A transdiode configuration with a BJT connected in the negative feedback loop.
A necessary condition for successful operation of a log amplifier is that the input voltage, Vin, is always positive. This may be ensured by using a rectifier and filter to condition the input signal before applying it to the log amp input. As Vin is positive, Vout is obliged to be negative (since the op amp is in the inverting configuration) and is large enough to forward bias the emitter-base junction of the BJT keeping it in the active mode of operation. Now,
where is the saturation current of the emitter-base diode and is the thermal voltage. Due to the virtual ground at the op amp differential input,
The output voltage is expressed as the natural log of the input voltage. Both the saturation current and the thermal voltage are temperature dependent, hence, temperature compensating circuits may be required.