A Comprehensive and Unified Procedure for Symbolic Analysis of Analog Circuits

Abstract

The objective here is to develop a uniform and comprehensive procedure for symbolic analysis of linear circuits using the Sum of the Tree Products (STP) of the circuit. We achieve this goal in two stages. In the first stage a circuit with active devices, such as VCCSs and I/O ports, is changed to a nullor circuit, i.e., to a circuit with only passive components and nullors. The nullor circuit is also partitioned into two parts, a passive circuit and an all-nullor circuit. It is shown that the magnitude of the STP, i.e., the determinant of the NAM, of the circuit is equal to the STP of the passive portion of the circuit, and the sign (0, 1, or −1) of the STP comes from its all-nullor part. Another significant development in this presentation is the replacement of the regular STP methodology with a rather new Admittance Method ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AM</i> ). It is shown that by doing this the entire two-graph theory for active circuits as well as the use of 2-tree procedures for I/O ports analysis are eliminated. It is these new developments that substantially simplifies the circuit analysis and makes it quite efficient for symbolic representation of transfer functions.