Evaluating Pulling Effects in Oscillators Due to Small-Signal Injection

This paper presents a hybrid numerical-analytical approach to evaluate and quantify injection pulling, effects in RF oscillators. The method employs the Floquet v(1)(t) eigenvector to project the perturbation signal into the phase domain. An original closed-form expression for the frequency shift induced by small-signal harmonic perturbations is derived. It is shown that such closed-form expression accurately predicts frequency shift under weak pulling, quasi-lock, as well as locked conditions. An estimation of the main spectrum components of the pulled response is also derived. The proposed macromodeling approach has the peculiarity to be applicable to any oscillator topology.