is 50 μa. Besides, totl 5. Eperimentl Results Tests re mde on the first proposed CM universl filter. The commercill vilble ctive structures, AD8s, with BJTs nd known s 60MHz 00V/μs monolithic op mp C re used the test circuit where one of the AD8s is used to obt current source. Pssive components re chosen s R = 00 Ω, R = R = R = kω, R = 00 Ω, C = C = 00 pf nd power suppl voltges re djusted to V DD = -V SS = V. Three AD8 Cs re used test circuit given Fig. 8. For this test circuit, Q.6 nd f MHz re clculted. Besides, both idel nd eperimentl results re given Fig. 9.

7 0 H. ALPASLAN, E. YUCE, CURRENT-MODE UNVERSAL FLTER DESGN WTH DUAL PORT UNTY GAN CELLS V R AD8 z w c HP AD8 z w BP Fig. 8. Test circuit designed with AD8 Cs. R R R AD8 Fig. 9. Eperimentl results of the first suggested CM secondorder universl filter. 6. Conclusion n this work, we present grounded prllel loss ctive ductor simultor nd two versions of sgle put multi output CM universl filters for simultneousl providg HP, LP, BP outputs. All the troduced configurtions this pper consist of two s nd CF. The suggested prllel grounded loss ductor cludes grounded cpcitor, which is dvntgeous C fbriction. B ddg n etr CF to the filter circuits, ll-pss nd notch filter output currents cn be esil obted. n ddition to these, ll the topologies cn esil be constructed b emplog commercill vilble ctive devices such s AD8s. Non-idel g nd X-terml prsitic resistor effects re emed this pper. The climed theor, simultion results nd eperimentl results re comptible with themselves. References [] MARSCOTT, A. An ctive nlog filter rchitecture ensurg c z w R LP unit-g nd low sensitivit. Circuit Sst. Signl Process, 00, vol. 9, p , 00. [] SUN, Y. Design of high frequenc tegrted nlogue filters. The nstitution of Engeerg Tech., April 5, 00. [] GHAUS, M. S. Anlog ctive filters. EEE Trns. on Circuits nd Sstems, 98, vol., p. -. [] RAUT, R., SWAMY, M. N. S. Modern Anlog Filter Anlsis nd Design: A Prcticl Approch. Wile-VCH, st edition, 00. [5] FER, G., GUERRN, N. C. Low Voltge, Low Power CMOS Current Conveor. Sprger, st edition, 00. [6] WENG, R.-M., LEE, M.-H. Novel universl biqud filters usg onl three followers. nt. Journl of Electronics, 997, vol. 8, p [7] WENG, R.-M., LEE, M.-H. Novel universl biqud filters usg onl two unit-g cells. nt. Journl of Electronics, 000, vol. 87, p [8] CELMA, S., SABADELL, J., MARTNEZ, P. Universl filter usg unit-g cells. Electronic Letters, 995, vol., p. 87 to 88. [9] ABUELMA ATT, M. T., AL-QUAHTAN, M. A. Current-mode universl filters usg unit-g cells. Electronic Letters, 996, vol., p [0] ALZAHER, H. A., SMAL, M. Current-mode universl filter usg unit-g cells. Electronic Letters, 999, vol. 5, p. 98 to 00. [] CHANG, C.-M., LAO, T.-S., YU, T.-Y., LN, E.-S., TENG, C.- H., HOU, C.-L. Novel universl current-mode filters usg unitg cells. nt. Journl of Electronics, 00, vol. 88, p. -0. [] GUPTA, S. S., SENAN, R. New voltge-mode/current-mode universl biqud filter usg unit-g cells. nt. Journl of Electronics, 006, vol. 9, p [] SENAN, R., GUPTA, S. S. Universl voltge-mode/current-mode biqud filter relised with current feedbck op-mps. Frequenz, 997, vol. 5, p [] LU, S.-., CHEN, J.-J., HWANG, Y.-S. New current mode biqud filters usg current followers. EEE Trns. on Circuits nd Sstems : Fund. Theor nd Applictions, 995, vol., p. 80 to 8. [5] SOULOTS, G., HARTANTS,. Current-mode filters bsed on current mirror rrs. nt. J. Circ. Theor. Appl., 007, vol. 6, p [6] ALZAHER, H. A. A CMOS digitll progrmmble universl current-mode filter. EEE Trns. on Circuits nd Sstems : Epress Briefs, 008, vol. 55, p [7] PAARMANN, L. D. Design nd Anlsis of Anlog Filters: A Signl Processg Perspective. Kluwer Acdemic Publisher, 00. [8] YUCE, E. Full tegrble mied-mode universl biqud with specific ppliction of the CFOA. nterntionl Journl of Electronics nd Communictions (AEU), 00, vol. 6, no., p [9] YUCE, E. A novel flotg simultion topolog composed of onl grounded pssive components. nterntionl Journl of Electronics, 00, vol. 97, no., p [0] AD8 monolithic op mp. [Onle] Avilble t: http: // [] SURAKAMPONTORN, W., REWRUJA, V., KUMWACHARA, K., DEJHAN, K. Accurte CMOS-bsed current conveors. EEE Trnsctions on nstrumenttion nd Mesurement, 99, vol. 0, p

8 RADOENGNEERNG, VOL., NO., APRL 0 [] FABRE, A., SAAD, O., WEST, F., BOUCHERON, C. Current controlled bndpss filter bsed on trnsler conveors. Electronic Letters, 995, vol., p [] FABRE, A., SAAD, O., WEST, F., BOUCHERON, C. Low power current-mode second-order bndpss F filter. EEE Trnsctions on Circuits nd Sstems-: Anlog nd Digitl Signl Processg, 997, vol., p [] YUCE, E., MNAE, S. Universl current-mode filters nd prsitic impednce effects on the filter performnces. nterntionl Journl of Circuit Theor nd Applictions, 008, vol. 6, p [5] OGATA, K. Modern Control Engeerg. Prentice Hll, th edition, 00. About Authors Hlil ALPASLAN received the B.Sc. nd the M.Sc. degrees from Pmukkle Universit, Deprtment of Electricl nd Electronics Engeerg Denizli, Turke 00 nd 005, respectivel. He is currentl PhD student t Pmukkle Universit, nstitute of Science nd Technolog, Deprtment of Electricl nd Electronics Engeerg Denizli, Turke. He hs been workg s reserch ssistnt t Pmukkle Universit sce 00. His reserch terests clude nlog current mode circuits, nlog tegrted circuit design, unit g cells nd current conveors. Erkn YUCE ws born 969 Nigde, Turke. He received the B.Sc. degree from Middle Est Technicl Universit, the M.Sc. degree from Pmukkle Universit nd the PhD. degree from Bogzici Universit, ll Electricl nd Electronics Engeerg 99, 998 nd 006, respectivel. He is currentl n Associtive Professor t the Electricl nd Electronics Engeerg Deprtment of Pmukkle Universit. His current reserch terests clude nlog circuits, ctive filters, snthetic ductors nd CMOS bsed circuits. He is the uthor or co-uthor of bout 90 ppers published scientific journls or conference proceedgs.