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This paper derives two kinds of Q factor formulas for use in estimating frequency stability of sinusoidal oscillators. To cover various circuit topologies, we consider a general black-box model having DC input and RF output ports. Assuming a small deviation in DC supply voltage or RF load impedance, the frequency shift caused by such deviation is formulated by a perturbation technique. As a versatile criterion to indicate the tolerance of circuit itself, we introduce oscillator Q against each deviation. Since the theory is described in the linear impedance domain, it gives oscillator designers a clear vista on the stability of practical circuits.

Dedicated <I>Q</I> factor formulas stemming from oscillation frequency stability against source and load deviations