Simulation of high-Q oscillators

Abstract

We present a new technique, based on a continuation method, for oscillator analysis using harmonic balance. Whh the use of Krylov subspace iterative linear solvers, harmonic balance has become a very powerful method for the analysis of general nonlinear circuits in the frequency domain. However, application of the harmonic balance method to the oscillator problem has been difficult due to the very small region of convergence. The main contribution of this paper is a robust and efficient continuation method that overcomes this problem.

Modelling and Discretization of Circuit Problems

“…In the limit, however, the sub-matrix Y in (21.21) becomes singular and one really needs (21.12) to gauge the complete problem. In [19,87,256] this problem was solved (in the frequency-domain) by introducing an artificial element in the circuit, a voltage source, of which the applied voltage E osc had to be determined in such a way that the current through this source became 0. In that case the artificial element can be eliminated from the circuit and the solution on the remaining circuit gives the oscillator solution.…”

“…The two-step approach [19,87,256] assumes that for given parameters f, E k , the driven non-linear problem F D (x(f, E k )) = 0 is solved. For updating f, E k , NewtonRaphson can be used ("outer loop") in which one can exploit the Jacobian-matrix of the inner Newton-Raphson process for solving …”

“…In [19,87,150,256] oscillator algorithms are given for Harmonic Balance that resemble the approach described in Section 21 for the time domain. However, there are some modifications:…”

“…• The applied value of the artificial element is initialized by optimization techniques [87,129,256]. In [23,150] techniques using affine damping improved convergence.…”

Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods

“…Homotopy methods have also been applied for discovering more than one (potentially all) operating points of a nonlinear circuit [6], [8]. More recently, homotopy methods have been applied by several researchers for solving steadystate problems in circuits [2], [5], [7], [28]. Finally, initial results of the present paper were reported in [19].…”