Unified Computation of Parameter Sensitivity and Signal-Injection Sensitivity in Nonlinear Oscillators

In this paper, two relevant computational aspects related to the design of nonlinear oscillators are considered: sensitivity to electrical parameter variation and sensitivity to small-amplitude injected signals. First, the analysis of the perturbation induced by parameter fluctuation is theoretically investigated, and a set of formal equations is deduced that allows us to correctly decompose amplitude and period variations. Second, the analysis of the perturbation induced by a generic weak signal is considered. This analysis is based on a well-consolidated approach that employs the Floquet eigenvector v1 (t) to project perturbation into the phase domain. It is shown that the same system of equations that formalizes the parameter-sensitivity problem can be exploited to calculate the v1 (t) projection vector. An efficient and reliable numerical implementation of a formal perturbation analysis is then proposed that allows the oscillator designer to evaluate both parameter sensitivity and signal-injection sensitivity in a homogeneous frame.