[sdiy] Temperature Compensated Exponential Converter Using SSM2164

[David G. Dixon]

Here's a bit of extra analysis for your reading enjoyment:

I tried several months ago to simulate 2164 like Sam Hoshuyama did, and
failed miserably.  (I think it had to do with the current sources.)  In any
case, I have been simulating circuits with 2164 (for which no SPICE model
exists) quite happily by assuming the following function:

log(I_out/I_in) = -1.5*V_C

This gives 33.3mV/dB, or 33mV/dB if one ignores all but two "sig figs".

With the gain temperature coefficient of 3300ppm/K, this is modified to:

log(I_out/I_in) = -1.5*V_C/(1 + 0.0033(t-25))

where t = temperature in celsius.

This function satisfactorily reproduces the gain vs temperature plot in the
datasheet.

I have solved this function at five temperatures between 5 and 45 degrees C,
and seven input voltages between -3 and +3V, and minimized the sum of square
errors between the calculated and desired values of log(I_out/I_in), and
have thereby obtained the following values:

Tempco voltage: 0.289V

Feedback resistance: 54.4k

These "best fit" values are actually constant to four significant figures.

It bears noting that the temperature compensation is not perfect, and
deteriorates rapidly as control voltages go above 0V (i.e., the sum of
square errors gets geometrically larger with increasing control voltages
above ground).  Hence, it would be prudent to rig the circuit so that the
audio range corresponded to negative control voltages in order to avoid the
need for high-frequency compensation.  (Gurus?  Am I on solid ground here?)

This tempco voltage is pretty close to Sam's value of 0.268, and this
feedback resistance will be accommodated by the 27k + a 50k trimmer.  I
would probably opt for 43k + a 20k trimmer, but that's just me being anal.

One question for Sam and/or the gurus: what is the purpose of the 22k
resistor at the summing opamp's output?