Derivation of Floquet Eigenvectors Displacement for Optimal Design of LC Tank Pulsed Bias Oscillators

Abstract

The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.

CMOS Phase and Quadrature Pulsed Differential Oscillators Coupled through Microstrip Delay-Lines

“…This oscillator class aims to reach high performance in terms of phase noise with reduced energy requirements with respect to their non-pulsed counterparts. Basing on the results of Floquet Theory applied to a single oscillator [1], we extended the pulsed bias concept to a coupled phase and quadrature system in [2]. We proved that the pulsed bias approach allows to minimize noise injection onto the Floquet Eigenvector with unitary eigenvalue, leading to decrease phase noise of generated fundamental in particular at low frequency offsets [3] [4].…”