[sdiy] Temperature compensation results

[René Schmitz]

Hi Ian and Martin,
> finally someone comes up with the question of offset voltage
> in the transistor pair and if it is perhaps usefull, or
> harmfull to the stability.

To me, it appears Ian has come up with the answer. (To the question if 
matching is necessary or not.)

My initial lack of understanding has stumbled me upon the following 
reasoning: If the offset must be applied after the TC-scaling to get a 
"absolute drift" for compensation, then what happens if the offset is 
introduced before the TC and scaled along. (I'd prefer calling this 
"absolute drift" "tune drift" instead, because thats what it effectively 
is for our application)

Also for the following recall the definition of offset voltage: Its a 
voltage that must be externally *applied* to get the same collector 
current in a differential pair. As such it is a circuit property not a 
transistor property.

Usual case: OP, long tail pair etc.

So in that case we have Ic1 = Ic2, Vb2 = Vb1+Voff (To say the 
transistors aren't similar. And I apply a correction voltage to the 
second transistor.)

In the following I am using the Ebers Moll Transistor Model.

So this comes down to:

Ic1 = Is1 * exp (Vb1 * q /(k*T)) -1
Ic2 = Is2 * exp (Vb1+Voff * q /(k*T)) -1

Now Ic >> Is

Ic1 = Is1 * exp (Vb1 * q /(k*T))
Ic2 = Is2 * exp (Vb1+Voff * q /(k*T))

If Ic1 = Ic2 we have:

Is1 * exp (Vb1 * q /(kT)) = Is1 * exp (Vb1+Voff * q /(kT))

-> Is1/Is2 = exp (Vb1+Voff * q /(kT)) / exp (Vb1 * q /(kT))
= exp (Voff * q /(kT))   (1)

Or Voff = (ln(Is1/Is2) * (k*T)) / q

So if Is1 = Is2 (i.e. Transistors are matched) then Voff = 0.
if Is1 != Is2 the offset Voltage must rise with T to keep Ic1=Ic2.
this shows that the better the matching, the better the drift will be.

But this is only for the normal case of a long tail pair or a current 
mirror (Is1/Is2 is called mirror gain).

Now to the humble exponentiator:

Ic2 != Ic1; Iref := Ic2; Iout := Ic1;

Iout = Iref * Is1/Is2 * exp (dVbe q / (kT))
= Iref exp ((dVbe + Voff) q / (kT))


So if our offset is scaled along with T there is no harm done if the 
transistors are dissimilar.

If Voff is independant of T, then Iref is effectively linearly
varied by T. Which can be used to compensate for a tune drift.

> My observation is that across a few cm 0.4C temperature difference
> can exist even with forced air motion and thus heat exchange.
> I'd expect (have no measurements) that in the real application
> the temperature difference will be larger, depending on board orientation
> faceplate and everything else. There may be even draft or convection
> inside the instrument.

Sure that is to be considered. (And to avoid confusion, the above is 
just the dissected influence of Vbe matching alone, many other factors 
have to be considered, like thermal coupling, as you say, gradients and 
so on.)

> The dual transistor expo circuit is a local approach, i.e. the reason
> of drift is known to be the transistor, so another transistor
> is integrated, or glued to that very source of error in order
> to compensate. In the next level a tempco resistor is glued
> to the pair in order to kill the remaining effect.
> This works quite well, because it is quite well known what is happening.

Right, and we tend to overlook the big picture. There is more in an 
oscillator than just an expo convertor. The stability of reference 
currents or trip points is influential too, often in a linear T 
dependancy. Which generates that "absolute drift".

> I *assume* that a non local compensation approach (i.e. compensation
> circuit not near to physical thermo process that you want to compensate,
> and perhaps physically not even related to the bunch of residual tempcos
> in the circuit) will suffer from such temperature gradients.
> I could imagine that even the sign of compensation may be wrong
> under certain circumstances.

Indeed. I think it is somewhat difficult to archeive that on a board. 
There are influences like TC of summing resistors, the cap, even things 
like offset drifts of OPs, that all boil down to a single drift figure.
It would mean to ovenize or insulate the whole board. (Maybe not the 
worst idea, but more effort.)


Cheers,
  René

-- 
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159