On 9/18/12 1:49 PM, Magnus Danielson wrote:
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.
That is basically what I have now.. I guess the next question that
leads to is "how big is the phase step", and that depends on what the
oscillator did (in a statistical sense) during the flywheel time, which
in turn, I should be able to figure out from the Allan Deviation data.
A lot of classical loop analyses (in terms of the statistics) makes the
assumption that the phase detector response is linear (that is, that the
error signal is linearly proportional to phase error), which is
reasonable for small delta phase. But in the phase step case, that
might not be.
I suppose then, it's more like looking at the acquisition behavior analysis.
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