---
title: "Frequency modulation"
subject: "Data Communication"
chapter: 5
key: "semester_5/data_communication:fm-explain"
source: https://www.bctengineer.com/q/semester_5/data_communication/fm-explain
site: BCT Engineering
---

# Frequency modulation

Data Communication · Chapter 5: Data Encoding and Modulation

- Asked in: 2073 Shrawan, 2+4 marks
- Video: [Frequency Modulation FM (Definition, Basics, Formula, Waveforms & Modulator) Explained](https://www.youtube.com/watch?v=6Y9n8dMYL-o) — Engineering Funda
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/fm-explain
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-5

## Question

What is frequency modulation (FM)? Explain with suitable equations and waveforms.

## Short answer

Frequency modulation varies instantaneous carrier frequency in proportion to message amplitude, keeping amplitude constant. Message m(t)=Am cos(2πfmt); carrier c(t)=Ac cos(2πfct). Instantaneous frequency fi=fc+kf m(t), max deviation Δf=kf Am. FM wave: s(t)=Ac cos(2πfct+β sin 2πfmt), β=Δf/fm. Power constant; Carson's rule bandwidth ≈2(Δf+fm).

## Answer

**Frequency modulation (FM)** is a method in which the instantaneous frequency of the carrier is varied in proportion to the instantaneous amplitude of the message signal, while the amplitude of the carrier stays constant.

#### Equations
Carrier: c(t) = Ac cos(2πfct). Message: m(t) = Am cos(2πfmt).

Instantaneous frequency: fi(t) = fc + kf·m(t) = fc + kf·Am cos(2πfmt)

where kf is the frequency sensitivity (Hz/V). The maximum frequency deviation is Δf = kf·Am.

FM wave: s(t) = Ac cos(2πfct + β sin(2πfmt))

where the modulation index β = Δf / fm.

- Narrowband FM: β << 1, bandwidth ≈ 2fm.
- Wideband FM: bandwidth by Carson's rule, BW = 2(Δf + fm) = 2fm(β + 1).

Power is constant: P = Ac²/2R, independent of the message.

#### Waveforms
```text
Message m(t):   _.-'''-._       _.-'''-._
              _/        \_____/        \_

FM output:   |||||||||   | | | |   |||||||||
             (dense at positive peaks, sparse at negative
              peaks; amplitude constant)
```
At the positive peak of the message the carrier frequency is highest (fc + Δf); at the negative peak it is lowest (fc - Δf); at zero message it is fc. Commercial FM broadcasting uses Δf = 75 kHz with a 200 kHz channel spacing.

## Check yourself

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

1. In FM, the message varies:
   A. Instantaneous carrier frequency; amplitude constant
   B. Carrier amplitude
   C. Phase only with fixed frequency
   D. Bandwidth
   Answer: A. FM. (Key point: Definition)

2. β:
   A. fm/Δf
   B. Δf/fm
   C. Δf x fm
   D. Am/Ac
   Answer: B. Definition. (Key point: Index)

3. FM power:
   A. Rises with message
   B. Zero
   C. Constant, independent of message
   D. Depends on β
   Answer: C. Constant amplitude. (Key point: Power)

4. At positive message peak frequency is:
   A. fc - Δf
   B. fc
   C. 0
   D. fc + Δf
   Answer: D. Highest. (Key point: Peak)

## Related in Data Communication

- [Single tone FM parameters](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afm-single-tone-numeric) — Data Communication, chapter 5
- [AM versus FM](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aam-vs-fm-compare) — Data Communication, chapter 5, asked 2×

## Related in other subjects

- [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
- [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
- [Modulation; AM and FM modulated waves](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Amodulation-am-fm-wave) — Basic Electronics Engineering, chapter 5
- [Angle modulation; Armstrong method of FM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-modulation-armstrong) — Communication Systems, chapter 3