A Generalization of the Groszkowski’s Result in Differential Oscillator Topologies

The paper presents a generalization of the Groszkowski's result in differential oscillators, providing novel equations to describe the oscillation frequency dependence on the harmonic content. The effect of the common-mode oscillation is rigorously included. Moreover, an additional term, arising from the dependence of the transistor current on the drain voltage, which is dominant any time ohmic operation occurs, is disclosed here for the first time. This framework is applied to Van der Pol oscillators, both nMOS and CMOS, designed in a 28-nm bulk CMOS technology. The results correctly match the oscillation frequency dependence derived from detailed circuit simulations. The analysis shows that, when even harmonics are relevant, the classical Groszkowski's result is not able to account for close-in phase noise performance. The novel theoretical framework fully justifies, instead, the simulation results and sheds new light on the flicker noise up-conversion mechanisms in the considered oscillator structures.