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Off-Resonance Oscillation, Phase Retention, and Orthogonality Modeling in Quadrature Oscillators

Two important drawbacks of parallel coupled LC quadrature oscillators (P-QOSC) which have not heretofore been addressed thoroughly in the literature are obviated simultaneously in this paper. The first, has to do with the inevitable off-tune operation of the tank which results in quality factor (Q) degradation, and hence, phase noise deterioration. The other, stems from process, voltage, and temperature (PVT) variations which exacerbate quadrature accuracy. Here, a feedback loop is presented which generates a control signal by mixing the quadrature outputs and tunes the injection strength in the coupled oscillators autonomously. A complex coupling factor is implemented which compensates the phase error to prohibit phase noise degradation. The operation of proposed loop is comprehensively studied mathematically. Measurement results of a 0.18 μm CMOS prototype with an active area of 0.5 mm2 and an overall power consumption of 5 mW corroborate the functionality of the proposed method. Finally, experimental results prove FoM of 185 dB for the core oscillator and a quadrature phase error of less than 0.8°.