Flicker Noise Up-Conversion due to Harmonic Distortion in Van der Pol CMOS Oscillators

Harmonic content modulation of the oscillator output voltage can contribute to flicker noise up-conversion in LC-tuned oscillators. The paper reports a quantitative analysis of the effect in Van der Pol oscillators using the framework of the impulse sensitivity function (ISF). It is shown that most of the up-conversion efficiency results from the first harmonic of the ISF, which is not perfectly in quadrature to the output voltage waveform, and from the first harmonic of the transistor current, which is slightly lagging the voltage waveform. A closed-form expression of 1/f³ phase noise in voltage-limited LC-tuned oscillator is derived that is in good agreement with circuit simulations. The paper also shows that the values of both phase shifts are determined by the non-linearity of the active element and are linked to the relevant oscillator parameters, i.e., excess gain and tank quality factor.