Application of the envelope-transient method to the analysis and design of autonomous circuits
The envelope transient enables a very efficient simulation of circuits with two different time scales, such as those that contain modulated signals (for example, amplifier or mixers), where an accurate prediction of intermodulation distortion is needed. The method has also been extended to oscillator analysis, where it requires additional techniques in order to avoid convergence to degenerate mathematical solutions, for which the circuit is not actually oscillating. It allows an efficient analysis of transients in these circuits and an accurate prediction of the phase-noise spectrum. This article presents an overview of the envelope-transient method and its most recent applications to the simulation of autonomous circuits, such as free and forced oscillators, frequency dividers, and phase-locked loops. Using this method, the operation bands of these circuits (which are delimited by qualitative stability changes or bifurcations) can be determined in a straightforward manner. This technique can also be applied to predict intermodulation distortion in self-oscillating mixers and to simulate the response of synchronized oscillators containing modulated signals. (c) 2005 Wiley Periodicals, Inc.
envelope transient oscillator self-oscillating mixer synchronization harmonic balance phase noise frequency synthesizer