---
title: "Modulation; AM and FM modulated waves"
subject: "Basic Electronics Engineering"
chapter: 5
key: "semester_2/basic_electronics_engineering:modulation-am-fm-wave"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/modulation-am-fm-wave
site: BCT Engineering
---

# Modulation; AM and FM modulated waves

Basic Electronics Engineering · Chapter 5: Communication System

- Asked in: 2071 Magh, 1+2+2 marks
- Video: [What is Modulation ? Why Modulation is Required ? Types of Modulation Explained.](https://www.youtube.com/watch?v=mHvV_Tv8HDQ) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/modulation-am-fm-wave
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-5

## Question

What is modulation? Explain AM and FM modulated wave.

## Short answer

Modulation is the process of varying a carrier's amplitude, frequency, or phase in accordance with a message signal. AM varies amplitude: v=Vc(1+m sin ωmt) sin ωct, bandwidth 2fm. FM varies frequency: v=Vc sin(ωct+mf sin ωmt), with mf=Δf/fm, constant amplitude, Carson's rule bandwidth, higher noise immunity.

## Answer

**Modulation** is the process of changing a property (amplitude, frequency or phase) of a high-frequency carrier wave in accordance with the instantaneous value of a low-frequency message signal.

It is needed for practical antenna size (antenna length is about λ/4, so a 1 kHz signal would need 75 km), for multiplexing many signals, for reducing noise and interference, and for longer range.

#### AM modulated wave

The amplitude of the carrier varies according to the message; the carrier frequency is constant.

v = Vc (1 + m sin ωm t) sin ωc t, m = Vm/Vc (modulation index, m ≤ 1 to avoid distortion).

- Frequencies: fc, fc + fm, fc − fm. Bandwidth = 2 fm.
- Simple and cheap, but noise affects amplitude and power efficiency is low.
- Used in medium-wave broadcasting (535 to 1605 kHz).

```text
   /\            /\
 /\/  \/\      /\/  \/\    <- envelope follows
 \/\  /\/      \/\  /\/       message
   \/            \/
```

#### FM modulated wave

The frequency of the carrier varies according to the message; the amplitude is constant.

v = Vc sin(ωc t + mf sin ωm t), mf = Δf/fm.

- Bandwidth by Carson's rule: BW = 2 (Δf + fm).
- High noise immunity because noise mainly changes amplitude, and the receiver limits amplitude. Better sound quality, but needs larger bandwidth.
- Used in FM broadcasting (88 to 108 MHz) and TV sound.

```text
 |||| | |  |   |  | | ||||   <- constant height,
 closer when message high        spacing varies
```

## Check yourself

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

1. What is modulation?
   A. Amplifying the message only
   B. Removing noise
   C. Converting analog to digital
   D. Varying a property of a high-frequency carrier according to the message
   Answer: D. Amplitude, frequency or phase may be varied. (Key point: Modulation)

2. Why does a 1 kHz signal need modulation for radiation?
   A. Antenna would be too small
   B. Antenna length λ/4 would be about 75 km
   C. Wave would be absorbed by air
   D. It has too high a frequency
   Answer: B. Modulating to a high carrier gives practical antennas. (Key point: Need for modulation)

3. What is FM bandwidth by Carson's rule?
   A. 2fm
   B. Δf/fm
   C. fc + fm
   D. 2(Δf + fm)
   Answer: D. FM needs larger bandwidth than AM. (Key point: FM bandwidth)

4. Why is FM less noisy than AM?
   A. Noise changes frequency only
   B. Noise mainly changes amplitude, and the FM receiver limits amplitude
   C. FM uses smaller bandwidth
   D. FM uses lower carrier frequency
   Answer: B. Amplitude limiting removes most noise. (Key point: FM noise immunity)

## Related in Basic Electronics Engineering

- [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
- [Short note: Amplitude modulation](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Ashort-note-am) — Basic Electronics Engineering, chapter 5
- [Communication system and AM block diagram](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Adefine-comm-am) — Basic Electronics Engineering, chapter 5

## Related in other subjects

- [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
- [ISB modulation; AM vs FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisb-am-vs-fm) — Communication Systems, chapter 2
- [AM transmitter 10 kW/11.8 kW: modulation index and power](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-10kw-11-8kw) — Communication Systems, chapter 2
- [Angle modulation; single tone FM time and frequency domain](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-single-tone-fm-time-freq) — Communication Systems, chapter 3