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I was watching some PLL video lectures by Professor Elad Alon, and he explains why intuitively the jitter transfer function of the loop filter to the PLL output has a bandpass characteristic. He says that when you inject noise at the output of the loop filter, because there is an integration function before it (in the loop filter), any noise at DC is thrown away. I was not quite clear about this because while I understand an integrator's response to noise before it, what impact does an integrator have on a noise source injected at its output? Or am I interpreting this completely wrong?

The time stamp for this statement is here: http://www.infocobuild.com/education/audio-video-courses/electronics/EE290C-Spring2011-Berkeley/lecture-17.html at 35:35 minutes.

Also, at another point, he says the VCO's transfer function has a high-pass characteristic, because with the pole at 0, the infinite DC gain would cause any noise injected into it to go to zero. I am not quite sure I understand how this works-- is it because infinite DC gain of an integrator just mean that there is no steady state error at DC, and this is an analog of no jitter ? Sorry if these are stupid questions, it's been a long time since I started studying PLLs and I am quite rusty.

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Injecting noise at the filter output means adding a noise signal there. However this will cause the PLL frequency to increase, and ultimately the loop will adjust the freq/phase to lock. At that point, the input to the integrator will have had its perturbations and ultimately leave the output at the correct value for lock.

DC at the output is a little like initial conditions in a circuit or the constant term in an integration -- it is somewhat arbitrary and doesn't matter in the end.

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File from microcap v12, Spectrum-Soft.com

This schematic (and file) will help you understand what you want.
Just try and enjoy it changing parameters.
It is not the CD4046 or similar (not same phase comparators), but a general PLL.
You can see also, by inspecting the VCO input, that filter is a second-order system.

enter image description here

enter image description here

I have added some noise on input (~ 1V).
One can see really the impact on the filter output, which is also the input of VCO.
One can see also that "output" is clean, so noise is "disappeared".

enter image description here

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