Determination of the steady state of an oscillator by a combined time-frequency method

A novel method for the computation of the steady state of nonlinear oscillators including distributed elements is presented which exploits advantages of both time-domain and frequency-domain simulation. The oscillator network is divided into a linear subnetwork described by a hybrid matrix in the frequency domain and a nonlinear differential equation solved in the time domain. The periodic steady state of the oscillator is shown to be equivalent to the solution of a boundary value problem, where the boundary conditions are given at a set of points along the time axis. For the solution of the boundary value problem the multiple shooting algorithm is applied. It is shown that the bandwidth in the nonlinear subnetwork can be chosen arbitrarily high regardless of the number of harmonics at the ports connecting the subnetworks. In order to demonstrate the feasibility of the method and to discuss the error mechanisms it is applied to two examples: a Clapp oscillator including a piecewise-linear characteristic and an integrated GaAs MESFET oscillator at 10.7 GHz