---
title: "Short note: Envelope detector"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:short-note-envelope-detector"
source: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-envelope-detector
site: BCT Engineering
---

# Short note: Envelope detector

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2076 Bhadra (CS I), 4 marks
- Video: [AM Demodulation - Envelope Detector Explained (with Simulation)](https://www.youtube.com/watch?v=4JrryefRNFk) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-envelope-detector
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Write a short note on envelope detector.

## Short answer

An envelope detector consists of a diode, capacitor, and resistor. The capacitor charges quickly via the diode on carrier peaks and discharges slowly through R, tracking the AM envelope. After a DC block, the message is recovered. Time constant must satisfy 1/fc ≪ RC ≪ 1/W.

## Answer

An **envelope detector** is a simple non-coherent demodulator for DSB-FC AM. Its output follows the envelope (peaks) of the AM wave, which is $A_c[1 + k_am(t)]$.

```text
          D
 AM in --|>|---+-------+---- output
               |       |
               C       R
               |       |
 ------------- +-------+---- ground
```

**Working**

- On the positive half cycle the diode conducts and the capacitor charges quickly to the peak through the small source resistance ($r_sC \ll 1/f_c$).
- When the input falls below the capacitor voltage, the diode is off and $C$ discharges slowly through $R$.
- The output is a slightly rippled copy of the envelope; a DC-blocking capacitor removes the carrier DC level, giving $m(t)$.

**Time constant condition**

$$
\frac{1}{f_c} \ll RC \ll \frac{1}{W}
$$

- If $RC$ is too small: large carrier ripple.
- If $RC$ is too large: **diagonal clipping** (output cannot follow a falling envelope). To avoid it, $RC \le \dfrac{\sqrt{1-\mu^2}}{\mu\,\omega_m}$.

**Advantages:** very simple, cheap, no local carrier needed; used in all AM broadcast receivers.

**Limitations:** works only for DSB-FC with $\mu \le 1$; distortion by diagonal clipping and negative peak clipping; poor at low SNR (threshold effect).

## Check yourself

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

1. How does an envelope detector follow the AM envelope?
   A. The diode conducts only on negative half cycles
   B. The capacitor charges quickly through the diode to the peaks and discharges slowly through R
   C. The capacitor charges slowly and discharges fast
   D. It multiplies by a local carrier
   Answer: B. Fast charge and slow discharge give the envelope. (Key point: Working principle)

2. What condition must RC satisfy?
   A. RC << 1/fc
   B. RC >> 1/W
   C. RC = 0
   D. 1/fc << RC << 1/W
   Answer: D. It must smooth carrier ripple but still follow the message. (Key point: Time constant)

3. What causes diagonal clipping?
   A. RC too large so the output cannot follow a falling envelope
   B. RC too small
   C. Carrier frequency too low
   D. mu being too small
   Answer: A. The capacitor discharges more slowly than the envelope falls. (Key point: Diagonal clipping)

## Related in Communication Systems

- [Envelope detector; can it demodulate DSB-SC?](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenvelope-detector-dsbsc) — Communication Systems, chapter 2, asked 2×
- [Envelope detector circuit and waveforms](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenvelope-detector-circuit) — Communication Systems, chapter 2
- [Square law detector limitation; envelope detector](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asquare-law-detector-limitation-envelope) — Communication Systems, chapter 2
- [Envelope detector; why not for DSB-SC and SSB](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenvelope-detector-why-not-dsbsc-ssb) — Communication Systems, chapter 2
- [ASK and FSK modulators/demodulators; PSK with envelope detector](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aask-fsk-mod-demod-psk-envelope) — Communication Systems, chapter 7
- [Envelope detector and choice of time constant](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aenvelope-detector-time-constant) — Communication Systems, chapter 2, asked 2×