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ModulationPosted on November 24, 2011 by john in Tutorials with 5 Comments

When audio signals are transmitted over thousands of kilometres through radiotransmission, the audio frequencies that lie within the frequency range of 15 Hertz to 20KiloHertz has very small signal power and thus cannot be transmitted via antenna forcommunication purposes. The radiation of electrical energy is only possible at frequenciesabove 20 KiloHertz. The main advantage of high frequency signals is that they can betransmitted over very long distances by dissipating very small power. Thus, the audio signalsmust be sent along with the high frequency signals for communication. This can be done bysuperimposing electrical audio signals on a high frequency wave called the carrier wave. Thecarrier wave is generated from radio-frequency oscillators and is undamped in nature. Thus,when the audio-frequency signal is superimposed on a carrier wave, the resulting wave getsall the characteristics of the audio signal. The method of superimposing an audio signal overthe carrier wave is called modulation.

After modulation is done, the resulting wave can be given to the antenna and the signal canbe transmitted over a long distance.

Principle of Transmission and Reception

The speech or music that is to be broadcasted consists of a series of compressions andrarefractions. A microphone acts as a transducer to convert these parameters into itscorresponding varying current measures. With the difference in the measure of sound, thecorresponding change in the frequency of electrical current is also produced, and they lie inthe audio-frequency range and therefore, it is known as an audio-frequency signal. Since thesignal strength of this low frequency signal is less, it has to be given to an audio-frequencyamplifier to strengthen the signal to a desired level. These low frequency signals cannot besent over long distances by radiating it out directly from the aerial. Thus, the audio frequencysignal has to be modulated with a radio-frequency carrier wave. The carrier wave can beproduced using any oscillator. The radio frequency waves have constant amplitude and travelthrough space with the velocity of light. This is why you can see and hear live broadcasts withvery little delay.

The resulting modulated wave is radiated out of the transmitter antenna and travels throughspace till it reaches the receiver antenna. The receiving aerial consists of a receiver thatseparates both the carrier signal and audio-frequency signal. The process of the receiver bywhich he audio frequency is separated from the carrier signal is called demodulation. Thedemodulated audio signal is sent to the loudspeakers for the user to hear. If there was nodemodulation, the high frequency currents would have reached the loudspeaker and wouldhave caused signal errors. Radio frequency current also cannot be heard by humans. Thisshows why modulation and demodulation is important in a communication system.

What is Modulation?

The best way to define modulation is:

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The process of impressing low-frequency information to be transmitted on to a high-frequency wave, called the carrier wave, by changing the characteristics of either itsamplitude, frequency, or phase angle is called modulation.

Another definition for modulation is:

The process of altering the characteristics of the amplitude, frequency, or phase angle of thehigh-frequency signal in accordance with the instantaneous value of the modulating wave iscalled modulation.

Functions of the Carrier Wave

The main function of the carrier wave is to carry the audio or video signal from thetransmitter to the receiver. The wave that is resulted due to superimposition of audio signaland carrier wave is called the modulated wave.

Need for Modulation

The reason why low frequency signals cannot be transmitted over long distances throughspace is listed below:

1. Short Operating Range – When a wave has a large frequency, the energy associated withit will also be large. Thus low frequency signals have less power that does not enablethem to travel over long distances.

2. Poor Radiation Efficiency – The radiation efficiency becomes very poor for low frequencysignals.

3. Mutual Interference – If all audio frequencies are send continuously from differentsources, they would all get mixed up and cause erroneous interference air. If modulationis done, each signal will occupy different frequency levels and can be transmittedsimultaneously without any error.

4. Huge Antenna Requirement – For a effective signal transmission, the sending andreceiving antenna should be at least 1/4 of the wave length of the signal. Thus, for smallfrequencies, the antenna will have kilometres of length. But if the signal has the range ofMegaHertz frequency, then the antenna size would be less. The carrier wave cannot beused alone for transmission purposes. Since its amplitude, frequency, and phase angleare constant with respect to some preference.

Types of Modulation

The sinusoidal carrier wave can be given by the equation

v = V Sin(w t + θ) = V Sin(2f t + θ)

V   – Maximum Value

f Frequency

θ  – Phase Relation

Since the three variables are the amplitude, frequency, and phase angle, the modulation canbe done by varying any one of them. Thus there are three modulation types namely:

Amplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)

Click on the links given above to know more.

In India, radio broadcasting is done through amplitude modulation. Television broadcasting isdone with amplitude modulation for video signals and frequency modulation for audiosignals.

Amplitude Modulation (AM)

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 DefinitionThe method of varying amplitude of a high frequency carrier wave in accordance with theinformation to be transmitted, keeping the frequency and phase of the carrier waveunchanged is called Amplitude Modulation. The information is considered as the modulatingsignal and it is superimposed on the carrier wave by applying both of them to the modulator.The detailed diagram showing the amplitude modulation process is given below.

Amplitude Modulation

As shown above, the carrier wave has positive and negative half cycles. Both these cycles arevaried according to the information to be sent. The carrier then consists of sine waves whoseamplitudes follow the amplitude variations of the modulating wave. The carrier is kept in anenvelope formed by the modulating wave. From the figure, you can also see that theamplitude variation of the high frequency carrier is at the signal frequency and the frequencyof the carrier wave is the same as the frequency of the resulting wave.

Analysis of Amplitude Modulation Carrier WaveLet v = V Sin w t

v = V Sin w t

v – Instantaneous value of the carrier

V – Peak value of the carrier

W – Angular velocity of the carrier

v – Instantaneous value of the modulating signal

V – Maximum value of the modulating signal

w – Angular velocity  of the modulating signal

f – Modulating signal frequency

It must be noted that the phase angle remains constant in this process. Thus it can beignored. The amplitude of the carrier wave varies at  f .

The amplitude modulated wave is given by the equation

A = V + v = V + V Sin w t = V [1+ (V /V Sin w t)]

= V (1 + mSin w t)

m – Modulation Index. The ratio of V /V .

Instantaneous value of amplitude modulated wave is given by the equation

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v = A Sin w t = Vc (1 + m Sin w t) Sin wct

= V Sin w t + mVc (Sin w t Sin w t)

v = V Sin wct + [mV /2 Cos (wc-wm)t – mVc/2 Cos (wc + wm)t]

The above equation represents the sum of three sine waves. One with amplitude of Vc and afrequency of w /2 , the second one with an amplitude of mV /2 and frequency of (w – w )/2and the third one with an amplitude of mV /2 and a frequency of (w + w )/2 .

In practice the angular velocity of the carrier is known to be greater than the angular velocityof the modulating signal (w >> w ). Thus, the second and third cosine equations are moreclose to the carrier frequency. The equation is represented graphically as shown below.

Amplitude Modulation Frequency Spectrum

Frequency Spectrum of AM WaveLower side frequency – (w – w )/2

Upper side frequency – (w +w )/2

The frequency components present in the AM wave are represented by vertical linesapproximately located along the frequency axis. The height of each vertical line is drawn inproportion to its amplitude. Since the angular velocity of the carrier is greater than theangular velocity of the modulating signal, the amplitude of side band frequencies can neverexceed half of the carrier amplitude.

Thus there will not be any change in the original frequency, but the side band frequencies (w– w )/2  and (w +w )/2  will be changed. The former is called the upper side band (USB)frequency and the later is known as lower side band (LSB) frequency.

Since the signal frequency w /2  is present in the side bands, it is clear that the carriervoltage component does not transmit any information.

Two side banded frequencies will be produced when a carrier is amplitude modulated by asingle frequency. That is, an AM wave has a band width from (w – w )/2  to (w +w )/2 , thatis, 2w /2  or twice the signal frequency is produced. When a modulating signal has morethan one frequency, two side band frequencies are produced by every frequency. Similarlyfor two frequencies of the modulating signal 2 LSB’s and 2 USB’s frequencies will be

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The side bands of frequencies present above the carrier frequency will be same as the onespresent below. The side band frequencies present above the carrier frequency is known to bethe upper side band and all those below the carrier frequency belong to the lower side band.The USB frequencies represent the some of the individual modulating frequencies and theLSB frequencies represent the difference between the modulating frequency and the carrierfrequency.  The total bandwidth is represented in terms of the higher modulating frequencyand is equal to twice this frequency.

Modulation Index (m)The ratio between the amplitude change of carrier wave to the amplitude of the normalcarrier wave is called modulation index. It is represented by the letter ‘m’.

It can also be defined as the range in which the amplitude of the carrier wave is varied by themodulating signal.

m = V /V

Percentage modulation, %m = m*100 = V /V * 100

The percentage modulation lies between 0 and 80%.

Another way of expressing the modulation index is in terms of the maximum and minimumvalues of the amplitude of the modulated carrier wave. This is shown in the figure below.

Amplitude Modulated Carrier Wave

From the figure we know that

2 V = V – V

V = (V – V )/2

V = V – V

= V – (V -V )/2

=(V + V )/2

Substituting the values of Vm and Vc in the equation m = Vm/Vc , we get

M = V – V /V + V

As told earlier, the value of ‘m’ lies between 0 and 0.8. The value of m determines the strengthand the quality of the transmitted signal. In an AM wave, the signal is contained in thevariations of the carrier amplitude. The audio signal transmitted will be weak if the carrierwave is only modulated to a very small degree. But if the value of m exceeds unity, the

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transmitter output produces erroneous distortion.

Power Relations in an AM waveA modulated wave has more power than had by the carrier wave before modulating. Thetotal power components in amplitude modulation can be written as:

P = P + P + P

Considering additional resistance like antenna resistance R.

P = [(V /√2)/R] = V /2R

Each side band has a value of m/2 V and r.m.s value of mV /2√2. Hence power in LSB andUSB can be written as

P = P = (mV /2√2) /R = m /4*V C/2R = m /4 P

P = V /2R + [m /4*V C/2R] + [m /4*V C/2R] = V /2R (1 + m /2) = P (1 + m /2)

In some applications, the carrier is simultaneously modulated by several sinusoidalmodulating signals. In such a case, the total modulation index is given as

Mt = √(m1 + m2 + m3 + m4 + …..)

If Ic and It are the r.m.s values of unmodulated current and total modulated current and R isthe resistance through which these current flow, then

P /P = (It.R/Ic.R) = (It/Ic)

P /P = (1 + m /2)

It/Ic = 1 + m /2

Limitations of Amplitude Modulation1. Low Efficiency- Since the useful power that lies in the small bands is quite small, so the

efficiency of AM system is low.2. Limited Operating Range – The range of operation is small due to low efficiency. Thus,

transmission of signals is difficult.3. Noise in Reception – As the radio receiver finds it difficult to distinguish between the

amplitude variations that represent noise and those with the signals, heavy noise isprone to occur in its reception.

4. Poor Audio Quality – To obtain high fidelity reception, all audio frequencies till 15KiloHertz must be reproduced and this necessitates the bandwidth of 10 KiloHertz tominimise the interference from the adjacent broadcasting stations. Therefore in AMbroadcasting stations audio quality is known to be poor.

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5 thoughts on “Modulation”

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Louis J. Bruno May 24, 2013 at 12:30 pm

What happened to the FM and PM explanation?

Reply

Safi Khan December 1, 2011 at 3:01 am

it is good to learn but it is good and easy to learn with circuits today.

Reply

Peter November 25, 2011 at 1:48 am

I have gone through this peace and am happy.

Reply

Joseph Vella-Zarb November 24, 2011 at 9:52 pm

Re: Need for Modulation.<>

Allow me to clarify the above note because it is not quite correct.

Interference will occur if the same CARRIER frequency is transmitted, at the same time, fromdifferent sources.A carrier frequency on its own has no information and, if you tune in to this frequency on thereceiver, all you will hear is silence.If, on the other hand, the carrier frequency is modulated with information (for example, speechor music) and your receiver is tuned to the carrier frequency, this signal is demodulated in thereceiver and you can hear the information. Demodulation, as the name implies, is the extractionof what was modulated in the transmitter.

Reply

jawid akhtar November 24, 2011 at 6:27 pm

I went through the topic Modulation. It was defined very simply and precisely. I appreciate andhope the same thing will keep on going.

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