A Criterion on Existence and Uniqueness of Behavior in Electric Circuit

Abstract

Behavior of electric circuits can be observed by solving circuit equations symbolically as well as numerically. In general, symbolic computation for circuits with certain number of circuit elements needs much more time than numerical computation. It is reasonable to check the existence and uniqueness of the solution to circuit equations beforehand in order to avoid computation for the case of no solution. Indeed, some circuits have no solution; in that case, one should notice it and avoid to wait meaningless computation. This paper proposes a new theorem to check whether given circuit equations have a solution and their voltages and currents of all circuit elements are uniquely determined or not. The theorem is suitable for developing a computer algorithm and helps quick symbolic computation for electric circuits.