Transient Analysis of Electronic Circuits Including Zener Diodes

Abstract

This paper addresses the transient analysis of the electronic circuits incorporating Zener diodes. It starts with suggesting a new Zener diode model. The model is based on efficiently utilized step functions of the applied voltage. It includes also the diode’s main technical parameters such as its resistances in both the forward and reverse current directions as well as its Zener’s breakdown voltage. The sharp discontinuities of the step-functions are dealt with by adopting equivalent approximations in terms of inverse hyperbolic tangent expressions. The resulting idealized step-shaped dependence of the diode’s resistance on voltage exhibits an extremely small value for positive voltages and extremely high resistances for negative voltages with magnitudes larger than the Zener voltage. Otherwise, the diode shows a resistance which is equal to the high reverse value. A compact Mathematica code written using the recent Version 12.2 is derived and applied in order to perform the time-domain analysis of three representative case studies. In addition to the usual display of the circuits’ currents and voltages as functions of time, parametric plots are also presented for illustrating their trajectories, in which the breakdown phenomenon of the diode is clearly manifested and recognized. Voltage sources of both sinusoidal as well as ramp-shaped time wave forms are considered. The computed results are presented in order to demonstrate the advantage, the applicability and the clear ease of implementation of the suggested procedure.