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Transmission Lines
Lecture 10
Types of transmission lines

Open-wire transmission line
This simply consists of two parallel wires,closely spaced and
separated by air. Nonconductive spacers are used to keep
the distance between the two wires constant. The distance
between the wires is between 2 and 6 inches. The real
advantage: it is simple to construct. Because there is no
shielding, radiation losses are high and can easily pick up
noise.
Twin lead

This is similar to the open wire, except that instead
of spacers a solid dielectric is used along the whole
length of the wire. This provides uniform spacing
along the entire length. The distance between the
wires is about 5/16 inch. Common dielectrics used
include teflon and polyethylene.
Twisted pair cable

In this two insulated conductors are
twisted together
Shielded pair
Two parallel wires separated by a solid dielectric material are
enclosed in a conductive metal braid, which is connected to
ground and hence acts as a shield. The braid also prevents
signals from radiating beyond its boundaries. It also stops
electromagnetic interference from reaching the wires
Coaxial


Parallel transmission lines are suitable for low frequency
applications. At high frequencies, their radiation and
dielectric losses become excessive. Coaxial cables are
therefore used at high frequencies. The basic coaxial is
made of a centre conductor surrounded by an outer
concentric conductor.
There can be two types rigid air filled or solid flexible
lines. The rigid air filled lines can be expensive to
manufacture and the air insulator must be moisture free.
The equivalent circuit of
transmission line

For any given transmission line, resistance and
inductance will occur along the line and
capacitance and conductance will occur between
the lines. These are called primary constants
and are uniformly distributed along the length of
the line. To make analysis simple these
parameters are lumped together per unit length
to form an artificial electrical model of the line.

At radio frequencies the inductive
reactance is much larger than the
resistance, the capacitive susceptance is
also much larger than the conductance.
Both R and G may therefore be ignored
resulting in what is called a lossless line
Transmission Characteristics
These are called the secondary constants and are determined
from the primary characteristics. They are the:
characteristic impedance and
the propagation constant
Characteristic impedance


Maximum power transfer is only possible if the load matches the
characteristic impedance of the line. This is the impedance measure
at the input of a transmission line when its length is infinite.
The relationship between the capacitance and the inductance per
unit length and the characteristic impedance is given as
L
Zo 
C
Propagation Constant

This is used to express the attenuation and phase shift
per unit length of the transmission line. This can be
expressed as
    j






is the propagation constant
is attenuation coefficient
is the phase shift coefficient
Reflected Wave and standing
wave ratio

When a transmission line terminates in a load that does not
match the characteristic impedance of the line then reflected
waves result. A summation of the incident and reflected
waves at different points along the line will give rise to
different rms voltage (current) values along the line. The
ratio of the largest rms value to the smallest is called
standing wave ratio. It is an indication of how close we are
to transmitting maximum power to the load.
Z L Vrms max I rms max
SWR 


Z o Vrms min I rms min
Reflection Coefficient

This is defined as reflected voltage
(current) divided by the incident voltage
(current).
V
I
Kr 

refl
Vinc

refl
I inc
This coefficient can also be expressed in
terms of the SWR or the load resistance
and characteristic
impedance
K 1
Z Z
SWR 
r
1  Kr
Kr 
L
o
Z L  Zo
Antenna resistance


Reflected Power
The reflected power is given as
2
Vrefl
Prefl 
RL

The incident power is given as
Vinc2
Pinc 
RL
2
Prefl Vrefl
 2  K r2
Pinc Vinc
Quarter-wave matching

A quarter wavelength section of a
transmission line can be used to match a load
to a transmission line. The value of the
characteristic impedance of quarter
wavelength section can found as follows:
2
o
Z
ZT 
ZL
Microstrip Lines
Microwave frequencies are from 1 to 300 GHz.
At these frequencies the wavelength is very small and these can a
serious effect on the circuit. The circuits at these frequencies are
extremely short and for such circuits, coaxial cable parallel open
and other forms of transmission lines are impractical. In this case
microstrip lines are used. The tracks or traces on the circuit board
are varied to produce the desired characteristic impedance.
Different configurations are in common use; examples of these
are:
Zo 
60

ln
4t

0.67b 0.8  c
h

Single-conductor microstrip
87
5.98h
Zo 
ln
  1.41 0.8b  c
Parallel coupled microstrip)
Zo 
120

ln
h
bc
Advantages of fiber optic systems

Bandwidth.

One of the most significant advantages that fiber has over
copper or other transmission media is bandwidth.
Bandwidth is directly related to the amount of information
that can be transmitted per unit time. Today's advanced
fiber-optic systems are capable of transmitting several
gigabits per second over hundreds of kilometers.
Thousands of voice channels can now be multiplexed
together and sent over a single fiber strand.
Less Loss.
Currently, fiber is being manufactured to exhibit less than a
few tenths of a decibel of loss per kilometer. Imagine glass
so pure that you could see through a window over 75 miles
(120 km) thick! Repeaters can now be spaced 50 to 75
miles apart from each other.
Noise Immunity and Safety

Since fiber is constructed of dielectric material, it is immune to
inductive coupling or crosstalk from adjacent copper or fiber
channels. In other words, it is not affected by electromagnetic
interference (EMI) or electrostatic interference. This includes
environments where there are electric motors, relays, and even
lightning. Likewise, since fiber-optic cables transmit light instead of
current, they do not emit electrical noise, nor do they arc when there
is an intermittent in the link. Thus they are useful in areas where
EMI must be kept to a minimum. With the telecommunications
highways of the air as congested as they are, the use of fiber is an
attractive alternative.
Less Weight and Volume

Fiber-optic cables are substantially lighter in weight and
occupy much less volume than copper cables with the same
information capacity. Fiberoptic cables are being used to
relieve congested underground ducts in metropolitan and
suburban areas. For example, a 3-in. diameter telephone
cable consisting of 900 twistedpair wires can be replaced
with a single fiber strand 0.005 in. in diameter
(approximately the diameter of a hair strand) and retain the
same information-carrying capacity. Even with a rugged
protective jacket surrounding the fiber, it occupies
enormously less space and weighs considerably less.
Security

Since light does not radiate from a fiber-optic cable,
it is nearly impossible to secretly tap into it without
detection. For this reason, several applications
requiring communications security employ
fiber-optic systems. Military information, for
example, can be transmitted over fiber to prevent
eavesdropping. In addition, fiber-optic cables
cannot be detected by metal detectors unless they
are manufactured with steel reinforcement for
strength.
Flexibility

We normally think of glass as being extremely brittle. If one were
to attempt to bend a 1/8 in. thick glass window, it would certainly
break at some point. One reason for this is that the glass we are
familiar with has a considerable amount of surface flaws,
although it appears polished. The outer surface of the glass
would bend considerably more than the inside. The surface flaws
would initiate the crack in the same manner that long scratches
are intentionally used to crack and form glass windows. The
surface of glass fiber is much more refined than ordinary glass.
This, coupled with its small diameter, allows it to be flexible
enough to wrap around a pencil. In terms of strength, if enough
pressure is applied against it, a 0.005-in. strand of fiber is strong
enough to cut one's finger before it breaks.
Economics
Presently, the cost of fiber is comparable to copper, at
approximately $0.20 to $0.50 per yard, and is expected
to drop as it becomes more widely used. Since
transmission losses are considerably less than for
coaxial cable, expensive repeaters can be spaced farther
apart. Fewer repeaters means a reduction in overall
system costs and enhanced reliability.
Reliability
Once installed, a longer life span is expected with fiber over its
metallic counterparts since it is more resistant to corrosion
caused by environmental extremes such as temperature,
corrosive gases, and liquids. Many coating systems made of
lacquer, silicons, and ultraviolet-cured acrylates have been
developed to maintain fiber strength and longevity.
DISADVANTAGES OF FiBER-OPTIC
SYSTEMS

In spite of the numerous advantages that
fiber-optic systems have over conventional
methods of transmission, there are some
disadvantages, particularly because of its
newness. Many of these disadvantages are
being overcome with new and competitive
technology.
Interfacing Costs

Electronic facilities must be converted to optics
to interface to fiber. Often these costs are
initially overlooked. Fiber-optic transmitters,
receivers, couplers, and connectors, for example,
must be employed as part of the communication
system. Test and repair equipment is costly. If
the fiber-optic cable breaks, splicing can be a
costly and tedious task. Manufacturers, however,
are continuously introducing new and improved
field repair kits.
Strength

Fiber, by itself, has a tensile strength of
approximately 1 lb, as compared to coaxial
cable at 180 lb (RG591J). Surrounding the
fiber with stranded KevIar* and a protective
PVC jacket can increase the pulling strength
up to 500 lb. Installations requiring greater
tensile strengths can be achieved with steel
reinforcement.
Remote Powering of Devices

Occasionally it is necessary to provide
electrical power to a remote device.
Since this cannot be achieved through
the fiber, metallic conductors are often
included in the cable assembly. Several
manufacturers now offer a complete line
of cable types, including cables
manufactured with both copper wire and
fiber.
Propagation Modes

The term mode is important in fibre
optics, it describes the propagation
characteristics of an electromagnetic
wave as it travels through a particular
type of fibre. Mathematically it can be
said to be the spatial distribution of
energy of the electromagnetic wave.
Two modes of transmission can be
distinguished in a fibre.
Single Mode

When there is only one path along which
the ray of light travels, along the centre
axis of the fibre, then that fibre is said to
be a single mode fibre.
Multimode

Where there are a number of paths along
which the ray may travel then the fibre is
said to be multimode fibre.
The number of modes a fibre can
support is a function of the wavelength
as well as the diameter of the fibre and
the index of refraction. Mathematically it
can be described using the following
equation:
2
d 2
2
n

n
1
2 
 

No. of Modes

2

Multimode step index

Useful in local applications that do not
require great transmission speeds. Core
diameter range between 50 – 1000 mm.
It is this large core size that supports
many modes and permits the use of
simple and inexpensive LED transmitters.
Light pulses in this type of fibre tend to
broaden as they reach their destination.
This is known as modal dispersion
Single mode step index

In this the core of the fibre is made
much smaller. The index of refraction is
also reduced. This leads to an increase
in the critical angle. Light rays tend to
travel along the same path hence
reducing modal dispersion. They offer
the best performance in terms of
information capacity and distance
Multimode graded index

The refractive index is graded from the
core outwards. This produces a bending
effect on the rays and helps them arrive
at end at the same time.
Flexibility
Cells and Cellular traffic
Splitting of the
geographical region
into “cells.” The
frequency f c1 is used
in multiple cells
separated by a fixed
distance.
Introduction to Wireless Systems by P. M. Shankar
Copyright © 2002 John Wiley and Sons. All rights reserve d
The power from the primary channel and the total
power from the co-channels in the cell subscribing to
the primary channel.
Introduction to Wirele ss Systems by P. M. Shankar
Copyright © 2002 John Wiley and Sons. All rights reserve d
Figure 4.3.
Different geometrical shapes
for cells.
(a) Square.
(b) Triangular.
(c) Circular.
(d) Hexagonal, where R is
the “radius” of the hexagon.
Introduction to Wirele ss Systems by P. M. Shankar
Copyright © 2002 John Wiley and Sons. All rights reserve d