---
title: "Short note: Modulation index"
subject: "Communication Systems"
chapter: 2
key: "semester_6/communication_systems:short-note-modulation-index"
source: https://www.bctengineer.com/q/semester_6/communication_systems/short-note-modulation-index
site: BCT Engineering
---

# Short note: Modulation index

Communication Systems · Chapter 2: Amplitude Modulation

- Asked in: 2072 Magh (CS I), 4 marks
- Video: [Importance of Modulation Index in Amplitude Modulation in Analog Communication by Engineering Funda](https://www.youtube.com/watch?v=TgKBbue1Whc) — 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/short-note-modulation-index
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-2

## Question

Write a short note on modulation index.

## Short answer

In AM, the modulation index μ = Am/Ac = (Amax−Amin)/(Amax+Amin), and efficiency η = μ²/(2+μ²). In FM and PM, β = Δf/fm or β = kpAm, setting the number of sidebands and bandwidth by Carson’s rule. In AM, transmitters aim for μ near 100% to maximise sideband power without overmodulation.

## Answer

The **modulation index** tells how much a carrier parameter is changed by the message.

#### In AM

Ratio of message amplitude to carrier amplitude:

$$
\mu = \frac{A_m}{A_c} = \frac{A_{max} - A_{min}}{A_{max} + A_{min}}
$$

- $\mu < 1$: under-modulation, envelope follows the message.
- $\mu = 1$: 100% modulation, maximum efficiency (33.3%) without distortion.
- $\mu > 1$: over-modulation; envelope distortion, extra sidebands, envelope detector fails.

For several tones, $\mu_t = \sqrt{\mu_1^2 + \mu_2^2 + \dots}$.

Power relation: $P_t = P_c(1 + \mu^2/2)$. A higher $\mu$ puts more power in the sidebands and gives a stronger, clearer received signal.

**Example:** $A_{max} = 8$ V, $A_{min} = 2$ V gives $\mu = 6/10 = 0.6$ (60%).

#### In FM and PM

$$
\beta = \frac{\Delta f}{f_m} \ (\text{FM}), \qquad \beta = k_pA_m \ (\text{PM})
$$

$\beta$ is the peak phase deviation in radians; it decides the number of significant sidebands and the bandwidth (Carson's rule $B = 2(\beta + 1)f_m$). Unlike AM, $\beta$ can exceed 1. Example: $\Delta f = 75$ kHz, $f_m = 15$ kHz gives $\beta = 5$.

## Check yourself

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

1. The modulation index of AM can be found from the envelope as:
   A. (Amax + Amin)/(Amax - Amin)
   B. (Amax - Amin)/(Amax + Amin)
   C. Amax/Amin
   D. Amax - Amin
   Answer: B. mu = Am/Ac = (Amax - Amin)/(Amax + Amin). (Key point: AM index definition)

2. What happens when mu > 1?
   A. Efficiency reaches 100%
   B. The wave becomes DSB-SC
   C. The carrier is suppressed automatically
   D. The envelope is distorted, extra sidebands appear and the envelope detector fails
   Answer: D. The envelope no longer equals the message, so distortion results. (Key point: Over-modulation)

3. For several tones the total modulation index is:
   A. mu1 + mu2 + ...
   B. sqrt(mu1^2 + mu2^2 + ...)
   C. mu1 x mu2 x ...
   D. The largest mu
   Answer: B. Sideband powers add, so mu_t = sqrt(sum of mu squared). (Key point: Multi-tone index)

4. For FM, the modulation index beta is:
   A. Always less than 1
   B. Am/Ac
   C. Delta f / fm, which can exceed 1
   D. fm / Delta f
   Answer: C. beta = Delta f / fm is the peak phase deviation and, unlike AM, can exceed 1 (for example 75/15 = 5). (Key point: Index in FM)

## Related in Communication Systems

- [Two-tone AM: net modulation index, power, spectrum](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-two-tone-50-20-12) — Communication Systems, chapter 2, asked 2×
- [AM modulation index; square law modulator](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-index-square-law-modulator) — Communication Systems, chapter 2
- [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
- [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
- [DSB-FC single tone expression and modulation index](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-single-tone-index) — Communication Systems, chapter 2
- [Double-tone AM expression, bandwidth and modulation index](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adouble-tone-am-bw-index) — Communication Systems, chapter 2

## Related in other subjects

- [Single-pulse PWM: modulation index and Fourier series](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Asingle-pulse-pwm-fourier) — Power Electronics, chapter 5