Eugene
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If you have access to SpectreRF, I think there's an appendix in the SpectreRF user's manual called "Introduction to the PLL Library", or something like that. The appendix includes a description of a phase domain model of a 3-state PFD. There are two fundamental steps in the derivation. First, you must pull the VCO and reference integrators into the PFD model. This saves on convergence errors and makes the DC analysis of the phase domain model linearize about frequency, which is something that has a meaningful equilibrium value. More importantly, this step gives the PFD memory, which is necessary to capture the hysteretic nature of the relationship between average output and phase error. Surprisingly, this step still works for fractional N PLLs because the sigma delta noise enters the loop linearly AFTER being integrated. Thus, for fractional Ns, you also absorb the sigma delta noise integrator into the PFD too. Now the PFD has memory and can accurately simulate cycle slips, which leads to the second fundamental step. Replace the integrator with a resettable integrator. As the integrator integrates frequency error to produce phase error, it resets at +-2Pi. The appendix describes a few other tricks but these two are the key steps.
Please note that Cadence was issued a patent for the PFD model. I am fairly sure that means you can use it from within the Cadence tool set. I am not sure what it means beyond that. I have enough trouble reading technical stuff, let alone technical stuff written in legalese.
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