Verification of Analog and Mixed-Signal Circuits Using Symbolic Methods

Abstract

With the rapidly increasing complexity of hardware, traditional validation techniques are becoming insufficient. This has led to a substantial interest in the formal verification of digital components. There has been relatively little research, however, into the application of formal verification methods to the analog/mixed-signal domain. Therefore, the overall goal of this work is to provide a system for efficient and meaningful analysis of analog/mixed-signal circuits. This encompasses two major efforts: modeling and symbolic analysis. The continuous nature of analog circuits requires a modeling method that is capable of representing continuous behavior and the discrete nature of digital circuits requires a modeling method that is capable of representing discrete behavior. This dual requirement necessitates a hybrid model—a model that can simultaneously represent continuous and discrete behavior. This work details the development of a specialized hybrid Petri net model with capabilities similar to hybrid automata. Analysis is greatly complicated by the addition of continuous behavior to the model. To help alleviate this, infinite numbers of states are often grouped into equivalence classes represented by symbolic structures. The analysis methods described here represent ranges of continuous variables using groups of inequalities which are then either mapped to Binary Decision Diagram variables so that necessary operations can be performed efficiently, or handed over to an advanced Satisfiability Modulo Theories solver for analysis. After describing the verification system in detail, experiences applying the techniques to several case studies are described and performance results are provided.

Type

Related