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SUMMARYWe present a systematic non-linear analysis of di erential voltage controlled oscillators (VCOs), both bipolar and MOS. Using the standard device models, we derive the second-order non-linear equation describing the behaviour of these oscillators, which is formulated in a perturbation form. The solution of this equation is obtained as a particular case of the solution of the most general equation of second-order oscillators, which is solved through a suitable perturbation method. Unlike a pure numerical analysis, simple analytical relationships are derived for predicting the steady-state oscillation, its transient behaviour and for ascertaining the existence of a stable oscillation in di erential VCOs. These relationships, leading to results which well agree with the SPICE simulations, are useful in both analysis and design.

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