[sdiy] Temperature Compensated Exponential ConverterUsingSSM2164

[David G. Dixon]

I've done a little bit more careful analysis over a more realistic
temperature range of 19 to 31 deg C, and -3V to +3V control voltage, and
have now determined that, within these ranges, assuming perfectly matched
2164 VCAs, it should be possible to achieve 1V/oct conformance to within
0.02%.  This means, for example, that if A440 is exactly 440Hz, then A880
will be within +/- 0.18Hz of 880Hz!  In other words, with proper trimming of
the tempco voltage V_TC and the feedback resistance R_FB, virtually perfect
tempco can be achieved.  However, one does depend on the other, and the
result is VERY sensitive to achieving the correct value of V_TC.

In case you are curious, here are the relationships (assuming 1V/oct,
3300ppm/K, and 33.3mV/dB):

R_FB = R_CV * log(2)*[1.0033^(1.0033/0.0033)]/1.5 = 0.546

(i.e., R_FB = 54.6k if R_CV = 100k) and

V_TC = log(1.0033)*(1.0033/0.0033)/1.5 = 0.290

The values are somewhat sensitive to the gain coefficient (1/1.5), but
completely insensitive to the gain temperature coefficient (0.0033).  Here
are a few sensitivity results based on minimization of the sum of square
errors to demonstrate the point:

GC      GTC      R ratio   V_TC
----------------------------------------------
1/1.5   0.0033   0.54542    0.28945  (baseline)

1/1.5   0.0030   0.54544    0.28946
1/1.5   0.0036   0.54540    0.28943

1/1.45  0.0033   0.56423    0.29943
1/1.55  0.0033   0.52782    0.28011

A change of +/- 10% in the GTC only changes the values at the fifth decimal
place!  Similar changes to the GC have more significant effects, but these
changes are far beyond expected tolerance levels.

I think we have a winner!