Comparator: Noisy sine to square wave, how much phase noise?
Depending on how the spectral density is provided, it is essentially asin
Determine the phase error due to the hysteresis:
\$ \Theta_{low} = sin^{-1}(-0.3) \$
\$ \Theta_{high} = sin^{-1}(0.3) \$
This is the phase error purely due to the hysteresis if a pure sinewave was applied.
Assuming you have or have converted your spectral density into magnitude & equally assuming it is normally distributed. generate the MEAN and 1 standard deviation.
LOW:
\$ \Theta_{low_error\_mean} = sin^{-1}(-0.3) - sin^{-1}(-0.3 + mean) \$
\$ \Theta_{low\_error\_+\sigma} = sin^{-1}(-0.3) -sin^{-1}(-0.3 + \sigma) \$
HIGH:
\$ \Theta_{high\_error\_mean} = sin^{-1}(0.3) - sin^{-1}(0.3 + mean) \$
\$ \Theta_{high\_error\_+\sigma} = sin^{-1}(0.3) -sin^{-1}(0.3 + \sigma) \$
With the mean and the standard deviation "phase error" you can reconstruct a phase error distribution curve.
However... if the spectral density isn't normally distributed you will need to derive errors at a number of specific points to reconstruct a phase error curve specific to the information you have
The noise is sampled only once per zero crossing, or twice per cycle of the 1 MHz signal. Therefore, as long as the bandwidth of the noise is significantly wider than 1 MHz, its spectrum is folded many times into the 1 MHz bandwidth of the sampled signal, and you can treat the PSD of the phase noise as essentially flat within that bandwidth.
The amplitude of the output phase noise is related to the amplitude of the input signal noise by the slope of the sine wave (in V/µs) at the comparator threshold voltages. Analysis is simpler if the thresholds are symmetric around the mean voltage of the sinewave, giving the same slope for both. The amplitude of the phase noise (in µs) is simply the noise voltage divided by the slope, in whatever units you want to use, such as the RMS value of noise that has a Gaussian distribution. In other words, the PDF of the phase noise is the same as the PDF of the original voltage noise (after scaling).