An introduction to the design of chaotic oscillators is presented from an electrical engineering point of view. Oscillators are amplifiers with unstable bias points. The basic design principle behind chaotic oscillators is the connection of two electronic circuits which are not in harmony. A number of configurations which may serve as the physical mechanisms behind chaotic behavior are listed. The behavior of an oscillator is explained by means of eigenvalue studies of the linearized Jacobian of the differential equations for the mathematical model of the oscillator. The basic design principle is demonstrated by means of different simple examples.

1.1 Introduction and General Remarks

Radio amateurs and electronic engineers have observed chaotic performance of electronic circuits since the invention of the triode amplifier by Lee de Forest in 1906. The phenomena observed were called noise, nonlinear distortion, parasitic oscillations, intermittent operation or asynchronous heteroperiodic excitation. It was considered unwanted and impossible to investigate analytically. Edwin H. Armstrong (1890-1954) invented the regenerative circuit for HF oscillations in 1912 (superheterodyne 1918, FM 1937). He possibly observed chaos ^{[1] [2]}. Balthasar van der Pol (1889-1959) reports about chaos as "an irregular noise" ^{[3] - [6]}. Today (year 2001) we are able to investigate the phenomena by means...