Still More on the $1/f^{2}$ Phase Noise Performance of Harmonic Oscillators

Modeling tank losses in a harmonic oscillator by means of an equivalent parallel resistance may lead to an optimistic estimate of phase noise, as recently experienced in a class-D CMOS oscillator. The discrepancy is significant if two conditions are fulfilled: The single-ended portion of the tank capacitance displays a non-negligible loss, and the loop gain of the oscillator is very large; in the latter case, a phase noise boost is likely to occur. In this brief, we derive phase noise equations that capture such behavior in a class-B oscillator, which is easier to approach than a class-D oscillator. The results, however, are (qualitatively) valid in general. Furthermore, the phase noise caused by the oscillator active core is always proportional to the phase noise caused by the tank losses independently of the amount of phase noise boost. The agreement between theoretical and simulation results is excellent.