A sufficient condition for piecewise-linear equations including n ideal diode functions to have 2{sup}l (l≤n) solutions

摘要

The maximum number of dc operating points for a circuit consisting of m transistors. Linear passive resistors and dc sources attracts much attention in the field of nonlinear circuits. Using Ebers-Moll's equivalent circuit, a circuit equation for the above circuit can be written in the form: f{sub}k (x{sub}k) + a{sub}(k1)x{sub}1+...+a{sub}(kn)X{sub}n = b{sub}k (k = 1,2,...n), where n = 2m. Usually f{sub}k(x{sub}k) is a monotone increasing function. In this paper we consider f{sub}k(x{sub}k) to be a ideal diode function. Then the circuit equation is described by a piecewise linear equation with 2{sup}n subregions. We discuss the number of solutions for this equation and show that the equation has exactly 2{sup}l solutions (0≤l≤n) if the matrix obtained by multiplying arbitrary l columns of [a{sub}(ij)] by -1 is a diagonally dominant matrix.