Admittance Matrix Models for the Nullor Using Limit Variables and Their Application to Circuit Design

A framework for symbolic analysis and synthesis of linear active circuits has previously been proposed which is based on the use of admittance matrices and infinity-variables. The notation has the important advantage that it can describe both ideal circuit elements, for which an infinite limit is implied, and nonideal circuit elements for which matrix elements are considered finite. The nullor is a very important circuit element because it can represent the ideal operational amplifier and the ideal transistor. For the nonideal case, the use of finite matrix elements implies that the operational amplifier and transistor are both modelled as a voltage-controlled current source, which is fine if the transistor is a field effect transistor or if the operational amplifier is of the transconductance type, but not otherwise. The purpose of this paper is to apply the$scriptstyle infty$-variable framework in order to derive alternative models for the nullor that can be used to model voltage, current and transresistance operational amplifiers and bipolar junction transistors. We also show that the$scriptstyle infty$-variable description of an ideal transistor can include a factor to represent transistor geometry.