[time-nuts] PLL behavior

[Magnus Danielson]

On 09/18/2012 05:28 PM, Jim Lux wrote:
> I'm looking for info on behavior of a PLL (with VCXO) when the reference
> comes and goes periodically. When the reference is gone, the PLL will
> "flywheel" according to whatever the loop filter does. (we can turn off
> the "input" to the filter, so we're not trying to track noise)..
>
> What I'm particularly interested in is the behavior in the PLL when the
> reference returns.
>
> The overall situation is where we are trying to make a frequency/phase
> measurement over 10-100 seconds, where the reference has a 50% duty
> cycle, and is on for a second, off for a second.
>
>
> I can fairly simply model this, or just try it, but I'm looking for some
> references to an analytical approach.

The leakage of your filter will cause the frequency to have drifted a 
little during the off period, so one way of modelling it would be that 
you would treat it like a frequency step. However, if you think a little 
about it, the drift will most likely not be that great so you would only 
shifted a somewhat in phase, and what you get is a phase step response.

It's really trivial to analyze and it has already been done to great extent.

It helps if you realize that a dirac delta has the LaPlace form of I(s) 
= 1, and then that a phase step has the formula I(s) = /|phi / s and 
that a phase ramp/frequency step has the formula I(s) = /|omega / s^2.
Applying these I(s) to you PLLs H(s) gives you the O(s) for your 
response to these stress-tests. Apply inverse LaPlace transform for 
impulse responces.

You can cheat and look it up in standard books.

Cheers,
Magnus