SYMBOLIC ANALYSIS METHODS AND APPLICATIONS

This tutorial paper outlines the state of the art in symbolic analysis. Symbolic analysis is defined as a technique providing closed-form analytic information complementary to numerical simulation results. The different application areas of symbolic analysis in the analog design world are then discussed. Symbolic analysis is mainly used as a means to obtain insight into circuit behavior, to generate analytic models for automated circuit sizing and in applications requiring repetitive evaluation of characteristics. The present capabilities and limitations of symbolic analysis, both in functionality and efficiency, are then discussed. The major analysis methods are presented, and algorithmic details are provided for symbolic approximation, hierarchical decomposition and symbolic distortion analysis. Finally, existing symbolic simulators are compared, and directions for future research are pointed out.