[sdiy] expo accuracy? or integrator accuracy?, or both?

[Magnus Danielson]

From: "Czech Martin" <Martin.Czech at Micronas.com>
Subject: [sdiy] expo accuracy? or integrator accuracy?, or both?
Date: Fri, 7 Feb 2003 11:02:25 +0100

Dear Martin,

> An expo vco has at least two components:
> expo current converter and integrator.
> The expo converter is always pretty much the same
> structure, the integrator can come as analog computer
> integrator (feedback) or simple capacitor with buffer.

Actually, you're wrong, but your point is not lost... there are infact more
than two components. You've missed any input network such as summing
amplifiers and you've missed the reset/schmitt-trigger network. Both can have
temperature dependent effects which changes the frequency. Also, throughout the
part of a VCO which can affect the frequency will any component's temperature
dependence be of interest.

Your point is correct however, there's more things in there which is dependent
on temperature and we tend to focus on only one part. In general, we know we
have many components which vary with temperature, but we need to single out
those who performs the worst (i.e. which has the greatest influence on
frequency stability, the actual value change as such may be of less importance)
and be able to handle with it.

> There are some published results from such vcos
> (EN as well as WWW). The problem is that they
> treated both components together (aka vco), most of
> them stated that they couldn't really understand
> why the vco was going sharp or flat or strange in that
> particular way, it remained open.

I've tried to separate it as the expo-converter and CCO (Current Controlled
Oscillator) for quite some time. One must realize the difference. Often is the
differance between a saw and tri oscillator only in the CCO part, not in the
expo-converter (which BTW has voltage in, current output).

> A few mails ago there was a thread about what transistor
> pair should be used. 
> There is much writing about expo converters, tempcos etc.
> I will not bore you to death with that.
> But what about the integrator?
> How can one say that this or the other transistor pair
> is sufficient if the error source can not be distinguished?

I think you should view it like this: Often the greatest error is found to be
in the expo-converter, hence the almost manic concentration on it.
There are indeed observations which is inconclusive on the blame of the expo.

> The integrator can have the following problems:
> -capacitor dielectric absorption
>  (this is ugly, because it is different for different
>   circuits and frequencies, so component manufacturers
>   can not spec it. It is what I understand least.
>   Polystyrene, polypropylene 
>   tend to have low absorption, I have seen that by experiment,
>   but different brands
>   are different, I thought that mica was good, but
>   Bob Pease published that it isn't)
>   Anyway, it can make the integration slower, by 0.1% - 1%.

Right.

> -limited gain of amplifier
>  (this is easier to understand, the inverting integrator
>  circuit will get slower if gain goes down. Gain can go
>  down with heat, lower supply, 

Exactly.

> -offset voltage (fortunately no issue)

Right.

> -amplifier input bias current (easy to understand,
>  steals current, will get worse with temperature,
>  leads to shift of some Hz down, parts with less then
>  30pA are expensive and sometimes slow)

Indeed.

> -dominant pole of amplifier (most compensated amplifiers
>  will have a pole at ~ 10Hz, with -20dB per decade, substantial!)

Which affects its ability to balance things yes, but as such doesn't explain
the temperature dependence we are after. However, the answer is quite simple,
the temperature dependence of the dominant pole is of interest. It would be
interesting to see how great the effect would be.

> -output resistance of amplifier (inverting integrator)
> -other sources of leakage (reset, sync)

I've had a report from Jörgen Bergfors that he suspected that the LM311 in one
of his experimental oscillators seemed to be the temperature-dependent part.
I have not done any experiments myself on this. However, it is quite clear that
a shift in the comparators input balance or ability to drive the reset will
induce frequency error.

> I do not know yet, but I feel that the total integrator
> error can be substantial and it could be that it can 
> be of the same magnitude than expo source error.
> I do not need to mention that said effects introduce
> also temperature dependency into the system, this is certainly
> important for leakage and absorption.

There are *many* sources of errors. Just looking at one or rather obsesively
focusing on one is naturally unwise. We must however separate sources of
errors into three categories:

* static (compensateable) - these we compensate for by tuning and trimming if
  we need to.
* static (uncompensatable) - these are the onces we don't compensate for due to
  cost basically, we just have to learn to live with them.
* dynamic - these are anoying since even after a precission calibration these
  put the box out of trim anyway

We might learn to live with some leakage, some static frequency error etc. due
to natural variation in components specs. What we should try to do is to
reduce the major dynamic effects and keep the number of trims down to a
minimum.

> Since some of the effects are not really observable or 
> can not be manipulated in experiment, I thought it would
> help to set up a simulation model. I know that (non)linear 
> differential equation solvers of the SPICE type have problems,
> but very soon we have third order (amplifier with single pole,
> integration cap with soakage cap), this is very cumbersome
> to solve with analytic methods.

Look at GnuCAP, which used to be Al's Curcuit Simulator. Al is still developing
it and seems more than reasnoble.

You can also do physical experiments - changing around components even if they
are flawed can give you a good sense on what going on if you have characterized
those flaws.

> What's up with Martin Czech, is he ill to ask such questions?
> No, he's just curious. And he wants to measure the performance
> of the japanese dual transistors (finally) with a current
> integrator and he wants to know how much error the measurement
> instrument will possible have. If it's about 1% it will be useless.
> 
> I apologize that I torture your mind with such a long mail.

There's nothing wrong with Martin Czech, the point is exactly correct in that
there are other effects in play besides the expo-pair. It's just that expo-
converters have been the main cause of problems previously.

Cheers,
Magnus