Symbolic analysis methods and applications for analog circuits: a tutorial overview

This tutorial paper gives an overview of the history and present state of the art in symbolic analysis of electronic circuits at the so-called circuit level. Symbolic analysis is defined as a technique generating a closed-form analytic expression for a circuit characteristic with the circuit´s elements represented by symbols. Such analytic information complements the results from numerical simulations. The paper then describes the different application areas of symbolic analysis for the design of analog 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, and in applications requiring the repetitive evaluation of circuit characteristics. Next, the present capabilities and limitations of symbolic analysis, both in functionality and efficiency, are discussed. The major symbolic 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