The effect of parameter mismatches in RF VCO

We investigate the effect of the parameter mismatches on the oscillation frequency of a popular voltage controlled oscillator, whose behavior is schematized by a system of two mutually coupled oscillators. A perturbation analysis of this system is carried out using the method of two time scale. The existence of synchronization phenomena leading to a locking frequency is shown, which significantly differs from the natural frequencies of the tanks. Circuit simulations confirm the presence of a synchronized oscillation which is consistent with the prediction of the presented analysis.