Temperature Compensation with a linear RTD from Vishay for a logarithmic converter
Back in my youth, I used to contemplate the circuit ideas in the wonderful book of "The Art of Electronics" by Horowitz and Hill (ISBN 0-521-37095-7).
Among the multitude of exposed circuits, I found in the fundamental chapter on opamps on page 255, a proposed schematics for a fast logarithmic converter with a peculiar temperature compensation. The idea has come to me recently to simulate this circuit with spice in order to fully visualize what such circuit does. I have developped full spice models for such temperature dependant resistances ( PTS surface mount from Vishay) and I couldn't wait to reproduce in simulation the original circuit idea. Such log converter was really important as being used in all sort of computations of dB conversion etc... The conversion is based on the fact that the base -emitter voltage of a npn transistor is proportional to the logarithm of the collector current. But at the same time it depends on temperature. And that's the reason of the presence of an RTD which is a temperature linearly depending resistance. here the two circuits one with RTD (circuit above) and its equivalent with a fixed resistor (under)
We apply different Vin levels and we record the output voltage Vout1 (with compensation) and Vout2 (without compensation) for three temperatures (-40 °C/25°C and 125°)
We see that Vout1 (lower pane) is perfectly stabilized in temperature, and changes linearily in function of the log of the input voltage. At the contrary, vout2 presents a spread in temperature for any fixed Vin.
The sweeping in temp for different input voltages shows even better the compensation effect (green compensated against blue non compensated)
If we introduce the PTS tolerances ( TOL0= 0.6 and TOLS= 0.01) then we can rerun the simulation, and we see the influence of these tolerances on the compensation: Fopr Vin = 5V, all the fixed resistors having +/-1% tolerance.
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