Here’s an excerpt from a topic about temperature compensators in exponential converters on Muffwigglers forum:
Frequency drift is caused by the two transistors in the exponential converter being at different temperatures and minimised by them being on the same substrate. This is temperature balancing. Temperature compensation with tempco resistors tries to stop the Volts/oct changing by matching the exponential term which is proportional to absolute temperature. At 25 deg C the amount of change for 1 deg is 1/(273 + 25) = 0.33557% or 3355.7ppm. That is where the figure comes from, it is not 3300pmm or 3000ppm or 3500ppm or anything else.
Note that the normal tolerance of tempco resistors is ±10% and changes with every reel of wire that they are made from. 3300pm -10% is way off (2970ppm). I have had some special ±1% tempcos made and 3316ppm to 3389ppm is not close enough either, but that was the best the manufacturers could guarantee.
If you buy a keyboard synthesizer the tempcos are probably from the same batch and equally wrong so the VCOs are also equally wrong and will track each other, but may not be absolutely in tune. If you take two synthesizer modules of different design and different tempco types, or even the same design with different batches of tempcos, the chances of them matching are very small unless each have been calibrated exactly to 3355ppm, e.g. using Ian Fritz’s method. Just sticking a 10% part in doesn’t cut it, it’s just better than not putting it in at all.
(…) the transistor temperature changes every time you play another note. If you go up an octave the current through the transistor doubles and its temperature rises.
Thermistors can be made with various technologies and are non-linear. Tempcos are usually wirewound resistors, sometimes a foil, but have a precise temperature coefficient proportional to absolute temperature.
Tempco resistors compensate for the change in temperature of a transistor where the relationship between collector current and Vbe is given by exp( q.Vbe/k.T). Vbe is the applied CV attenuated and to get an octave needs to be ~18mV. q is the electron charge and a standard constant, k is Boltzman’s constant, the only other variable is T in degrees K. As T increases the exponent term gets smaller, so to compensate Vbe needs to be multiplied by T. This is usually done by having a tempco resistor as part of the attenuator that drops volts to 18mV.
Does it make a difference? You’ve got the equation, do the maths with real figures…
OK, most people would rather gnaw their legs off, so here’s the result:
For a five octave keyboard and a 25 deg C change in temperature (not unreasonable real world changes) without compensation the error would be 464 cents! An unusable keyboard. With a tempco of various coefficients the error would be:
3000ppm: -49 cents
3300ppm: -7.7 cents
3400ppm: +6.1 cents
3500ppm: +19.9 cents
So you can see that standard common 3000 and 3500ppm parts are still going to be out of tune and you need very close to 3355 ppm to be immune to temperature changes. Don’t forget that these coefficients have a +/-10% variation too, some may be the value you want, but try finding them…