I'm pretty visually oriented so my questions come from that angle,
so I'm picturing the output of a pll of two signals that are
identical in frequency which will be a flat dc level. Does the whole
loop then try to bring the dc level to zero or is matching frequencies
enough?
If there's just some DC gain from the pd output to the vco input
(maybe just g=1, even), the loop will usually settle with some
non-zero pd output, namely the voltage necessary to pull the vco to
the target frequency. Since it almost always takes some non-zero dc
voltage to pull the vco to the target, there must be a steady-state
phase error, so the waveforms are locked in frequency but have some
fixed phase offset, whatever it takes to tune the vco. This is a
first-order pll.
But if you add an integrator in the path from the phase detector
output to the vco input, the loop will settle at zero frequency error
and zero phase error (ignoring any residual offset errors in the pd or
the integrator.) The integrator will slowly creep the vco input over
time such as to servo the pd output to zero. This is a second-order
pll.
The vco-phase detector combination is itself mathematically an
integrator - just imagine applying a small DC voltage at the vco
input... the pd output will then be a ramp (although the ramp
eventually folds over, but that's another story... no integrator can
ramp forever!) So the type-1 servo loop is an integrator with negative
feedback, which is usually very stable. The type 2 loop has *two*
integrators in a feedback loop, which tends to be unstable,
oscillating or ringing badly (two integrators tend to chase each
others' tails, so to speak) so some additional compensation is needed
to keep the lock stable.
Beyond this, a good book on pll's would be helpful. Unfortunately,
many are mainly mathematical in approach, which is fine for coming to
workable solutions but somewhat lacking if you want an instinctive
visual feel for what's happening.
My favorite pll uses a d-type flipflop as the phase detector in a
type-1 loop. It's inherently stable, but has zero phase error, because
the phase detector gain is infinite. Mathematically, it's sort of a
mess.
I can picture the visual way to obtain phase difference of two
different frequencies of equal amplitude by just drawing a horizontal
line through the two waves at any amplitude and this will give the
rolling phase difference. But what will be the effect on the phase
detector output if one of the waves is say twice the amplitude.? If
there is a difference how does the phase detector deal with this?
Some phase detectors (like a linear multiplier) give an output that
depends on one or both input amplitudes, so loop behavior varies with
input signal level (vco level is usually pretty much constant.) Most
pd's don't care about input amplitude for reasonable input levels, but
just compare phases; that simplifies loop analysis. An XOR gate is a
nice phase detector that pretty much ignores input level. Just imagine
turning either sine input into a square wave of, say, +-1 volt fixed
signal level, using a comparator or some such, and then comparing
phases.
John