Application of Nullors in Symbolic Single Port Transfer Functions Using Admittance Method

This article has two objectives. The first one is to develop an Admittance Method (AM) for active circuits, which is a replacement for the Sum of the Tree Products (STP) used for symbolic analysis of circuits. A similar but very limited method is developed earlier (1976) for passive circuits. The second objective is to replace the active devices (mainly VCCS) in circuits with nullors, and prepare them for a smooth application of the AM. The method is replacing the well-known 2-graph methodology, and it is ideal for symbolic representation of circuits, especially for low component density. The core of the AM technique is based on parallel and series (P/S) operations that continuously combines the components until it is reduced to a single element. In case the P/S operations are exhausted but the circuit is still not a single element, we leave the P/S and remove as many elements from the circuit to regenerate new P/S operations. We continue it until the circuit terminates with a single element. It is shown that the admittance of the final element represents a port transfer function (admittance) with the numerator being the determinant of the Nodal Admittance Matrix (NAM). In case of active circuits, with g
_m
, the method works when the dependent sources are replaced with nullors.