Fast VCOs/V->F converters

[Arthur Harrison]

I did the math, and perhaps its even correct! (; :

Assume a 1MHz VCO with a non-linearity of 0.1% is used
to drive a 64-sample wavetable.  For argument's sake, also
assume that the VCO's non-linearity curve is monotonic and
that the end-point deviation is negative, i.e., a predicted value
of 1MHz full-scale actually yields 99.9% of 1MHz, or 999kHz.
(Granted, these are only assumptions; the real departures
from an ideal transfer function may have some unpleasant
surprises.)

For A-440, the clock rate would need to be (64 X 440) = 28,160Hz.
Based on the non-linearity assumptions,  the deviation at 28,160 Hz
would be (28,160  /  1,000,000) X  -0.1%  =  -0.0028%, so the
result would be 439.988Hz, and that may be close enough to
A-440's exact value for many single-voiced applications (one
half-tone down, G#, is 415.31Hz).

Considering a higher pitch, say A-14,080, the clock rate would need
to be (64 X 14,080) = 901,120Hz.  Here, the deviation would approach
the worst-case value:  (901,120  /  1,000,000) X  -0.1% =  -0.0901%,
so  the resulting frequency would be 14,067.31Hz.  One half-tone down,
G#, is 13,290Hz.  Again, this might not be too obtrusive for
single-voiced applications, however, the beat frequency of this "A" with
a true "A" would be 12.69Hz.  This would probably be objectionable.

Conclusion:  Douglas' comments re: the limitations of monolithic F-V-driven
wavetable is correct if such a scheme is used in conjunction with more
precise digital synthesizers, in the higher registers.

Perhaps the 2.5MHz, 0.05% non-linearity Jim Williams' V-to-F design,
mentioned by Karl, would work in a wave table application if the samples
were reduced to 32 and the upper frequency limit was constrained to 10kHz.
Here, [(10kHz X 32) / 2.5MHz] X 0.05% = 0.64Hz deviation.  This might have
merit, since waveforms with fundamentals above several kilohertz sound
like sines, anyway.

I concur with Douglas' comments on the "hook" for polystyrene caps, and
was wondering if mica dielectrics would provide an improvement.

-Art


-----Original Message-----
From: Douglas R. Kraul <dkraul at mindspring.com>
To: DIY <synth-diy at mailhost.bpa.nl>
Date: Sunday, November 22, 1998 5:58 AM
Subject: Re: Fast VCOs/V->F converters


>This has been a while so bear with me...
>
>Linear V-F converters can yield disappointing results when used as VCO
>substitutes. Do the math on the linearity spec taking into account the fact
>that the advertised linearity (.05%) in this case is on the *full scale*
>range of the frequency output.  I think that you'll find the error
expressed
>in cents to be too high for practical use.
>
>Almost all VCO and similar devices use an integrate and dump circuit
>technique.  These devices fail at higher frequencies primarily do to delays
>in the control path - how long it takes to detect the time to reset and how
>long it takes to respond.  Parasitic effects also become problems at higher
>frequencies.  Semiconductor junctions have capacitance that varies with
>junction conditions.  Smaller capacitors in the integrator will make these
>effects more pronounced.
>
>Finally, capacitors themselves do strange things under transients like when
>they are discharged.  Polystyrene (sp?) are the best and were used almost
>exclusively in the finest VCOs of days past.  The problem is sometimes
>called "hook" and really amounts to the capacitors having  more capacitance
>at higher discharge rates, hence the oscillators go flat.
>
>These effects are problems even at the upper end of the normal VCO range.
>At higher frequencies they become even more pronounced.  Newer technology
>semiconductors could improve these problems but I doubt it.  Again, the
true
>pro VCO designs of the mid 70's used compensating tricks to keep them from
>going flat.  Emu's stuff was by far the best.  Most of the tricks also
>relied on oscillator matching in order to prevent the errors from being
>obvious - the famous tracking adjustments.
>
>As for using a frequency multiplier approach, waveform shaping is about the
>best but not practical above 4x or so do to again circuit errors.  Stay
away
>from PLL approaches because loop stability can be a big error factor in
>musical uses.
>
>All that said, good luck.  Just go into it with your eyes open that it is a
>serious technical challenge.
>
>-----Original Message-----
>From: Arthur Harrison <theremin1 at worldnet.att.net>
>To: DIY <synth-diy at mailhost.bpa.nl>
>Cc: Karl Helmer Torvmark <karlto at invalid.ed.ntnu.no>
>Date: Saturday, November 21, 1998 7:14 PM
>Subject: Re: Fast VCOs/V->F converters
>
>
>>Karl H. wrote:
>>>
>>>I've been thinking about doing a wavetable oscillator project lately, and
>>>like several others people have remarked, getting a fast enough VCO to
>>>drive it is difficult.
>>>
>>>However, I've just looked through my favorite Linear Technology appnote
>>>(AN14 - Designs for High Performance V-to-F converters), and the "Fast
>>>Response 1Hz->2.5MHz V->F converter" design looks promising. Now, how do
>>>we convert this from a V->F to a I->F converter (so we can use a regular
>>>expo. converter)? Anybody with more analog design experience that me care
>>>to comment?
>>
>>An I to V converter could be an operational amplifier (signal fed to
>>the summing node).  Perhaps the exponential function may be
>>implemented directly in this stage's feedback loop.
>>
>>There are some Ananlog Devices VCOs, too, that might have a large
>>enough range.
>>
>>>If it can be made to work, it can provide 20Hz-20kHz bandwidth with a 64
>>>byte wavetable with speed to spare, also fast response ensures you can
use
>>>FM on it as well. Linearity of the V-F itself is spec'ed to 0.05%.
>>
>>Sounds good to me!
>>
>>-Art
>>
>>
>