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

An Analog CMOS Universal Membership Function Circuit With Fully Independent, Adjustable Parameters R. G. Carvajal, A. Torralba, F. Colodro and L. G. Franquelo Dpto. de Ingenier´ıaElectr´ onica EscuelaSuperior de Ingenieros, Avda. ReinaMercedes s/n, Sevilla–41012(SPAIN) e–mail: [email protected] Abstract— A novel CMOS membershipfunctioncircuit (MBC) is presented. It is based on a linear tunable transconductor proposed in [1] and implementstrapezoidal/triangularfunctions withall parameters(slope,position,width,heightandamplitude)independentlyand continuouslyadjustable. It is suitableto be usedin analog fuzzy circuitsworking in current mode. The computersimulationsthatverify thecharacteristicsandperformancesof thiscircuitare shown. I. INTRODUCTION In the last few years several implementations of analog fuzzy controllers have been proposed using either, a voltage-mode [2], [3] and a currentmode approach [3], [4], [5]. The advantages of the current-mode approach are a greater and flexible range of values and higher speed (the voltagemode basic building block is the OperationalAmplifier which is inherently slower than the OTA). MostoftheCMOScurrent-modecircuitsproposed to build a MBC are based on the differential pair. This circuit produces sigmoidal type shapes and has good programming properties. But triangular/trapezoidal are the most used shape in fuzzy literature. In this paper a novel CMOS MBC is presented. It is based on a linear tunable transconductor proposed in [1]. This OTA has excellent properties in termsoflinearity and tunability, and withthe help of current mirrors it is possible to build triangular and trapezoidal shapes. Furthermore, with the help of MAX-MIN circuits, it is possible to generate any type of piecewise linear (PWL) function [6]. Besides, the MBCs obtained with this method are fully and continuously programmable. This paper is organized as follows. Section II describes the architecture of the MBC. The way to generate triangular, trapezoidal and PWL circuits is detailed in Section III. Section IV presents some results and advances future research. II. ARCHITECTURE OF TH MBC Figure 1 shows the OTA circuit used to build the MBC. A linear relation between the differential output current and the differential input voltage can be seen in the equation shown in this figure. This relation depends on the control voltage V c and it is possible to modify the gain by changing its value. 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 - Figure 1: OTAcircuit I V I V I V I V MIN MAX a) b) Figure 2: Kind of MBF shapes The functionsshownin figure 2a(Z-functions)can be generated with this circuit. As the inference process in the main fuzzy hardware applications is carried out by means of MAX/MIN operators, V 1 V 2 1 I2 I bias V bias V Vdd bias V Vdd amp I 1 I 2 I - IZ-func I V Vc Vss Vdd Vss I V V I Figure 3: Z-functions circuitry it is easy to see that if the position and slope of the Z-functions are controlled, any type of triangular/trapezoidal shapes can be constructed with the help of MAX/MIN operators (figure 2b). MAX/MIN operators are needed to perform the inference process and this type of MBC only duplicatesthenumberofinputsoftheMAX/MINcircuits. Thecomplexityoftheinferenceprocessdoes notgrowexcessivelybecausethenumberofinputs of MAX/MIN operators is equal to the number of inputs of the controller and this number is usually small. To build a Z-function is necessary to truncate the left and right side of the OTA response. This operation is carried out by means of current mirrors as can be seen in figure 3. A fuzzy controller input directly drives one OTA input, while the other defines the position of the Z-function on the Xaxis. The amplitude of the Z-function can be programmedby thecurrent source I amp and the slope with the value of the voltage V c . III. USE OF THE Z-FUNCTION Withthe Z-functionit ispossibletogenerate triangular and trapezoidal shapes. We only need two Z-functions to build one MBC as can be seen in figure 4. In this figure a MIN circuit is required, but in usual applications this circuit is part of the MIN circuit who performsthe inference process. The MAX circuit proposed in [7] and later imI MBF2 I MBFK I MBFmax I MBF1 V Vdd bias Figure 5: Max Circuitry proved in [8] for fuzzy hardware applications, is shown in figure 5. The way tobuild a MIN circuit (with MAX circuits) with the technique proposed in [9] is also shown is figure 6. This circuit has O(n)complexityand is very suitableforthisapplication. Changing the MIN circuit of figure 4 by a MAX I MBF1 I amp I MBF1 I amp MBFmin I Vbias I MBF1 I MBFr MAX CIRCUIT I MBFmax Figure 6: Min Circuitry 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 Circuit MBF2 IMBF2 Figure 4: Membership Function Generator MIN V I V I Figure 7: An example of PWL function generation circuit thecomplementaryshapecan beproduced. Furthermore it is easy to see that we can construct any PWL function by combining several Zfunctions with MAX/MIN circuits (figure 7). In the next section the results obtained with this circuit and the tunability of all the parameters is shown. IV. SIMULATION RESULTS HSPICE simulations using a standard 0.7 m CMOS technology have been performed. In figure 8 the tunabilityof the positionof the shapesis shown. In figure 9 the gain tunability of the OTA circuit can be seen. This figure has been obtained changing the V c of one OTA. As said before, the position of the Z-function is controlled by the value of one of the two OTA input voltages. Changing the same input of the second OTA the membership function aperture can be modified (figure 10). Finally in figure 11 the transient analysis of the MIN circuit is shown. This simulation also shows how to generate PWL functions by means of several OTAs and MAX/MIN circuits (MIN circuits in this case). Presently, membership function circuit is being sent to fabrication in order to experimentally test the circuit behavior. Besides new OTA topologies are being explored to eliminate the gain dependence on the transistorsthreshold voltages. V. ACKNOWLEDGMENTS The authors would like to acknowledge financial supportbyCICYT through theTIC86-0860project. REFERENCES [1] S. C. Huang and M. Ismail, “Linear tunable COMFET transconductors”, Electronics Letters, vol 29, pp. 459-461,March 1993. Figure 8: Tunability of the position ofthe MBC Figure 9: Tunability of the slope of the MBC [2] ShuweiGuo,Liliane Petersand HartmutSurmann, “Design and Application ofan Analog FuzzyLogic Controller”. IEEE Transactions on Fuzzy Systems vol. 4, no. 4, November 1996. [3] J.Ramirez–Angulo,K.Treece, P.Andrewsand T. Choi. “Current–Mode and Volage–Mode VLSI fuzzy processor architecture”. Proc. Int. Conf. on Circuits and Systems, ISCAS’95,pp 1156–1159,Seattle 1995. [4] Kyoto Tsukano and Takahiro Inoue, “Sysnthesis of Operational Transconductance Amplifier–Based Analog Fuzzy Functional Blocks and Its Application”.IEEE Transactions on Fuzzy Systems, vol. 3 no.1, February 1995. [5] L. Lemaitre, M. J. Patyra and D. Mlynek “Analysis and design of CMOS fuzzy logic controller in current mode”. IEEE Journal of Solid–StateCircuits,vol.29,pp317–322,March 1994. [6] E. S´ anchez-Sinencio, J. Ram´ırez Angulo, B. Linares-Barranco and A. Rodr´ıguezV´ azquez, “Operational Transconductance Amplifiers Figure 10: Tunability of the with of the MBC Figure 11: Transient analysis of the MIN circuit for nonlinear function systheses”. IEEE Journal of Solid-State Circuits, pp 1576-1585, Dec. 1989. [7] J. Lazzaro, S. Ryckebusch, M. A. Mahowald and C. A. Mead. “Winner–Take–All Networks of O(n) Complexity”. Advances in Neural Information Processing Systems, vol. 1, D.S. Toureztky, ed. Morgan Hauffmann, 1989. [8] Bin-Da Liu and Chun-Yueh Huang. “Array Based Fuzzy Inference Mechanism Implemented with Current–Mode CMOS Circuits”.Proc. Int. Conf. on Circuits and Systems, ISCAS’94 vol. 5, London, June 1994. [9] M. Sasaki, T. Inoue, Y. Shirai and F. Ueno. “Fuzzy Multiple–Input Maximum and Minimum Circuits in Current Mode and Their Analyses Using Bounded-Difference Equations”. IEEE Transactions on Computers, vol. 39, no. 6, June 1990.