A Comparison of Range Arithmetic Methods in Symbolic-Numeric Circuit Analysis Applications

In this paper we compare the performance of several range arithmetic methods in evaluating problems in symbolicnumeric circuit analysis. Symbolic-numeric circuit analysis involves solving systems of linear equations in order to obtain the values of currents and voltages in a given circuit. Symbolic circuit expressions contain a large number of product terms and long chains of arithmetic operations which make computations difficult. When analysis of circuit behaviour over a range of parameter values is required the symbolic expressions can be evaluated using one of the range arithmetic methods reported in literature. The range arithmetic methods considered in this paper are affine arithmetic (AA), Extensions to AA (EAA) suggested by Messine, and generalized interval arithmetic (GIA) suggested by Kolev. One important difference between these range arithmetic methods is the method by which two affine numbers, or two generalized interval numbers, are multiplied. In this paper, each range arithmetic method is evaluated based on the performance of the multiplication operation which is predominant in symbolic circuit expressions. We show that the performance of the multiplication rule in each method determines the accuracy of computations. We present the benefits and problems associated with using each of the range arithmetic methods. We also show that GIA gives tighter bounds and efficiently simulates the effects of uncertainties in circuit parameters when solving problems in circuit analysis.