# Leeson's equation

Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum.

Leeson's expression[1] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per Hertz) is[2]

$L(f_m) = 10 \log \bigg[ \frac{1}{2} \bigg( \bigg(\frac{f_0}{2 Q_l f_m}\bigg)^2 + 1\bigg)\bigg(\frac{f_c}{f_m} + 1\bigg)\bigg(\frac{FkT}{P_s}\bigg) \bigg]$
where f0 is the output frequency, Ql is the loaded Q, fm is the offset from the output frequency (Hz), fc is the 1/f corner frequency, F is the noise factor of the amplifier, k is Boltzmann's constant, T is absolute temperature in Kelvins, and Ps is the oscillator output power.

## References

1. ^ Leeson, D. B. (February 1966), "A Simple Model of Feedback Oscillator Noise Spectrum", Proceedings of the IEEE 54 (2): 329–330, doi:10.1109/PROC.1966.4682
2. ^ Rhea, Randall W. (1997), Oscillator Design & Computer Simulation (Second ed.), McGraw-Hill, ISBN 0-07-052415-7, p. 115.