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.

Analysis of the Transient Dynamics of Microwave Oscillators

“…In previous works [19], [20] the time-varying harmonic component 1 ( ) X t was treated as a narrow-band signal, assuming that its high-order time derivatives were negligible. Under this assumption, (5) can be expressed as:…”

“…1(b). The results of this numerical technique should approach those of the analytical derivation in (20) to (27). However, there will be discrepancies due to the fact that ( 27) relies on a derivative of the fundamental-frequency admittance function Y with respect to the excitation amplitude V, whereas the circuit-level simulation is based on a conversion-matrix representation of the nonlinear elements.…”

“…To extend the numerical model in order to account for the build-up transient, the preliminary work [19], [20] presents the derivation of a first-order envelope-domain equation from a single observation node. The model relies on a full extraction of an outer-tier admittance function ( , ) Y V  from HB, which depends on the excitation amplitude V and frequency .…”

“…Y V  enables a general procedure for a realistic prediction of the oscillator behavior. However, the first-order assumption [19], [20] will fail if the transient effects cannot be accurately described through a firstorder Taylor series expansion in j . To cope with this limitation, this work considers a general dependence on j .…”