4.

6 / Key Terms, Review Questions, And Problems   145

4.6 Key Terms, Review Questions, And Problems

Key Terms

antenna guided media satellite

antenna gain index of refraction shielded twisted pair
atmospheric absorption infrared (STP)
attenuation insertion loss single-mode propagation
attenuation-to-crosstalk isotropic antenna sky wave propagation
ratio (ACR) jacket step-index multimode
broadcast radio line of sight (LOS) subscriber loops
buffer coating microwave frequencies terrestrial microwave
cladding multipath total internal reflection
coaxial cable near-end crosstalk (NEXT) transmission medium
core loss transponder channels
directional antenna omnidirectional antenna transponders
downlink optical fiber strand twisted pair
earth stations optical LOS unguided media
effective area parabolic reflective antenna unshielded twisted pair
fiber optic cable radio (UTP)
free space loss radio LOS uplink
global positioning system reflection wavelength division
(GPS) refraction multiplexing (WDM)
graded-index multimode refractive index wireless transmission
ground wave propagation scattering

Review Questions
4.1.
Why are the wires twisted in twisted-pair copper wire?
4.2.
What are some major limitations of twisted-pair wire?
4.3.
What is the difference between unshielded twisted pair and shielded twisted pair?
4.4.
Describe the components of optical fiber cable.
4.5.
What are some major advantages and disadvantages of microwave transmission?
4.6.
What is direct broadcast satellite (DBS)?
4.7.
Why must a satellite have distinct uplink and downlink frequencies?
4.8.
Indicate some significant differences between broadcast radio and microwave.
4.9.
What two functions are performed by an antenna?
4.10.
What is an isotropic antenna?
4.11.
What is the advantage of a parabolic reflective antenna?
4.12.
What factors determine antenna gain?
4.13.
What is the primary cause of signal loss in satellite communications?
4.14.
What is refraction?
4.15.
What is the difference between diffraction and scattering?
146   Chapter 4 / Transmission Media

Problems
4.1.
Suppose that data are stored on 8.54-Gbyte single-sided, double-layer DVDs that
weigh 15 g each. Suppose that an Eurostar rail service train, London to Paris via
Chunnel, carries 104 kg of these DVDs. The great circle distance of the line is 640 km
and the traveling time is 2 hours, 15 minutes. What is the data transmission rate in bits
per second of this system?
4.2.
A telephone line is known to have a loss of 20 dB. The input signal power is measured
as 0.5 W, and the output noise level is measured as 4.5 mW. Using this information,
calculate the output signal-to-noise ratio in dB.
4.3.
Given a 100-watt power source, what is the maximum allowable length for the follow-
ing transmission media if a signal of 1 watt is to be received?
a. 24-gauge (0.5 mm) twisted pair operating at 300 kHz
b. 24-gauge (0.5 mm) twisted pair operating at 1 MHz
c. 0.375-inch (9.5 mm) coaxial cable operating at 1 MHz
d. 0.375-inch (9.5 mm) coaxial cable operating at 25 MHz
e. optical fiber operating at its optimal frequency
4.4.
Coaxial cable is a two-wire transmission system. What is the advantage of connecting
the outer conductor to ground?
4.5.
Show that doubling the transmission frequency or doubling the distance between
transmitting antenna and receiving antenna attenuates the power received by 6 dB.
4.6.
It turns out that the depth in the ocean to which airborne electromagnetic signals can
be detected grows with the wavelength. Therefore, the military got the idea of using
very long wavelengths corresponding to about 30 Hz to communicate with subma-
rines throughout the world. It is desirable to have an antenna that is about one-half
wavelength long. How long would that be?
4.7.
The audio power of the human voice is concentrated at about 300 Hz. Antennas of
the appropriate size for this frequency are impracticably large, so that to send voice
by radio the voice signal must be used to modulate a higher (carrier) frequency for
which the natural antenna size is smaller.
a. What is the length of an antenna one-half wavelength long for sending radio at
300 Hz?
b. An alternative is to use a modulation scheme, as described in Chapter 5, for trans-
mitting the voice signal by modulating a carrier frequency, so that the bandwidth
of the signal is a narrow band centered on the carrier frequency. Suppose we
would like a half-wave antenna to have a length of 1 m. What carrier frequency
would we use?
4.8.
Stories abound of people who receive radio signals in fillings in their teeth. Suppose
you have one filling that is 2.5 mm (0.0025 m) long that acts as a radio antenna. That
is, it is equal in length to one-half the wavelength. What frequency do you receive?
4.9.
You are communicating between two satellites. The transmission obeys the free space
law. The signal is too weak. Your vendor offers you two options. The vendor can use
a higher frequency that is twice the current frequency or can double the effective area
of both of the antennas. Which will offer you more received power or will both offer
the same improvement, all other factors remaining equal? How much improvement
in the received power do you obtain from the best option?
4.10.
In satellite communications, different frequency bands are used for the uplink and
the downlink. Discuss why this pattern occurs.
4.11.
For radio transmission in free space, signal power is reduced in proportion to the
square of the distance from the source, whereas in wire transmission, the attenuation
is a fixed number of dB per kilometer. The following table is used to show the dB
reduction relative to some reference for free space radio and uniform wire. Fill in the
missing numbers to complete the table.
 4.6 / Key Terms, Review Questions, And Problems   147

Distance (km) Radio (dB) Wire (dB)

 1 -6 -3
 2
 4
 8
16

4.12.
Section 4.2 states that if a source of electromagnetic energy is placed at the focus of
the paraboloid, and if the paraboloid is a reflecting surface, then the wave will bounce
back in lines parallel to the axis of the paraboloid. To demonstrate this, consider the
parabola y2 = 2px shown in Figure 4.15. Let P(x1, y1) be a point on the parabola, and
PF be the line from P to the focus. Construct the line L through P parallel to the
x-axis and the line M tangent to the parabola at P. The angle between L and M is b,
and the angle between PF and M is a. The angle a is the angle at which a ray from F
strikes the parabola at P. Because the angle of incidence equals the angle of reflec-
tion, the ray reflected from P must be at an angle a to M. Thus, if we can show that
a = b, we have demonstrated that rays reflected from the parabola starting at F will
be parallel to the x-axis.
a. First show that tan b = (p/y1). Hint: Recall from trigonometry that the slope of a
line is equal to the tangent of the angle the line makes with the positive x-direction.
Also recall that the slope of the line tangent to a curve at a given point is equal to
the derivative of the curve at that point.
b. Now show that tan a = (p/y1), which demonstrates that a = b. Hint: Recall from
trigonometry that the formula for the tangent of the difference between two
angles a1 and a2 is tan(a2 - a1) = (tan a2 - tan a1)/(1 + tan a2 * tan a1).

M
y

b
P(x1, y1)
L

0 F(p/2, 0) x

Figure 4.15  Parabolic Reflection

148   Chapter 4 / Transmission Media
4.13.
It is often more convenient to express distance in km rather than m and frequency in
MHz rather than Hz. Rewrite Equation (4.4) using these dimensions.
4.14.
Suppose a transmitter produces 50 W of power.
a. Express the transmit power in units of dBm and dBW.
b. If the transmitter’s power is applied to a unity gain antenna with a 900 MHz carrier
frequency, what is the received power in dBm at a free space distance of 100 m?
c. Repeat (b) for a distance of 10 km.
d. Repeat (c) but assume a receiver antenna gain of 2.
4.15.
A microwave transmitter has an output of 0.1 W at 2 GHz. Assume that this transmit-
ter is used in a microwave communication system where the transmitting and receiving
antennas are parabolas, each 1.2 m in diameter.
a. What is the gain of each antenna in decibels?
b. Taking into account antenna gain, what is the effective radiated power of the
transmitted signal?
c. If the receiving antenna is located 24 km from the transmitting antenna over a
free space path, find the available signal power out of the receiving antenna in
dBm units.
4.16.
Section 4.3 states that with no intervening obstacles, the optical line of sight can be
expressed as d = 3.571h, where d is the distance between an antenna and the hori-
zon in kilometers and h is the antenna height in meters. Using a value for the Earth’s
radius of 6370 km, derive this equation. Hint: Assume that the antenna is perpendicu-
lar to the Earth’s surface, and note that the line from the top of the antenna to the
horizon forms a tangent to the Earth’s surface at the horizon. Draw a picture showing
the antenna, the line of sight, and the Earth’s radius to help visualize the problem.
4.17.
Determine the height of an antenna for a TV station that must be able to reach
­customers up to 80 km away.
4.18. Suppose a ray of visible light passes from the atmosphere into water at an angle to
the horizontal of 30º. What is the angle of the ray in the water? Note: At standard
atmospheric conditions at the Earth’s surface, a reasonable value for refractive index
is 1.0003. A typical value of refractive index for water is 4/3.