Q. How do you estimate accumulated phase error?
A. I estimate accumulated phase error in a
coarse way, based on the work of John McNeill
at WPI and Mozhgan Mansuri at UCLA.
If the VCO noise is random, I expect
the noise to accumulate with the square root of
the number of VCO cycles. However, eventually
the PLL feedback loop will begin to correct
the phase error that is slowly accumulating.
So, I simply multiply the RMS VCO period jitter by
roughly the number of VCO cycles in the bandwidth of
the PLL.
If the damping > 1, PhaseError = PeriodJitter(rms) * sqrt(fvco/fn).
If the damping < 1, PhaseError = PeriodJitter(rms) * sqrt(fvco/(fn*damping)).
where
fn is the natural frequency in Hz.
fvco is the VCO frequency in Hz.
According to Mozghan Mansuri's analysis,
phase error is less dependent on the damping factor if
the damping factor is much greater than one.
Reference:
"Jitter Optimization Based on Phase-Locked Lopp Design Parameters",
Mozhgan Mansuri & Ken Yang, IEEE Journal of Solid-State Circuits,
Nov. 2002, p. 1375.