[sdiy] Temperature compensation results

[René Schmitz]

Hi Ian, Martin and all,

> This argument is fine as long as the mismatch offset is independent of 
> T.  If it comes from different T dependences in Is1 and Is2 then the 
> situation is much more complicated.

This is how the Temperature dependance of Is is modelled in the Gummel 
Poon Transistor model: (used in SPICE)

IS(T) = IS(T0) (T/T0)^XTI  exp[ EG/VT ((T/T0) - 1) ]

EG is the bandgap voltage
XTI is usually 3.
VT = kT/q
T0 is the temperature at which the model parameters were extracted.

I think XTI is a mere modelling parameter, its a question which physical 
meaning it has. I know that the number of carriers depends as 
T^(3/2)*exp(-EG/2VT). Which would also explain the form of the equation.

At least we see that Is(T) depends on Is(T0) in a linear fashion.
If Is(T) were itself some nonlinear function of Is(T0) then bad things 
could happen. For example you could find two transistors with an offset 
of zero which aren't really matched, just happen to have the same Ic at 
some specific temperature.

Its the crucial question here if EG and XTI would be the same for say 
two randomly picked 2N3904s. Or the transistors inside a CA3046 or 
2SC1583. So we are back to the point "geometry" vs. "defects". But thats 
only natural, since a transistor model can't answer those questions. 
Only experiments can.

> Gradients in themself may not be a show stopper, as long as they are 
> reproducible and non-fluctuating.  Turbulent air flow and drafts are 
> what need to be controlled, I think.

Agreed. But then, I think you would need to do your calibration in the 
target environment, where you have the final gradient.

Cheers,
  René

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