Techniques and Applications of Symbolic Analysis for Analog Integrated Circuits: A Tutorial Overview

This tutorial paper gives an overview of the state of the art in symbolic analysis techniques for analog integrated circuits. Symbolic analysis allows to generate closed-form analytic expre-ssions for a circuit's small-signal characteristics with the circuit's elements and the frequency variable represented by symbols. Such analytic information complements the results from numerical simulations. The paper then describes the different application areas of symbolic analysis in the design of analog integrated circuits. Symbolic analysis is mainly used as a means to obtain insight into a circuit's behavior, to generate analytic models for automated circuit sizing, for behavioral model generation and in applications requiring the repetitive evaluation of circuit characteristics. Recent extensions of both the functionality (such as towards symbolic distortion or pole-zero analysis) and the efficiency of symbolic analysis for larger circuits (through new algorithmic developments) are discussed. Finally, an overview and comparison of existing tools is presented.