  We study an abstract model of an oscillator realized by an amplifier embedded
in a positive feedback loop. The power and frequency stability of the output of
such an oscillator are limited by quantum noise added by two elements in the
loop: the amplifier, and the out-coupler. The resulting frequency instability
gives the Schawlow-Townes formula. Thus the applicability of the
Schawlow-Townes formula is extended to a large class of oscillators, and is
shown to be related to the Haus-Caves quantum noise limit for a linear
amplifier, while identifying the role of quantum noise added at the
out-coupler. By illuminating the precise origin of amplitude and frequency
quantum noise in the output of an oscillator, we reveal several techniques to
systematically evade them.
