Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Leeson's equation

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

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

$L(f_m) = 10 log igg[ frac{1}{2} igg( igg(frac{f_0}{2 Q_l f_m}igg)^2 + 1igg)igg(frac{f_c}{f_m} + 1igg)igg(frac{FkT}{P_s}igg) igg]$
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.

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