A general theory of phase noise in transconductor-based harmonic oscillators

We present a rigorous phase noise analysis of a generic harmonic oscillator where the active core can be modeled as a transconductor. Phase noise equations are derived without any specific assumption on the nature of the resonator in the oscillator; furthermore, we provide closed-form 1/f² phase noise equations when the resonator consists of an arbitrary number of cascaded LC tanks, each tuned at a different harmonic of the oscillation frequency. We also show that the phase noise caused by transconductor white noise is always proportional to the phase noise caused by resonator losses, and that no flicker noise from the transconductor is up-converted into phase noise in an oscillator with an odd-symmetric voltage waveform. The phase noise for a number of different oscillators/resonators has been simulated, always obtaining an exceedingly good agreement between theoretical predictions and numerical results.