Determination of the correlation spectrum of oscillators with low noise

A general expression for the correlation spectrum of an oscillator, described by a set of nonlinear ordinary differential equations with intrinsic noise sources, is derived by a first-order perturbation theory. The analytical derivations are well suited to the numerical determination of the correlation spectrum by Poincare mapping methods. The theory is applied to a lumped circuit model of Colpitts oscillator. It is concluded that the noise behavior of complex oscillator circuits used in microwave engineering can be simulated by the derived method.>