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simulation results. Note that almost all the current is supplied by References

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id and the ripple current is compensated by io. Fig. 4shows theexperimental waveforms. No ripple exists in the output voltage V,.Fig. 5 represents the total harmonic distortions THDs) at 1, 10and SOW output, respectively. Fig. 6shows the total power effi-ciency. 2

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JEO N G , I.H., SE ONG, H H., YI, J H., , and CHO, G.H.: A class Dswitching power amplifier with high efficiency and wide bandwidthby dual feedback loops. IEEE Int. Conf. Consumer Electronics(ICCE), 1995, pp. 428429LAI, z. and SM ED LEY , K.M.: A low distortion switching audio poweramplifier. IEEE Power Electronics Specialist Conf. (PESC), 1995,Vol. I, pp. 17k-180JEONG, 1 H., JUNG, N . S , and CHO, G.H.: A high efficiency class Aamplifier with variable power supply. 100th Audio EngineeringSociety Convention, Copenhagen, 1996

Implementation of Chuas chaotic circuitusing current feedback op ampsR. Senani and S.S. Gupta

The authors present a new, current feedback op-amp-based,implementation of Chuas chaotic circuit. The workability of theproposed implementation has been experimentally verified usingAD844 type current feedback op amps. This implementationoffers several advantages over an earlier one based upontraditional voltage-mode op-amps.

Conclusions: This Letter has presented a novel audio amplifier thathas the advantages of both analogue and digital amplders. Thehigh fidelity of an analogue amplifier and excellent efficiency of adigital amplifier are simultaneously achieved in one board. A typi-cal 50W prototype has demonstrated that the proposed amplifierhas excellent THD up to 0.005 ,and high efficiency of - 90 atoutput = 50W.

bFig. 1 Schematic drawing and V-I characteristics of Chuas circuitU Chuas circuitL = 28.53mH, C, = 5nF, C = 50nF, R = variablemo = -0.5, m, = -0.8, BP = -1v-l characteristics of Chua diode

The purpose of this Letter is to present a new, CFOA-basedimplementation of Chuas circuit. The workability of the proposedrealisation has been experimentally verified using ADS44 typeN.S. Jung, J.H. Jeong and G.H. Cho (Korea Advanced Institute of CFOAs. The new implementation offers Several advantages OverScience and Technology (KAIST), 373-1, Kusong-dong, YuSong-gu, the previously reported inductorless realisation of [4] based onTaejon, 305-701,Korea) VOAs.

ELECTRONICS LETTERS 30th Apr il 1998 Vol 4 No 9 829

23 Junuury 1998EE 1998Electronics Letters Online No: 19980595

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vc2

................................................................................NL

........................................................................

Fig. 2 New implementation of Chuas circuit using CFOAs

The proposed CFOA implementation is shown in Fig. 2, whereeach CFOA is characterised by the instantaneous terminal rela-tions i = 0, v, = v,, i, = i and v, = v, [7]. The detailed characteri-sation of the CFOA-based subnetworks NL and NR s as follows:i) The Chua diode NR:With resistors RN1 nd Rm shorted, eachof the CFOAs A, and A, is configured as a negative impedanceconverter NIC) and the circuit is basically a parallel connection

of two negative resistors -R, and -RN4.With resistors RN,andRm added and the bias voltages of the two CFOAs made differ-ent, the circuit allows realisation of the required characteristics ofa Chua diode using RNl= 9.558kR,Rm = 542Q R, = 5.482w2,RN4= 1.606kR;+VI = M.05V DC and f V = f11.23V DC, yield-ing m, = 0.8, m, = 0.5 and BPI = -1, as codirmed from the V-Icharacteristic of Fig. 3.

Fig. 3 V-I characteristics of CFOA-based Chua diode NR

Fig. 4 Double scroll attractor obtained fr om hardware implementationof Fig. 2, using AD844 CFOAs

ii) The synthetic inductor NL:CFOAs AZ A, and A,, togetherwith the associated components, simulate an ideal inductor ofvalue L = C,R,R,. However, when the parasitic impedances of the

CFOAs are considered i.e. parasitic resistance R and parasiticcapacitance C, at the compensation pin z-terminal) and the inputresistance R at the x-input), it is found that choosing RI =3.744k0, R2 = 1.459162, and CO= 5nF, and considering C, =4.5pF, R, = 50Q and R, = 3MR [7], the circuit realises an induc-tor of value 28.53mH with R = 1.88R and thus, can be consid-ered to be almost an ideal inductor of 28.53mH. Note that in thesubcircuit NL, he current through the inductor is available exter-nally at the z-output terminal of A,. Thus, a novel feature of thecircuit of Fig. 2, possible only due to the use of CFOAs, is thatnot only the state variables x capacitor voltage K1 nd y capac-itor voltage Vc2 ut the third state variable z inductor current iLis also accessible in a direct manner.The realisation of Fig. 2has been experimentally verified usingcommercially avdable ADS 44 type CFOAs. In Fig. 4we displaythe experimentally observed double scroll attractor obtained withL = 28.53mH, C, = 5nF, C, = 50nF, R = 1.503kR with CFOAsA,, A and A, biased with +15V DC). The various other chaoticattractors observable from the circuit of Fig. la with Chua dioderealised by the two op-amp circuit of [3])have also been found tobe realisable from the new implementation of Fig. 2.

A comparison with the recently proposed CM chaos generatorof [8] and the inductorless realisation of the Chua oscillator usingVOAs published earlier in [4] is now in order. Whereas the circuitof [8] is a CM chaos generator, the proposed implementation ofFig. 2is simultaneously a voltage-mode as well as current-modechaos generator. In comparison to [4], it may be noted that in theproposed circuit, the CFOA-based Chua diode NR employs feweronly four) resistors than the six resistors in the VOA-basedKennedys circuit of [3]. On the other hand, the CFOA-based syn-thetic inductor NL,although it employs three CFOAs in contrastto the single op-amp-based circuit in [4], offers the following novelfeatures: i) employment of a minimum number only three) ofpassive components, ii) easy incorporation of the CFOA-parasit-ics into the design, iii) lack of resistor-matching or capacitor-matching conditions, and iv) explicit availability of the third statevariable z inductor current iL as a current output. It appears thatthe last feature may lead to interesting possibilities in the contextof interconnections of two or more chaotic Chua oscillators [9].This, however, needs further investigation.

EE 1998Electronics Letters Online No: 19980621R. Senani (Department of Electronics and Communication Engineering,Delhi Institute of Technology, Old I.G. Block, Kashmere Gate, Delhi110 006, India)S.S. Gupta (727, Sector I , Pushp Vihar, New Delhi 110 017, India)

4 March 1998

References1 CHUA, L.o.: Chuas circuit: an overview ten years later, J . CircuitsSyst. Comput., 1994, 4 2 ) ,pp. 117-1592 MATSUMOTO, T.: A chaotic attractor from Chuas circuit, IEEE

Trans. CAS, 1984, CAS-31 pp. 1055-10583 KENNEDY, M.K.: Robust op-amp realization of Chuas circuit,Frequenz, 1992, 46 pp. 66-804 MORGUL, 0 : Inductorless realisation of Chuas oscillator,Electron.Lett., 1995, 31 (17), pp. 1403-14045 ABUELMA ATTI, M.T.: Chaos in an autonomous active-R circuit,IEEE Trans. Circuits Syst. I: Fundam. theory appl., 1995, 42 (l),pp. 1-56 TAMASEVICIUS, A., MYKOLAITIS, G., and NAMAJUNAS, A.: Doublescroll in a simple 2D chaotic oscillator, Electron. Lett., 1996, 32(14), pp. 1250-12517 TOUMAZOU, c., and LIDGEY, J.: Current feedback op-amps: ablessing in disguise?, IEEE Circuits Devices Mag., 1994, 10 (l),8 ELWAKIL, A.s., and SOLIMAN, A.M.: Current mode chaos generator,

Electron. Lett., 1997, 33 20), pp. 1661-16629 CHUA, L.o., ITOH, M., KOCAREV, L., and ECKERT, K.: Chaossynchronization in Chuas circuit in MADAN, R.N. (Ed.): Chuascircuit: A paradigm for chaos (World Scientific Publishing Co.Pvt. Ltd, Singapore, 1993), pp. 309-324

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