AW: Fast VCOs/V->F converters

[Haible Juergen]

	>What I am referring to is the inherent error in the loop itself.
No
	>feedback loop is perfect.  Everyone has a certain amount or error.
In a PLL
	>the phase detector outputs a signal that is related to the phase
difference
	>between the reference osc and the incoming signal.  This output is
then
	>integrated(low pass filtered) and applied to the ref osc control.
This loop
	>has a certain "gain" that determines the phase error that one will
see at
	>any instance at the ref osc.  The loop also has a time constant
determined
	>by the integrator (the cut-off of the low pass).  This not only
determines
	>how fast the PLL response to a step change in incoming freq but
also how
	>much "hunting around" the PLL does.  The more "loop gain" the lower
the
	>error but it is finite.  Loop components also contribute to the
error though
	>the feedback tends to minimize the effects.  However, feedback can
only fix
	>errors that have predictable characteristic and "good behavior"
like
	>monotonically.

What you describe is probably the same thing, just different words.
Your standard 2nd order PLL with PI-filter behaves much like a
2-pole band pass filter. You can linearize the PD for small changes
(i.e. at the end of a transient), the gain and time constant of the
loop filter can be described as one pole and one zero, and a second
pole comes from the VCO (phase information in / frequency out).
So you get an overall 2-pole filter response. It's important that the
VCO + PD contributes a "perfect" pole at s = 0. The trick
is comparing phase instead of frequency, so the finite gain of
your PD and loop filter will result in a finite *phase* error, but *zero*
frequency error. The PLL locks to a certain phase difference,
i.e. the phase is different from the input signal, but the frequency is
the same. That's for the ideal system without noise, and for the
static case, of course. So I'm ready to believe all you wrote about
jitter measurements without hesitation. My point is just that
it isn't the mere PLL configuration that's responsible for that.
If you were going to build an ordinary BP filter (from noisy
components, and with a certain Q factor to amplify noise of the
input signal), you will get a similar behaviour: connect a comparator
to the BPF output to detect the zero crossing, and you'll notice
a comparable jitter, too.

Or did I get that wrong ?

	> All of this may sound like splitting hairs, and in normal PLL
applications
	> they almost never show their nature.  But musical applications of
osc to
	> produce pitches tend to be very unforgiving.

It may sound like splitting hairs, especially since we have long
agreed that PLLs are not the best solution for our original problem.
But I think it's an interesting topic by itself.

JH.