[sdiy] FW: Knob resolution

[John Loffink]

Forwarding from an Analog Heaven discussion (I hate cross posts - messes up
my Outlook Mail Rules that redirects everything to the proper directory).

John Loffink
The Microtonal Synthesis Web Site
http://www.microtonal-synthesis.com
The Wavemakers Synthesizer Web Site
http://www.wavemakers-synth.com


-----Original Message-----
From: John Loffink [mailto:jloffink at austin.rr.com] 
Sent: Wednesday, December 31, 2003 11:48 AM
To: 'Paul Schreiber'; 'analogue at hyperreal.org'
Subject: RE: [AH] Knob resolution

Knob resolution is defined according to two parameters in the Potentiometer
Handbook by Bourns.

The first parameter is Output Smoothness (OS).  The test circuit for this
parameter is a stable voltage source across the potentiometer and the pot
wiper going to a resistive load 100 times the pot value.  This feeds to a
bandpass filter with bandwidth from 10 Hz to 100 Hz.  The pot is swept
across its full range, ideally by a controlled motor, and the voltage output
read on a digital scope or strip recorder.  The bandpass filter takes out
the DC component of the signal.  OS percentage equals the peak difference
within 1% of total electrical travel divided by the voltage source across
the pot x 100.

This somewhat equates the stairstepping artifact heard in digitized pots,
but note this parameter defines the worst case output smoothness while a
digitized pot has an output smoothness that is constant across all steps.  I
have not performed this experiment, but expect that the smoothness should be
much finer than the Adjustability defined below.  This parameter should not
be affected by knob size or backlash.

The second parameter defined by Bourns is Adjustability (A) and could be
considered the "resolution" of the pot.  As noted by Paul, this value can be
affected by several parameters including knob size, element type, backlash,
etc.  This parameter can be defined by resistance or voltage.  The voltage
method is more accurate but requires specialized test equipment that accepts
a reference voltage.  Taking just the resistance case, Ar% is defined as the
achieved reading minus the target reading, divided by the total resistance
and times 100.

Ar% = (Achieved Reading - Target Reading)/(Total Resistance) x 100

Suggested Target readings are 30%, 50% and 75% of the Total Resistance.  No
more than 20 seconds is used to adjust the knob.

I took these readings on a Spectrol 10K linear pot Model 249 with a cermet
element.  This had a Moog/MOTM style knob, Alco #PKES-90B-1/4, 0.8620" in
diameter.  Readings were taken with an Extech 5/6 digit DMM, MM560.  These
were the results:

Total Measured Resistance = 9.469K
30% Target = 2.8407K, Actual = 2.832K, Ar% (.30) = .0919%
50% Target = 4.7345K, Actual = 4.7245K, Ar% (.50) = .1056%
75% Target = 7.10175, Actual = 7.092K, Ar% (.75) = .1030%

Averaging these three results together, Ar% is 0.10%.  This is 1000 steps of
Adjustability or "resolution."  In a digitized pot, this equates to 10 bits
of A/D resolution.  Avoidance of stair stepping artifacts may require finer
bit resolution.

As a practical matter, the only time I've needed to set a knob that finely
is when setting note values from an analog sequencer or setting the fine
tuning on a VCO.

John Loffink
The Microtonal Synthesis Web Site
http://www.microtonal-synthesis.com
The Wavemakers Synthesizer Web Site
http://www.wavemakers-synth.com