Quality Factor Analysis for Cross-Coupled $LC$ Oscillators Using a Time-Varying Root Locus

An extraction of an effective oscillator Q factor in cross-coupled LC 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 Q-factor degradation mechanisms in large-signal LC oscillators and to compare different oscillator topologies. The obtained effective Q factor is validated through SpectreRF simulations and phase noise measurements of a voltage-controlled oscillator fabricated on a 130-nm process.