Graph-Pair Decision Diagram Construction for Topological Symbolic Circuit Analysis

Symbolic circuit analysis is concerned with analytical construction of circuit response in the frequency (or time) domain, for which an efficient data structure is required. Recent research has justified that the binary decision diagram (BDD) is a superior data structure with the following distinguishing feature: a large number of product terms can be compactly represented by a BDD, on which numerical computations and analytical deductions can be performed directly. Using BDD for symbolic circuit analysis requires an efficient method for construction. In this paper, a graph-based construction method, called graph-pair decision diagram (GPDD), is developed. Given a small-signal circuit, a pair of graphs representing the circuit is created, from which a GPDD is constructed by successively reducing the graph pair. The GPDD algorithm, which generates cancellation-free symbolic terms, differs from the existing determinant decision diagram (DDD) algorithm. Detailed theory and implementable algorithms for the GPDD construction are developed, and a runtime performance comparison to DDD is made. It is demonstrated that the runtime performance using GPDD is comparable to that of DDD in terms of time and memory complexity for exact symbolic analysis, although the GPDD algorithm has to generate a much larger number of symbolic product terms.