Find all solutions of piecewise-linear resistive circuits using an LP test

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. It is shown that the LP test can deal with nonseparable functions of more than one variable by using more than two-dimensional rectangles. It is also shown that, for bipolar transistor circuits, the LP test becomes more efficient and more powerful by surrounding the exponential functions by right-angled triangles. The proposed algorithm is simple, efficient, and can be easily implemented.