Large-signal analysis of CMOS - LC VCOs

A nonlinear perturbation model of a complementary LC-tuned voltage controlled oscillator is derived, which consists of two mutually-coupled second-order equations. The first-order approximate periodic solution of describing equations is found, obtaining closed-form expressions for both the amplitude and the harmonics of oscillation, as well as for the correction of the oscillation frequency due to the nonlinear effect of varactors. The accuracy of presented formulae was validated by circuit simulations.