--- title: "Limiter-discriminator FM demodulation" subject: "Communication Systems" chapter: 3 key: "semester_6/communication_systems:limiter-discriminator" source: https://www.bctengineer.com/q/semester_6/communication_systems/limiter-discriminator site: BCT Engineering --- # Limiter-discriminator FM demodulation Communication Systems · Chapter 3: Angle Modulation - Asked in: 2071 Bhadra (CS I), 7 marks - Video: [LECT-23: DEMODULATION OF FM WAVE USING FREQUENCY DISCRIMINATOR.](https://www.youtube.com/watch?v=7Cdh1lRus34) — EPOV CHANNEL - 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 - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3 ## Question Describe the limiter-discriminator method for demodulation of FM wave. ## Short answer The limiter removes amplitude noise, outputting a constant-amplitude FM wave. A differentiator (discriminator) converts frequency variations into amplitude variations, producing an AM-FM signal whose envelope follows the message; an envelope detector then extracts the message, with a DC block removing the constant term. ## Answer The **limiter–discriminator** is a direct method of FM demodulation. It first removes amplitude variations (limiter), then converts frequency variations into amplitude variations (discriminator), and finally detects the envelope. ```text FM in +-------+ +-----+ +-----------+ +--------+ m(t) ----->| Hard |>| BPF |>|Discrimina-|>|Envelope|----> |limiter| | fc | |tor (d/dt) | |detector| +-------+ +-----+ +-----------+ +--------+ ``` #### 1. Limiter and band-pass filter The received FM signal is $A(t)\cos[2\pi f_c t + \phi(t)]$, where $A(t)$ varies due to noise and fading. The hard limiter clips it into a rectangular wave of fixed amplitude whose zero crossings carry the frequency information. The BPF centred at $f_c$ removes the harmonics. The output is a constant-amplitude FM wave: $$ s(t) = A_c\cos\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right] $$ #### 2. Discriminator An ideal discriminator has a transfer function $H(f) = j2\pi a f$ over the FM band, i.e. it acts as a differentiator: $$ \frac{ds(t)}{dt} = -A_c\left[2\pi f_c + 2\pi k_f\, m(t)\right]\sin\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right] $$ The output is a hybrid AM–FM wave whose **envelope** $2\pi A_c[f_c + k_f m(t)]$ varies linearly with $m(t)$ (provided $f_c > k_f |m(t)|_{max}$, so the envelope never becomes negative). Practical discriminators: - **Slope detector:** a tuned circuit detuned so that $f_c$ sits on the linear slope of its response; output amplitude rises with frequency. Simple but not very linear. - **Balanced slope detector:** two tuned circuits at $f_c + \delta$ and $f_c - \delta$, each with a diode detector; outputs subtracted. Gives a wider linear range and cancels the DC term. - **Foster–Seeley discriminator / ratio detector:** phase-shift discriminators with good linearity. #### 3. Envelope detector A diode detector recovers $2\pi A_c[f_c + k_f m(t)]$. A DC-blocking capacitor removes the $2\pi A_c f_c$ term, giving an output proportional to $m(t)$. **Why the limiter is essential:** the discriminator output amplitude depends on $A_c$. Without the limiter, any amplitude noise on the received signal would appear directly in the output. The limiter makes the detector respond only to frequency changes, which is the main reason for FM's noise immunity. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the BPF after the hard limiter do? A. Removes the harmonics of the clipped wave, keeping the fundamental centred at fc B. Differentiates the signal C. Removes the message D. Increases the amplitude variations Answer: A. The hard limiter produces a rectangular wave; the BPF at fc keeps only the constant-amplitude FM fundamental. (Key point: Limiter and BPF) 2. What transfer function does an ideal discriminator have over the FM band? A. H(f) = constant B. H(f) = 1/(j2π a f) C. H(f) = j2π a f, i.e. a differentiator D. H(f) = a f^2 Answer: C. A gain rising linearly with frequency, H(f) = j2π a f, differentiates the FM wave and gives an AM-FM wave. (Key point: Ideal discriminator) 3. The envelope 2π Ac [fc + kf m(t)] follows m(t) correctly provided what? A. fc < kf |m|max B. beta is less than 1 C. fc > kf |m(t)|max, so the envelope never goes negative D. Ac is very small Answer: C. If fc exceeds the maximum deviation kf|m|max, the envelope stays positive and the envelope detector can recover it. (Key point: Envelope condition) 4. What is the advantage of a balanced slope detector over a simple slope detector? A. It needs no diodes B. It does not need a limiter C. It works at any carrier frequency D. Two tuned circuits at fc +/- delta with subtracted outputs give a wider linear range and cancel DC Answer: D. Subtracting the outputs of two oppositely detuned circuits gives an S-shaped, more linear characteristic with no DC term. 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