AW: VC Phaser using the LM13600

[Magnus Danielson]

>>>>> "HJ" == Haible Juergen <Juergen.Haible at nbgm.siemens.de> writes:

 >>> phase(degrees) = -2*arctan(2*pi*f*RC) for a lagging type filter
 HJ> and
 >> 
 >>> phase(degrees)= -180-2*arctan(2*pi*f*RC) for a leading type
 HJ> filter.
 >> 
 >> Well, I suppose my question should have been: Which of the
 HJ> commercial >phasers use lagging and which use leading filters? Can the
 HJ> Hammond scanning >vibrato be considered leading or lagging?
 >> 
 >> I suppose my phaser (and the Small Stone) would be of the leading
 HJ> type, as the >frequency shift gets lower at higher frequencies (if f=0 then
 HJ> phase is -180 >degrees). But if you look at the oscilloscope, the signal
 HJ> moves left when the >phase shift is increased. Because the oscilloscope
 HJ> trace moves from left to right, >it must mean the signal is delayed and
 HJ> therefore lagging! Right?

 HJ> I have a stupid question: Does this leading / lagging distinction
 HJ> make any sense at all ? I mean, you only can *delay* a signal
 HJ> anyway, and the phase shift is just the delay normalized to an
 HJ> angle for a certain frequency. I'd say the 180 degree difference
 HJ> in the above equation is just a signal inversion. (I know there
 HJ> are cases where it's useful to speak of lead and lag, but I doubt
 HJ> it is when you build delay units like phasers.)

Well, for the all-pass filter, you got n poles at -v on the real axis
and n zeros at +v on the real axis. Thus

                n
         (s - v)
H  (s) = --------
 AP             n
         (s + v)

where n is typically 4 or 6. The phase responce becomes

                     -w              -w              w
phi(jw) = n * arctan -- - n * arctan -- = 2*n*arctan -
                     -v               v              v

For this type of all-pass filters there is not really much more to
add, this is the way they behave.

Now, an all-pass filter is not all there is to a phaser, you need to
sum the output of the all-pass with the input. This has the responce
of
                                                     n            n
                                        n   c (s + v)  + c (s - v)
                                 (s - v)     1            2
H  (s) = c  + c H  (s) = c  + c  -------- = ---------------------
 PH       1    2 AP       1    2        n                 n
                                 (s + v)           (s + v)

So, dependent on how set mix c1:c2 is set, the zeros are moved from -v
(the pole positions, no effect) to +v (the all-pass zero
position). This will ofcourse change the phase behaviour between these
two cases.

Then, you could also throw in some feedback term, just for the fun of
it, this will spread the poles and the phase responce will not be as
simple.

As for lead/lag - you can't break the casuallilty without getting into
trouble with Einstein. There have been some trouble regarding how low
intensity (photon per photon) interferometers actually work with this
respect and the best explanation comes from the transaction
description of this interaction. Also, further trouble have been in
the discussions of how fast a jump over a barriers (such as in a
tunnel diod) actually takes, there are people discussing speeds in
superluminar levels (that is, _faster_ than light). In Germany they
had some fun and sent Mozart at 4.5 times the speed of light, without
any noticable distorsion over a distance of 11 cm. Hope this is
confusing ;)

Cheers,
Magnus