An analog CMOS universal membership function circuit with fully independent, adjustable parameters

An Analog CMOS Uni e sal Membe ship Func ion Ci cui Wi h Fully Independen , Adjus able Pa ame e s R. G. Ca ajal, A. To alba, F. Colod o and L. G. F anquelo Dp o. de Ingenie ´ıaElec ´ onica EscuelaSupe io de Ingenie os, A da. ReinaMe cedes s/n, Se illa–41012(SPAIN) e–mail: [email p o ec ed] Abs ac — A no el CMOS membe ship unc ionci cui (MBC) is p e- sen ed. I is based on a linea unable ansconduc o p oposed in [1] and implemen s apezoidal/ iangula unc ions wi hall pa ame- e s(slope,posi ion,wid h,heigh andampli ude)independen lyand con inuouslyadjus able. I is sui able o be usedin analog uzzy ci - cui swo king in cu en mode. The compu e simula ions ha e i y hecha ac e is icsandpe o manceso hisci cui a e shown. I. INTRODUCTION In he las ew yea s se e al implemen a ions o analog uzzy con olle s ha e been p oposed us- ing ei he , a ol age-mode [2], [3] and a cu en - mode app oach [3], [4], [5]. The ad an ages o he cu en -mode app oach a e a g ea e and lexi- ble ange o alues and highe speed ( he ol age- mode basic building block is he Ope a ionalAm- pli ie which is inhe en ly slowe han he OTA). Mos o heCMOScu en -modeci cui sp oposed o build a MBC a e based on he di e en ial pai . This ci cui p oduces sigmoidal ype shapes and has good p og amming p ope ies. Bu iangu- la / apezoidal a e he mos used shape in uzzy li e a u e. In his pape a no el CMOS MBC is p esen ed. I is based on a linea unable ansconduc o p o- posed in [1]. This OTA has excellen p ope ies in e mso linea i y and unabili y, and wi h he help o cu en mi o s i is possible o build iangu- la and apezoidal shapes. Fu he mo e, wi h he help o MAX-MIN ci cui s, i is possible o gen- e a e any ype o piecewise linea (PWL) unc ion [6]. Besides, he MBCs ob ained wi h his me hod a e ully and con inuously p og ammable. This pape is o ganized as ollows. Sec ion II de- sc ibes he a chi ec u e o he MBC. The way o gene a e iangula , apezoidal and PWL ci cui s is de ailed in Sec ion III. Sec ion IV p esen s some esul s and ad ances u u e esea ch. II. ARCHITECTURE OF TH MBC Figu e 1 shows he OTA ci cui used o build he MBC. A linea ela ion be ween he di e en ial ou pu cu en and he di e en ial inpu ol age can be seen in he equa ion shown in his igu e. This ela ion depends on he con ol ol age V c and i is possible o modi y he gain by changing i s alue. V 1 V 2 1 I 2 I bias V 1 I 2 I 2 IKn 1 IV cV ss Tn V Teq V V 1V 2 = ( -2-- - ) * ( - ) Vc Vss Vdd - Figu e 1: OTAci cui I V I V I V I V MIN MAX a) b) Figu e 2: Kind o MBF shapes The unc ionsshownin igu e 2a(Z- unc ions)can be gene a ed wi h his ci cui . As he in e ence p ocess in he main uzzy ha dwa e applica ions is ca ied ou by means o MAX/MIN ope a o s, V 1 V 2 1 I2 I bias V bias V Vdd bias V Vdd amp I 1 I 2 I - IZ- unc I V Vc Vss Vdd Vss I V V I Figu e 3: Z- unc ions ci cui y i is easy o see ha i he posi ion and slope o he Z- unc ions a e con olled, any ype o ian- gula / apezoidal shapes can be cons uc ed wi h he help o MAX/MIN ope a o s ( igu e 2b). MAX/MIN ope a o s a e needed o pe o m he in e ence p ocess and his ype o MBC only du- plica es henumbe o inpu so heMAX/MINci - cui s. Thecomplexi yo hein e encep ocessdoes no g owexcessi elybecause henumbe o inpu s o MAX/MIN ope a o s is equal o he numbe o inpu s o he con olle and his numbe is usually small. To build a Z- unc ion is necessa y o unca e he le and igh side o he OTA esponse. This op- e a ion is ca ied ou by means o cu en mi o s as can be seen in igu e 3. A uzzy con olle in- pu di ec ly d i es one OTA inpu , while he o he de ines he posi ion o he Z- unc ion on he X- axis. The ampli ude o he Z- unc ion can be p o- g ammedby hecu en sou ce I amp and he slope wi h he alue o he ol age V c . III. USE OF THE Z-FUNCTION Wi h he Z- unc ioni ispossible ogene a e ian- gula and apezoidal shapes. We only need wo Z- unc ions o build one MBC as can be seen in igu e 4. In his igu e a MIN ci cui is equi ed, bu in usual applica ions his ci cui is pa o he MIN ci cui who pe o ms he in e ence p ocess. The MAX ci cui p oposed in [7] and la e im- I MBF2 I MBFK I MBFmax I MBF1 V Vdd bias Figu e 5: Max Ci cui y p o ed in [8] o uzzy ha dwa e applica ions, is shown in igu e 5. The way obuild a MIN ci cui (wi h MAX ci cui s) wi h he echnique p oposed in [9] is also shown is igu e 6. This ci cui has O(n)complexi yand is e y sui able o hisappli- ca ion. Changing he MIN ci cui o igu e 4 by a MAX I MBF1 I amp I MBF1 I amp MBFmin I Vbias I MBF1 I MBF MAX CIRCUIT I MBFmax Figu e 6: Min Ci cui y I MBF Vpos1 Vpos2 I MBF Vslop2 Vslop1 Vpos2 Vpos1 IN V I amp I amp Vslop1 Vslop2 I amp I MBF1 I VIN I1 V slop2 I2 Vpos2 I= 1 -I 2 MIN Ci cui MBF2 IMBF2 Figu e 4: Membe ship Func ion Gene a o MIN V I V I Figu e 7: An example o PWL unc ion gene a ion ci cui hecomplemen a yshapecan bep oduced. Fu he mo e i is easy o see ha we can con- s uc any PWL unc ion by combining se e al Z- unc ions wi h MAX/MIN ci cui s ( igu e 7). In he nex sec ion he esul s ob ained wi h his ci - cui and he unabili y o all he pa ame e s is shown. IV. SIMULATION RESULTS HSPICE simula ions using a s anda d 0.7 m CMOS echnology ha e been pe o med. In ig- u e 8 he unabili yo he posi iono he shapesis shown. In igu e 9 he gain unabili y o he OTA ci cui can be seen. This igu e has been ob ained changing he V c o one OTA. As said be o e, he posi ion o he Z- unc ion is con olled by he alue o one o he wo OTA in- pu ol ages. Changing he same inpu o he sec- ond OTA he membe ship unc ion ape u e can be modi ied ( igu e 10). Finally in igu e 11 he ansien analysis o he MIN ci cui is shown. This simula ion also shows how o gene a e PWL unc ions by means o se - e al OTAs and MAX/MIN ci cui s (MIN ci cui s in his case). P esen ly, membe ship unc ion ci cui is being sen o ab ica ion in o de o expe imen ally es he ci cui beha io . Besides new OTA opologies a e being explo ed o elimina e he gain depen- dence on he ansis o s h eshold ol ages. V. ACKNOWLEDGMENTS The au ho s would like o acknowledge inancial suppo byCICYT h ough heTIC86-0860p ojec . REFERENCES [1] S. C. Huang and M. Ismail, “Linea unable COMFET ansconduc o s”, Elec onics Le - e s, ol 29, pp. 459-461,Ma ch 1993. Figu e 8: Tunabili y o he posi ion o he MBC Figu e 9: Tunabili y o he slope o he MBC [2] ShuweiGuo,Liliane Pe e sand Ha mu Su - mann, “Design and Applica ion o an Analog FuzzyLogic Con olle ”. IEEE T ansac ions on Fuzzy Sys ems ol. 4, no. 4, No embe 1996. [3] J.Rami ez–Angulo,K.T eece, P.And ewsand T. Choi. “Cu en –Mode and Volage–Mode VLSI uzzy p ocesso a chi ec u e”. P oc. In . Con . on Ci cui s and Sys ems, ISCAS’95,pp 1156–1159,Sea le 1995. [4] Kyo o Tsukano and Takahi o Inoue, “Sys- n hesis o Ope a ional T ansconduc ance Ampli ie –Based Analog Fuzzy Func ional Blocks and I s Applica ion”.IEEE T ansac ions on Fuzzy Sys ems, ol. 3 no.1, Feb ua y 1995. [5] L. Lemai e, M. J. Pa y a and D. Mlynek “Analysis and design o CMOS uzzy logic con olle in cu en mode”. IEEE Jou nal o Solid–S a eCi cui s, ol.29,pp317–322,Ma ch 1994. [6] E. S´ anchez-Sinencio, J. Ram´ı ez Angulo, B. Lina es-Ba anco and A. Rod ´ıguezV´ azquez, “Ope a ional T ansconduc ance Ampli ie s Figu e 10: Tunabili y o he wi h o he MBC Figu e 11: T ansien analysis o he MIN ci cui o nonlinea unc ion sys heses”. IEEE Jou - nal o Solid-S a e Ci cui s, pp 1576-1585, Dec. 1989. [7] J. Lazza o, S. Ryckebusch, M. A. Mahowald and C. A. Mead. “Winne –Take–All Ne - wo ks o O(n) Complexi y”. Ad ances in Neu- al In o ma ion P ocessing Sys ems, ol. 1, D.S. Tou ez ky, ed. Mo gan Hau mann, 1989. [8] Bin-Da Liu and Chun-Yueh Huang. “A - ay Based Fuzzy In e ence Mechanism Im- plemen ed wi h Cu en –Mode CMOS Ci - cui s”.P oc. In . Con . on Ci cui s and Sys ems, ISCAS’94 ol. 5, London, June 1994. [9] M. Sasaki, T. Inoue, Y. Shi ai and F. Ueno. “Fuzzy Mul iple–Inpu Maximum and Min- imum Ci cui s in Cu en Mode and Thei Analyses Using Bounded-Di e ence Equa- ions”. IEEE T ansac ions on Compu e s, ol. 39, no. 6, June 1990.