[sdiy] YuSynth vco tracking

[cheater cheater]

Doing this subsequently in smaller steps makes it easier to achieve in
practice, because if you make big adjustments you can easily
overshoot.

On Mon, Apr 19, 2010 at 19:27, David G. Dixon <dixon at interchange.ubc.ca> wrote:
> I was just reading some web forum entries which led me to the YuSynth VCO
> page.  According to the instructions for tracking adjustment, one is to set
> the pitch at 55Hz at CV = 0V, then adjust T2 (the CV summer gain trim) until
> the pitch is 110Hz at CV = 1V.  OK.  Then, it says to repeat this procedure
> all the way up to CV = 6 or 7V (presumably from 0V every time).
>
> What does this achieve?  Why would one make six or seven adjustments to the
> same trimmer?  Unless the overall tracking is perfect, won't this only
> ensure optimum tracking at the last octave adjusted?  In other words, if one
> has to make changes to the trimmer after perfecting the first (one octave)
> adjustment, then won't that first octave be off?

No. Think of it this way: You have a curve e^x (ideal tuning) and
another curve which is a*e^(bx+c) + d (current tuning). Of course it
would be more like 2^x, but it's easier to think of e^x. The constants
a, b are positive, c and d are real numbers.

Those two exponential curves will be in one of the following relations:
- they meet in one point
- they meet in two points (octave scaling a is below or above where it
should be, or linear scaling b is)
- they meet in no points (octave scaling and linear scaling are
perfect, there is a non-zero frequency shift d. the oscillator will
beat with a perfect oscillator by a fixed frequency)
- they meet in all points (a, b, c, and d are set perfectly)

I can't remember the proof, but I don't think the curves can meet in
exactly n points for any n > 2.

The potentiometers you are adjusting are, I believe, b, and I might be
wrong, but I think d. By adjusting b you test how curvy your curve is,
for an example look here:

http://www.wolframalpha.com/input/?i=plot+e^x%2C+e^%282x-2%29%2B1+from+-1+to+2

>  Is this procedure designed
> to give the best "average" tracking?

Yes. Ideally, you could get the ideal curve (in the above thought
experiment, e(x)), but because the electronic circuits are imperfect,
and because the probability is 0 that out of all possible real numbers
you will gt a=1, b=1, c=0, d=0, this is not possible.

If you only go for tuning two frequencies (e.g. 0V and 1V), then the
frequencies between 0V and 1V might *either* overshoot or undershoot.
By fitting the curves on every octave you can set up a best-fit for
the imperfect analog electronics.

> I don't get it.

Hope this helps :-)

D.