Quality Factor Analysis for Cross-Coupled [Formula Omitted] Oscillators Using a Time-Varying Root Locus

An extraction of an effective oscillator [Formula Omitted] factor in cross-coupled [Formula Omitted] oscillators using time-varying root locus is proposed. The extraction utilizes root computations and analytical expression of the cross-coupled-pair admittance. The methodology permits to investigate the [Formula Omitted]-factor degradation mechanisms in large-signal [Formula Omitted] oscillators and to compare different oscillator topologies. The obtained effective [Formula Omitted] factor is validated through SpectreRF simulations and phase noise measurements of a voltage-controlled oscillator fabricated on a 130-nm process.