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I am working on a project that involves time synchronization and we want to derive worst case bounds for the accuracy of the current time given measurements with known error as input. Unfortunately all the PLL literature I have found focuses on small-signal cases and transient response rather then error propagation. I see some reference to more statistically grounded techniques but haven't really found a great source. Any ideas where I might look next?

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    $\begingroup$ I'm not sure what kind of error you're talking about.But, you should be able to use the small-signal case to infer the response to a disturbance. $\endgroup$ – Ben Jun 22 '19 at 19:56
  • $\begingroup$ Yes, I'm also a bit confused. Could you try to put this into formulas? Maybe looking into "classical" control loop theory (ignoring that you're specifically looking at a PLL) helps you: control loops that have an integrating component should reach 0 error asymptotically. $\endgroup$ – Marcus Müller Jun 22 '19 at 20:08
  • $\begingroup$ isn’t worst case loosing lock? $\endgroup$ – user28715 Jun 22 '19 at 23:40
  • $\begingroup$ @StanleyPawlukiewicz the question is "for how long", and "loosing lock; what happens next?", because if your PLL then, free-runningly, might simply bring the oscillator to some maximum or minimum frequency that might or might not drift – and the error that poses depends on these operational bounds (which would be a very nonlinear aspect of your control model), and on how you define "error" $\endgroup$ – Marcus Müller Jun 23 '19 at 11:00

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