Spectral purity
Frequency synthesis

An ideal oscillator provides a signal of constant frequency ν₀ and amplitude V₀: V(t) = V₀ cos (2πν₀t).

In practice, noise sources internal to the oscillator circuit induce random modulation of the signal's phase and amplitude. The real signal is then represented by :

where ϕ(t) and α(t) are random variables representing phase modulation and amplitude modulation of the signal by noise, respectively. We then define the power spectral densities S_ϕ(f ) and S_α(f ), which characterize the frequency distribution of ϕ(t) and α(t). In the case of an oscillator, the saturation...