---
title: "Envelope detector; why not for DSB-SC and SSB"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:envelope-detector-why-not-dsbsc-ssb"
source: https://www.bctengineer.com/q/semester_6/communication_systems/envelope-detector-why-not-dsbsc-ssb
site: BCT Engineering
---

# Envelope detector; why not for DSB-SC and SSB

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2069 Bhadra (CS I), 6+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/envelope-detector-why-not-dsbsc-ssb
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Describe how envelope detector can be used for demodulation of standard AM wave. Explain why DSB-SC and SSB can not be demodulated using envelope detector.

## Short answer

Envelope detector tracks the peaks of AM wave, requiring μ≤1 to avoid distortion. DSB-SC envelope is |m(t)| because carrier phase reverses when m(t) negative, causing rectified output. SSB envelope is constant for a tone and not proportional to m(t). Both need synchronous detection.

## Answer

An **envelope detector** is a diode–RC circuit that tracks the peaks (envelope) of a standard AM wave $A_c[1+\mu m(t)]\cos\omega_ct$, giving $A_c[1+\mu m(t)]$ and hence $m(t)$ after removing DC.

#### Circuit

```text
        D
 o----->|-----+--------+-----o
 AM           |        |
 input   C  ===       > RL   v_o
              |        >
 o------------+--------+-----o
```

#### Operation

1. **Charging:** in each positive carrier half cycle, when the input is above the capacitor voltage, the diode conducts and $C$ charges through the small source resistance $R_s$ almost to the peak.
2. **Discharging:** once the input falls below the capacitor voltage, the diode is cut off and $C$ discharges slowly through $R_L$.
3. Repeating every carrier cycle, the capacitor voltage follows the envelope with a small saw-tooth ripple at $f_c$.
4. A low-pass RC filter smooths the ripple and a blocking capacitor removes the DC term $A_c$, leaving $\mu A_c m(t)$.

```text
 AM in:   /\/\/\  /\/\/\
         /\/\/\/\/\/\/\/\  (peaks follow m)
 Out:      ___      ___
         _/   \____/   \_  (envelope)
```

#### Design conditions

- $R_sC \ll 1/f_c$ (fast charge)
- $1/f_c \ll R_LC \ll 1/W$ (small ripple, yet follows the message)
- For a tone, to avoid diagonal clipping: $R_LC \le \dfrac{\sqrt{1-\mu^2}}{\mu\omega_m}$
- $\mu \le 1$ (no over-modulation)

#### Why DSB-SC cannot be envelope detected

$s_{DSB}(t) = A_cm(t)\cos\omega_ct$. Its envelope is $A_c|m(t)|$, not $m(t)$. When $m(t)$ goes negative, the carrier phase reverses by 180°, but the peaks stay positive. The envelope detector outputs $|m(t)|$, a rectified (full-wave) copy of the message, which is badly distorted.

```text
 m(t):    /\      /\         |m(t)|:  /\  /\  /\
        _/  \    /  \_    ->         /  \/  \/  \
             \__/
```

Example: for $m(t) = \cos\omega_mt$ the output contains $|\cos\omega_mt|$, which has components at $0, 2f_m, 4f_m, \dots$ and none at $f_m$.

#### Why SSB cannot be envelope detected

$s_{SSB}(t) = \frac{A_c}{2}[m(t)\cos\omega_ct \mp \hat m(t)\sin\omega_ct]$. Its envelope is

$$
a(t) = \frac{A_c}{2}\sqrt{m^2(t) + \hat m^2(t)}
$$

which is not proportional to $m(t)$. For a single tone $m = A_m\cos\omega_mt$, $\hat m = A_m\sin\omega_mt$, so the envelope is constant, $A_cA_m/2$: the detector gives only DC and the message is lost completely.

Both DSB-SC and SSB therefore need **coherent (synchronous) detection**, or a large carrier must be added at the receiver so that the envelope again follows $m(t)$.

## Check yourself

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

1. The envelope of DSB-SC is
   A. Ac|m(t)|
   B. constant
   C. Ac m(t)
   D. Ac(1+m(t))
   Answer: A. Phase reversals do not make the envelope negative. (Key point: DSB-SC envelope)

2. For m = cos wm t, the DSB-SC envelope output contains
   A. only fm
   B. fm and 3fm
   C. components at 0, 2fm, 4fm, ... and none at fm
   D. only fc
   Answer: C. |cos| is full-wave rectified. (Key point: Rectified output)

3. The SSB envelope is
   A. Ac m(t)
   B. (Ac/2) sqrt(m^2 + m^2hat)
   C. Ac(1+m)
   D. (Ac/2) m(t)
   Answer: B. Not proportional to m(t); constant for a single tone. (Key point: SSB envelope)

4. How can DSB-SC or SSB be demodulated?
   A. Increase mu
   B. Coherent detection, or add a large carrier
   C. Use a lower fc
   D. Use a longer RC
   Answer: B. Adding a large carrier restores an envelope proportional to m(t). (Key point: Remedy)

## 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×
- [DSB-AM vs SSB; ring modulator for DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbam-ssb-compare-ring-modulator) — Communication Systems, chapter 2
- [DSB-SC vs SSB; synchronous demodulation of DSB-SC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbsc-vs-ssb-synchronous-demod) — Communication Systems, chapter 2
- [Compare DSB-AM, DSB-SC, SSB, VSB; SSB by phase discrimination](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompare-am-variants-ssb-phase) — Communication Systems, chapter 2
- [SSB vs AM and DSB-SC; balanced modulator](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Assb-vs-am-balanced-modulator) — Communication Systems, chapter 2
- [Phase error in coherent DSB-SC detection; AM demodulation by PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aphase-error-dsbsc-am-pll) — Communication Systems, chapter 2