A method for the analysis of transistor circuits having multiple DC solutions

Abstract

The paper deals with circuits containing bipolar and MOS transistors. Both BJTs and MOSFETs are characterized by the Ebers–Moll-type models composed of two diodes and two current-controlled current sources. The basic and still open question of finding multiple DC solutions is discussed. To find all the DC solutions, the diodes are considered as piecewise-linear and represented by the series connection of an ideal diode, a voltage source and a linear resistor. Thus, the ideal diodes are the only nonlinear elements of the circuits. To find all the DC solutions, a method having combinatorial nature is applied. The main achievements of the paper are new algorithms enabling us to discard a huge number of combinations of the ideal diodes states immediately, without any solving of equations, or by performing a considerably reduced amount of computation. The method guarantees finding all the DC solutions of the piecewise-linear circuits. Next, each of the obtained solutions is corrected in succession by means of a controlled SPICE simulation. Four numerical examples of circuits containing bipolar and MOS transistors are presented, showing the efficiency of the proposed approach.