--- title: "Limiter-discriminator FM demodulation; need for pre-emphasis" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:limiter-discriminator-pre-emphasis" source: https://www.bctengineer.com/q/semester_6/communication_systems/limiter-discriminator-pre-emphasis site: BCT Engineering --- # Limiter-discriminator FM demodulation; need for pre-emphasis Communication Systems · Chapter 3: Angle Modulation - Asked in: 2071 Magh (CS I), 6+2 marks - Video: [Foster Seeley Phase Discrimination Method for FM Demodulation in Communication Engineering](https://www.youtube.com/watch?v=49OxjEmLj7s) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/limiter-discriminator-pre-emphasis - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question Explain demodulation of FM using limiter-discriminator method. Why pre-emphasis is needed in FM during transmission? ## Short answer The limiter clips amplitude variations, the differentiator (discriminator) converts frequency to amplitude variations, and an envelope detector recovers the message. Pre-emphasis boosts high audio frequencies at the transmitter because FM noise power increases with frequency; at the receiver a de-emphasis network restores the signal and reduces high-frequency noise, improving SNR. ## Answer #### FM demodulation by limiter–discriminator A limiter–discriminator converts frequency variations of the FM wave into amplitude variations and then detects the envelope. ```text FM in +---------+ +-----+ +---------+ +--------+ m(t) ----->| Limiter |>| BPF |>|Differen-|>|Envelope|----> |(hard | | | |tiator | |detector| | clipper)| +-----+ |(slope) | +--------+ +---------+ +---------+ ``` 1. **Limiter and BPF:** the received FM wave has unwanted amplitude variations due to noise and fading. The hard limiter clips it to a square-like wave of constant amplitude; the BPF centred at $f_c$ keeps only the fundamental. Output: $s(t) = A_c\cos[2\pi f_c t + \phi(t)]$, $\phi(t) = 2\pi k_f\int_0^t m(\tau)d\tau$. 2. **Discriminator (differentiator):** its output is proportional to frequency: $$ \frac{ds(t)}{dt} = -A_c\left[2\pi f_c + 2\pi k_f\, m(t)\right]\sin\left[2\pi f_c t + \phi(t)\right] $$ This is a wave that is both FM and **AM**; its envelope is $2\pi A_c [f_c + k_f m(t)]$, which follows the message. 3. **Envelope detector:** recovers $2\pi A_c[f_c + k_f m(t)]$. A DC-blocking capacitor removes the constant $2\pi A_c f_c$, leaving an output proportional to $m(t)$. In practice the differentiator is a **slope detector** (a tuned circuit operated on the slope of its response), a **balanced slope detector** (two tuned circuits, one above and one below $f_c$, giving better linearity), or a Foster–Seeley discriminator. The limiter is essential: without it, amplitude noise would pass straight to the envelope detector. #### Why pre-emphasis is needed - In FM, the output noise power spectral density after detection increases with the **square of frequency** (a parabolic noise spectrum; the noise voltage itself rises linearly, which is why it is called triangular noise), so high audio frequencies suffer more noise. - High-frequency components of speech and music have small amplitudes, so their SNR is poorest. - **Pre-emphasis** (an RC high-pass network, time constant 75 μs, corner 2.1 kHz) boosts high audio frequencies before modulation. At the receiver a matching **de-emphasis** network attenuates them back, and also attenuates the high-frequency noise. The result is an SNR improvement of about 10–13 dB with no overall distortion of the message. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In what order do the blocks of the limiter-discriminator demodulator operate? A. Envelope detector, differentiator, limiter B. Limiter and BPF, differentiator, envelope detector C. Differentiator, limiter, envelope detector D. Limiter, envelope detector, differentiator Answer: B. The limiter and BPF give constant amplitude FM, the differentiator makes an AM-FM wave, and the envelope detector recovers the message. (Key point: Chain of the limiter-discriminator) 2. After differentiating the FM wave, the envelope is proportional to what? A. A constant B. The message integral C. fc + kf m(t), so it follows the message D. m(t)^2 Answer: C. The derivative has amplitude 2π Ac [fc + kf m(t)], which varies linearly with m(t); the DC term is removed by a blocking capacitor. (Key point: Differentiator output) 3. What would happen without the limiter? A. The output would have double the frequency B. The discriminator would stop working at fc C. The differentiator would give no envelope D. Amplitude noise would pass straight to the envelope detector output Answer: D. The envelope detector responds to any amplitude variation, so the limiter is needed to make the detector respond only to frequency changes. (Key point: Why the limiter is essential) 4. Why is pre-emphasis used in FM transmission? A. Detected noise power density rises with f^2, and high audio components are weak, so they are boosted before modulation B. To reduce the transmitter bandwidth C. To make the carrier amplitude constant D. To remove low audio frequencies Answer: A. FM output noise grows as f^2 so high frequencies have poor SNR; boosting them at the transmitter and de-emphasising at the receiver improves SNR by about 10-13 dB. (Key point: Need for pre-emphasis) ## Related in Communication Systems - [Limiter-discriminator FM demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator) — Communication Systems, chapter 3 - [Need for pre-emphasis and de-emphasis in FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneed-pre-de-emphasis-fm) — Communication Systems, chapter 3 - [Amplitude limiter; FM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pll-fm) — Communication Systems, chapter 3, asked 2× - [Pre-emphasis in FM broadcasting; stereo encoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apre-emphasis-stereo-encoder) — Communication Systems, chapter 3, asked 2× - [Armstrong (indirect) FM generation; pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-indirect-pre-emphasis) — Communication Systems, chapter 3 - [Short note: Pre-emphasis and de-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ashort-note-pre-de-emphasis) — Communication Systems, chapter 3, asked 4×