A fundamental problem of exponential VCOs?

[Haible Juergen]

Hi!

I spent some thoughts on beating between a pair of exponential
(V/Octave) VCOs.

I found that I run into one problem quite often: When I detune the VCOs
so much
that I get a decent beat rate of 0.2 to 1 Hz (which I find very
pleasant), the VCOs
sound very detuned in higher octaves, *regardless* of the scale
adjustment of each
VCO.
I thought that a fairly constant (or only slightly changing) beat rate
over the whole 
frequency range would be a good start for experiments. Then I did some
simple
calculations and found that this is impossible with exponential VCOs.

On an exponential VCO we usually have 2 trimmers (I omit the HFT here),
detune
and scale.
If you have perfect matching of scales of the two VCOs, you can produce
some beating
with the Detune trimmer. Then you'll *always* have a certain beat rate
at a certain note
*and* the double beat rate one octave higher. And so on. So you can only
choose between
too much detuning in ithe upper range or almost non-existing beating in
the lower range.

Then I thought of compensating this by slightly changing the Scale
trimmer of one VCO.
I start with some arbitrary amount of mistracking, then I use the Detune
trimmer to get
the VCOs in tune at some note in the upper range of the keyboard, and
watch how
the beating increases if I go up or down the keyboard. Going down, it
sounds quite
pleasant - basically the effect I wanted to accomplish. But going up,
things become
unpleasant very fast. No much use of notes above your chosen "reference
note".
Maybe in that range the HFT trimmer would already have some effect and
you could
slightly compensate for this (making the Scale of one VCO slightly flat,
and over-compensating
with HFT), but I have not really analyzed this, and probably it will not
work good enough.

To me, it looks like this: Most of us use exponential VCOs to get rid of
the offset voltage
adjustments you need in linear (V/Hz) VCOs. But exactly this (offset
misadjustment) would
be the means to get a constant beat rate term over the whole keyboard !!

To be more precise: The offset must be introduced *after* the
exponential converter.
We get *rid* of this by generating an exponential current which charges
some capacitor
directly. The only way to *introduce* an offset here would be an offset
*current*. Maybe
some leakage current has some (positive) effect, but it's really hard to
control such small
amounts of current. (If 1kHz corresponds to some uA, then a 0.2 Hz
difference would
correspond to some nA ... ) (Method A)

Another way to introduce an offset is using an exponential
voltage-to-voltage converter
(just drive the collector current into a resistor instead of the VCO
capacitor), and use
this voltage to drive a linear VCO. Some Korg Synths did this (Polysix,
Trident), and
as far as I know the first Moog Modular VCOs as well. Problem here: You
must take care
that the offset voltage doesn't grow too *large*, which reduces the
usable range to 
approx. 5 or 6 octaves. (To cover a larger range with linear VCOs, you
have to switch
resistors, or do some waveshaping/dividing tricks.) (Method B)

So we have two possibillities to make controlled use of a constant term
in beat rate:
Either use method A and find a way to control very small amounts of
current
(a linear current sorce in parallel of your exponential one, adjustable
from 0 to
a few nanoamperes), or
use Method B and extend the usable range with an opamp that has
extremely low
offset voltage drift.

I encourage you to make experiments, if this sounds reasonable to you.
If not, please tell me - comments invited (;->)

Before I close, I'd like to take a look at some typical commercial
synths. Maybe
there is some connection between their VCO architecture and the
"richness" of
their sound:

Category 1 - Linear VCOs (with or without expo converter in front of the
VCO core)

Korg Trident, Polysix
Moog Taurus 1, some Modular VCOs (the ones with driver + VCO modules)
Yamaha CS-50/60/80


Category 2 - Expo VCOs with cheap expo converter (maybe some leakage,
                   or other aberration from perfect V/Oct courve ?)

Old-style Minimoog,
Oberheim SEM


Category 3 - Expo VCO with perfect expo converter (by autotune that
includes a table
                   to correct scale imperfections)

OB-8



These are just examples, of course. And most analogue synths would be
somewhere
in between category 2 and 3, as they don't have scale correction, but a
pretty precice
straight forward expo converter. (later Minimoogs, Roland SH-synths,
OB-Xa, and many,
many more) 
I just wanted to show that there might be some *tendency*, some *trend*
from very
rich sounding synths at one end to very precice sounding instruments on
the other
end. And that the reason for this is not black magic, but of some
physical nature.
And, that this may have something to do with a linear term in VCO
detuning.
I am quite sure about the extremes (category 1 and 3), but not of the
things between.
Maybe temperature drift has more effect than the basic architecture in
some synths.

Please tell me what you think. 

JH.