A log amplifier, which may spell log as logarithmic or logarithm and which may abbreviate amplifier as amp or be termed as a converter, is an electronic amplifier that for some range of input voltage ${\displaystyle V_{\text{in}}}$ has an output voltage ${\displaystyle V_{\text{out}}}$ approximately proportional to the logarithm of the input:

where ${\displaystyle V_{\text{ref}}}$ is a normalization constant in volts, ${\displaystyle K}$ is a scale factor, and ${\displaystyle \ln }$ is the natural logarithm. Some log amps may mirror negative input with positive input (even though the mathematical log function is only defined for positive numbers), and some may use electric current as input instead of voltage.

Log amplifier circuits designed with operational amplifiers (opamps) use the exponential current–voltage relationship of a p–n junction (either from a diode or bipolar junction transistor) as negative feedback to compute the logarithm. Multistage log amplifiers instead cascade multiple simple amplifiers to approximate the logarithm's curve. Temperature-compensated log amplifiers may include more than one opamp and use closely-matched circuit elements to cancel out temperature dependencies. Integrated circuit (IC) log amplifiers have better bandwidth and noise performance and require fewer components and printed circuit board area than circuits built from discrete components.

Log amplifier applications include:

A log amplifier's elements can be rearranged to produce exponential output, the logarithm's inverse function. Such an amplifier may be called an exponentiator, an antilogarithm amplifier, or abbreviated like antilog amp. An exponentiator may be needed at the end of a series of analog computation stages done in a logarithmic scale in order to return the voltage scale back to a linear output scale. Additionally, signals that were companded by a log amplifier may later be expanded by an exponentiator to return to their original scale.

The basic opamp diode log amplifier shown in the diagram utilizes the diode's exponential current-voltage relationship for the opamp's negative feedback path, with the diode's anode virtually grounded and its cathode connected to the opamp's output ${\displaystyle V_{\text{out}}}$, used as the circuit output. The Shockley diode equation gives the current–voltage relationship for the ideal semiconductor diode in the diagram to be:

where ${\displaystyle I_{\text{D}}}$ flows from the diode's anode to its cathode, ${\displaystyle I_{\text{S}}}$ is the diode's reverse saturation current and ${\displaystyle V_{\text{T}}}$ is the thermal voltage (approximately 26 mV at room temperature). When ${\displaystyle -V_{\text{out}}\gg V_{\text{T}},}$ the diode's current is approximately proportional to an exponential function:

Rearranging this equation gives the output voltage ${\displaystyle V_{\text{out}}}$ to be approximately: