Unified large-signal stability and noise theory for synchronised oscillators

Abstract

A unified model is developed which is capable of analysing large-signal performance, stability, and noise of synchronised oscillators under rather general conditions. The passive circuitry is arbitrary; the active subnetwork may in principle contain one-port or two-port devices with or without harmonic content. However, only one-port devices operating at a single frequency are treated explicitly. The active device is modelled by its describing function (i.e. its effective admittance) with respect to both carrier and noise signals. The noise analysis directly leads to a new stability criterion, which clearly shows the restrictions and even failure of the hitherto-used criteria. These results are proved by measurements. Finally, the application of the nonlinear theory to the analysis of multiple-device oscillators is illustrated by results. ) b -modulation frequency in bias circuit b > 0u 5 0i = phase at particular frequencies = real part of a complex frequency u v b -normalised frequencies = time List of symbols Indexes b c = u = / = / = r = Currents i = y y b ,y 0 = y c y t y L = y rb ,y ru ,y rl = y r iu,y r ii Voltages