[sdiy] Tempco adjuster idea

[Ian Fritz]

Hi all --

Has anyone thought of making a circuit to compensate for tempco resistors 
that have incorrect coefficients? I've come up with an idea for this which 
is really quite simple, but I don't remember seeing it before.

The ideal tempco resistor (for compensating exponential current generators) 
has what's called a PTAT (proportional to absolute temperature) response. 
This means that the resistance is of the form R = AT, where A is a constant 
and T is absolute temperature.  This dependence cancels the 1/T factor in 
the exponential of the transistor I-V response function. The corresponding 
temperature coefficient (1/R)(dR/dT) is just 1/T, or 3350ppm/K at room 
temperature.

So what if you buy some tempcos and their coefficients are different from 
this?  Since they are normally made of metals, their resistance will still 
have a linear T dependence, but they will not be PTAT.  In other words, 
their resistance can be well approximated as R = AT + B, where the constant 
B is the resistance extrapolated back to T = 0.  If B is positive then the 
coefficient is too low, and conversely if B is negative then it is too high.

So to correct for an incorrect coefficient one just needs to make a circuit 
that cancels the B term.  This looks easy to do, at least on paper, and the 
only drawback is that it takes several amplifiers instead of just one to 
condition the control voltage inputs.

The circuit I designed has four opamps.  The first one is a unity-gain 
inverting summer for the control signals.  The second and third op amps are 
driven in parallel from the first.  The second op amp is an inverter with 
with a gain of 0.1 and with the tempco resistor as the feedback resistor. 
(E.g., 10k input resistor, 1k tempco feedback resistor). The third opamp is 
a "switch-hitter" with gain adjustable over the range of -0.1 to 0.1.  This 
produces the signal needed to buck out the B coefficient.  The fourth op 
amp sums the outputs of the second and third, with the bucking signal 
attenuated to about 20% of the compensated signal.  A final 5.5 to 1 
voltage divider feeds the compensated 18 mV/Oct signal to the base of the 
converter transistor.

The circuit should work with just about any tempco resistance value, as 
long as the second op amp's input resistor is chosen to be ten times as 
large.  The only potential problem I can think of with this idea is that 
noise and offsets could add up with four amplifiers in the 
circuit.  Keeping impedances low and using high-quality modern op amps 
should help alleviate these problems.

I hope to try this idea out in the near future so that I can use 
the  3200ppm/K units that KRL sold me.

Any comments most welcome.

   Ian