A robust and efficient oscillator analysis technique using harmonic balance
This paper is concerned with the efficient determination of the fundamental frequency of oscillators which appear in electronic systems. As remarked in the introduction the simulation of these oscillators leads to high dimensional differential algebraic systems (DAEs) and application of standard methods of DAEs is highly inefficient due to the fact that time integration requires large intervals to reach the steady state. Then in the standard literature it is usual to use the Fourier transform to convert the DAEs to a set of nonlinear algebraic equations and the so called harmonic balance method achieves the solution of these equations by means of Newton type nonlinear solvers. In this context the authors propose a continuation type technique which allows to get good starting values for the solution of these nonlinear algebraic equations with the aim to improve the convergence and the efficiency of the quasi Newton iterative solver. Further the authors present an overview of the Krylov methods which are used in Newton iteration. Finally an example is presented to show the efficiency and robustness of the new method.
differential algebraic equations of oscillators
scientific article; zbMATH DE number 1417825