Modulation index of an AM signal is ratio of __________ to the _______.

Peak message signal amplitude, Peak carrier amplitude

Peak carrier amplitude, Peak message signal amplitude

Carrier signal frequency, Message signal frequency

Message signal frequency, Carrier signal frequency

Function of frequency mixer in super heterodyne receiver is

Multiplication of incoming signal and the locally generated carrier

Amplitude Modulation - Definition, Types, Solved Examples, AM Uses

Amplitude modulation is a process by which the wave signal is transmitted by modulating the amplitude of the signal. It is often called AM and is commonly used in transmitting a piece of information through a radio carrier wave. Amplitude modulation is mostly used in the form of electronic communication.

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Currently, this technique is used in many areas of communication, such as in portable two-way radios, citizens band radios, VHF aircraft radios and in modems for computers. Amplitude modulation is also used to refer to mediumwave AM radio broadcasting.

What Is Amplitude Modulation?
Types of Amplitude Modulation
Communication Systems and Modulation
What Is Modulation?
Amplitude Phase
Need for Modulation
Common Terms
Expression for Amplitude Modulated Wave
Frequencies of Amplitude Modulated Wave
Advantages and Disadvantages of Amplitude Modulation
Solved Problems
NCERT Questions on Amplitude Modulation

What Is Amplitude Modulation?

Amplitude modulation, or just AM, is one of the earliest modulation methods that is used in transmitting information over the radio. This technique was devised in the 20th century at a time when Landell de Moura and Reginald Fessenden were conducting experiments using a radiotelephone in the 1900s. After successful attempts, the modulation technique was established and used in electronic communication.

In general, amplitude modulation definition is given as a type of modulation where the amplitude of the carrier wave varies in some proportion with respect to the modulating data or the signal.

As for the mechanism, when amplitude modulation is used, there is a variation in the amplitude of the carrier. Here, the voltage or the power level of the information signal changes the amplitude of the carrier. In AM, the carrier does not vary in amplitude. However, the modulating data is in the form of signal components consisting of frequencies either higher or lower than that of the carrier. The signal components are known as sidebands, and the sideband power is responsible for the variations in the overall amplitude of the signal.

The AM technique is totally different from frequency modulation and phase modulation, where the frequency of the carrier signal is varied in the first case and in the second one, the phase is varied.

Types of Amplitude Modulation

There are three main types of amplitude modulation. They are

Double Sideband-suppressed Carrier Modulation (DSB-SC)
Single Sideband Modulation (SSB)
Vestigial Sideband Modulation (VSB)

Also Read: Amplitude Modulation Derivation

Designations by ITU

The International Telecommunication Union (ITU) designated different types of amplitude modulation in 1982. They are as follows:

Designation	Description
A3E	Double-sideband a full-carrier
R3E	Single-sideband reduced-carrier
H3E	Single-sideband full-carrier
J3E	Single-sideband suppressed-carrier
B8E	Independent-sideband emission
C3F	Vestigial-sideband
Lincompex	Linked compressor and expander

Communication Systems and Modulation

We are studying modulation under communication systems. They are used to transmit and receive messages (information) from one place to another place in the form of electronic signals, and they are carried out in two different ways.

(i) Analog signal transmission

(ii) Digital signal transmission

So, we can represent an analogue electronic signal (information) as follows:

$\begin{array}{l}\left.\begin{matrix} m(t)={{A}_{m}}\cos ({{\omega }_{m}}t+\theta ) \\ (or) \\ m(t)={{A}_{m}}\sin ({{\omega }_{m}}t+\theta ) \end{matrix}\right\}…………….1\end{array} $

We can represent the analogue electronic signal either as a sine (or) cosine wave. Every wave will have an amplitude and phase.

Where m(t) = Modulating signal (input signal) or baseband signal

A_m = Amplitude of the modulating signal

(ω_mt + Ɵ) = Phase of the signal phase contains both frequency (ω_mt) ad angle (Ɵ) term

What Is Modulation?

Basically, it is a process in a communication system. For communication, we need some fundamental elements. One is the high-frequency carrier wave, and the other is the information that has to be transmitted (modulating signal) or input signal. These are essential for communication which is done using a device from one place to another. All in all, we need the help of the communication system.

An electronic communication system converts our message (information) into an electronic signal, and the electronic signal is carried out by carrier waves to the destination.

Amplitude Modulation Graph

Message (information)

Modulating signal

The superposition of modulating signal onto a carrier wave is known as modulation.

Modulation is defined as,

Varying any one of the fundamental parameters of a carrier wave in accordance with the modulating signal. A carrier wave can be represented as a sine or cosine.

C(t) = A_c sin (ω_ct + Ɵ)

Also Read: Frequency Modulation vs Amplitude Modulation

Amplitude Phase

If we vary the amplitude of the carrier wave in accordance with the modulating signal (input signal), it is known as amplitude modulation.

Similarly, it can be frequency modulation and phase modulation, too. In other words, modulation is the phenomenon of “superimposition of the modulating signal (input signal) into the carrier wave”.

Why Do We Need Modulation?

Practically speaking, modulation is required for

High range transmission
Quality of transmission
To avoid the overlapping of signals

High Range Transmission: (Effective Length of Antenna)

For effective communication, the length of the antenna should be λ/4 times the modulating signal.

H_min = λ/4

λ – Wavelength of the modulating signal or transmitting signal H> λ/4

For example, if I need to transmit a signal of a frequency of f = 20 kHz

As we know, c = f λ

3 × 10⁸ = 20 × 10³ (λ)

$\begin{array}{l}\frac{3\times {{10}^{8}}}{2\times {{10}^{4}}}=\lambda\end{array} $

$\begin{array}{l}\lambda =\frac{3}{2}\times {{10}^{4}}\end{array} $

$\begin{array}{l}{{H}_{\min }}\simeq \frac{\lambda }{4}=\frac{3}{8}\times {{10}^{4}}=0.375\times {{10}^{4}}m\end{array} $

H_min = 3750 m

H_min = 3750 m is practically impossible; for that, we can transmit our modulating signal onto a carrier wave of frequency 1MHz. What we did here is we raised our transmission frequency from 20kHz to 1mHz.

Now, let us find out what the H_min is needed for good transmission.

c = fλ

3 × 10⁸ = 1×10⁶ (λ)

If we increase the transmitting frequency, wavelengths

$\begin{array}{l}\frac{3\times {{10}^{8-6}}}{1}=\lambda\end{array} $

will decreases so, H_min also decreases.

3 × 10² = λ

$\begin{array}{l}\Rightarrow f\uparrow and \; \lambda \downarrow \to H\min \downarrow\end{array} $

λ = 300 m

$\begin{array}{l}H_{min} = {}^{\lambda }/{}_{4}=\frac{300}{4}=75m\end{array} $

This is practically possible, so we need modulation to increase the transmission frequency to transmit a low-frequency signal.

Quality of Transmission: (Power of Transmission by Antenna)

Since, from the Q-factor, we know sharpness or quality is maximum when power is maximum.

Sharpness or quality α power

Power radiated by a linear antenna is

$\begin{array}{l}P\alpha \frac{1}{{{\lambda }^{2}}}\Rightarrow Power=\frac{\ell }{{{\lambda }^{2}}}\end{array} $

Where l = Length of the antenna

λ = Wavelength of the transmitting signal

$\begin{array}{l}\left.\begin{matrix} for\,small(\lambda ) \\ (or) \\ High\,frequency \end{matrix}\right\} \to \text{Transmission power is high to quality of transmission high}\end{array} $

$\begin{array}{l}\left.\begin{matrix} for\,high(\lambda ) \\ (or) \\ small\,frequency \end{matrix}\right\} \to \text{Transmission power is small to quality of transmission low}\end{array} $

Avoiding the Overlapping of Signals

Two different transmitting stations transmit signals of the same frequency. They will get mixed up or overlap one another. To avoid this, we need to modulate these signals by different carrier waves.

When we talk about amplitude modulation, it is a technique that is used to vary the amplitude of the high-frequency carrier wave in accordance with the amplitude of the modulating signal. But the frequency of the carrier wave remains constant. Now, let us see what carrier waves and modulating signals are.

Common Terms

Carrier Wave (High Frequency)

Carrier Wave

The amplitude and frequency of a carrier wave remain constant. Generally, it will be high frequency, and it will be a sine or cosine wave of electronic signal; it can be represented as

C(t) = A_c sin w_ct ……………. 1

Modulating Signal

Modulating Signal

The modulating signal is nothing but the input signal (electronic signal), which has to be transmitted. It is also a sine or cosine wave; it can be represented as

m(t) = A_m sin w_mt

Where

A_c and A_m = Amplitude of the carrier wave and the modulating signal

sin w_ct = Phase of the carrier wave

sin w_mt = Phase of the modulating signal

Expression for Amplitude Modulated Wave

We have carrier wave and modulating signals,

$\begin{array}{l}\left.\begin{matrix} m(t)={{A}_{m}}\,\sin \,{{\omega }_{m}}t\,and \\ \\ c(t)={{A}_{c}}\sin {{\omega }_{c}}t \end{matrix}\right\} \to 1\end{array} $

m(t) = Modulating signal

c(t) = Carrier wave

A_m and Ac are the amplitude of modulating signal and carrier wave, respectively, in amplitude modulation. We are superimposing modulating signal into a carrier wave and also varying the amplitude of the carrier wave in accordance with the amplitude of the modulating signal, and the amplitude-modulated wave C_m(t) will be

C_m(t) = (A_c + A_m sin ω_mt) sin ω_ct ……………….. 2

This is the general form of an amplitude-modulated wave.

C_m(t) is the amplitude-modulated wave

Where,

A = A_c + A_m sin ω_mt = Amplitude of the modulated wave

sin w_ct = Phase of modulated wave

$\begin{array}{l}{{C}_{m}}(t)={{A}_{c}}\left( 1+\frac{{{A}_{m}}}{{{A}_{c}}}\sin \,{{\omega }_{m}}t \right)\sin {{\omega }_{c}}t\end{array} $

$\begin{array}{l}={{A}_{c}}\sin {{\omega }_{c}}t+\frac{{{A}_{m}}}{{{A}_{c}}}{{A}_{c}}\sin {{\omega }_{m}}t\,\sin {{\omega }_{c}}t\end{array} $

Where,

$\begin{array}{l}\frac{{{A}_{m}}}{{{A}_{c}}}=\mu = \text{modulation index}\end{array} $

C_m (t) = A_c sin ω_ct + A_cμ sin ω_mt sinω_ct

We can rewrite the above equation as

$\begin{array}{l}\sin A\sin B=\frac{1}{2}\left[ \cos (A-B)-\cos (A+B) \right]\end{array} $

$\begin{array}{l}={{A}_{c}}\sin {{\omega }_{c}}t+{{A}_{c}}\mu \frac{1}{2}\left[ \cos ({{\omega }_{c}}-{{\omega }_{m}})-\cos \left( {{\omega }_{c}}+{{\omega }_{m}} \right) \right]\end{array} $

$\begin{array}{l}{{c}_{m}}(t)={{A}_{c}}\sin {{\omega }_{c}}t+\frac{{{A}_{c}}\mu }{2}\cos ({{\omega }_{c}}-{{\omega }_{m}})-\frac{{{A}_{c}}\mu }{2}\cos \left( {{\omega }_{c}}+{{\omega }_{m}} \right)……\,3\end{array} $

From equation 3, we can see amplitude modulated wave is the sum of three sine or cosine waves.

Frequencies of Amplitude Modulated Wave

There are three frequencies in amplitude modulated wave – f₁, f₂ and f₃– corresponding to ω_c, ω_c + ω_m and ω_c – ω_m, respectively.

ω₁ = ω_c → it is corresponding f₁ = f_c

ω₂ = ω_c + ω_m → it is corresponding f₂ = f_c + f_m

ω₃ = ω_c – ω_m → it is corresponding f₃ = f_c – f_m

Where f_c → Carrier wave frequency

f_c + f_m → Upper side band frequency

f_c – f_m → Lower side band frequency

f_m → Modulating signal frequency

In general, f_c > > f_m

Bandwidth: (BW) It is the difference between the highest and lowest frequencies of the signal.

BW = Upper sideband frequency – Lower sideband frequency (f_c – f_m)

$B W = f_{m a x} - f_{m i n}$

BW = f_c + f_m – f_c + f_m = 2 f_m

BW = 2f_m = Twice the frequency of the modulating signal

Modulation Index

It is the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

$\begin{array}{l}\mu =\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{\text{Amplitude of modulating signal}}{\text{Amplitude of carrier wave}}\end{array} $

Amplitude Modulated Waveform

The waveform representation of amplitude modulated wave is given below.

Amplitude Modulated Wave

1. Carrier wave

2. Modulating signal

3. Superposition of the carrier wave and modulating signal

4. Amplitude modulated wave

Summary:

Carrier wave, c(t) = A_c sin w_ct

Modulating single m(t) = A_m sin w_mt

Amplitude modulate wave (m(t) = (A_c + A_m sin ω_mt) sin ω_ct

$\begin{array}{l}\text{modulation index}(\mu )=\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{\text{Amplitude of modulating signal}}{\text{Amplitude of carrier wave}}\end{array} $

Frequencies of modulated wave → f_c, f_c + f_m, f_c – f_m

Bandwidth (w) = f_c + f_m – (f_c – f_m) = 2f_m

Advantages and Disadvantages of Amplitude Modulation

Advantages	Disadvantages
Amplitude modulation is easier to implement.	When it comes to power usage, it is not efficient.
Demodulation can be done using a few components and a circuit.	It requires a very high bandwidth that is equivalent to that of the highest audio frequency.
The receiver used for AM is very cheap.	Noise interference is highly noticeable.

Applications of Amplitude Modulation

While amplitude modulation use has decreased over the years, it is still present and has several applications in certain transmission areas. We will look at them below.

Broadcast Transmissions: AM is used in broadcasting transmission over the short, medium and long wavebands. Since AM is easy to demodulate, radio receivers for amplitude modulation are, therefore, easier and cheaper to manufacture.
Air-band Radio: AM is used in VHF transmissions for many airborne applications, such as ground-to-air radio communications or two-way radio links, for ground staff personnel.
Single Sideband: Amplitude modulation in this form is used for HF radio links or point-to-point HF links. AM uses a lower bandwidth and provides more effective use of the transmitted power.
Quadrature Amplitude Modulation: AM is used extensively in transmitting data in several ways, including short-range wireless links, such as Wi-Fi to cellular telecommunications and others.

These are some of the important applications of amplitude modulation.

Demodulation Methods

The most simple AM demodulator is made up of a diode that acts as an envelope detector. The product detector, which is another type of demodulator, can offer better-quality demodulation but with a complex additional circuit.

Solved Problems

Question 1:

A carrier wave of frequency f = 1mHz with a pack voltage of 20V is used to modulate a signal of frequency 1kHz with a pack voltage of 10v. Find out the following:

(i) μ

(ii) Frequencies of the modulated wave

(iii) Bandwidth

Solution:

(i)

$\begin{array}{l}\mu =\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{10v}{20v}=\frac{1}{2}=0.5\end{array} $

(ii) Frequencies of modulated wave

f → f_c, f_c + f_m and f_c – f_m

f_c = 1mHz, f_m = 1kHz

f_c + f_m = 1×10⁶ + 1×10³ = 1001 ×10³ = 1001 kHz

f_c – f_m = 1×10⁶ – 1×10³ = 999 × 10³ = 999 kHz

(iii) Bandwidth: (W)

(W) = Upper side band frequency – Lower side band frequency

= f_c + f_m – (fc – fm)

= 2f_m = 1001 kHz – 999 kHz = 2 kHz

Question 2:

y = 10 cos (1800 πt) + 20 cos 2000 πt + 10 cos 2200 πt. Find the modulation index (μ) of the given wave.

Solution:

As we know, the expression for amplitude modulated wave is

C_m(t) = (A_c + A_m cos ω_mt) cos ω_ct ……………… 1

So, we have to bring the given wave equation into the known form

y = 10 [cos(1800 πt) + cos (2200πt)] + 20 cos 2000 πt

We can rewrite the above equation as

$\begin{array}{l}\cos A+\cos B=2\cos \left( \frac{A+B}{2} \right)\cos \left( \frac{A-B}{2} \right)\end{array} $

cos(2000 πt) + cos (1800 πt) = 2 cos 2000 πt cos 200 πt

$\begin{array}{l}y=10\left[ 2\cos (2000\pi t)\cos (200\pi t) \right]+20\cos 2000\pi t\end{array} $

$\begin{array}{l}y=\cos 2000\pi t\left[ 20+20\cos (200\pi t) \right]……2\end{array} $

Compare equations 1 and 2.

A_c = 20

A_m = 20

Then, the modulation index (μ)

$\begin{array}{l}\mu =\frac{Am}{Ac}=\frac{20}{20}=1\end{array} $

We can also find the frequencies of the modulated wave and B and width

(ii) Frequencies off the modulated wave

We know frequencies are fc, fc + fm and fc – fm from the modulated wave expression.

$\begin{array}{l}y=\cos 2000\pi t[20+20\cos (200\pi t)]\,…………\,3\end{array} $

y = (A_c + A_m cos ω_mt) cos ω_ct ……………….. 4

Comparing equations 3 and 4, we get

cos ω_mt = cos (200 πt)

ω_m = 200 π

2 πf_m= 200 π

f_m = 100 Hz

Similarly,

cos ω_ct = cos 2000 πt

ω_c = 2000 π

2πf_c = 2000 π

f_c = 1000 Hz

f_c, f_c + f_m and f_c – f_m, respectively, 1000 Hz, 1100 Hz and 900 Hz.

(iii) Bandwidth (W)

W = f_c + f_m – (f_c – f_m) = 2f_m

W = 200 Hz

NCERT Questions on Amplitude Modulation

1. Why are carrier waves of higher frequency compared to modulating signals?

Answer:

(i) High-frequency carrier waves effectively reduce the size of the antenna, which increases transmission range.

(ii) They convert wideband signal into a narrowband signal which can easily be recovered at the receiving end.

2. Define modulation index.

Answer:

The modulation index is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave (μ).

$\begin{array}{l}\mu =\frac{{{A}_{m}}}{{{A}_{c}}}\end{array} $

3. What happens if μ > 1?

Answer:

As we know, the range of modulation index (μ) should be 0 < μ < 1 if μ > 1. It is said to be over-modulated, and distortion will take place in the modulated signal.

4. Why do we need modulation?

Answer:

To transmit the low-frequency signal to a longer distance.
To reduce the length of the antenna.
Power radiated by the antenna will be high for high frequency (small wavelength).
To avoid the overlapping of modulating signals.

5. Why is the amplitude of the modulating signal kept less than the amplitude of the carrier wave?

Answer:

To avoid overmodulation. Typically, in overmodulation, the negative half cycle of the modulating signal will be distorted.

Frequently Asked Questions on Amplitude Modulation

Explain Amplitude Modulation.

The amplitude of the wave is altered in proportion to the message signal, such as an audio signal, in amplitude modulation. Amplitude modulation is a modulation technique extensively used in electronic communication to send messages through radio waves.

What is the difference between amplitude modulation and frequency modulation?

The distinction is in the modulation or alteration of the carrier wave. To add sound information into amplitude modulation radio, the broadcast’s amplitude, or overall strength, is changed. The carrier signal’s frequency (the number of times per second that the current changes direction) is altered with frequency modulation.

Which one is preferable: amplitude modulation or frequency modulation?

Because of the increased bandwidth, FM has better sound quality and is the preferable one.

Amplitude Modulation

Table of Contents

What Is Amplitude Modulation?

Types of Amplitude Modulation

Designations by ITU

Communication Systems and Modulation

What Is Modulation?

Amplitude Phase

Why Do We Need Modulation?

High Range Transmission: (Effective Length of Antenna)

Quality of Transmission: (Power of Transmission by Antenna)

Avoiding the Overlapping of Signals

Common Terms

Expression for Amplitude Modulated Wave

Frequencies of Amplitude Modulated Wave

Amplitude Modulated Waveform

Advantages and Disadvantages of Amplitude Modulation

Applications of Amplitude Modulation

Demodulation Methods

Solved Problems

NCERT Questions on Amplitude Modulation

Frequently Asked Questions on Amplitude Modulation

Explain Amplitude Modulation.

What is the difference between amplitude modulation and frequency modulation?

Which one is preferable: amplitude modulation or frequency modulation?

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