I am trying to find a mathematical model to understand the correlated phase noise. In the link https://www.markimicrowave.com/blog/does-a-mixer-add-phase-noise/ I see the ref phase noise is almost the same after upconversion and then down-conversion. How does correlated noise gets canceled as though the mixer has not added any noise at all. I am looking for a signal processing angle to this problem and any math that supports the theory will be extremely helpful as well.

Many thanks in advance !

Did your same post on Stack Exchange not answer your question?

Not exactly. I understand the multiplication in time domain is convolution in the frequency domain. my question was - what happens when the RF & LO phase noise (PN) are highly correlated. here the author has assumed the RF phase noise is negligible and LO phase noise dominates. I want to understand how correlated PN at RF & LO ports (essentially the same PN profile) leads to cancellation of the PN in the IF port as shown in the marki link above in my OP.

I updated that post to focus on the phase noise cancellation, bottom lined here:

This occurs in down-conversion only and not in up-conversion given the output in this case is the difference of the frequency AND phase of the input ports. Where the difference term alone is selected using a low pass filter at the mixer output and the phase noise terms are correlated, the phase noise will cancel given the difference between the matching phase modulations. The further details with the math are here: https://dsp.stackexchange.com/questions/87286/corr...

Krishk- Did the update get to the root of your question or is there still some confusion here? It may help to know that for small angles beta, the sidebands due to a sinusoidal phase modulation in dBc with peak phase deviation beta are -20log10(beta/2). So the power in the phase fluctuations is directly what we would measure with a spectrum analyzer as the power in the sidebands. This is another way to see how the phase noise spectrum when translated by a mixer when multiplied with a much cleaner tone, and observed at a different carrier frequency with the same phase noise profile in dBc/Hz, will still have the same phase versus time waveform. (Frequency translation does not change the phase, in contrast to frequency multiplication).