Design criteria based on Floquet eigenvectors for the class of LC-CMOS pulsed bias oscillators

We present an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time-varying bias. The paper refers to parallel tank oscillators in which the energy restoring can be modeled by current pulses controlled by the oscillation voltage. The goal is to show, for the proposed class, the possibility to guide the design of oscillators phase noise through eigenvectors. Floquet eigenvectors in fact are acknowledged to give a correct decomposition of noise perturbations in the oscillator state space along the stable orbit. An analytical parametric model is derived and eigenvectors displacement is evaluated versus design parameters. In particular, minimization conditions of the effect of stationary and time-varying noise are deduced from analytical expression. & 2011 Elsevier Ltd. All rights reserved.