Some Contraction Methods for Locating and Finding All the DC Operating Points of Diode-Transistor Circuits

Abstract

Some Contraction Methods for Locating and Finding All the DC Operating Points of Diode-Transistor CircuitsThe paper is focused on the analysis of diodetransistor circuits having multiple DC solutions (operating points) and brings two methods enabling us to find all the solutions. The first method contracts and eliminates some hyperrectangular regions where the solutions are sought. It is based on the idea of framing of the nonlinear functions appearing in the mathematical description of the circuit by linear ones and exploits the Woodbury formula in matrix theory. The other method finds quickly and easily preliminary bounds on the location of all the solutions. The method employs some monotonic functions and generates convergent sequences leading to a shrinked hyperrectangle that contains all the solutions. Both the proposed methods are rigorously proved. They constitute the core of an algorithm which efficiently finds all the DC operating points of diode-transistor circuits. It is illustrated via numerical examples.