Detailed Study of Phase and Amplitude Imbalances in Quadrature LC CMOS Oscillators

Conventional analyses of phase and amplitude imbalances in quadrature LC CMOS oscillators are typically performed in the time-domain under large-signal conditions, where tank series losses are approximated as a fixed parallel resistance to simplify the analysis. However, this simplification fails to accurately capture the effects of practical tank losses, which are inherently represented as a series resistance in real LC oscillators. To address this limitation, a novel theoretical framework is developed for analyzing phase and amplitude imbalances in quadrature LC CMOS oscillators. The analysis is carried out in the phasor-domain using a modified small-signal circuit model (MSSCM). Unlike prior studies, the proposed approach explicitly incorporates the series resistance of the inductor as the dominant tank loss, resulting in a nonlinear formulation for phase and amplitude imbalances. Closed-form expressions for these errors are derived across three fundamental topologies: series-coupled, parallel-coupled, and source-injection-coupled accounting for Q variations. Additionally, the maximum steady-state oscillation amplitude under mismatch conditions is derived. The accuracy of the proposed model is validated through extensive simulations, showing strong agreement with numerical results. This comprehensive analysis offers deeper insight into the mechanisms underlying phase and amplitude imbalances and, ultimately, presents multiple techniques for the simultaneous compensation of these errors across different quadrature oscillator topologies.