Communication Systems
Week 15
Dr. Farah Haroon
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Transmission Lines
Definition
 Types
 Balanced and Unbalanced Lines
 Characteristic Impedance
 Standing Waves

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Transmission-Line Basics



Transmission lines in communication carry
telephone signals, computer data in LANs,
TV signals in cable TV systems, and signals
from a transmitter to an antenna or from an
antenna to a receiver.
A TL is an electrically suitable confinement
used to guide the flow of energy between
two points within a system.
Their electrical characteristics are critical
and must be matched to the equipment for
successful communication to take place.
Transmission-Line Basics

The two primary requirements of a
transmission line are:
1. The line should introduce minimum
attenuation to the signal.
2. The line should not radiate any of the
signal as radio energy.
Balanced Vs Unbalanced Lines
◦ Transmission lines can be balanced or
unbalanced.
◦ A balanced line is one in which neither wire is
connected to ground.
◦ The signal on each wire is referenced to ground.
◦ In an unbalanced line, one conductor is connected
to ground.
◦ Open-wire line has a balanced configuration.
◦ Balanced-line wires offer significant protection
from noise pickup and cross talk.
◦ Coaxial cables are unbalanced lines.
◦ Coaxial cable and shielded twisted-pair
provide significant but not complete
protection from noise or cross talk.
◦ Unshielded lines may pick up signals and cross
talk and can even radiate energy, resulting in
an undesirable loss of signal.
◦ A device called a balun is used to convert
from balanced to unbalanced lines and vice
versa.
Types of Transmission Lines
◦ Parallel-wire line is made of two parallel
conductors separated by a space of ½ inch to
several inches.
◦ A variation of parallel line is the 300-Ω twinlead. Spacing between the wires is maintained
by a continuous plastic insulator.
◦ The most widely used type of transmission
line is the coaxial cable. It consists of a solid
center conductor surrounded by a dielectric
material, usually a plastic insulator such as
Teflon.
 A second conducting shield made of fine wires
covers the insulator, and an outer plastic sheath
insulates the braid.
◦ Coaxial cable comes in sizes from ¼ inch to
several inches in diameter.
◦ Twisted-pair cable uses two insulated solid
copper wires covered with insulation and
loosely twisted together.
◦ Two types of twisted-pair cable are
 Unshielded twisted-pair (UTP) cable
 Shielded twisted-pair (STP) cable
Types of Transmission-Line
Figure Common types of transmission lines. (a) Open-wire line. (b) Open-wire line
called twin lead. (c) Coaxial cable (d) Twisted-pair cable.
T-Line Equivalent Circuit


Transmission line parameters are distributed (e.g.
capacitance per unit length).
A transmission line can be modeled using a
network of resistances, inductances, and
capacitances, where the distributed parameters
are evenly distributed in microscopic values over
the entire length of the line.
R
L
G
C0
At low frequencies, the circuit elements are
lumped since voltage and current waves affect
the entire circuit at the same time.
 At microwave frequencies, such treatment of
circuit elements is not possible since voltage
and current waves do not affect the entire
circuit at the same time.
 The circuit must be broken down into unit
sections within which the circuit elements are
considered to be lumped.
 This is because the dimensions of the circuit are
comparable to the wavelength of the waves

Wavelength of Cables
◦ The electrical length of conductors is typically
short compared to 1 wavelength of the frequency
they carry.
◦ A pair of current-carrying conductors is not
considered to be a transmission line unless it is at
least 0.1 λ long at the signal frequency.
◦ Therefore at low frequencies, very long pair of
conductors would act as transmission line.
◦ Whereas at high frequencies, even pair of
conductors of very short length would act as TL.
Characteristic Impedance
◦ When the length of transmission line is longer
than several wavelengths at the signal
frequency, the two parallel conductors of the
transmission line appear as a complex
impedance.
◦ An RF generator connected to a considerable
length of transmission line sees an impedance
that is a function of the inductance, resistance,
and capacitance in the circuit—the
characteristic or surge impedance (Z0).
Characteristic Impedance
Ratio of the amplitudes of a single pair of
voltage and current waves in the absence
of reflections of an infinite long line.
 Input impedance

Characteristic Impedance
• Characteristic Impedance
• For
lossless line,
• Propagation
 
Z0 
R  jL
G  jC
L
Z0 
C
constant
R 
jL G  jC     j
Z0 of 2 Wire Parallel Line
Z0 of Coaxial Cable
Reflections

If the transmission line is terminated in a
resistor equal in value to the characteristic
impedance of the line as calculated by the
formula Z=(L/C)0.5 , then the voltage and
current are compatible and no reflections
occur.

When the resistive load termination is not
equal to the characteristic impedance, part of
the power is reflected back and the
remainder is absorbed by the load. The ratio
of the two voltages is called voltage reflection
coefficient.
Standing Waves



When a signal is applied to a transmission
line, it appears at the other end of the line
some time later because of the propagation
delay.
If the load on the line is an antenna, the
signal is converted into electromagnetic
energy and radiated into space.
If the load at the end of the line is an open
or a short circuit or has an impedance other
than the characteristic impedance of the line,
the signal is not fully absorbed by the load.
Standing Waves
When a line is not terminated properly,
some of the energy is reflected and moves
back up the line, toward the generator.
 This reflected voltage adds to the forward
or incident generator voltage and forms a
composite voltage that is distributed along
the line.
 The pattern of voltage and its related
current constitute what is called a standing
wave.
 Standing waves are not desirable.

Standing Waves
Matched Lines
◦ A matched transmission line is one
terminated in a load that has a resistive
impedance equal to the characteristic impedance
of the line.
◦ Alternating voltage (or current) at any point on a
matched line is a constant value. A correctly
terminated transmission line is said to be flat or
nonresonant line.
◦ The power sent down the line toward the load is
called forward or incident power.
◦ Power not absorbed by the load is reflected
power.
Standing Waves
Figure A transmission line must be terminated in its characteristic impedance
for proper operation.
Standing Waves
◦ The magnitude of the standing waves on a
transmission line is determined by the ratio of the
maximum current to the minimum current, or the
ratio of the maximum voltage to the minimum
voltage, along the line.
◦ These ratios are referred to as the standing wave
ratio (SWR).
SWR =
Imax
Imin
=
Vmax
Vmin
Voltage standing wave ratio expressed in decibels
is called the
SWR (dB) = 20 log10SWR
SWR is equal to 1 when load is perfectly
matched.
 SWR=Z0/RL or SWR=RL/Z0
 It is infinite when no power is absorbed at load
and Vmin = 0.


Relationship between VSWR and Reflection
Coefficient:
SWR = (1 + |G|/1 - |G|
G  (SWR – 1)/(SWR + 1)
Voltage
Standing Waves
Vmax = Ei + Er
l
2
Vmin = Ei - Er
With a mismatched line, the incident and reflected
waves set up an interference pattern on the line
known as a standing wave.
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Reflection Coefficient
The reflection coefficient is defined as:
Er
G
Ei
or
It can also be shown that:
Ir
Ii
Z L  Zo
G
 G 
Z L  Zo
Note that when ZL = Zo, G = 0; when ZL = 0, G = -1;
and when ZL = open circuit, G = 1.
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Problems
Q1. A lossless line of 100Ω characteristic
impedance connects a 100 kHz generator to a
140 Ω load. Calculate the voltage reflection
coefficient and voltage standing wave ratio.
Q2. A transmission line has the following per
unit length equivalent circuit parameters:
L = 0.75 μH/m, C = 300 pF/m, R = 1 Ω/m,
G = 0.001 S/m at 5 GHz. Find
(i) the length l of a line in wavelengths
(ii) characteristic impedance Z0 .
(iii) characteristic impedance Z0 of lossless line.
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