A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

The paper is devoted to the analysis of diode–transistor circuits having multiple DC solutions. The transistors are characterized by the Ebers–Moll model and the circuits are described by the Sandberg–Willson equation, without any piecewise-linear approximations. A new method for finding bounds on the location of all the solutions is offered. The method contracts a hyperrectangular region that includes the solutions in a systematic manner, considering in succession all the individual equations. It does not require much computation power and is very fast. The method is very useful as a preliminary step of the algorithms for finding all the DC solutions, making them more efficient. A numerical example is given to illustrate the proposed approach.

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