Review Questions and Problem Solutions on Antennas, Fading, and Modulation

This article provides review questions and problem solutions on antennas, fading, and modulation. It covers topics such as isotropic antenna, radiation pattern, fading, diffraction, QAM modulation, and more.

Review Questions
Solution 5.1
An isotropic antenna is an unreal and unpractical antenna whose radiations spread in all the
direction and that to with the same intensity. This radiation is both horizontal and vertical.
The radiation is in the form of a sphere with a gain of 1decibel. Its efficiency is 100 percent.
Since, this is just a hypothetical antenna, its gain is actually used as a reference for measuring
the gain of practical antennas. Many times the gain of the antennas is calculated in decibels
over isotropic (dBi). It is the ratio of the transmitted power in a specific direction by a
particular antenna to the total power that an isotropic antenna would transmit [1].
Solution 5.2
Radiation pattern depicts the radiation from the source at different angles. It tells about those
angles at which the radiation is maximum and minimum. The relative filed strength can be
easily observed using them [2].
Solution 5.3
Fading is the phenomena which is observed at the receiving end. Due to many factors, the
signal is attenuated before it reaches the antenna. Some of the factors include multipath
distractions, environment or shadowing offered by the obstacle is there are present around the
receiving antenna. Due to the presence of various reflecting objects, the signal that is
originally transmitted gets reflected through them and reaches the receiving end. As a result
of this multiple reflections, many copies of the same original signal reaches the antenna such
that there is a difference in the extent of detonation, phase shift as well as unequal delays.
These multiple copies gets interfered with each other or we can say superposition happens,
the interference could be constructive or destructive. If the interference is destructive, the
overall receiving signal is highly attenuated and modified whereas if the interference is
constructive, then the attenuation is low. The objects surrounding the transmitter also causes
fading as they fall under the path of propagation [3].
Solution 5.4
1. The property of the diffraction is related to the waves while scattering is related to
both waves and particles.

2. Diffraction is a phenomenon of wave propagation while scattering is the phenomenon
involving the interaction of various waves.
3. In order to prove that light has a way of nature also, diffraction is used while
Compton scattering of light along with other forms, can be considered as the proof for
the lights particle nature [4].
Solution 5.5
1. Fast fading changes very fast to change the frequency whereas slow fading does not
changes quickly when the frequencies changed.
2. Fast fading arises because of the interference, which can be constructive or
destructive. These interferences are caused due to multipath distraction of the source
signal whereas in the case of slow fading the mobility is the main factor that arises
them.
3. Fast fading is caused due to high Doppler spread whereas slow fading due to low
Doppler spread.
4. When the coherence time is less than the symbol period, Fast fading occurs whereas
when it is much greater than symbol slow fading happens.
5. In the case of fast fading the channel impulse response varies very quickly within the
duration of the symbol. The reverse happens in the case of slow fading when the
impulse response varies very slowly as compared to the signal that is transmitted.
Solution 5.6
1. When the coherent channel bandwidth is greater than the transmitted signal’s
bandwidth, flat fading happens. When the coherent channel bandwidth is less than the
transmitted signal’s bandwidth, frequency selective fading happens.
2. In the case of light reading, the channel has got a constant gain and the phase response
is linear. Whereas in the case of frequency selective fading, the channel introduces
many inter-symbol interferences.
3. The RMS delay spread is less than the signal symbol period. Whereas in the case of
frequency selective fading the RMS delay spread is more than the signal symbol
period [5].

Solution 5.7
1. Digital signals are less prone to the interference caused due to the noise as compared
to the analog signals because in the case of digital signals there is no need to find out
the exact amplitude, frequency over the face of the signal. Instead the time period of
the pulse train is evaluated.
2. Use of multiplexing is easier and effective in the case of digital signals as compared
to the analog signals.
3. The storage of the digital signals is easier as compared to the analog signals [6, 7].
Solution 5.8
When the message bit stream contains logical ‘0’, the carrier wave is not allowed to
propagate. Whereas when the message bit stream contains logical ‘1’, the carrier is allowed to
propagate [8].
Solution 5.9
QAM or Quadrature Amplitude Modulation is a technique in which the two message signals
that can either be analog or digital, can be simultaneously modulated using amplitude
modulation and phase modulation (in the case of two analog message signals) or amplitude
shift keying and phase shift keying (in the case of two digital message signals). In the case of
analog message, the first message signal is amplitude modulated with a carrier wave of some
angular frequency while the second analog message is modulated with a carrier wave such
that it is phase shifted by 90° to the first carrier wave. Both the amplitude modulated signals
are then multiplexed and transmitted. In the case of digital message, everything is same
except that in the place of amplitude modulation and phase modulation, amplitude shift
keying and phase shift keying are employed. The multiplexed modulated signal is received at
the receiver and the modulated using QAM receiver. It is a bandwidth saving scheme [9].
Problem Questions
Solution 5.2
Frequency of the signal (f) =30 Hz
Required wavelength of the antenna =1/2 λ
Length of the antenna =?

Since, wavelength =speed of the signal/ frequency;
Or, λ =c/ f;
=3x108/ 30;
=107 m = 10000 km
Therefore, length of the antenna = λ /2;
=10000/ 2 = 5000 km
Solution 5.3
a) Since, wavelength (λ) = speed of the wave(c)/ frequency (f);
Substituting the values, λ =3x108/ 300 =1000 km;
Since, length of the antenna (L) is half the wavelength;
Therefore, L =1000/ 2= 500 km
b) The length of the antenna (L) = λ/ 2; and it is given as 1 m. Therefore, 1 = λ/ 2; λ= 2
m;
Since, wavelength =speed of the signal/ frequency;
Or, λ =c/ f;
Therefore, f =c/ λ; f =3x108/ 2; f =150 MHz
Solution 5.4
The length of the antenna (L) = λ/ 2; and it is given as 0.0025 m. Therefore, 0.0025 = λ/ 2; λ=
0.005 m;
Since, wavelength =speed of the signal/ frequency;
Or, λ =c/ f;
Therefore, f =c/ λ; f =3x108/ 0.005; f =60 GHz
Solution 5.5
The equation is given as, Pt/ Pr = (4пfd)2 /c2;
Here, ‘f’ is the frequency, ‘d’ is the length, ‘c’ is the speed of the wave, ‘Pt’ is the radiated
power and ‘Pr’ is received power.
Converting the units of length in km and units of frequency in MHz,
(4п Hz m)2 / (ms-1)2 =16п2 Hz2 m2 s2/m2 = 16п2 (10-6)2 Hz2 (10-3)2 m2 s2 / (10-6)2 (10-3)2 m2

(Dividing numerator and denominator by 10-6 so that Hz can be converted to MHz and by 10-3
so that m can be converted to km)
= 16п2 MHz2 km2 s2 / (10-6)2 km2 (Since, 1Hz = 10-6 MHz and 1m =10-3km)
= (4пfd)2 / (10-6 c)2;
Review Questions
Solution 6.3
A directional radiation pattern consists of a main lobe that is directed towards a particular
direction and a very small or no (theoretically) backward lobe. A directional antenna directs
the RF energy into one particular direction only and hence the radiation pattern looks like
this. As the gain increases, the distance covered by the antenna also increases but at the same
time the effective covering angle decreases. Thus, with increasing gain the lobes are more in
length. This pattern is helpful when all the energy is to be directed somewhere at a point
without radiating it in the case of isotropic antenna. This pattern increases the radiation
strength [10].
Solution 6.4
Radiation pattern depicts the radiation from the source at different angles. It tells about those
angles at which the radiation is maximum and minimum. The relative filed strength can be
easily observed using them.

References
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