Road map representation of s-expanded symbolic network functions

A new two-graph approach is presented for the generation of exact symbolic network functions in the form of rational polynomials of the complex frequency variable s for analogue circuits. The closed-loop circuit representation is used, but the numerator and denominator of the desired transfer function are obtained separately without using any sorting process. In this method each symbolic expression for a coefficient at particular power of s is obtained immediately without any operation on polynomials. For compact representation of terms in symbolic network functions a new notation of expressions called the road map is presented. This notation has also the advantage that in the process of the repetitive evaluation of transfer function for the analyzed network we do not have to calculate the whole expression but only to update the terms which are changed. We consider R,C,L,E,I,cs networks (R,C,L,E,I,cs stand for resistors, capacitors, inductors, independent voltage and current sources, and all types of controlled sources, respectively).