Symbolic State Equations for Analog Circuit with Excess Elements

A new method, using a normal tree (NT) and symbolic simulator Maple V, to systematically formulate symbolic state equations for linear timeinvariant analog circuits with excess elements is presented. Our objective is to develop an algorithm so that a computer program can be written to formulate the symbolic normal-form equations of a large class of analog circuits containing linear resistors, inductors, magnetic couplings, and capacitors, independent voltage and current sources, and the four types of linear controlled sources. Using the symbolic normal-form of the state equations in the numerical solving of these equations we obtain a higher accuracy. The state matrix in the symbolic form is used to obtain a simplified expression of any circuit function, preserving a “cluster” of poles and zeros. The method of symbolic computation to find the state-space model, without any inverse of literal matrix, may greatly facilitate cancellation and simplification of subexpressions. According to our method a program was implemented, called SYSEG – SYmbolic State Equation Generation. The SYSEG program is very easy to use, and it has been tested with many and various analog circuits.