--- title: "Demodulation of DSB-FC AM" subject: "Communication Systems" chapter: 2 key: "semester_6/communication_systems:dsbfc-demodulation-method" source: https://www.bctengineer.com/q/semester_6/communication_systems/dsbfc-demodulation-method site: BCT Engineering --- # Demodulation of DSB-FC AM Communication Systems · Chapter 2: Amplitude Modulation - Asked in: 2075 Bhadra (CS I), 8 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/dsbfc-demodulation-method - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2 ## Question Describe any one method of demodulating DSB-FC AM signal. ## Short answer Envelope detector: diode conducts on positive half-cycles, charging a capacitor to peak; capacitor discharges through resistor between peaks, following the AM envelope. A DC-blocking capacitor removes carrier bias to yield m(t). The RC time constant must be large relative to carrier period and small relative to message period. ## Answer DSB-FC (conventional AM) can be demodulated by the **square law detector** or the **envelope detector**. The envelope detector is the most widely used method and is described here. #### Envelope detector An envelope detector is a diode–RC circuit whose output follows the envelope $A_c[1 + k_am(t)]$ of the AM wave. ```text D AM in o---|>|----+--------+-------||----o m(t) s(t) | | Cc C R (DC block) | | o----------+--------+-------------o ``` **Input:** $s(t) = A_c[1 + k_am(t)]\cos\omega_ct$, with $|k_am(t)| \le 1$. #### Working 1. **Charging:** During each positive half cycle, when the input exceeds the capacitor voltage, the diode conducts and $C$ charges rapidly to the peak value. The charging time constant $r_fC$ ($r_f$ = diode + source resistance) is very small compared to the carrier period. 2. **Discharging:** When the input falls below the capacitor voltage, the diode is reverse biased; $C$ discharges slowly through $R$ until the next positive peak. 3. The capacitor voltage thus follows the **positive peaks** (envelope) with a small carrier-frequency ripple. 4. A coupling capacitor $C_c$ removes the DC term $A_c$, leaving $A_ck_am(t)$, i.e. the message. ```text AM input Detector output /\ /\/\/\ /\ ___ / \/ \/ \ _/ \_ _/ (follows envelope, \ /\ /\ / \__/ small ripple) \/ \/\/\/ \/ ``` #### Choice of time constant $$ \frac{1}{f_c} \ll RC \ll \frac{1}{W} $$ - $RC \gg 1/f_c$: the capacitor does not discharge much between carrier peaks (low ripple). - $RC \ll 1/W$: the voltage can follow the fastest change of the envelope. #### Distortions - **Diagonal clipping:** if $RC$ is too large, the output cannot follow a fast-falling envelope. Avoid by $$ RC \le \frac{\sqrt{1 - \mu^2}}{\mu\,\omega_m} $$ - **Negative peak clipping:** caused when the AC load (after $C_c$) is much smaller than the DC load $R$; keep $\mu \le R_{ac}/R_{dc}$. - **Over-modulation** ($\mu > 1$): envelope no longer equals $m(t)$, so the output is distorted. #### Advantages and limitations - Very simple, cheap, no local oscillator or synchronisation needed: used in all broadcast AM receivers. - Works only for DSB-FC with $\mu \le 1$; cannot demodulate DSB-SC or SSB; shows a threshold effect at low input SNR. **Example design:** for $f_c = 1$ MHz and $W = 5$ kHz, $1\ \mu s \ll RC \ll 200\ \mu s$; choose $RC \approx 20\ \mu s$ (e.g. $R = 10$ kΩ, $C = 2$ nF). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In an envelope detector, what happens when the input falls below the capacitor voltage? A. The diode is reverse biased and C discharges slowly through R B. The diode conducts and C charges to the new peak C. C discharges rapidly through the diode D. The coupling capacitor shorts the input Answer: A. The diode turns off, so C can only discharge through R until the next positive peak, which makes the output follow the envelope. (Key point: Charging and discharging) 2. Which condition on RC gives correct envelope detection? A. RC << 1/fc B. 1/fc << RC << 1/W C. RC >> 1/W D. RC = 1/fc exactly Answer: B. RC must be long compared with the carrier period (low ripple) but short compared with 1/W so the output can follow the envelope. (Key point: Time constant choice) 3. What is the purpose of the coupling capacitor Cc after the detector? A. To remove the carrier ripple B. To increase the charging speed C. To block the DC term Ac and leave Ac*ka*m(t) D. To provide synchronisation Answer: C. The detector output is Ac[1 + ka m(t)]; Cc blocks the DC part Ac so only the message term remains. (Key point: Role of coupling capacitor) 4. What causes diagonal clipping in an envelope detector? A. RC too small, giving large ripple B. Over-modulation with mu < 1 C. AC load much smaller than DC load D. RC too large, so the output cannot follow a falling envelope Answer: D. If RC is too large the capacitor discharges too slowly and the output lags behind a fast-falling envelope. (Key point: Diagonal clipping) ## Related in Communication Systems - [Compare AM systems; one method of DSB-FC generation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-types-compare-dsbfc-method) — Communication Systems, chapter 2 - [Single tone DSB-FC AM in time and frequency domain](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asingle-tone-dsbfc-time-freq) — 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 - [Switching modulator for DSB-FC AM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aswitching-modulator-dsbfc) — Communication Systems, chapter 2 - [Define AM; switching modulator for DSB-FC](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adefine-am-switching-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