An efficient and practical algorithm is proposed for finding all DC solutions of nonlinear circuits. This algorithm is based on interval analysis and linear programming techniques. The proposed algorithm is very efficient and can be easily implemented by using the free package GLPK (GNU Linear Programming Kit). By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2 000 nonlinear circuit equations in practical computation time.

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter, an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits containing bipolar transistors. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution in a given region using linear programming (LP). In the LP test, an LP problem is formulated by surrounding the exponential functions in the Ebers-Moll model by right-angled triangles, and it is solved by LP, for example, by the simplex method. In this paper, it is shown that the LP test can be performed by the dual simplex method, which makes the number of pivotings much smaller. Effectiveness of the proposed technique is confirmed by numerical examples.

An efficient algorithm is proposed for finding all dc solutions of piecewise-linear (PWL) circuits. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region using the dual simplex method. The proposed algorithm also uses a special technique that decreases the number of regions on which the LP test is performed. By numerical examples, it is shown that the proposed algorithm could find all solutions of large scale problems, including those where the number of variables is 500 and the number of linear regions is 10500, in practical computation time.