Amplitude Modulation – Definition, Expression, Types And Solved Examples with solution


What is Amplitude modulation

Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio carrier wave. In Amplitude modulation, the amplitude of carrier signal is changes in accordance with instantaneous amplitude of the massage signal. It means the information is contains the amplitude of modulating signal. Amplitude modulation is commonly uses in electronics communication system and it is also used in medium wave amplitude modulation radio broadcasting.

Amplitude modulation is the one of the oldest modulation method to transmit the information. This technique was introduced in 20th century by Landell de Moura and Reginald when performing experiments using radio telephone in 1900s.

Amplitude Modulation Single Sideband Modulation and Double Sideband Modulation of AM

Top figure is the modulating wave, which is baseband or massage signal. Next figure is the carrier wave which is very high frequency. The last figure shows the modulated wave which contains the information. Here you can see the positive and negative peaks of the carrier wave, connected with imaginary line, and when the receiver receives this radio signal this line recreating the same shape of the modulating signal. These imaginary lines on the carrier wave called as Envelope. This envelope is exactly same the massage signal.

Amplitude Modulation – Characteristics

Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio carrier wave.

  • In Amplitude modulation, the amplitude of a carrier signal changed accordance with the massage signal. It utilizes low carrier frequency for long distance communication. Sometimes, AM signals are bouncing off the ionosphere. AM signal is traveled long distance.
  • AM was developed in 1870. The first audio transmission introduce and AM has more effected by noise
  • Sound quality in AM  system is poor, however, can transmit long distances
  • AM frequency spectrum from 535 kHz – 1705 kHz. Amplitude modulation index ranges from 0 to 1
  • It has two side bands. AM circuit is easy to design. AM has less bandwidth like 10 kHz.
  • For MF (medium frequency) & HF( high frequency) communication we use AM

Common Terms Amplitude modulation

Carrier Wave (High frequency)

Carrier waves are those waves in which the amplitude, frequency and phase are constant. It is high frequency and sine or cosine wave of electronics signal. The mathematical expressions of carrier wave are given below.

C(t) = Ac sin wct ……………. (1)

Modulating signal

It is a low signal frequency and massage signal. It is also known as massage signal. This signal goes to modulation processes and then it is prepared for transmission.

Modulated Signal

Those signals are modulating signal which has to be transmitted through channel. It is may be sine or cosine wave

m(t) = Am sin wmt

Ac and Am is Amplitude of the carrier wave and the modulating signal.
Sin wct is phase of carrier wave.
Sin wmt is phase of modulating signal.

Expression for Amplitude Modulated Wave

We have carrier wave and modulating signal,

m(t)= Am ​sinωm​t and
c(t)= Ac ​sinωc​t​
c(t) is carrier wave.
m(t) is modulating signal
Am is amplitude of modulating signal.
Ac is the amplitude of carrier signal.
We are varying the amplitude of carrier signal is change in accordance with the amplitude of the massage signal. It will be
Cm(t) = (Ac + Am sin ωmt) sin ωct ……………….. (2)
Equation (2) shows the general form of amplitude modulated wave.
Cm(t)  is the amplitude-modulated wave.

A = Ac + Am sin ωmt is the amplitude of the modulated wave
Sin wct is phase of modulated wave.
Cm(t) = Ac(1+ Am / Ac sin ωmt)sinωc​t
=Ac sin ωmt + ​( AmAc/Ac​)sin ωmt sin ωct

Am​​/Ac = μ =modulation index
sinA sinB=1/2​[cos(A−B) − cos(A+B)]
Cm(t) = Ac sin ωc​t + Ac ​μ 1​/2[cos(ωc​−ωm​) − cos(ωc ​+ωm​)]
Cm(t) = Ac ​sin ωc ​t + Ac ​μ​/2 cos(ωc ​− ωm ​) − Ac ​μ/2 ​cos(ωc ​+ ωm ​)………….(3)
Equation (3) shows Amplitude modulated wave. It three component carrier signal, upper side signal and lower side signal.

Frequencies of Amplitude Modulation

There are three frequencies component in amplitude modulated wave carrier frequency, upper frequency and lower frequency corresponding to ωc, ωc + ωm and ωc – ωm respectively.

ωc, it is corresponding fc
ωc + ωm, it is corresponding fc + fm
ωc – ωm, it is corresponding fc – fm

Where fc is carrier wave frequency
fc + fm  Upper side band frequency (USB)
fc – fm Lower side band frequency(LSB)
fm  is modulating signal frequency
Generally, fc > >> fm

Bandwidth (BW)

Band with is the differences of upper side band frequency and lower side band frequency.

BW = upper side band frequency – lower side band frequency (fc – fm)
BW = fc + fm – (fc – fm )
BW = fc + fm – fc + fm ) = 2 fm
BW = 2fm = twice of the modulating frequency.

The band width of amplitude modulation is the twice of the modulating frequency.

Modulation Index

μ=​ Am​​/Ac

Modulation index is the ratio of the modulating signal to the carrier signal.
We can calculate modulation index value by using above formula.
Modulation index has one more formula and it is derive by the equation (3). When the maximum and minimum amplitude is given,
Let Amax and Amin are maximum and minimum amplitudes of the modulated wave.
When cos(2πfmt) is  1 we will get the maximum amplitude of modulation.
⇒ Amax = Ac + Am…………..(4)
When cos(2πfmt) is  -1 we will get the minimum amplitude of modulation.
⇒ Amin = Ac – A…………..(5)
Addition of equation of (4)  and (5) we get,
Amax + Amin = Ac + Am + Ac – A= 2 Ac
Ac = (Amax + Amin )/2 …………..(6)
Subtraction of equation of (4)  and (5) we get,
Amax – Amin = Ac + Am – (Ac – Am) =2 Am
Am = (Amax – Amin )/2…………..(7)
Ratio of the Equation (7) and (6) will be.
μ =​ Am​​/Ac = {(Amax – Amin )/2}/{(Amax + Amin )/2}
μ = (Amax – Amin )/(Amax + Amin ) …………..(8)

Critical Modulation

When modulation Index (m) =1. Note, during critical modulation Vmin =0
μ = Am​​/Ac = (Amax – Amin )/(Amax + Amin )
= (Amax / Amax)
= 1
When modulation index is 1, than the Amax = Amax

Amplitude Modulation Single Sideband Modulation and Double Sideband Modulation Critical Modulation



Types of Amplitude Modulations.

  • Single Sideband Modulation (SSB-SC).
  • Double sideband-suppressed carrier modulation (DSB-SC).
  • Vestigial Sideband Modulation (VSB).

Sideband of Amplitude Modulation

Amplitude modulation contains two side bands upper side band and lower side band. Side band is the frequency ranges, which are lower side band and upper side band. Both side bands contain same information.

Single Sideband Modulation (SSB-SC)

The processes in which the single side and carrier are suppressed and only one side band is transmitted is called single sideband suppress carrier system. It simply labeled by SSB-SC. As we know the two sidebands carry same information, so we suppress one side band and other side band is transmitted. Single side band suppress carrier save power consumption.  The single side band suppress carrier shows the following figure.

Amplitude Modulation Single Sideband Modulation and Double Sideband single side band suppress 

Double sideband-suppressed carrier modulation (DSB-SC)

In double side band suppressed carrier modulation the upper side band and lower side band is transmitted but carrier is not transmitted. In double side band transmission the power is distributed to the two sides. It simply labeled by DSB-SC.

Double sideband-suppressed-carrier(DSB-SC)

Advantage of side band transmission

  • It required less bandwidth than AM and DSB signal
  • More number of signal is allowed for transmission
  • Less power consumption
  • Less noise is present
  • Fading of signal is less occur

Disadvantage of side band transmission

  • It is complex process in generation and detection of singles side band signal.
  • Quality of signal is affected during transmission

Vestigial Sideband

The signal Along with the upper sideband, a part of the lower sideband is also being transmitted is known as vestigial sideband. A guard band VSB is very small width to avoid the interference on either side. It is mostly used in television transmissions.

Advantages Vestigial Sideband

  • It has highly efficient.
  • Reduction in bandwidth size.
  • Design of filter is easy and not need high accuracy.
  • Low-frequency components transmission is possible, without any difficulties.
  • VSB has good phase characteristics.

Disadvantages Vestigial Sideband

  • Bandwidth in VSB is greater than when compared to SSB.
  • VSB Demodulation is complex.

Application of amplitude modulation

Amplitude modulation is used in various type of application. Even through amplitude modulation is not widely used. Here some applications of amplitude modulation.

Broadcast Transmissions – Amplitude Modulation

Amplitude modulation is widely used in broadcast transmission on the long, medium and short wave band. In amplitude modulation, the demodulation of wave is easy it means the radio receiver is capable to easily demodulation of AM wave.

Air band radio

In VHF transmission, many airborne application uses AM. AM is use for ground to air radio communication.

Single sideband

In AM, the single side band is still used for high frequency links. In single sideband has low bandwidth and less power is consume for transmission of signal. This form of modulation is still used for many point to point high frequency links.

Quadrature amplitude modulation

Quadrature amplitude modulation is mostly used for transmission of data in short range wireless such as Wi-Fi to cellular communication. It is form by having two carrier 90° out of phase.

Amplitude demodulation

Amplitude demodulation is one of the simplest ways of modulating a radio signal or carrier. The simplest way to archive a demodulation of AM signal is uses a single diode rectifier circuit.
The other way of method for demodulation signal use synchronous techniques and provide low levels of distortion and improved reception.

Advantages & disadvantages of amplitude modulation

Advantages Disadvantages
Implementation is simple. It has high levels of noise because most noise is amplitude based.
The demodulation circuit is simple. It is less efficient in terms of its power consumption.
AM receiver circuit is cheap as no specialized components are needed. It is less efficient in terms of its use of bandwidth, requiring a bandwidth equal to twice maximum frequency.

AM overview

  • AM is simplest method for modulation but it is not effective for use.
  • AM is subjected higher level of noise the other mode.
  • AM will be difficult to change quickly.
  • The theory of behind AM is straightforward, and can be handled using trigonometric calculations to manipulation.
  • Two signals are multiplied together and how they create the carrier and two sidebands.

What is Over Modulation and Sidebands of AM?

When m>1, this is over modulation.
(Vm / Vc) > 1
Therefore Vm > Vc, it means modulating signal is grater the carrier signal.


Power Calculations of AM Wave

Consider the equation (3) which is given below,
Cm(t) = Ac ​sin ωc ​t + (Ac ​μ​/2) cos(ωc ​− ωm ​) − (Ac ​μ/2) ​cos(ωc ​+ ωm ​)………….(3)
The total power of amplitude modulation is the sum of carrier upper sideband and lower sidebands frequency component.
Pt = Pc + PUSB +PLSB
The standard formula for power of signal is,
P= V2rms /R = ( Vmax / 2)2 /2
Vrms is the rms value of signal.
Vm is the peak value of signal.

Carrier power

Pc = ( Ac/√2)2 /R= Ac2/2R

Upper sideband power

PUSB = (Ac μ/2√2)2/R= (Ac2μ2 )/8R
Similarly, Lower sideband power is equal to the upper side band power.
PLSB = (Ac μ/2√2)2/R= (Ac2μ2 )/8R

The total power of Amplitude modulation is

Pt = Pc + PUSB +PLSB
Pt = Ac2/2R + (Ac2μ2 )/8R + (Ac2μ2 )/8R
Pt = (Ac2/2R)(1+ μ2/4 + μ2/4)
Pt = Pc (1+ μ 2/ 2)

When the modulation index (μ) is 1, then the power of AM wave is equal to 1.5 times the carrier power.

Current relation in amplitude modulation wave

We know, the formula of power in AM,
Pt = Pc (1+ μ 2/ 2)
Pt / Pc = 1+ μ 2/ 2
It2/ Ic2= 1+ μ 2/ 2
It2= Ic2 (1+ μ 2/ 2)

Some question based on amplitude modulation

Que (1). A 400 watt carrier is modulated to a depth of 75 percent. Calculate the total power in the modulated wave.

Sol– we know,

Pt = Pc (1+ μ 2/ 2)
= 400(1+ 0.75 2/ 2)

Que (2). A broadcast radio transmitter radiates 10 kw. When the modulated percentage is 60. How much of this carrier power?

Sol– we know,

Pc = Pt /(1+ μ 2/ 2)
=10/(1+ 0.62/2)
=8.47 kw

Que (3). A DSB-SC transmitter radiates 1kw when the modulating percentage is 60. How much of carrier power is required if we want to transmit the same massage by AM transmission.

Sol– Given, PDSBSC=1kw
μ =0.6
Carrier power, Pc = PDSBSC (2/μ2)

We required 5.56 kw to transmit the carrier component.

Some Questions:-

  1. The antenna current of an AM transmitter is 8 amperes (8 A) when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation. Determine the antenna current when the percent of modulation changes to 0.8.
  2. A certain transmitter radiates 9 kW with the carrier unmodulated, and 10.125 kW when the carrier is sinusoidal modulated. Calculate the modulation index, if another sine wave is simultaneously transmitted with modulation index 0.4, determine the total radiated power.
  3. The antenna current of an AM broadcast transmitter, modulated to a depth of 40 percent by an audio sine wave, is 11 A. It increases to 12 A as a result of simultaneous modulation by another audio sine wave. What is the modulation index due to this second wave?
  4. A 400 W carrier is amplitude modulated to a depth of 100%. Calculate the total power in case of AM and DSBSC techniques. How much power saving (in W) is achieved for DSBSC? If the depth of modulation is changed to 75%, then how much power (in W) is required for transmitting the DSBSC wave? Compare the powers required for DSBSC in both the cases and comment on the reason for change in the power levels.
  5. A 1000-kHz carrier is simultaneously modulated with 300-Hz, 800-Hz and 2-kHz audio sine waves. What will be the frequencies present in the output?
  6. A broadcast AM transmitter radiates 50 kW of carrier power. What will be the radiated power at 85 percent modulation?
  7. When the modulation percentage is 75, an AM transmitter produces 10 kW. How much of this is carrier power? What would be the percentage power saving if the carrier and one of the sidebands were sup- pressed before transmission took place?
  8. A 360-W carrier is simultaneously modulated by two audio waves with modulation percentages of 55 and 65, respectively. What is the total sideband power radiated?
  9. A transistor class C amplifier has maximum permissible collector dissipation of 20 W and a collector efficiency of 75 percent. It is to be collector-modulated to a depth of 90 percent, (a) Calculate (i) the maximum unmodulated carrier power and (ii) the sideband power generated. (b) If the maximum depth of modulation is now restricted to 70 percent, calculate the new maximum sideband power generated.
  10. When a broadcast AM transmitter is 50 percent modulated, its antenna current is 12 A. What will the current be when the modulation depth is increased to 0.9?
  11. The output current of a 60 percent modulated AM generator is 1.5 A. To what value will this current rise if the generator is modulated additionally by another audio wave, whose modulation index is 0.7? What will be the percentage power saving if the carrier and one of the sidebands are now suppressed?

Multiple-Choice Questions

Each of the following multiple-choice questions consists of an incomplete statement followed by four choices (a, b, c and d). Circle the letter preceding the line and correctly complete each sentence.

a. Analog communication involves

  1. analog message, analog carrier and analog modulated signal
  2. analog message, carrier can be analog or digital, but the modulated signal is analog
  3. analog message, analog carrier and no restriction on the nature of modulated signal
  4. modulated signal which is analog and no restriction on message and carrier

b. Amplitude modulation is defined as the system of modulation in which

  1. amplitude of carrier is varied in accordance with the modulated signal
  2. amplitude of carrier is varied in accordance with the message signal
  3. amplitude of message is varied in accordance with the carrier signal
  4. amplitude of message is varied in accordance with the modulated signal

c. The peak amplitude of the basic amplitude modulated wave is given by

  1. Vc + Vm
  2. Vm
  3. Vc
  4. Vc + Vm sin ωmt,

d. The instantaneous voltage of the AM wave is

  1. V +V
  2. V sin ωmt
  3. Vc sin ωmt + Vm sin ωmt
  4. Vc (1 + m sin ωmt) sin ωmt

e. The modulation index of AM is given by

  1. Vc/Vm
  2. Vc/Vm
  3. (Vc + Vm)/2
  4. (Vc – Vm)/2

f. The AM wave will have

  1. carrier, LSB and USB
  2. LSB and USB
  3. LSB or USB
  4. one sideband and vestige of other

g. The bandwidth of AM wave is given by

  1. fc + fm
  2. fc – fm
  3. 2fm
  4. 2Fc

h. If Vc , Vl and Vu, are the peak amplitudes of carrier, LSB and USB, then the relation among them in AM is

  1. Vc > Vu >Vl
  2. Vc > Vl >Vu
  3. Vc = Vl = Vu
  4. Vc > Vu  =-Vl

i. fc, >> fm the frequency of AM wave can be approximated by

  1. fc
  2. fm
  3. fc – fm)/2
  4. (fc – fm)/2

j. The expression for total power in AM wave is

  1. Pt = Pc (1+ μ 2/ 8)
  2. Pt = Pc (1+ μ 2/ 4)
  3. Pt = Pc (1+ μ 2/ 2)
  4. Pt = Pc (1+ μ / 2)

k. The maximum power of AM wave under distortionless condition is

  1. 5Pc
  2. Pc
  3. 2Pc /3
  4. Pc /3

l. The instantaneous voltage of DSBSC can be related to that of AM by

  1. VDSBSC = Vam– Vc sin ωct
  2. VDSBSC = Vam
  3. VDSBSC = Vc sin ωct
  4. VDSBSC = Vc sin ωct Vm sin ωmt

m. The peak amplitude of the DSBSC wave is given by

  1. Vc
  2. Vm
  3. Vc sin ωct
  4. Vm sin ωmt

n. The instantaneous voltage of the DSBSC wave is

  1. Vm+ Vm
  2. Vc sin ωct
  3. Vc sin ωc t + Vm sin ωm t
  4. mVc sin ωm t sin ωm t
Also read:- Need of modulation, Frequency modulation

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