but so far I only found the classical equation
You'll find a lot more in a serious literature search. You can also refer to SPICE FET models, that also include temperature
dependencies, but they aren't suitable for a basic compensation of temperature effects.
If you refer to the simple quadratic characteristic as quoted above, two reservations apply:
- It's only valid for a central range of the characteristic. Low current (subtreshold range) as well as high current range
(series resistances get important) are not reproduced correctly
- both parameter (IDSS and Vp) are temperature dependant
For square or square root functional circuits, you can easily cancel Vp temperature effects by using a FET pair. So the IDSS temperature dependency
is the more important problem.
I reviewed my 1984 diploma thesis (about wideband square root circuits) and found this representation of FET temperature dependant behaviour:
Code:
ID = β/2 (VGS - VP)²
β = β0 (T/T0)^-k
k = 1.2 ... 2
I also found empirical measurements of deviation from quadratic behaviour, that can bring FET function generator circuits down to earth...