AW: Re[2]: tempco resistors

[Haible_Juergen#Tel2743]

>>   Ya know while we're on the subject, I'd be interested if somebody
>  >   *would* open the matched-transistor can of worms! I don't think I'm 
up
>  >   to it.
>
>Yes! Yes!
>If the temp-co of one transistor is cancelled by the other, where does this 

>extra temp-dependancy come in?

I'll try to leave most of the worms in the box, i.e. won't go into full
math, so I risk to say something wrong. Anyway, I'll try to say it
without writhing down the full equations.

(1) the current thru one transistor follows some exponential law (if you
      leave out bulk resistance and similar effects) if you plot it
against the BE voltage.  So the idea is to fix the base at GND, apply
some control voltage at the emitter, and use the collector current
to charge a capacitor. The root of all evil is that in the exponent
of this exponential equation there isn't just the BE voltage and
some factor, but also the temperature as a factor. This means,
that the *absolute BE* voltage is scaled by temperature before
the expo law applies.

(2) the operating point for the BE voltage is way above zero for practical
      applications, so say it has some amount (a few hundred millivolts)
for the lowest frequency in your VCO. I'd call this "bias BE voltage".
>From this point onward, you want to have some V/8ve characteristic.
So you can think of your total BE voltage as a sum of the bias BE voltage
and some delta BE voltage for a certain VCO frequency. The temperature
applies as a factor to the total BE voltage, i.e. to both components
at the same time. So your bias will shift with temperature, and the
V/8ve factor for the delta will change with temperature as well.

(3) You can compensate for the *bias* shift by adding to your input voltage
another voltage that also changes with temperature. This is achieved
by a simple emitter follower, and  you have to keep the current thru
the emitter follower constant. This is achieved by a loop that measures
the current thru the emitter follower (usually with a resistor in its 
collector
path and an opamp - or even with a transistor and a zener diode, as in
the EMS synthi's ...)
This way the input voltage is "pre-shifted" with a similar temperature
dependency as the expo transistor has, and thus compensates
for the *bias* BE voltage shift.
(And yes, you can also look at the whole thing as a differential pair,
but maybe its easier to understand, if you split it into two stages like
this - and  believe me, it's just the same thing alltogether.)

(4) As the constant-current-emitter-follower only does some voltage
      *shift* (but no scaling), it can only compensate for the temperature
dependency of the bias BE voltage in the expo transistor. The
*delta* BE voltage is still affected with the temperature term, so scaling
has to be compensated for by other means (tempco resistor,
analogue multiplier, etc.).

Hope this wasn't all too wrong - I tried to keep it simple.


>Also, if the transistor pair is driving an OTA to control the frequency,
>doesn't the transconductance of the OTA have a temp-co? Does this affect 
the
>ocillator (or filter) frequency?

Depends on how far the OTA is overdriven. With full overdrive, you just
switch direction of the current that is forced in at the emitter of the
ota's differential pair.
But even VCO's that don't overdrive the ota, are reportedly working well.
After all, you don't make use of the ota's transistors as expo current
sources here ... but I'd have to look at details once more.

JH.