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Short note: Applications of log-antilog amplifiers

Short answer

Log and antilog amplifiers convert multiplication, division, powers, and roots into addition, subtraction, and scaling of log voltages. Applications include analog multipliers, dividers, multifunction converters, true RMS converters, signal compression, dB meters, and linearizing exponential sensors. They are one-quadrant and need temperature compensation.

Write a short note on applications of log and antilog amplifier.

A log amplifier gives an output proportional to the logarithm of its input, Vo = −V_T ln(Vi/(R·Is)), and an antilog amplifier gives Vo = −R·Is·e^(Vi/V_T). Used together, they turn multiplication, division and powers into simple addition, subtraction and scaling of voltages.

Main applications:

  1. Analog multiplier: log V1 + log V2, then antilog → Vo ∝ V1·V2.
  2. Analog divider: log V1 − log V2, then antilog → Vo ∝ V1/V2.
  3. Raising to a power / taking roots: scale the log output by m (resistor ratio), then antilog → Vo ∝ Vi^m (m = 2 for squaring, m = 0.5 for square root).
  4. Multifunction converter: Vo = Vy·(Vz/Vx)^m, one circuit giving multiply, divide, power and root.
  5. True RMS converter: squaring, averaging and square-rooting a signal using log-antilog blocks.
  6. Signal compression: a log amp compresses a wide dynamic range (e.g. 1 mV to 10 V) into a small output range, used in audio, sonar, radar and pH/light measurement.
  7. Decibel (dB) meters: output directly proportional to log of signal level.
  8. Linearising sensors that have exponential response (e.g. photodiodes, thermistors).

Limitation: simple log amps work only for one polarity of input (one-quadrant) and need temperature compensation because V_T and Is depend on temperature.

✓ Answer checked by Claude Opus 5.5 (high effort)

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