--- title: "Envelope detector; can it demodulate DSB-SC?" subject: "Communication Systems" chapter: 2 key: "semester_6/communication_systems:envelope-detector-dsbsc" source: https://www.bctengineer.com/q/semester_6/communication_systems/envelope-detector-dsbsc site: BCT Engineering --- # Envelope detector; can it demodulate DSB-SC? Communication Systems · Chapter 2: Amplitude Modulation - Asked in: 2076 Baisakh (CS I), 6+2 marks; 2064 Shrawan (CS I), 5+3 marks (asked 2 times) - 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-dsbsc - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2 ## Question Explain the process of demodulation of AM wave using envelope detector. Does envelope detector demodulate DSB-SC AM wave? Explain. ## Short answer An envelope detector charges a capacitor to the carrier peaks and discharges slowly, following the AM envelope. It cannot demodulate DSB-SC because the envelope is |m(t)|, producing a rectified and distorted output; DSB-SC requires coherent detection. ## Answer The **envelope detector** is a simple non-coherent demodulator whose output follows the envelope of the AM wave. Since standard AM has envelope $A_c[1+k_am(t)]$, which is a shifted copy of $m(t)$, it recovers the message without any local carrier. #### Circuit ```text D o---->|---+------+--------o | | AM in C R vo(t) ~ envelope | | o---------+------+--------o ``` #### Working 1. **Positive half cycle:** when the input exceeds the capacitor voltage, the diode conducts and $C$ charges quickly to the peak of the carrier through the small source resistance ($R_sC\ll1/f_c$). 2. **Between peaks:** when the input falls below the capacitor voltage, the diode becomes reverse-biased and $C$ discharges slowly through $R$. 3. On the next peak the diode conducts again and recharges $C$. Thus the capacitor voltage follows the **peaks** of the carrier, i.e. the envelope, with a small ripple at $f_c$. 4. A DC-blocking capacitor removes the DC ($A_c$) and a small RC low-pass filter removes ripple, giving $m(t)$. **Time constant condition:** $$ \frac{1}{f_c}\ll RC\ll\frac{1}{W} $$ - If $RC$ is too small, the output follows the carrier cycles (large ripple). - If $RC$ is too large, the capacitor cannot follow a falling envelope (**diagonal clipping**); for a tone with index $\mu$ we need $RC\le\frac{\sqrt{1-\mu^2}}{\mu\,\omega_m}$. ```text AM wave envelope detector output /\ /\/\ ___ ___ / \/ \/\ / \ __ / \ __ (small ripple) ``` Requirements: $\mu\le1$ (no over-modulation) and $f_c\gg W$. #### Can an envelope detector demodulate DSB-SC? **No.** A DSB-SC wave is $s(t)=A_cm(t)\cos\omega_ct$. Its envelope is $A_c\lvert m(t)\rvert$, not $m(t)$. Whenever $m(t)$ becomes negative, the carrier phase reverses by $180°$ but the envelope stays positive, so the detector output is the **rectified** message $\lvert m(t)\rvert$, which is badly distorted. For example, a tone $\cos\omega_mt$ comes out as $\lvert\cos\omega_mt\rvert$, which contains $2f_m$ and higher harmonics. DSB-SC therefore needs **coherent (synchronous) detection**, using a carrier recovered by a Costas loop or squaring loop. (Envelope detection would only work if a large carrier were re-inserted, which converts it back to standard AM.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does the capacitor voltage follow the envelope in an envelope detector? A. It charges quickly through the diode at peaks and discharges slowly through R between peaks B. It discharges instantly each cycle C. The diode is always off D. R is zero Answer: A. The diode conducts at peaks charging C fast; between peaks C discharges slowly, tracing the peaks. (Key point: Capacitor behaviour) 2. Which time-constant condition is correct? A. RC << 1/fc B. 1/fc << RC << 1/W C. RC >> 1/W D. RC = 0 Answer: B. RC must be long relative to the carrier period (remove ripple) but short relative to message variations (follow envelope). (Key point: Time constant) 3. What is the envelope of a DSB-SC wave Ac m(t) cos wct? A. Ac m(t) B. Ac |m(t)| C. Ac [1 + m(t)] D. Ac Answer: B. The envelope is always positive, so it equals Ac|m(t)|, not m(t). (Key point: DSB-SC envelope) 4. What does an envelope detector output for a DSB-SC tone cos wm t? A. cos wm t exactly B. |cos wm t|, containing 2fm and harmonics C. A constant DC D. Zero Answer: B. Phase reversals at m(t) zero crossings are lost, giving a rectified message; DSB-SC needs coherent detection. (Key point: Failure result) ## Related in Communication Systems - [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 - [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 - [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 - [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 - [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