Determining multi-valued input-output characteristics in the circuits containing bipolar transistors

The paper deals with the DC circuits including bipolar transistors represented by the Ebers-Moll model. An important question, how to determine specific multi-valued input-output characteristics, is considered. A general approach for finding the characteristics in nonlinear circuits, based on some known ideas, is developed in this paper. Unfortunately, this approach is not effective in a case of transistor circuits due to particular properties of the functions, which describe the bipolar transistors. The paper shows how to overcome these difficulties and make the approach effective. For this purpose, a transformation is suggested to obtain a circuit representation with suitable nonlinear functions. Next, an improvement is made for solving scalar nonlinear equations arising in the computation process. As a result we obtain an effective and useful tool for determining the characteristics. It is illustrated via a numerical example.