From: matthews@eecs.ucdavis.edu (Thomas W. Matthews)
Newsgroups: rec.audio.high-end
Subject: Re: Source for high-quality pots / impedance questions
Date: 7 Oct 92 16:50:38 GMT
Organization: Division of Electrical Engineering and Computer Science, UC Davis
NNTP-Posting-Host: 129.89.7.4
Originator: tjk@csd4.csd.uwm.edu


Just a brief comment on potentiometers and impedance.  Restricting our
attention to standard potentiometers (not L-pads, etc.), let's call the
three terminals of the device the driven, ground, and output
terminals.  The impedance seen "looking into" the output terminal (also
called the output impedance of the device) depends on the position of
the potentiometer's moveable tap (in other words, where the pot is
"set").  Under the simplifying assumption that the driven terminal of
the pot is driven by a very low impedance source, the output impedance
of the pot is:

     Rp*X*(1-X)

where Rp= value of pot (fixed resistance between driven and ground terminals)
      X= electrical position of pot control (X=0 for min; X=1 for max).

The maximum output impedance of the pot is seen when it is set at its
*electrical* center.  For a linear taper pot, this would be the same as
its mechanical center.  However, for volume controls (audio taper) the
electrical center is located about 30 degrees counter clockwise from
the maximum clockwise (full up) position.  When the pot is set at its
electrical center, the signal voltage at the output is one-half that
present at the driven input (assuming no load on the output, which is
the assumption made by pot manufacturers) corresponding to a loss of 6
db.  And readers can probably recognize that -6 db should be near the
maximum (-0 db).  BTW, the maximum output impedance of the pot is 1/4
the value of the pot (under the above assumptions).

What does all this mean to the user?

Suppose a "passive preamp" uses a 10K Ohm pot.  If driven by a 120 Ohm
source (as someone mentioned in a previous posting) we can use the
above results.  The maximum output impedance of the pot and the input
impedance of the following device can be considered as a voltage
divider.  Suppose the input impedance of the following device is 25K
ohms.  When the pot is set at -6 db, the signal will be 0.83 db lower
than its supposed to be due to the load of the following device;  this
is the maximum error that occurs anywhere in the pot's range of
adjustment.  Since users can simply turn (or slide) the pot to where it
sounds best, this "error" is no big deal.  However, if the input
impedance of the following device is too low, the user may find that
most of the adjustable range of volume occurs in the last 30 degrees or
so of the pot.  This reduces the resolution of control right in the
range where a passive preamp user is most likely to need it.

If the following device and the cable connecting to it have significant
capacitance, the output impedance of the pot will cause a lower
high-frequency cutoff than if the caple and input were driven by a
lower impedance source.  This high-frequency cutoff is not likely to be
below 20 KHz, so classical theory says it doesn't matter; but high-end
folks may care.

Now, suppose that the device driving the pot does not have a low output
impedance.  The user will notice that the pot doesn't seem to adjust
the volume in the upper range of its travel; perhaps even the upper
_half_ of its range is useless.  And there will likely be a lot of
loss.  Normally, audio equipment should have a low output impedance.
Sometimes, however, a device will have an output level control (a pot)
just previous to its output with no buffer amplifier in that path.  In
that case the output impedance of the device depends on the position of
the output level control just as in the above discussion.

Conclusions:

 1  Place passive preamps as close to their following devices as possible.
 2  If most of the adjustment of the passive preamp occurs in the last (upper)
        part of its range, do what you can to raise the input impedance of
        the following device or lower the impedance of the pot.
 3  If the passive preamp is driven by a device that has an output level control
        and that device has no electronics after the output level control,
        then set the output level control all the way up.

I hope I've provided some useful information and not wasted too much bandwidth!  
This got longer than I intended.

Tom Matthews