Phase Noise Derivation

[@xlai]

Thank you for the explanation. A helpful supplement to Razavi's book.

[@user-gi2vw2kd4l]

Very helpful brief concept. Thank you.

[@milkarton]

Perfectly explained, thank you.

[@santhoshk8703]

Beautiful explanation

[@javidmusayev1092]

I see two issues with this derivation. First, A(w0) need not be -1 as in Barkhausen criterion, because in real oscillators it would be the nonlinearity (voltage limitation) that would suppress the large swing oscillation. It does not mean that A(w0) becomes one (e.g. in ring oscillator example it is not 1). Second and even more important point is that the phase noise conceptually is a sampled noise. Therefore, input noise sources at low frequencies up-convert to frequencies around the carrier when phase noise is observed. This phenomenon cannot be described by such linear model where Vin is passed through H(w), because none of the low-frequency components of Vin would appear around w0 according to the given derivation.