Abstract
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 $\mu{\text m}$ CMOS prototype with an active area of 0.5 ${\text{mm}}^{2}$ 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 $^{\circ}$ .
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