Computing Multivalued Input–Output Characteristics in the Circuits Containing Bipolar Transistors

Abstract

The paper deals with dc circuits including bipolar transistors represented by the Ebers-Moll model. An important question how to efficiently compute multivalued input-output characteristics of these circuits is considered. A switching variables approach for tracing a multivalued single-branched characteristic, which can be considered as some kind of continuation method, is developed. A new strategy of switching variables is proposed and the generalized implicit function theorem is used as the mathematical background. Unfortunately, this approach suffers from major shortcomings when it is directly applied to bipolar transistor circuits, due to specific nonlinearities of the transistor model, causing the sharp-turning-point problem. To overcome this problem, a variable transformation is proposed, which leads to smooth solution curves. An efficient algorithm combining the developed variant of switching variable method with the proposed transformation is described. A generalized version of the algorithm enables us to compute multivalued characteristics composed of disconnected branches, under the assumption that at least one point on each branch can be found. It is illustrated via four examples of realistic transistor circuits including a voltage regulator, the Schmitt trigger, a line receiver, and their combination.