You need to distinguish between the PSD of the output signal (which will flatten out) and the PSD of the jitter sequence (which will not). See for example the distinction between S_phi and L in section 3.2 of https://designers-guide.org/analysis/PLLnoise.pdf
Thank you for your reply. I read through your suggested material. I am just wondering if you could give me some more references that discuss the difference of these two ways of viewing phase noise: timeaverage noise spectrum and the jitter sequence spectrum. I am not seeing intuitively, from large signal point of view, why the former phase noise flattens at close-in frequency but not in the case of the jitter sequence spectrum. Thank you.
If you really want to dig into this, you should take a look at Alper Demir's paper https://scholar.google.com/scholar?cluster=7162988792433147977, which is reference  of Ken Kundert's paper that I mentioned above.
Here is a short intuitive explanation: What you call timeaverage noise spectrum is really the spectrum of the signal including the noise. Jitter or phase noise does not change the amplitude and thus the power of the signal, so the area under the PSD curve must remain constant. This means that larger jitter or phase noise will cause a wider peak that will flatten out at a lower level in the PSD of the signal.
The jitter sequence spectrum, on the other hand, only captures the deviation of the zero crossings from their original position (relative to the ideal period). For a free-running oscillator without any absolute timing reference, the average spread of its jitter due to white noise increases linearly with time without any limit (which is the first main result of Demir's paper). This also means that the jitter sequence spectrum will increase without any limit as you go to lower frequencies.
Thanks for the further explanation. Is there a way to run a transient noise simulation to see the Lorentian effect on the ring oscillator? Do I need to sample the clock output voltage waveform and take the DFT to obtain the spectrum? If so, I imagine that the sampling frequency must be very high as compared to the fundamental freq of the clock, which will make the simulation very long?
Yes, I guess that this would be the way. Because you are looking at behavior very close to the oscillation frequency, the frequency step would have to be very small, so the simulation time would have to be very long. You probably also need to set the parameters of the transient noise analysis carefully. I have never tried this, so I don't have any experience here. I almost never use transient noise because pnoise is usually faster and also gives more information like for example the noise summary.
Dear StanleyChe and Frank,
Long time coming, but i have spent some time studying the use of the Lorentzian feature within spectre pss/pnoise domain and its use in general. I also used an example ring oscillator to carefully examine pss/pnoise results and Transient noise phase noise based results. I used both Cadence's ViVA PN() function to extract phase noise from the Transient noise results as well as a methodology I developed a number of years back. The note also includes some background information to (hopefully) shed some light on my conclusions and recommendations to Cadence. I have submitted it as an SR, but if you have "absolutely nothing to do" and have still an interest, I placed the note at URL:
Just wanted to keep you abreast of my findings sicne you both piqued my interest!