New methodologies for the analysis and synthesis of oscillator circuits

Abstract

Advances in the analysis and synthesis of oscillator circuits, using harmonic balance (HB), are presented. They rely on the use of auxiliary generators, which can be introduced into the HB software to impose mathematical conditions or to extract a realistic oscillator model. In particular, a bifurcation-detection technique, for the accurate design of dual-frequency oscillators, and a semi-analytical function, for the prediction of oscillation transients, are described. In dual-frequency oscillators, each oscillation must be the only stable solution in a certain parameter interval. This is ensured through the calculation of two distinct primary-Hopf bifurcation loci, which should give rise to disjoint parameter regions. Conditions for the physical observability of concurrent oscillations are also given. With respect to the transient prediction, both the linear and nonlinear stages are considered. The analysis is based on the derivation of outer-tier semi analytical equation, from which a growth rate function is identified, which, unlike ordinary simulations, is not constrained to particular initial values. The methods have been applied to two FET-based oscillator circuits that have been manufactured and measured, obtaining good agreement with the simulation results.