Nonlinear Noise Theory for Synchronized Oscillators

A nonlinear theory of noise in synchronized oscillators is outlined, thus extending Kurokawa's work from small to arbitrary injection levels. The description is of phenomenological nature: it uses the describing function method of control theory for calculating the carrier waves, and the circuit theory of periodically driven nonlinear systems for an analysis of the noise sidebands. Simple expressions are derived for the various output noise and noise conversion factors in the case when the nonlinear characteristic of the active device can be described by a third-order (van-der-Pol) polynomial.