[sdiy] equations up

[Magnus Danielson]

From: Ian Fritz <ijfritz at earthlink.net>
Subject: Re: [sdiy] equations up
Date: Sun, 15 Jun 2003 16:01:40 -0600

> Magnus ---

Ian,

> At 09:27 AM 6/15/2003, Magnus Danielson wrote:
> 
> >You formula (2) for the CCO is inaccurate. It misses out the dependence on V+
> >for which also I0 depends.
> 
> The assumption that goes into Eqn. (2) is that any drift in the CCO core is 
> "tuning drift".  I probably should have been more explicit about that, but 
> since the emphasis of the document is on correcting converter inaccuracies 
> I don't see this as an important issue.

You fail to see my point I think. The point is, the V+ dependence of the
reference current and the V+ dependence of the reset-voltage reference (a
20k over 10k divider in the ASM-1) neatly cancels out... if you care to do the
math as I propose. However, other signals which does not depend on the V+ to
ground potential difference does not cancel the same way.

While your investigations concentrate on the temperature compensation alone,
my point was that the mear fashion other things where short-handed a specific
issue where being missed out. The assumption of stable supplies leaves a lot of
questions and really no answers. There is ways to remove the dependence of
low-frequency (downto DC) variations, but due care has to be taken or else the
improvement is lost, since both the reference-current and the comparator
reference-voltage must track or the cancelation effect turns into an error
induction path.

OK, CCO equation for the ASM-1 VCO is:

       3 * I
            in
f    = -------
 osc   V  * C2
        +

The expo-converter voltage is

              V                  V     V
               lin     (...)      +     lin     (...)
I   = (I    - ----) * e      = (---- - ----) * e
 in     ref   560k              1.5M   560k

put these together and you get...

            3 * V            3 * V
                 +                lin       (...)
f    = (-------------- - --------------) * e
 osc    V  * C2 * 1.5M   V  * C2 * 560k
         +                +

for this case out falls the V+'s of the first part, where as Vlin/V+ does not
cancel as well on the second. Compensate just one of the V+ from another source
and you are dependent on it. The bad thing about this form of V+ dependence is
that it only works for low frequency issues, where as the Iref V+ dependence
integrates through the C2 cap before it hits the reference, so it is not ideal.

If you have a different way of acheiving the reference voltage for the
comparator your story might be much different.

Start to see my point?

> I also assume that well-regulated, stable supplies are used for critical 
> voltages.  I would never use the AMS1 design for a serious VCO without 
> extensive modifications.

Please elaborate... without motivation it remains strong but empty words, and
if there is to learn, then I am awaiting to see what is to be learned.

I am aware that the exponential converter part of the ASM-1 VCO is not ideal,
so there is no big news. I have been following the various exponetial converter
compensations scheme with interest and I have also done some homework on this
(some of it has not been seen here).

> As far as your point on drift in I0, I do not believe that affects Eqn. (2).
> 
> >If you also toss in the scaled linjear input you
> >get another term there.
> 
> I don't understand what this means.

In the ASM-1 VCO, as many other similar VCOs, there is a "linear input" which is
really a scaled linear CV input. This input voltage has a relative dependence
on V+ (or whatever voltage gives the reference current), so that the scale of
this scaled linear CV input depends on it. This is my point. You need to bring
the formulas together the right way to realize it.

> >There are a few points to remember:
> >
> >* Supply voltage effects
> 
> Again, regulated sub-supplies for critical voltages are a must.

Indeed, but why are you fighting of making them explicit when there isn't that
difficult to do?

> >* Certain offsets can be compensated for variating voltage, but care must be
> >   taken.
> 
> I don't understand what that means either.  I think I *have* been careful, 
> since I was able to get my drift to under 50 ppm/K.

What part of the design did you change the heating on?

The PSU as well?

Did you change the line voltage?

Did you change the load on the PSU?

> >If you look at the ASM-1 homepage you will find enought hints from my work on
> >this...
> 
> I don't really see anything there on temperature drift except "put in a 
> tempco if you want to".  Maybe I didn't look in the right places.  Let me know.

I think you are concentrating too much on the temperature compensation to see
what I am refering to. I am refering to the slightly more elaborate modeling of
exponential converter and CCO, and what result they make. My point is still
valid IMHO in that certain voltages have a very direct effect on frequency, and
it is not hard to bring those effects to the awareness by just a slightly more
elaborate formulas. When those effects is understood it becomes fairly
straightforward to handle this compensation properly. The trouble is that there
is many ways to go wrong.

> Thanks for your interest.

Thanks for your work! Please be assured that I try to point out a few related
points which will easilly be missed.

Cheers,
Magnus