User:Zomphys/sandbox

Leeson frequency
The Leeson frequency is determined by the inverse of the ringing time of a resonator.

$$f_{L}={1 \over {\tau}_{ring}}={\nu_0 \over 2Q}$$

It serves as the point at which a measurement is sensitive to the Instantaneous phase $$\phi{(t)}$$. Meeasurements which probe the resonator at frequencies above the Leeson frequency result in instantaneous phase sensitivity and are therefore able to measure the spectrum of phase fluctuations $$S_{\phi}$$ in units of dBc/Hz. When measurements probe the resonator below the Leeson frequency, only averaged phase response is obtained allowing only for measurement of the spectrum of frequency fluctuations $$S_Y$$ in units of Hz2/Hz.

These two spectra are related by $$S_Y = {f^2 \over \nu_{0}^{2}}S_{\phi}$$