An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method

It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SPICE-oriented Newton homotopy method which can efficiently find out the multiple dc solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.