What does this PNP transistor + OPAMP circuit does?

I can solve the circuit for given DC input voltage with transistors Ies and alfa values. It amplifies the input signal for like 13 times. (Not linearly). But i couldn't understand the purpose of this circuit. Could you help me with that? Thanks in advance

• looks like a twist on the log amplifier using the PNP for the log conversion and a transimpedance amp
– user16222
Commented Dec 24, 2014 at 18:02

This is a standard textbook building block- an antilog amplifier. You'd normally have a diode from the emitter to ground to prevent the input from going too far negative and possibly damaging the transistor (by reverse B-E breakdown).

How it works:-

The transistor base-collector voltage is maintained at 0V by the op-amp through virtue of negative feedback.

Collector current is $i_C = I_S e^{(\frac{V_{BE}}{V_T})}$, so

$Vo = -(100K) I_S e^{(\frac{V_{i}}{V_T})}$

There is a temperature dependency, obviously in the thermal voltage $V_T = kT/q$, but also in the saturation current $I_S$, so practical antilog circuits use something like a thermistor to compensate for temperature variations.

It is an Antilog Amplifier.
The output voltage will be proportional to the antilog of input voltage.

The best way to understand and explain a circuit is to divide it into its constituent building blocks. Here we can think of this circuit as of a voltage-to-voltage converter (amplifier) consisting of two consecutively connected (cascaded) converters: an exponential voltage-to-current converter (the transistor) and a perfect current-to-voltage converter (the op-amp + resistor).