--- title: "Envelope detector circuit and waveforms" subject: "Communication Systems" chapter: 2 key: "semester_6/communication_systems:envelope-detector-circuit" source: https://www.bctengineer.com/q/semester_6/communication_systems/envelope-detector-circuit site: BCT Engineering --- # Envelope detector circuit and waveforms Communication Systems · Chapter 2: Amplitude Modulation - Asked in: 2071 Bhadra (CS I), 5 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-circuit - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2 ## Question Draw the circuit diagram and the waveforms and describe how envelope detector can be used for demodulation of standard AM wave. ## Short answer A diode and parallel RC circuit: capacitor charges rapidly through diode to carrier peaks; between peaks diode is off, capacitor discharges slowly through load resistor, so output follows envelope A_c[1+μm(t)]. Conditions: 1/f_c << R_LC << 1/W, μ≤1, to avoid excessive ripple and diagonal clipping. ## Answer An **envelope detector** is a simple non-coherent demodulator that recovers the message from a DSB-FC (standard AM) wave by following its envelope $A_c[1+\mu m(t)]$. It needs no local carrier, so it is used in almost all AM broadcast receivers. #### Circuit ```text D o----->|-----+--------+-----o AM diode | | input === C > RL v_o(t) s(t) | > (envelope) o------------+--------+-----o ``` #### Working 1. **Positive half cycle (charging):** when the input is higher than the capacitor voltage, the diode conducts. The capacitor charges quickly through the small source resistance $R_s$ to the peak of the carrier cycle. The charging time constant $R_sC$ is very small. 2. **Between peaks (discharging):** when the input falls below the capacitor voltage, the diode is reverse biased. The capacitor discharges slowly through $R_L$ with time constant $R_LC$. 3. At the next carrier peak the diode conducts again and tops up the capacitor. So the output is the envelope with a small RF ripple at $f_c$. 4. A following RC low-pass filter removes the ripple and a coupling capacitor blocks the DC term, leaving $m(t)$. #### Choice of time constant $$ \frac{1}{f_c} \ll R_L C \ll \frac{1}{W} $$ where $W$ is the message bandwidth. - If $R_LC$ is too small, the capacitor discharges too fast and the output has large RF ripple. - If $R_LC$ is too large, the capacitor cannot follow a falling envelope, giving **diagonal clipping**. Also $\mu \le 1$ is needed; with over-modulation the envelope no longer matches $m(t)$ and the output is distorted. #### Waveforms ```text AM input: /\ /\/\/\ /\ /\/\/\/\/ \/\/\/\/\ \/\/\/\/\ /\/\/\/\/ \/ \/\/\/ \/ Detector output (before filter): __/\/\__ __ _/ \_ _/ / \__/ (envelope + small ripple) After LPF: smooth copy of m(t) ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does the capacitor behave in an envelope detector? A. Charges quickly through the diode to the peak and discharges slowly through R_L B. Charges and discharges through R_L equally C. Charges slowly and discharges quickly D. Stays fully charged at all times Answer: A. The diode conducts at peaks (small Rs C), then is off while C discharges through RL. (Key point: Charging and discharging) 2. Which condition is correct for R_L C? A. 1/fc << R_L C << 1/W B. R_L C << 1/fc C. R_L C >> 1/W D. R_L C = 0 Answer: A. It must be long enough to smooth carrier ripple but short enough to follow the envelope. (Key point: Time constant) 3. What causes diagonal clipping? A. R_L C too large so the output cannot follow a falling envelope B. R_L C too small C. Modulation index below 0.5 D. Carrier frequency too high Answer: A. If the capacitor discharges too slowly, the output lags a decreasing envelope. (Key point: Diagonal clipping) ## 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 - [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 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× - [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 - [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 - [AM wave diagram, modulation index; why near 100%](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-diagram-index-100-percent) — Communication Systems, chapter 2 ## Related in other subjects - [Half wave rectifier with waveforms](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Ahalf-wave-rectifier) — Fundamental of Electrical and Electronics Engineering, chapter 4 - [Define AM and FM with waveforms](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aam-fm-waveforms) — Basic Electronics Engineering, chapter 5 - [Sequence detector 1011 state diagram and VHDL](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Avhdl-sequence-detector-1011) — Embedded System, chapter 9 - [AM superheterodyne radio receiver diagram](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aam-superheterodyne-receiver) — Basic Electronics Engineering, chapter 5