Symbolic pole/zero calculation using SANTAFE

The aim of symbolic analysis is to gain insight into circuit behavior. To study the behavior of analog circuits, the locations of the poles and zeros have to be known. Unfortunately, no general method exists to calculate the poles and zeros symbolically for polynomials of degree greater than four from transfer functions in coefficient form. The CAD tool SANTAFE (Symbolic Analysis of Transfer Functions) applies the signal-flow graph method, which permits to keep the result in a factorized or partially factorized form. The graphic view provided by a signal-flow graph offers insight into the internal interactions between the circuit elements and, as will be demonstrated, enables the user to perform circuit knowledge-based approximations. A novel procedure based on symbolic Newton-iteration, accurately calculates high-order transfer functions in the desired pole/zero form. Another special routine, based on element weight ratios rather than numerical values, enables the simplification of large symbolic expressions without numerical values for each parameter. With the program SANTAFE, even large networks can be analyzed symbolically. This will be shown with an example of a wide band BiCMOS operational amplifier