Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum. Leeson's expression for single-sideband phase noise in dBc/Hz and augmented for flicker noise: where is the output frequency, is the loaded quality factor, is the offset from the output frequency, is the corner frequency, is the noise factor of the amplifier, is Boltzmann's constant in joules/kelvin, is absolute temperature in kelvins, and is the available power at the sustaining amplifier input. There is often misunderstanding around Leeson's equation, even in text books. In the 1966 paper, Leeson stated correctly that " is the signal level at the oscillatoractive element input". F is the device noisefactor, however this does need to be measured at the operating power level. The common misunderstanding, that is the oscillator output level, may result from derivations that are not completely general. In 1982, W. P. Robins correctly showed that the Leeson equation is not just an empirical rule, but a result that follows from a linear analysis of an oscillator circuit. However, a used constraint in his circuit was that the oscillator output power was approximately equal to the active device input power. The Leeson equation is presented in various forms. In the above equation, if is set to zero the equation represents a linear analysis of a feedback oscillator in the general case, it is for this that Leeson is most recognised, showing a -20dB/ decade of offset frequency slope. If used correctly, the Leeson equation gives a useful prediction of oscillator performance in this range. If a value for is included, the equation also shows a curve fit for the flicker noise. The for an amplifier depends on the actual configuration used, because radio-frequency and low-frequency negative feedback can have an effect on. So for accurate results, must be determined from added noise measurements on the amplifier using R.F., with the actual circuit configuration to be used in the oscillator. Evidence that is the amplifier input power can be found in the derivation in further reading which also shows experimental results, Enrico Rubiola, The Leeson Effect also shows this in a different form.
