Conditions for «deterministic chaos» phenomenon occurrence in a non-linear rl-diode electric circuit of sinusoid current

Abstract

In this work, the phenomenon of «deterministic chaos» in a nonlinear RL-diode electrical circuit of a sinusoidal current was investigated. The diode is represented by an equivalent circuit, which in the general case includes a nonlinear resistor and two nonlinear capacitances – barrier and diffusion. With certain ratios of the frequency of the current and the parameters of the circuit, the transition process for the period of oscillation of the input voltage hasn’t time to finish. In this case, at the beginning of each period there is a residual voltage on the capacitances, that is, each new cycle of the transition process has non-zero initial conditions. It is noted that the residual voltage in each period is different; therefore, the current in the circuit in each period is also different. Thus, in this case, a continuous transition occurs, the parameters of which are chaotic. The simulation of the phenomenon of «deterministic chaos» was carried out in the environment of the MicroCap circuit simulation program. During the simulation for each type of diode, the set of circuit parameters f, R, L (frequency, load resistance, inductance) was divided into two subsets – a subset for which the transition process during the oscillation period of the input voltage has time to finish (the residual voltage on the capacitance is almost zero) and the mode of operation of the circuit can be considered deterministic, and a subset for which the transient process during the oscillation period of the input voltage doesn't attenuate (the residual voltage on the capacitance is significantly different from zero) and the mode of operation of the circuit can be considered chaotic. As a result, the recommended sets of parameters of the circuit for designing the generators of chaotic oscillations were determined.