Solving nonlinear resistive networks by a homotopy method using a rectangular subdivision

The authors present an efficient algorithm for solving bipolar transistor networks. Two types of formulation techniques are used for deriving a network equation, i.e., the topological formulation and the n-port formulation. The equation f(x)=0 is solved by a homotopy method, in which a homotopy h(x,t)=f(x)-(1-t)f(x/sup 0/) is introduced and the solution curve of h(x,t)=0 is traced from an obvious solution (x/sup 0/,0) to the solution (x*,1) which is sought. It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions. A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve.<>