The effect of parameter mismatches on the output waveform of an LC-VCO

The effect of parameter mismatches on the output waveforms of a popular voltage-controlled oscillator is investigated, schematizing the circuit as a system of two mutually coupled oscillators, whose describing equations are derived in a perturbation form. The circuit is studied using the method of two time-scales showing the existence of synchronization phenomena leading in presence of mismatches to a locking frequency, which significantly differs from the natural frequencies of the tanks, and to an oscillation amplitude different from that of the symmetric case. We also show that in-phase and quadrature oscillations at the drain nodes can be generated with a proper parameter setting. Circuit simulations confirm the presence of a synchronized oscillation, which is consistent with the prediction of the presented analysis. Copyright © 2009 John Wiley & Sons, Ltd.

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