You are being excessively stringent. If the phase-locked loop is fast
enough to track the planned-for phase excursions, it can track larger phase > > excursions than +/-pi radians (or +/-180 degrees if you aren't a
physicist).
You need to have some mechanism to keep track of the more-than-one-cycle
phase excursions, but that's what counters are for.
Floyd M. Gardners's book "Phaselock techniques" talks about this at length, > > and what sort of tracking errors various order of phase-locked loop can be > > expected to show.
Gardner talks about cycle skipping and near-skipping (which he calls
"clicks" and "anti-clicks" iirc) in a PLL at low signal to noise ratios.
I'm talking about a completely different situation--very high SNR, with
a phase shifter with a limited range. There's only one way for that to
lose lock, namely when the PFD runs into its sawtooth discontinuity at
+-pi and has to snap round to the other end of its range.[/QUOTE]
And what I had in mind - and totally failed to communicate - was that it istrivially easy to keep track of larger phase excursions, provided that youhave a second - quadrature - phase detector to keep track of the directionof the excursion when it crosses +/-pi.
Interferometers use this trick to measure distances which are multiple of the wave-length of the light (or other waveform) involved, and the more mundane Moire-fringe displacement measuring systems (which make Heidenhain loads of money) rely on the same idea.
http://en.wikipedia.org/wiki/Heidenhain
You do need the second detector - and it doesn't have to be exactly in quadrature with the first, or anything like it - and you end up with a necessarily digital system, because you add the "clicks" and subtract the "anti-clicks" into some kind of digital register,
As it is a digital system, you have to worry about keeping the sampling rate high enough to avoid aliasing, but that's a whole lot less stringent thanavoiding more that +/-pi of phase excursion.