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Thu Jan 6 20:35:57 EST 2011

## Nonlinear control

Taking the circuit output as f, the frequency of the oscillator or
filter that is driven by the exponential converter, and the input V,
the (average) voltage at the base of the BJT, we have the following
model.
f = f_0 exp((V - V_O) / V_T),
V_T = kT / q
* Voltage offset V_O expresses all component mismatches (transistor
V_BE offsets, capacitor and resistor errors). This can be
calculated once, or at a very low interval (power-on).
* Voltage scale V_T is entirely due to operating temperature, needs
to be compensated on-line.
As mentioned before it would be really interesting to be able to use
the feedback control that's necessary to stabilize the oscillator to
obtain an _explicit_ estimate of temperature so that this estimate can
then be used to drive other transistor in feedforward mode.
How would one do this? I suppose using an exact textbook Maximum
Likelihood estimator since the model is so simple and the data so
plentiful.

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