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

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.

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

Table of Content

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 is varied 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 respectively.

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) has also designated different types of amplitude modulation in 1982. These 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 the message (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 sine (or) cosine wave. Every wave will have an amplitude and phase.

Where m(t) – modulating signal (input signal) (or) Baseband signal.

Am ? 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 carried out by carrier waves to the destination.

Amplitude Modulation Graph

Message (information)

(or)

Modulating signal

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 also in other words modulation is the phenomenon of “Superimposition of 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

$\begin{array}{l}\frac{\lambda }{4}\end{array} $

times of the modulating signal.

H_min =

$\begin{array}{l}\frac{\lambda }{4}\end{array} $

λ – wavelength of the modulating signal (or) transmitting signal H>

$\begin{array}{l}\frac{\lambda }{4}\end{array} $

(example) if i need to transmit signal of 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? We raised our transmission frequency from 20kHz to 1mHz.

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

c = fλ

3 × 10⁸ = 1×10⁶ (λ)

If we increase transmitting frequency, wavelengths

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

will decreases so, Hmin also decreases.

3 × 10² = λ

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

λ = 300 m

H_min =

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

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

Quality of Transmission: (Power of Transmission by Antenna)

Since, from 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

$\begin{array}{l}\ell \to\end{array} $

length of the antenna

$\begin{array}{l}\lambda \to\end{array} $

wavelength of the transmitting signal

$\begin{array}{l}\left.\begin{matrix} for\,small(\lambda ) \\ (or) \\ High\,frequency \end{matrix}\right\} \to 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 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 on other to avoid this we need to modulate these signals by different carriers 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 are carrier waves and modulating signals.

Common Terms

Carrier Wave (High frequency)

Carrier Wave

Amplitude and frequency of a carrier wave remain constant. Generally, it will be high frequency and it will be sine (or) cosine wave of electronic signal it can be represented as

C(t) = A_c sin w_ct ……………. 1

Modulating Signal

Modulating Signal

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 signal,

$\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.

Am and Ac ? are Amplitude of modulating signal and carrier wave respectively in Amplitude modulation. We are superimposing modulating signal into 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 amplitude modulated wave C_m(t) ? is the amplitude-modulated wave.

Where,

A = A_c + A_m sin ω_mt → is the 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 =\bmod ulation\,index\end{array} $

C_m (t) = A_c sin ω_ct + A_cμ sin ω_mtsinω_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 modulating signal

Modulation Index

Is the ratio of Amplitude of modulating signal to the amplitude of the carrier wave.

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

Amplitude Modulated Waveform

Waveform representation of Amplitude modulated wave:

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}\bmod ulatin\,index(\mu )=\frac{{{A}_{m}}}{{{A}_{c}}}=\frac{Amplitude\,of\bmod ulcting\sin gal}{Amplitude\,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 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 the 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 is able to offer better-quality demodulation but with a complex additional circuit.

Solved Problems

Ex 1

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

(i) μ?

(ii) Frequencies of 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) Band width: (W)

(W) = upper side band frequency – lower side band frequency

= f_c + f_m – (fc – fm)

= 2f_m = 1001 kHz – 999 kHz = 2 kHz

Ex: 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.

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

So, we have to bring the given wave equation into 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 equation 1 and 2

A_c = 20

A_m = 20

Then 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, we can get it.

$\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 the equation 3 and 4

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 carrier waves are of higher frequency compared to modulating signal?

Answer:

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

(ii) Converts 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 0 < μ < 1 if μ > 1 it is said to be over modulated and distortion will take place in the modulated signal.

4. Why 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).
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.