Phase Noise in LC Oscillators: A Phasor-Based Analysis of a General Result and of Loaded $Q$

Recent work by Bank, and Mazzanti and Andreani has offered a general result concerning phase noise in nearly-sinusoidal inductance-capacitance (LC) oscillators; namely that the noise factor of such oscillators (under certain achievable conditions) is largely independent of the specific operation of individual transistors in the active circuitry. Both use the impulse sensitivity function (ISF). In this work, we show how the same result can be obtained by generalizing the phasor-based analysis. Indeed, as applied to nearly-sinusoidal LC oscillators, we show how the two approaches are equivalent. We analyze the negative-gm LC model and present a simple equation that quantifies output noise resulting from phase fluctuations. We also derive an expression for output noise resulting from amplitude fluctuations. Further, we extend the analysis to consider the voltage-biased LC oscillator and fully differential CMOS LC oscillator, for which the Bank´s general result does not apply. Thus we quantify the concept of loaded Q.