Exponential amplifier realized with op-amp is given in figure bellow.
Exponential amplifier provides a exponential output for a linear voltage input. In the given schematic, output voltage can be calculated via equaling currents. Input current is
In here, IS is the saturation current, VT is the thermal voltage and VD is diode voltage.
The same current flows through R1, so the output voltage is:
Input voltage is positive, and output is exponential, scaled and with minus sign.