Log amplifier

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:

${\displaystyle V_{\text{out}}\approx K\cdot \ln \left({\frac {V_{\text{in}}}{V_{\text{ref}}}}\right)\,,}$

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:

• Performing mathematical operations like multiplication (sometimes called mixing), division, and exponentiation.^[1] This ability is analogous to the operation of a slide rule and is used for:
  • Analog computers
  • Audio synthesis
  • Measurement instruments (e.g. power = current × voltage)
• Decibel (dB) calculation
• True RMS conversion
• Extending the dynamic range of other circuits, used for:
  • Automatic gain control of transmit power in radio frequency circuits
  • Scaling a large dynamic range sensor (e.g. from a photodiode^[2]) into a linear voltage scale for an analog-to-digital converter with limited resolution^[1]

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.^[3] 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.