---
title: "Non-synchronous FM demodulation"
subject: "Communication Systems"
chapter: 3
key: "semester_6/communication_systems:fm-nonsynchronous-demod"
source: https://www.bctengineer.com/q/semester_6/communication_systems/fm-nonsynchronous-demod
site: BCT Engineering
---

# Non-synchronous FM demodulation

Communication Systems · Chapter 3: Angle Modulation

- Asked in: 2070 Bhadra (CS I), 6 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/fm-nonsynchronous-demod
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3

## Question

Explain with necessary mathematical relations, the demodulation of FM wave using non-synchronous method.

## Short answer

Non-synchronous FM demodulation uses a limiter, bandpass filter, differentiator, and envelope detector. The FM signal is differentiated to produce an AM-FM signal whose envelope is proportional to the message, then envelope detection recovers m(t).

## Answer

**Non-synchronous (non-coherent) FM demodulation** recovers the message without generating a local carrier in phase with the received carrier. The standard method is **differentiation followed by envelope detection** (the discriminator method).

```text
FM  +-------+ +-----+ +------------+ +--------+ m(t)
--->|Limiter|>| BPF |>|Differentia-|>|Envelope|---->
    +-------+ +-----+ |tor j2pi af | |detector|
                      +------------+ +--------+
```

**Received FM (after limiter and BPF):**

$$
s(t) = A_c\cos\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right]
$$

**Step 1: Differentiation.** A circuit whose gain rises linearly with frequency, $H(f) = j2\pi a f$, acts as a differentiator:

$$
v_1(t) = a\frac{ds(t)}{dt} = -2\pi a A_c\left[f_c + k_f m(t)\right]\sin\left[2\pi f_c t + 2\pi k_f\int_0^t m(\tau)\,d\tau\right]
$$

$v_1(t)$ is still FM, but its **amplitude** now varies as $f_c + k_f m(t)$, i.e. it is an AM–FM wave.

**Step 2: Envelope detection.** Since $f_c \gg k_f|m(t)|$, the envelope is always positive:

$$
v_2(t) = 2\pi a A_c\left[f_c + k_f m(t)\right]
$$

**Step 3: DC removal.** A blocking capacitor removes $2\pi a A_c f_c$:

$$
y(t) = 2\pi a A_c k_f\, m(t) \;\propto\; m(t)
$$

**Practical circuits:**

- **Slope detector:** a tuned circuit with resonance slightly above $f_c$; the carrier sits on its sloping skirt, so amplitude varies with frequency. Simple but non-linear.
- **Balanced slope detector:** two tuned circuits at $f_c \pm \delta f$ with diode detectors connected back to back; the output is the difference, giving an S-shaped, more linear response and no DC.
- **Foster–Seeley discriminator and ratio detector:** use the phase shift of a double-tuned transformer.
- **Zero-crossing detector:** counts zero crossings; the average of a pulse train triggered at each crossing is proportional to the instantaneous frequency.

**Role of the limiter:** the envelope detector also responds to amplitude noise. The limiter makes the input amplitude constant so that only frequency variations reach the output.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does non-synchronous FM demodulation mean?
   A. It needs a local carrier locked in phase
   B. It recovers the message without generating a phase-locked local carrier
   C. It works only for narrowband FM
   D. It uses a pilot tone
   Answer: B. Non-coherent demodulation (differentiation plus envelope detection) needs no phase-synchronised local carrier. (Key point: Meaning of non-synchronous)

2. What is the amplitude of the differentiated FM wave?
   A. Proportional to fc + kf m(t)
   B. Constant
   C. Proportional to the integral of m(t)
   D. Proportional to m(t)^2
   Answer: A. d s/dt = -2π a Ac [fc + kf m(t)] sin(...), an AM-FM wave whose envelope carries the message. (Key point: Differentiator output)

3. What is the final step after envelope detection, and why?
   A. Squaring, to double the frequency
   B. Filtering with a BPF, to remove noise
   C. Integration, to get m(t)
   D. A DC-blocking capacitor removes 2π a Ac fc, leaving a term proportional to m(t)
   Answer: D. The envelope has a constant part 2π a Ac fc; blocking it leaves y(t) = 2π a Ac kf m(t). (Key point: DC removal)

4. Why is a limiter placed before the differentiator?
   A. It lowers the carrier frequency
   B. Because envelope detection also responds to amplitude noise, the limiter makes the amplitude constant
   C. It amplifies the message
   D. It increases deviation
   Answer: B. Without constant amplitude, noise on the envelope would appear at the output; the limiter lets only frequency variations through. (Key point: Limiter role)

5. How does a simple slope detector work?
   A. It counts zero crossings
   B. It uses two PLLs
   C. The carrier sits on the sloping skirt of a tuned circuit so output amplitude varies with frequency
   D. It uses a crystal filter at fc
   Answer: C. A tuned circuit with resonance slightly off fc converts frequency changes into amplitude changes, though non-linearly. (Key point: Slope detector)

## 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
- [FM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-demod-pll) — Communication Systems, chapter 3, asked 2×
- [PLL lock and capture range; FM demodulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apll-lock-capture-fm-demod) — Communication Systems, chapter 3
- [Limiter-discriminator FM demodulation; need for pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pre-emphasis) — Communication Systems, chapter 3
- [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
- [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×

## Related in other subjects

- [Plane wave in non-magnetic medium](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aplane-wave-non-magnetic-e-given) — Electromagnetism, chapter 4
- [Second-order non-linear kinematic wave; FDM principle](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Asecond-order-nonlinear-kinematic-principle) — Computational Techniques in Civil Engineering, chapter 5
- [Non-linear kinematic wave, trapezoidal river](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Akinematic-wave-trapezoidal-river) — Computational Techniques in Civil Engineering, chapter 5
- [First-order implicit non-linear kinematic wave](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Afirst-order-implicit-nonlinear-kinematic) — Computational Techniques in Civil Engineering, chapter 5