Periodic Steady-State Analysis of Free-running Oscillators

Abstract

A common problem in the simulation of electric circuits for RF (Radio Frequency) applications is finding a periodic steady-state (PSS) of such a circuit. Several approaches exist for solving this problem. For non-autonomous circuits, i.e. circuits that are driven by an input source with an a priori known period T, many methods exist (see [1], [2], [3]). However, when dealing with autonomous circuits, the situation is less satisfactory. For an autonomous circuit, the period T becomes an additional unknown, which makes the resulting system under-determined. A common solution method is harmonic balance, a frequency-domain method (see [4], [5]). Harmonic balance performs well if the waveform to be computed contains mostly low harmonics, but it becomes very expensive if a large number of harmonics is present. Therefore, there has been much interest in hybrid (see [6]) and pure time-domain methods (see [4]), such as shooting or finite difference. However, convergence of these methods is often problematic; typically there is only convergence when the initial guess for the period T ₀ is already very close to the actual solution T*