Simulation of switching circuits using transfer functions

Simulation of complex hardware circuits is the basis for many EDA tasks and is commonly used at various phases of the design flow. State-of-the-art simulation tools are based upon discrete event simulation algorithms and are highly optimized and mature. Symbolic simulation may also be implemented using a discrete event approach, or other approaches based on extracted functional models. The common foundation behind modern simulation tools is that of a switching or Boolean algebraic model that may be augmented with timing information. Recently, an alternative foundational model for conventional digital electronic circuits has been proposed, based upon linear algebra rather than Boolean switching algebra where the circuits are modeled as transfer functions in the form of linear transformation matrices. We demonstrate that this model can be effectively used as the basis for a simulation methodology. Our approach is motivated by the need to develop a truly unified EDA tool for mixed signal circuit design. Currently, industrial tools such as SPECTRE use two different internal engines; a SPICE-like engine and a Verilog-like engine. Our method will allow us to represent mixed signal circuit elements as transfer functions. Spatial complexity is significantly reduced through the use of binary decision diagrams (BDD) to represent the transfer functions. A prototype implementation is used to generate experimental results and to illustrate the viability of the linear algebraic model as a basis for EDA applications.

I. Introduction

The concept of a transfer function model for digital circuits is devised wherein the input stimulus and the output response are represented by an element in a finite-dimensioned Hilbert vector space. This work describes the use of our past results to implement and evaluate a prototype simulation tool. The prototype parses a structural netlist in Verilog and constructs the transfer matrix for the netlist in the form of a BDD. Constructing the transfer function of a structural circuit description can be accomplished by partitioning the netlist into a serial cascade of parallel stages, constructing the transfer matrices of each stage through a tensor matrix multiplication, and combining the stages using direct matrix multiplication [1]. The advantage of our simulation approach is that it supports symbolic simulation wherein any of the inputs, or subsets of the inputs can be assigned both binary values simultaneously. In one extreme, all possible input values can be symbolically simulated with one vector-matrix computation. In the other extreme, a single input assignment can be simulated with one vector-matrix product.