A DISCRETE-TIME APPROACH TO THE STEADY-STATE ANALYSIS AND OPTIMIZATION OF NONLINEAR AUTONOMOUS CIRCUITS

In this paper a method for the steady state analysis and optimization of non-linear autonomous circuits is described. After discretizing the linear part of the circuit, a system of non-linear algebraic equations is obtained. The final formulation is written entirely in the discrete-time domain, making it unnecessary to repeatedly take direct and inverse DFTs during the solution process. Furthermore, it is shown that the resulting formulation may be viewed as a generalization of the harmonic balance equations. An analytic method for computing the exact partial derivatives of the resulting equations with respect to the samples of the variables, the oscillation period and the circuit element values is described, making the proposed approach efficient for both analysis and optimization. Different globally convergent techniques for solving the non-linear system of equations are described, with emphasis on an algorithm based on fast simulated diffusion. Selected application examples are provided to validate the proposed approach.