INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, VOL. 25, 561—579 (1997) A FAMILY OF WIEN-TYPE OSCILLATORS MODIFIED FOR CHAOS A. S. ELWAKIL AND A. M. SOLIMAN* Electronics and Communications Engineering Department, Cairo University, Cairo, Egypt SUMMARY A family consisting of four Wien-type oscillator circuits are modified for chaos by direct replacement of one of the linear resistors with an asymmetrical-type non-linearity introduced by a junction field effect transistor (JFET) operating in its triode region and the addition of a single capacitor. The internal op amp dominant pole is found to play a major role in understanding the chaotic behaviour of the proposed circuits. Mathematical models that describe the observed behaviours are derived. The well known Wien bridge oscillator design equations are shown to be useful as a starting point for chaos modification. Experimental laboratory results, PSpice simulations and numerical simulations of the mathematical models are provided for this family of autonomous RC chaos generators.  1997 John Wiley & Sons, Ltd. Int. J. Circ. ¹heor. Appl., 25, 561 — 579 (1997) No. of Figures: 11 No. of Tables: 0 No. of References: 12 1. INTRODUCTION It has not been until recently that an increasing demand on chaotic signal generators has evolved. Since chaotic signals have been shown to be very useful in various applications including communica- tions, medical applications, neural networks and even music generation, the need for chaotic signal generators that are simple, easy to construct, easy to tune and operate in different frequency bands has increased. It is also generally required that the generated signal has a large voltage swing and persists for a wide and continuous range of parameter values and that periodic as well as chaotic waveforms can be easily sustained. Since Chua’s circuit has been the main source for studying and generating chaos in electronic systems, different realizations of this circuit have been introduced in literature in order to facilitate its implementation as in Reference 4. Recently, the chaotic performance of the well known Colpitts oscillator was investi- gated. —  This study suggested that more interest should be directed towards studying chaos in conventional oscillator structures. On the other hand, the need for simple RC chaos generators has urged some researchers to modify the Wien bridge oscillator for chaos. Although Wien oscillators are basically of second order, interest in their modification is largely due to their popularity and ease of design. In Reference 8, the proposed Wien bridge based chaos generator was formed by coupling a Chua dode with a Wien oscillator in parallel thus requiring three op amps, eleven resistors and three capacitors while in Reference 9, a simple and innovative modification was proposed requiring a single op amp, four resistors, three capacitors and a non-linear element. In this paper, a systematic method is proposed for modifying a family of Wien-type oscillators. The method is demonstrated on the whole family of Wien oscillators given in Reference 10 leading to circuits that require one op amp, three resistors, three capacitors and a single discrete two terminal non-linear element. The well-known linear case design equations of the oscillators are used as a starting point for * Correspondence to: A. M. Soliman, Electronics and Communications Engineering Department, Cairo University, Cairo, Egypt CCC 0098—9886/97/060561—19$17.50 Received 14 August 1996  1997 by John Wiley & Sons, Ltd. Accepted 24 April 1997