[sdiy] Plotting the phase of a filter with FFT or a Phase Comparator?

[cheater00 .]

Hi guys,
I have been looking for a good way to measure the phase shift of a
filter. One way is to use an FFT spectrograph, but it isn't always the
best idea:
- they're a bit cumbersome to use. tiny screens and even tinier
resolutions don't help.
- it's difficult to find an FFT which does audio frequencies, and if
you do they're usually a bit expensive
- there's little resolution in the low end (not great if you want to
e.g. design a filter network for a subwoofer, or see how your vcf
behaves in the low end of the spectrum)

An alternative I've found is to use a phase comparator. First off, I
stumbled upon something called a "phase writer", which is one of those
wax roll printers. What it does is it takes two sine waves as input -
one is the reference and one is the tested wave, and plot the phase
shift between them (either in the range -tau/2..tau/2 or 0..tau).

Historically, those items used to be used in time measurements, to
check clock drift apparently. If you have two waves that are very
close in frequency, you can look at the phase relationship, and it'll
be a saw-up or a saw-down. Imagine: both waves start at phase = 0. One
is slower so it starts lagging behind.. after one cycle of the slower
wave, that is when the slower wave is at phase = 0 again, the fast one
might be at phase = 0.001 tau. This accumulates and then once the
slower wave is at phase = 0, the fast one is at phase = 0.002 tau, and
so on, until the fast one reaches 1 tau, which again registers as
phase = 0. This means that for beating frequencies your phase
relationship graph will be a saw up or saw down.

Anyways, those seem to be useful for phase relationships that are
constant, too (they have to be, so that you can sync your clock
perfectly). Many of them only work down to say 50 Hz.

The less cumbersome version is the Phase Comparator (not really sure
if there's much of a connection with the circuit used in PLL's). It
takes two sine waves, again, but this time it outputs a DC voltage or
current which is proportional to the phase shift. Two that seem to be
useful for low-frequency work are the Dranetz 305 (apparently very
precise, and somewhat inexpensive), as well as the Tracor 905a (google
thinks it's a tractor if you don't include the "a" so beware). Manuals
or brochures are available for both.

A phase comparator can be used with a bistable or digital storage
scope to create plots (very slowly for frequencies below say 10 Hz)

Have you guys come across phase comparators before? Have you found
them to be useful? Do you know any models other than what I mentioned
above?

One thing that's bothering me about phase comparators is that they are
made to compare the phase of static frequencies, and they have a
settling time, which means you have to turn off the Z axis or the
storage in the scope while the comparator is settling. Ideally you'd
want to have a sweep, and no gating at all.

Is there any other equipment useful for this purpose that you could
recommend? I know there's the impulse method, but again that's
deconvolution/fft. I'm not sure there's a box which does that
specifically, it's always integrated into fft spectrographs.

BTW, can someone recommend good spectrographs which go down to 1Hz?

Cheers,
D.