---
title: "Short note: Applications of log-antilog amplifiers"
subject: "Advanced Electronics"
chapter: 6
key: "semester_4/advanced_electronics:short-note-log-antilog-applications"
source: https://www.bctengineer.com/q/semester_4/advanced_electronics/short-note-log-antilog-applications
site: BCT Engineering
---

# Short note: Applications of log-antilog amplifiers

Advanced Electronics · Chapter 6: Log-Antilog Circuit Applications

- Asked in: 2071 Chaitra, 3 marks; 2068 Chaitra, 3 marks (asked 2 times)
- Video: [LOGARITHMIC & ANTI LOGARITHMIC AMPLIFIER](https://www.youtube.com/watch?v=6kU_rsJBPhM) — Electrodiction
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/short-note-log-antilog-applications
- Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-6

## Question

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

## 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.

## Answer

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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is Vo proportional to Vi^m obtained?
   A. Scale the log output by m, then take the antilog
   B. Add m to the log output
   C. Take the antilog and multiply by m
   D. Divide the input by m
   Answer: A. m ln Vi = ln(Vi^m), with m = 2 for squaring and 0.5 for square root. (Key point: Power and roots)

2. Why is a log amp used for signal compression?
   A. It amplifies small signals linearly
   B. It removes noise
   C. It converts AC to DC
   D. It maps a wide dynamic range into a small output range
   Answer: D. A range such as 1 mV to 10 V gives a log output of only a few hundred mV. (Key point: Compression)

3. What is the output of the multifunction converter?
   A. Vo = Vz ln Vx
   B. Vo = Vy Vz Vx m
   C. Vo = Vy (Vz/Vx)^m
   D. Vo = Vy + Vz m
   Answer: C. One circuit gives multiplication, division, power and root. (Key point: Multifunction converter)

## Related in Advanced Electronics

- [RMS of sinusoid using log-antilog amplifiers](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Arms-sinusoid-log-antilog) — Advanced Electronics, chapter 6
- [BJT vs diode log amplifier; applications](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Abjt-vs-diode-log-amp) — Advanced Electronics, chapter 5
- [Design Vo = (Vx/Vy)^α·Vz with log-antilog](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Adesign-vx-vy-power-alpha) — Advanced Electronics, chapter 6, asked 2×
- [Multifunction converter using log-antilog](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Amultifunction-converter) — Advanced Electronics, chapter 6
- [Need for log-antilog circuits; analog multiplier](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Awhy-log-antilog-multiplier) — Advanced Electronics, chapter 6, asked 2×
- [Multiplier and divider using log-antilog](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Amultiplier-divider-log-antilog) — Advanced Electronics, chapter 6

## Related in other subjects

- [Tuned amplifier applications, bandwidth, Q factor](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Atuned-amplifier-applications-resonance-q) — Electronics Devices and Circuit, chapter 4