Module 1

Analog Communication

Communication is defined as a method of exchanging data and information.

When the communication is accomplished by using analog signals, then it is
referred to as Analog Communication. In more simple words, analog
communication is the exchange of information in the form of analog signals
that represent information in the form of continuous time functions. Sound
waves or voice signals are the common examples of analog signals.

Analog communication is most widely used in AM or FM radio broadcasting,

TV broadcasting, telephonic voice communication, and various measuring
and instrumentation applications.

Analog communication is known for its simpler design and high fidelity.
However, it is very sensitive to noise and electromagnetic interference. It also
has limited communication range.

Every communication has three essential elements: transmitter, channel and

receiver Here the transmitter is placed at one place and receiver is placed
another place and the channel is the physical medium that connect them.
The purpose of transmitter is to convert into suitable form of signal that can
transmitted through the channel.
If the o/p of the information source is a non-electric signal, then a transducer
converts it into electric form before it passes through the channel. Moreover,
noise is introduced in channel so receiver reconstruct it and send the
information to user for.
There are two basic type of communication namely point to point and
broadcast. The former take place over a link between a single transmitter and
receiver, while later one have large number of receiver corresponding to a
single transmitter.
Radio and TV comes under broadcast
For a signal to be transmitted to a distance, without the effect of any external
interferences or noise addition and without getting faded away, it has to
undergo a process called as Modulation. It improves the strength of the signal
without disturbing the parameters of the original signal.

What is Modulation?

A message carrying a signal has to get transmitted over a distance and for it
to establish a reliable communication, it needs to take the help of a high
frequency signal which should not affect the original characteristics of the
message signal.

The characteristics of the message signal, if changed, the message contained

in it also alters. Hence, it is a must to take care of the message signal. A high
frequency signal can travel up to a longer distance, without getting affected
by external disturbances. We take the help of such high frequency signal
which is called as a carrier signal to transmit our message signal. Such a
process is simply called as Modulation.

Modulation is the process of changing the parameters of the carrier signal, in

accordance with the instantaneous values of the modulating signal.

Need for Modulation

Baseband signals are incompatible for direct transmission. For such a signal,
to travel longer distances, its strength has to be increased by modulating with
a high frequency carrier wave, which doesn’t affect the parameters of the
modulating signal.

Advantages of Modulation
The antenna used for transmission, had to be very large, if modulation was
not introduced. The range of communication gets limited as the wave cannot
travel a distance without getting distorted.

Following are some of the advantages for implementing modulation in the

communication systems.
 Reduction of antenna size
 No signal mixing
 Increased communication range
 Multiplexing of signals
 Possibility of bandwidth adjustments
 Improved reception quality
Signals in the Modulation Process

Following are the three types of signals in the modulation process.

Message or Modulating Signal

The signal which contains a message to be transmitted, is called as a message

signal. It is a baseband signal, which has to undergo the process of
modulation, to get transmitted. Hence, it is also called as the modulating
signal.
Carrier Signal

The high frequency signal, which has a certain amplitude, frequency and
phase but contains no information is called as a carrier signal. It is an empty
signal and is used to carry the signal to the receiver after modulation.
Modulated Signal

The resultant signal after the process of modulation is called as a modulated

signal. This signal is a combination of modulating signal and carrier signal.

Types of Modulation

There are many types of modulations. Depending upon the modulation

techniques used, they are classified as shown in the following figure.
Amplitude Modulation

A continuous-wave goes on continuously without any intervals and it is the

baseband message signal, which contains the information. This wave has to
be modulated.

According to the standard definition, “The amplitude of the carrier signal

varies in accordance with the instantaneous amplitude of the modulating
signal.” Which means, the amplitude of the carrier signal containing no
information varies as per the amplitude of the signal containing information,
at each instant. This can be well explained by the following figures.
The first figure shows the modulating wave, which is the message signal. The
next one is the carrier wave, which is a high frequency signal and contains no
information. While, the last one is the resultant modulated wave.

It can be observed that the positive and negative peaks of the carrier wave,
are interconnected with an imaginary line. This line helps recreating the exact
shape of the modulating signal. This imaginary line on the carrier wave is
called as Envelope. It is the same as that of the message signal.

Mathematical Expressions

Following are the mathematical expressions for these waves.

Time-domain Representation of the Waves

Let the modulating signal be,

m(t)=Am cos(2πfmt)

and the carrier signal be,

c(t)=Ac cos(2πfct)

Where,
Am and Ac are the amplitude of the modulating signal and the carrier signal
respectively.
fm and fc are the frequency of the modulating signal and the carrier signal
respectively.
Then, the equation of Amplitude Modulated wave will be
s(t)=[Ac + Am cos(2πfmt)] cos(2πfct) ……………..(Equation 1)

Modulation Index

A carrier wave, after being modulated, if the modulated level is calculated,

then such an attempt is called as Modulation Index or Modulation Depth.
It states the level of modulation that a carrier wave undergoes.

Rearrange the Equation 1 as below.

𝐴𝑚
s(t)=Ac [1 + ( 𝐴𝑐 ) cos(2πfmt)] cos(2πfct)

⇒s(t)=Ac [1 + μ cos(2πfmt)] cos(2πfct) …………..(Equation 2)

Where, μ is Modulation index and it is equal to the ratio of Am and Ac.

Mathematically, we can write it as

𝐴𝑚
μ= ……………(Equation 3)
𝐴𝑐

Hence, we can calculate the value of modulation index by using the above
formula, when the amplitudes of the message and carrier signals are known.

Now, let us derive one more formula for Modulation index by considering
Equation 1. We can use this formula for calculating modulation index value,
when the maximum and minimum amplitudes of the modulated wave are
known.

Let Amax and Amin be the maximum and minimum amplitudes of the
modulated wave.

We will get the maximum amplitude of the modulated wave, when cos(2πfmt)
is 1.

⇒Amax=Ac+Am…………..(Equation 4)

We will get the minimum amplitude of the modulated wave, when cos(2πfmt)
is -1.

⇒Amin=Ac−Am………….(Equation 5)

Add Equation 4 and Equation 5.

Amax + Amin = Ac+Am+Ac−Am = 2Ac
 𝐴𝑚𝑎𝑥+𝐴𝑚𝑖𝑛
⇒Ac = …………….(Equation 6)
2

Subtract Equation 5 from Equation 4.

Amax – Amin = Ac+Am−(Ac−Am) = 2Am

𝐴𝑚𝑎𝑥−𝐴𝑚𝑖𝑛
⇒Am= ……………..(Equation 7)
2

The ratio of Equation 7 and Equation 6 will be as follows.

𝐴𝑚 (𝐴𝑚𝑎𝑥 − 𝐴𝑚𝑖𝑛 )/2

=
𝐴𝑐 (𝐴𝑚𝑎𝑥 + 𝐴𝑚𝑖𝑛 )/2

(𝐴 −𝐴 )
⇒ 𝜇 = (𝐴𝑚𝑎𝑥 +𝐴𝑚𝑖𝑛 ) … … … … … … (Equation 8)
𝑚𝑎𝑥 𝑚𝑖𝑛

Therefore, Equation 3 and Equation 8 are the two formulas for Modulation
index. The modulation index or modulation depth is often denoted in
percentage called as Percentage of Modulation. We will get the percentage of
modulation, just by multiplying the modulation index value with 100.

For a perfect modulation, the value of modulation index should be 1, which

implies the percentage of modulation should be 100%.

For instance, if this value is less than 1, i.e., the modulation index is 0.5, then
the modulated output would look like the following figure. It is called
as Under-modulation. Such a wave is called as an under-modulated wave.

If the value of the modulation index is greater than 1, i.e., 1.5 or so, then the
wave will be an over-modulated wave. It would look like the following figure.
As the value of the modulation index increases, the carrier experiences a
180o phase reversal, which causes additional sidebands and hence, the wave
gets distorted. Such an over-modulated wave causes interference, which
cannot be eliminated.

Bandwidth of AM Wave

Bandwidth (BW) is the difference between the highest and lowest frequencies
of the signal. Mathematically, we can write it as
BW=fmax−fmin

Consider the following equation of amplitude modulated wave.

s(t)=Ac [1+μ cos(2πfmt)] cos(2πfct)
⇒s(t)=Ac cos(2πfct) + Ac μ cos(2πfct) cos(2πfmt)

𝐴𝑐 𝜇 𝐴𝑐 𝜇
⇒s(t)=Ac cos(2πfct) + cos[2π(fc+fm)t] + cos[2π(fc−fm)t]
2 2

Hence, the amplitude modulated wave has three frequencies. Those are
carrier frequency fc, upper sideband frequency fc+fm and lower sideband
frequency fc−fm

Here,

fmax=fc+fm and fmin=fc−fm

Substitute, fmax and fmin values in bandwidth formula.

BW=fc+fm−(fc−fm)
⇒BW=2fm
Thus, it can be said that the bandwidth required for amplitude modulated
wave is twice the frequency of the modulating signal.

Power Calculations of AM Wave

Consider the following equation of amplitude modulated wave.

𝐴𝑐 𝜇 𝐴𝑐 𝜇
s(t)=Ac cos(2πfct) + cos[2π(fc+fm)t] + cos[2π(fc−fm)t]
2 2

Power of AM wave is equal to the sum of powers of carrier, upper sideband,

and lower sideband frequency components.
Pt=Pc + PUSB + PLSB

We know that the standard formula for power of cos signal is

2
𝑉𝑟𝑚𝑠 (𝑉𝑚 /√2)2
P= =
𝑅 2

Where,

Vrms is the rms value of cos signal.

Vm is the peak value of cos signal.

First, let us find the powers of the carrier, the upper and lower sideband one
by one.

Carrier power
(𝐴𝑐 /√2)2 (𝐴𝑐 )2
Pc= =
𝑅 2𝑅

Upper sideband power

(𝐴𝑐 𝜇/2√2)2 𝐴𝑐 2 𝜇 2
PUSB = =
𝑅 8𝑅

Similarly, we will get the lower sideband power same as that of the upper side
band power.
𝐴𝑐 2 𝜇 2
PLSB= 8𝑅

Now, let us add these three powers in order to get the power of AM wave.
(𝐴𝑐 )2 𝐴𝑐 2 𝜇 2 𝐴𝑐 2 𝜇 2
Pt = + +
2𝑅 8𝑅 8𝑅
𝐴𝑐 2 𝜇2 𝜇2
⇒Pt = (1 + + )
2𝑅 4 4
𝜇2
⇒Pt = Pc (1 + )
2
We can use the above formula to calculate the power of AM wave, when the
carrier power and the modulation index are known.

If the modulation index μ=1 then the power of AM wave is equal to 1.5 times
the carrier power. So, the power required for transmitting an AM wave is 1.5
times the carrier power for a perfect modulation.

Problem 1

A modulating signal m(t)=10 cos(2π×103t) is amplitude modulated with a

carrier signal c(t)=50 cos(2π×105t). Find the modulation index, the carrier
power, and the power required for transmitting AM wave.
Solution

Given, the equation of modulating signal as

m(t)=10 cos(2π×103t)

We know the standard equation of modulating signal as

m(t)=Am cos(2πfmt)

By comparing the above two equations, we will get

Amplitude of modulating signal as Am=10volts

and Frequency of modulating signal as

fm=103Hz=1KHz

Given, the equation of carrier signal is

c(t)=50 cos(2π×105t)

The standard equation of carrier signal is

c(t)=Ac cos(2πfct)

By comparing these two equations, we will get

Amplitude of carrier signal as Ac=50volts

and Frequency of carrier signal as fc=105Hz=100KHz

We know the formula for modulation index as

μ=Am/Ac

Substitute, Am and Ac values in the above formula.

μ=10/50=0.2
Therefore, the value of modulation index is 0.2 and percentage of
modulation is 20%.

The formula for Carrier power, Pc= is

𝐴𝑐 2
Pc = 2𝑅

Assume R=1Ωand substitute Ac value in the above formula.

Pc=(50)2 / 2(1) = 1250W

Therefore, the Carrier power, PcPc is 1250 watts.

We know the formula for power required for transmitting AM wave is

𝜇2
⇒ Pt = Pc (1 + )
2

Substitute Pc and μ values in the above formula.

Pt=1250 (1+ (0.2)2/2) = 1275W

Therefore, the power required for transmitting AM wave is 1275 watts.

Problem 2

The equation of amplitude wave is given by

s(t)=20[1+0.8cos(2π×10 t)]cos(4π×10 t). Find the carrier power, the total
3 5

sideband power, and the band width of AM wave.

Solution

Given, the equation of Amplitude modulated wave is

s(t)=20[1 + 0.8 cos(2π×103t)] cos(4π×105t)

Re-write the above equation as

s(t)=20[1 + 0.8 cos(2π×103t)] cos(2π×2×105t)

We know the equation of Amplitude modulated wave is

s(t)=Ac[1 + μ cos(2πfmt)] cos(2πfct)

By comparing the above two equations, we will get

Amplitude of carrier signal as Ac=20volts

Modulation index as μ=0.8

Frequency of modulating signal as fm=103Hz=1KHz

Frequency of carrier signal as fc=2×105Hz=200KHz

The formula for Carrier power, Pc is

𝐴 2
Pc= 2𝑅
𝑐

Assume R=1Ω and substitute Ac value in the above formula.

Pc=(20)2 / 2(1) = 200W

Therefore, the Carrier power, Pc is 200watts.

We know the formula for total side band power is

PSB=Pcμ2 / 2

Substitute Pc and μ values in the above formula.

PSB=200×(0.8)2 / 2=64W

Therefore, the total side band power is 64 watts.

We know the formula for bandwidth of AM wave is

BW=2fm

Substitute fm value in the above formula.

BW=2(1K)=2KHz

Therefore, the bandwidth of AM wave is 2 KHz.

Frequency Modulation

In amplitude modulation, the amplitude of the carrier signal varies. Whereas,

in Frequency Modulation (FM), the frequency of the carrier signal varies in
accordance with the instantaneous amplitude of the modulating signal.

Hence, in frequency modulation, the amplitude and the phase of the carrier
signal remains constant. This can be better understood by observing the
following figures.
The frequency of the modulated wave increases, when the amplitude of the
modulating or message signal increases. Similarly, the frequency of the
modulated wave decreases, when the amplitude of the modulating signal
decreases. Note that, the frequency of the modulated wave remains constant
and it is equal to the frequency of the carrier signal, when the amplitude of
the modulating signal is zero.

Mathematical Representation
The equation for instantaneous frequency fi in FM modulation is
fi=fc + kf m(t)
Where,
fc is the carrier frequency
kf is the frequency sensitivity
m(t) is the message signal
We know the relationship between angular frequency ωi and angle θi(t) as
ωi=dθi(t)/dt
⇒2πfi=dθi(t)/dt
⇒θi(t)=2π∫fidt
Substitute, fi value in the above equation.
θi(t)=2π ∫(fc+kfm(t))dt
⇒θi(t)=2πfct+2πkf ∫m(t)dt
Substitute, θi(t) value in the standard equation of angle modulated wave.
s(t)=Ac cos(2πfct+2πkf ∫m(t)dt)
This is the equation of FM wave.
If the modulating signal is m(t)=Am cos(2πfmt)), then the equation of FM wave
will be
s(t)=Ac cos(2πfct+βsin(2πfmt))
Where,
β = modulation index = (Δf/fm) = (kfAm)/fm

The difference between FM modulated frequency (instantaneous frequency)

and normal carrier frequency is termed as Frequency Deviation. It is denoted
by Δf, which is equal to the product of kf and Am.

FM can be divided into Narrowband FM and Wideband FM based on the

values of modulation index β.
Narrowband FM

Following are the features of Narrowband FM.

 This frequency modulation has a small bandwidth when compared to

wideband FM.
 The modulation index β is small, i.e., less than 1.
 Its spectrum consists of the carrier, the upper sideband and the lower
sideband.
 This is used in mobile communications such as police wireless,
ambulances, taxicabs, etc.

Wideband FM

Following are the features of Wideband FM.

 This frequency modulation has infinite bandwidth.

 The modulation index β is large, i.e., higher than 1.
 Its spectrum consists of a carrier and infinite number of sidebands,
which are located around it.
 This is used in entertainment, broadcasting applications such as FM
radio, TV, etc.

Demodulation

The process of extracting an original message signal from the modulated wave
is known as detection or demodulation. The circuit, which demodulates the
modulated wave is known as the demodulator.