I have a question regarding a measurement scheme of phase noise that I'm trying to implement. The idea is that I have two identical signal generators (I actually do) that generate a sinusoidal voltage signal $V(t) = V_a(t) \sin\left(2\pi\nu + \phi(t)\right)$ where $V_a(t)$ is the amplitude, $\nu$ the frequency (I'll just assume that this is implemented perfectly for now) and $\phi(t)$ the phase.
Now ideally both the amplitude and phase would be static values, but in practice they are both subjected to noise (think thermal noise, 1/f noise, etc). In general this noise has a vanishing mean, so I could for example write $V_a(t) = V_a + \delta V_a(t)$, $\phi(t) = \phi + \delta \phi(t)$ where $\left<V_a(t)\right> = V_a$ and $\left<\phi(t)\right> = \phi$. With this the signals produced by the generators become $V(t) = \left(V_a+\delta V_a(t)\right) \sin\left(2\pi\nu + \phi + \delta\phi(t)\right)$.
Now, the purpose of my investigation is to characterize $\delta\phi(t)$: I am trying to find its power spectral density. The way I do this is by measuring the voltage signal in a time series and using (discrete) Fourier transforms to find the voltage spectral density and then the power spectral density. However, in general the noise is quite hard to distinguish when it competes with the actual time alternating part due to $\nu$. So to get this out, we use a trick: using an IQ mixer with an LO and RF signal at the same frequency, we use the downconverted signal at their difference ($=0$) frequency to get a DC signal, which is actually slightly time varying due to the phase noise.
Great! So then we would have a signal of the type (setting $\phi = 0$) for convenience) $V(t) = \left(V_a+\delta V_a(t)\right) \sin\left(\delta\phi(t)\right)$.
But here is where my question comes in. We only want to measure the phase noise, not the amplitude noise, and I don't understand how this is achieved. In the scheme we use, one uses an IQ mixer (inputs LO and RF) with outputs I and Q, but we terminate Q and only use the output from I. Somehow this gives a signal in which the amplitude oscillations are not longer relevant. Personally, I don't see this however, and I can't really find any documentation on the whole I-Q picture that's helping me out there.
So my question is, how does using only the I channel from the mixer make it so that our output signal is unaffected by the amplitude noise, and that we only look at phase noise?