Applications of bifurcation theory to thyristor turn-on and turn-off

Abstract

We present a simple thyristor model that uses the gate voltage as the dependent variable and makes it possible to analyse the transverse behaviour of the device. The model leads to parabolic non linear partial differential equations in space and time, which are similar to Fisher's equation. A stationary analysis using bifurcation theory shows the existence of two stationary stable equilibrium points corresponding to the off- and on-state of the thyristor having in between an unstable point. A critical length, below which transverse non uniform current densities are not possible, is also predicted. A dynamical analysis in terms of wave type solutions shows that the steeper the wave front is, the smaller the propagation velocity. A numerical solution of the equations with more realistic boundary conditions, i.e., a cathode short-circuit and a turn on voltage at the gate, predicts that the conducting zone propagates with a velocity which is proportional to the anode voltage. This result unifies two previous expressions for the velocity in terms of the current that were obtained by two different groups on an experimental basis.