Ethiopian Institute of Technology-Mekele
Mekelle University
School of Electrical and Computer Engineering
Title: Developing High Performance of the Coaxial Cable Losses Based On
Dielectrics
A semester project submitted in partial fulfillment of the requirements for BSc in
Electrical and Computer Engineering (Electronics and Communication
Engineering)
Submitted By
Group Member
1. Ameteyesus
Gidey
Id.No:
.……...
261539/06
2. Mearg
Berhe
………
162489/06
3. Mearg
Ybabe
………...
162493/06
4. Merhawit Hadera
………..
262578/06
Advisor Name: Gebremedhn Wubet
June, 2017 GC
DECLARATION
We, the undersigned, declare that the work which is being presented in the semester project entitle,
“Developing high performance of the coaxial cable losses based on dielectrics” is our original
work, and has not been presented for a degree in this or any other university, and all sources of
materials used for the project have been fully acknowledged. This paper is submitted to Electronics
and Communication Chair, School of Electrical and Computer Engineering, Mekelle University,
is an authentic record of our own work carried out under supervision of Gebremedhn Wubet
(ADVISOR).
Name
Signature
1. Ameteyesus Gidey
______________
2. Mearg
Berhe
______________
3. Mearg
Ybabe
______________
4. Merhawit Hadera
______________
Place: Mekelle
Date of Submission: ________________
This semester project has been submitted for examination with our approval as a university
advisor.
Advisor’s name
Signature
Gebremedhn Wubet
___________________
I
Acknowledgement
At the outset we would thank God without his support, the work would not have been the light
of the day.
We are very thankful to our parents who have been a part of life supporting us through and we are
also thankful to our advisor Gebremedhn Wubet who has helped us in the process of research every
stage.
Lastly we are thankful to our friends who made a wonderful group to work with and we would
also like to thank the various individuals who have contributed in any way possible, thereby
allowing us to create as accurate a representation as possible within our given constraints.
II
Abstract
This semester project presents the analysis of high performance for coaxial cable with different
parameters. The modeling for performance of coaxial cable contains many parameters, in this
paper will discuss the more effective parameter is the type of dielectric mediums (Air, Polyimide,
Polyethylene, and Teflon). This analysis of the performance related to dielectric mediums with
respect to: dielectric losses and its effect upon cable properties, dielectrics versus characteristic
impedance, and the attenuation in the coaxial line for different dielectrics. The analysis depends
on a simple mathematical model for coaxial cables to test the influence of the insulators
(Dielectrics) performance.
The simulation of this work is done using Mat lab/Simulink and presents the results according to
the construction of the coaxial cable with its physical properties, the types of losses in both the
cable and the dielectric, and the role of dielectric in the propagation of electromagnetic waves.
Satisfied results are obtained that concluded the condition of high performance for coaxial cable.
The work has proven that the performance of the polyimide has better results than the Air,
polyethylene and Teflon and it give less attenuation, practically the polyethylene has wider using
because of its cheap price and easy to be made.
III
Contents
DECLARATION.......................................................................................................................................... i
Acknowledgement ....................................................................................................................................... II
Abstract ........................................................................................................................................................ III
List of Figures............................................................................................................................................. VI
List of Tables ............................................................................................................................................. VII
List of Acronyms ...................................................................................................................................... VIII
CHAPTER ONE ......................................................................................................................................... 1
Introduction ................................................................................................................................................. 1
1.1 Background ....................................................................................................................................... 1
1.2 Literature review .............................................................................................................................. 3
1.3 Problem statement and justification ............................................................................................... 5
1.4 Objectives........................................................................................................................................... 5
1.4.1 General objective........................................................................................................................ 5
1.4.2 Specific objectives ...................................................................................................................... 6
1.5 Methodology ...................................................................................................................................... 6
1.6 Organization of project .................................................................................................................... 7
CHAPTER TWO ........................................................................................................................................ 8
Coaxial Cable and Basic Parameters ........................................................................................................ 8
2.1 coaxial cable....................................................................................................................................... 8
2.1.1 Types of Coaxial Cable ............................................................................................................ 10
2.1.2 Advantages and disadvantages of a coaxial cable ................................................................. 11
2.1.3 How RF coax cable works ....................................................................................................... 14
2.2 Coax Cable Specifications & Parameters ..................................................................................... 15
2.2.1 Characteristic impedance specification.................................................................................. 15
2.2.2 Loss / attenuation specification ............................................................................................... 16
2.2.3 Power rating specification ....................................................................................................... 17
2.2.4 Velocity factor specification .................................................................................................... 17
2.2.5 Capacitance specification ........................................................................................................ 18
2.2.6 Maximum voltage..................................................................................................................... 18
IV
2.2.7 Coax mechanical dimensions specification ............................................................................ 18
2.2.8 Common dielectric materials .................................................................................................. 19
CHAPTER THREE .................................................................................................................................. 20
System Modeling ....................................................................................................................................... 20
3.1 Equivalent Circuit of the Coaxial Cable ....................................................................................... 20
3.2 Dielectric Losses .............................................................................................................................. 22
3.3 The Electrical Model of Coaxial Cable and simulation ............................................................... 23
CHAPTER FOUR..................................................................................................................................... 25
Simulation Result and Discussion............................................................................................................ 25
4.1 Simulation Result ............................................................................................................................ 25
4.2 Discussion......................................................................................................................................... 27
4.2.1 Characteristic Impedance ....................................................................................................... 27
4.2.2 Attenuation ............................................................................................................................... 28
CHAPTET FIVE....................................................................................................................................... 30
CONCLUSION AND FUTURE WORK ................................................................................................ 30
5.1 Conclusion ........................................................................................................................................... 30
5.2 Future Work ........................................................................................................................................ 30
References .................................................................................................................................................. 31
Appendix .................................................................................................................................................... 33
V
List of Figures
Figure No.
Name
Page No.
2.1
The cross section of coaxial cable
8
3.1
The electrical model of coaxial transmission line
20
3.2
Attenuation constant in coaxial cable
23
4.1
Characteristic impedance Vs. frequency
28
4.2
Attenuation of different di-electrics
29
VI
List of Tables
Table No.
Name
Page No.
3.1
Relative permittivity of the tested dielectrics
24
4.1
Mat lab results of air as a dielectric
25
4.2
Mat lab result of polyimide as a dielectric
26
4.3
Mat lab result of polyethylene as a dielectric
26
4.4
Mat lab result of Teflon as a dielectric
27
VII
List of Acronyms
C
Cable capacitance per unit length
d
Outside diameter of inner conductor
D
Inside diameter of the shield
Dc
Diameter of conductor
NTSC
National Television Systems Committee
PAL
Phase Alternate Line
PE
Polyethylene
PVC
polyvinyl chloride
Tan δ
Loss factor for insulation
RF
radio
S
Speed
Vo
Cable rated voltage to earth
Wd
Dielectric loss per unit length
ϵr
Dielectric relative permittivity
ϵ
Dielectric permittivity of the dielectric medium
μ
Magnetic permeability of dielectric medium
μr
Magnetic relative permeability of dielectric medium
σ
Conductivity of the inner conductor

Propagation constant equation
ω
Angular frequency
frequency
VIII
CHAPTER ONE
Introduction
1.1 Background
There are several types of transmission lines whose losses are small: coaxial cable, micro strip,
strapline, balanced line, single-wire line, waveguide, optical fiber. One advantage of coax over
other types of radio transmission line is that in an ideal coaxial cable can be installed next to metal
objects such as gutters without the power losses that occur in other types of transmission lines. It
has a large frequency range which allows it to carry multiple signals. Coaxial cable also provides
protection of the signal from external electromagnetic interference. However, coaxial cable is more
expensive to install, and it uses a network topology that is prone to congestion.
In recent years, coaxial cables have become an essential component of our information
superhighway. They are applied in a wide variety of residential, commercial and industrial
installations. Coaxial cables serve as transmission line for radio frequency signals. They are
applied in feed lines connecting radio transmitters and receivers with their antennas, computer
network connections, and distributing cable television signals. Short lengths of coaxial cables are
also used for connecting devices with test equipment, like signal generator.
Coaxial cable is perhaps the most commonly used transmission line type for RF and microwave
measurements and applications. In 1894 Heaviside, Tesla and others received patents for coaxial
line and related structures. A development of coax theory is often provided as part of basic physics
and engineering equation, which are generally used for transmission line and macroscopic
electromagnetic analysis. Accordingly, the analysis, measurement and application of coax are
usually considered to be quite mature and complete.
1
Coaxial cable is typically identified or classified based on its impedance or RG-type. Coaxial
cables that conform to U.S. Government specifications are identified with an RG designation.
The RG series was originally used to describe the types of coax cables for military use, and the
specification took the form RG plus two numbers. The RG designation stands for Radio Guide,
the U designation stands for Universal.
Technique Background MATLAB
MATLAB is a programming language for technical computing. MATLAB is used for algorithm
development, model prototyping, data analysis and exploration of data, visualization and numeric
computation.
MATLAB was first conceived as a teaching tool by Moler who was at the University of New
Mexico in the late 1970s. Moler wanted his students to have access to Linpack and Eispack matrix
software without having to use the Fortan programming language, which was complex; he came
up with the MATLAB system to solve this problem. The original MATLAB was designed
specifically to handle computations with matrices and mathematics. Little and Steve Bangert
developed PC MATLAB by porting Moler’s code from FORTRAN to C, adding user-defined
functions, improved graphics, and libraries of MATLAB routines, the toolboxes.
There is general agreement in the technical computing community that the main reasons for
MATLAB’s success are its intuitive, concise syntax, the use of complex matrices as the default
numeric data object, the power of the built-in operators, easily used graphics, and it is simple and
friendly programming environment, allowing easy extension of the language. It has been widely
used by engineers, mathematicians and scientists. MATLAB boats more than 1 million users
2
around the word. MATLAB now has been used in such varied areas as automobiles, airplanes,
hearing aids, cellphones, financial derivative pricing and academics.
1.2 Literature review
This section gives an idea in the analysis of developing high performance for coaxial cable losses
with different parameters of dielectric system. The modeling for the performance of the coaxial
cable contains many parameters with various developments in the past in the field of transmission
line, which includes matching impedance, and decreasing losses of coaxial cable for growing needs
of today’s advancement of transmission line.
K. Praveen Kumar et al. (2013): presented the effect of dielectric permittivity on radiation
characteristics of coaxial cable. Coax is a type of cable that has an inner conductor surrounded by
a tubular insulating layer. Many coaxial cables also have an insulating outer sheath or jacket. The
term coaxial comes from the inner conductor and the outer shield sharing a geometric axis.
Martin J. Van Der Burgt et al. (2014): presented “Coaxial Cables and Applications “that a coax
cable consists of two conductors separated by a dielectric material. The center conductor and the
outer conductor, or shield, are configured in such a way that they form concentric cylinders with
a common axis. Hence the term and name co-axial.
Temperature range of the cable is often limited by the choice of jacket material. The insulation, or
dielectric material, is used to provide separation between the conductors. It is desirable that the
material has stable electrical characteristics (dielectric constant and dissipation factor) across a
broad frequency range. The most common materials used are polyethylene (PE), polypropylene
(PP), fluorinated ethylene propylene (FEP), and poly-tetrafluoro ethylene (PTFE). PE and PP are
desirable in lower cost, power, and temperature range applications. The outer conductor is
typically made from a number of smaller aluminum or copper conductors combined together.
3
These conductors are woven together to form a braid around the dielectric core. For higher
frequency applications, a second braid or aluminum foil tapes are often added to improve
attenuation and shield effectiveness.
The jacket material serves as a protective covering from the environment and may also serve to
add in the overall flame retardant properties of the cable. Typical materials include polyvinyl
chloride (PVC), PE, FEP, and polyvinylidene fluoride (PVDF). Coax cables are typically
identified or classified according to their impedance or RG-type. RG, or Radio Guide, is the
manner that the military used to identify transmission lines. The RG number specified the physical
construction, materials, physical, mechanical and electrical requirements of the cable.
Luyan Qian et al. (2014): proposed a method of “Coaxial Cable Modelling and Verification",
coaxial cables are differ from the other shielded cable used for carrying lower frequency signals,
such as audio signals, in that the dimension of the cable are controlled to give a precise, constant
conductor spacing, which is needed for it to function efficiently as a radio frequency transmission
line.
Mohammed Qasim Taha et al. (2015): found that the analysis to the performance is related to the
dielectric media with respect to the losses and its effects upon the cable property, dielectric
versus characteristics impedance, and the attenuation in the coaxial line for different dielectrics.
The analysis depends on the mathematical model for coaxial cables to test the influence of the
insulators (di-electrics) performance. Lower-loss cables are achieved by using dielectric materials
with better insulating properties. Polyethylene has lower dielectric losses than PVC and is
sensitive to moisture under voltage stress (i.e. for high voltages only). The material breaks down
at high temperatures.
4
1.3 Problem statement and justification
Along the length of the coaxial cable the signal transmitting through it will be lost or attenuated.
A small percent may be escape the cable’s shielding, and more will be converted to heat. The
higher frequency, the greater losses. For long distance transmissions, repeater stations are
necessary for amplifying and retransmitting weakened signals.
Coaxial cable efficiency partly depends on keeping the physical dimension of the cable uniformly.
Bends that distort the cable’s cross-section interfere with signal and bounce it back toward the
source. Connections to equipment must a physical as well as electrical match for the cable. Many
types of cables and connectors have been developed to overcome these issues in nearly any
situation. Weight and complexity are still concerns.
Power radiated, or picked up by a coax cable is more of a problem in terms of interference. Signal
radiated by the coax cable may result in high signal levels being present where they are not wanted.
For example leakage from a coax cable carrying a feed from a high power transmitter may give
rise to interference in sensitive receivers that may be located close to the coax cable. Alternatively
a coax cable being used for receiving may pick up interference if it passes through an electrically
noisy environment. It is normally for these reasons that additional measures are taken in ensuring
the outer screen or conductor is effective. Double, or even triple screened coax cables are available
to reduce the levels of leakage to very low levels.
1.4 Objectives
1.4.1 General objective
The aim of this project is to check out the effect of developing high performance of the coaxial
cable losses based on the different dielectrics on the Transmitter and receivers side. Since the
losses of coaxial cable has a great impact on decreasing the quality of the signal. An analysis is
5
carried out to find the amount of losses on the transmission of the system using coaxial cable. So
that we can identify by how much did the system affected in the presence of coaxial cable losses.
1.4.2 Specific objectives

To identify the cause of coaxial cable loss.

To identify methods of coaxial cable loss.

To design the required performance of the coaxial cable based on different dielectrics.

To minimize the amount of the coaxial cable loss.
1.5 Methodology
This project is based on the study and simulation using scientific computer software, MATLAB.
The simulation result analysis by MATLAB, first we will identify the parameters of the system
and generate the MATLAB code. And separate and differentiate the parameters going to improve
the transmission system performance using coaxial cable. Then we will model and design the high
performance of the coaxial cable transmission system.
6
1.6 Organization of project
This semi semester project is written as a partial fulfillment of the requirement for degree in
electronics and communication engineering. The broad objectives of this project is to study
“Developing high performance of the coaxial cable losses based on dielectrics”. The paper is
organized in five chapters and its outline is as follows. Chapter one presents the background,
literature survey, problem statement, objectives and the methodology used. Chapter two provides
coax cable Specifications & Parameters:
Characteristic impedance specification, Loss /
attenuation specification, Power rating specification, Velocity factor specification, Capacitance
specification, Maximum voltage, Coax mechanical dimensions specification, Common dielectric
material Chapter three is concerned with System modeling and simulation, equivalent circuit of
the coaxial cable, dielectric losses, the electrical model of coaxial Cable, Chapter four presents
how model performance comparison, and analysis and interpretation result of Algorithm. And
Chapter five draws conclusion and recommendation.
7
CHAPTER TWO
Coaxial Cable and Basic Parameters
2.1 coaxial cable
Coax cable, coaxial feeder is normally seen as a thick electrical cable. The cable is made from a
number of different elements that when together enable the coax cable to carry the radio frequency
signals with a low level of loss from one location to another.
The coaxial cable has an inner conductor surrounded by a tubular insulating layer, surrounded by
a tubular conducting shield. Many coaxial cables also have an insulating outer sheath or jacket.
The term coaxial comes from the inner conductor and the outer shield sharing a geometric axis as
shown in fig.2.1.Historically, in 1880 an English mathematician Oliver Heaviside studied the socalled skin effect in telegraph transmission lines. He concluded that wrapping an insular casing
around a transmission line both increases the clarity of the signal and improves the durability of
the cable. He patented the first coaxial cable in England after that year. Four years afterwards (in
1884), the first Coaxial cable was made by an electrical engineering company named Siemens.
Figure 2.1.The cross section of coaxial cable
The main elements within a coax cable are:
1. Centre conductor
2. Insulating dielectric
3. Outer conductor
4. Outer protecting jacket or sheath
The overall construction of the coax cable or RF cable can be seen in the diagram below and from
8
this it can be seen that it is built up from a number of concentric layers. Although there are many
varieties of coax cable, the basic overall construction remains the same:
1. Centre conductor: The center conductor of the coax is almost universally made of copper.
Sometimes it may be a single conductor whilst in other RF cables it may consist of several
strands.
2. Insulating dielectric: Between the two conductors of the coax cable there is an insulating
dielectric. This holds the two conductors apart and in an ideal world would not introduce any
loss, although it is one of the chief causes of loss in reality. This coax cable dielectric may be
solid or as in the case of many low loss cables it may be semi-airspace because it is the dielectric
that introduces most of the loss. This may be in the form of long "tubes" in the dielectric, or a
"foam" construction where air forms a major part of the material.
3. Outer conductor: The outer conductor of the RF cable is normally made from a copper braid.
This enables the coax cable to be flexible which would not be the case if the outer conductor
was solid, although in some varieties made for particular applications it is. To improve the
screening double or even triple screened coax cables are sometimes used. Normally this is
accomplished by placing one braid directly over another although in some instances a copper
foil or tape outer may be used. By using additional layers of screening, the levels of stray pickup and radiation are considerably reduced. The loss is marginally lower.
4. Outer protecting jacket or sheath: Finally there is a final cover or outer sheath to the coax
cable. This serves little electrical function, but can prevent earth loops forming. It also gives a
vital protection needed to prevent dirt and moisture attacking the cable, and prevent the coax
cable from being damaged by other mechanical means.
Coaxial cable virtually keeps all the electromagnetic wave to the area inside it. Due to the
mechanical properties, the coaxial cable can be bent or twisted, also it can be strapped to
9
conductive supports without inducing unwanted currents in the cable. In frequency radiation
applications up to a few gigahertz, the wave propagation in the transverse electric and magnetic
mode only, that means the electric and magnetic fields are both perpendicular to the focal point of
propagation. Yet, at frequencies for which the wavelength (in the dielectric) is significantly shorter
than the circumference of the transmission line, transverse electric and transverse magnetic
waveguide modes can also spread.
Coaxial cable conducts electrical signal using an inner conductor normally a solid copper, stranded
copper or copper plated steel wire, surrounded by an insulating layer (dielectric) and all enclosed
by a shield. The cable is protected by an outer insulating jacket. The electromagnetic waves cannot
propagate through coaxial cable before they are either sucked or reflected because of the effect of
the Dielectric Materials. The speed (S) of electromagnetic waves propagating through a dielectric
medium is given by:
𝑆=
𝑐
(𝜇𝑟 𝜀𝑟)1/2
C= 0.3 G (m/s)-the velocity of light in a vacuum
Where;
 μr: Magnetic relative permeability of dielectric medium
 εr: Dielectric relative permittivity of the dielectric
Since K>1 for dielectric materials, it is concluded that: The velocity with which electromagnetic
waves propagate through a dielectric medium is always less than the velocity with which they
propagate through vacuum.
2.1.1 Types of Coaxial Cable
Coaxial cable can carry digital signals for internet connections, cable television, and other new
technology. Some types of coaxial cable have different uses in a residential or commercial project.
1. Hard Line Coaxial Cable
Hard line cables are often used for high signal strength applications, as with radio transmitters or
other devices. Hard line cables typically measure up to or more than 1/2 inch thick. For heavy duty
10
signal transmissions, a variety of popular brands are available. Each of these produce many
specialized types, with varying properties and capacities.
2. RG-6 Coaxial Cable
RG-6 is likely the most familiar coaxial cable on this list. Used for relaying cable TV and other
signals, "RG" stands for “radio guide” and references the capacity of the cable. However,
according to some consumer advocates, an RG rating does not often accurately indicate the overall
quality of the cable or the materials that it is made with. Since RG-6 is used for high-definition
signals, techs from cable companies are often replacing RG-5 cables with RG-6 in clients' homes.
As the current standard, RG-6 is the desirable cable rating for today’s home and commercial
entertainment systems. RG-6 comes in several varieties, some of which have more waterproofing
for underwater or moisture prone areas of installation.
3. Semi-Rigid Coaxial Cable
This type of coaxial cable has a harder shielding metal and is therefore less flexible. It may be
useful in situations where cables do not have to curve around obstacles.
4. Tri-axial Cable
This extra-strength cable has an additional layer of shield to discourage electromagnetic
interference. It can be helpful in conditions where the cable may be vulnerable to high-strength
electromagnetic forces.
5. Twin-Axial Cable
This paired cable represents another alternative to conventional coaxial cables for a number of
different installation types.
2.1.2 Advantages and disadvantages of a coaxial cable
The two major types of feed line for time-varying electrical signals are parallel conductors ("ladder
line", "twin lead", or "twisted pair") and coaxial cable ("coax"). Each has its advantages and
11
disadvantages. Coaxial has higher loss per unit distance than twisted pair, and when used with
mismatched loads, will radiate signal from the shield. However, when properly loaded with a
matched signal, coax is much quieter than twisted pair and far more immune to noise. Parallel
conductor feed lines generally have much lower loss but are much less immune to noise and will
readily couple to any conductive objects that are proximate to the cable. Thus, much greater care
is required when routing twin lead than when routing coax.
I.
The advantages of using coax include the following:
 Broadband system
Coax has a sufficient frequency range to support multiple channels, which allows for
much greater throughput.
 Greater channel capacity
Each of the multiple channels offers substantial capacity. The capacity depends on where you
are in the world. In the North American system, each channel in the cable TV system is 6MHz
wide, according to the National Television Systems Committee (NTSC) standard. In Europe,
with the Phase Alternate Line (PAL) standard, the channels are 8MHz wide. Within one of
these channels, you can provision high-speed Internet access-that's how cable modems operate.
But that one channel is now being shared by everyone using that coax from that neighborhood
node, which can range from 200 to 2,000 homes.
 Greater bandwidth
Compared to twisted-pair, coax provides greater bandwidth system wide, and it also offers
greater bandwidth for each channel. Because it has greater bandwidth per channel, it supports
a mixed range of services. Voice, data, and even video and multimedia can benefit from the
enhanced capacity.
 Lower error rates
12
Because the inner conductor is in a Faraday shield, noise immunity is improved, and coax
has lower error rates and therefore slightly better performance than twisted-pair. The error
rate is generally 10-9 (i.e., 1 in 1 billion) bps.
 Greater spacing between amplifiers
Coax's cable shielding reduces noise and crosstalk, which means amplifiers can be spaced
farther apart than with twisted-pair.
II.
Disadvantages of a coaxial cable
 Problems with the deployment architecture
The bus topology in which coax is deployed is susceptible to congestion, noise, and security
risks.
 Bidirectional upgrade required
In countries that have a history of cable TV, the cable systems were designed for broadcasting,
not for interactive communications. Before they can offer to the subscriber any form of twoway services, those networks have to be upgraded to bidirectional systems.
 Great noise
The return path has some noise problems, and the end equipment requires added intelligence
to take care of error control.
 High installation costs
Installation costs in the local environment are high.
 Susceptible to damage from lightning strikes
Coax may be damaged by lightning strikes. People who live in an area with a lot of lightning
strikes must be wary because if that lightning is conducted by a coax, it could very well fry the
equipment at the end of it. Compared with optical fiber, coaxial cable enjoys the advantages of
relatively cheaper price and more convenient installment. As a result, in the monitor system within
a small scope, as the transmission distance is very close, transmitting the monitoring image with
13
coaxial cable cannot distort the image so that it can meet actual requirement. Moreover, coaxial
cable can compensate for different rate by doing balance adjustment in order to distort as less video
signal from receiving terminal.
Generally, coaxial cable is still the most common means of data transmission over short
distances. The advantages are:
 they are cheap to make
 cheap to install
 easy to modify
 good bandwidth
 great channel capacity
 noise immunity due to low error rate
2.1.3 How RF coax cable works
A coaxial cable carries current in both the inner and the outer conductors. These current are equal
and opposite and as a result all the fields are confined within the cable and it neither radiates nor
picks up signals.
This means that the cable operates by propagating an electromagnetic wave inside the cable. As
there are no fields outside the coax cable it is not affected by nearby objects. Accordingly it is ideal
for applications where the RF cable has to be routed through or around buildings or close to many
other objects. This is a particular advantage of coaxial feeder when compared with other forms of
feeder such as two wire (open wire, or twin) feeder.
When working with coaxial cables on your television, take care to avoid "signal leakage." This
occurs when cable systems are not fully contained within the cable system and can cause the signal
strength to deteriorate and leak into the surrounding area. Cable TV companies monitor this and
may even disconnect your service as a result.
14
Understanding the difference between these types of coaxial cables can help homeowners and
others make informed choices when installing cabling in homes, small businesses, and other
settings.
2.2 Coax Cable Specifications & Parameters
Definitions and explanations of the variety of specifications and parameters used to define the
performance of a type of coax cable. When choosing a type of coax cable to be used, it is necessary
to understand its performance. Coax cable specifications define the performance so that decision
can be made about which type to use for a given application. In order to understand the
performance of the coaxial cable it is necessary to understand the specifications for the different
parameters.
2.2.1 Characteristic impedance specification
Possibly one of the most defining coax cable specifications is its characteristic impedance. This is
the impedance seen looking into an infinitely long length of cable by a signal source. The
dimensions of the cable along with the dielectric used determine the overall impedance. This
specification is measured in ohms and is resistive.
The most common impedance figures are:

50/52 ohms: This cable is the form that is generally used for professional RF applications
and gives the minimum loss for a given weight.

75 ohms: This impedance is more widely used in domestic applications for television and
Wi-Fi RF signal and gives the minimum weight for a given loss.

93 ohms: Coax with this impedance specification was used in many early computers, linking
the computers themselves and also monitors. It was used because of its low capacitance level.
Other values of impedance are available although they are considerably less widely used. Some
searching may be required to locate coaxial cable with an unusual impedance level.
15
2.2.2 Loss / attenuation specification
Attenuation or loss is key specification of the coax cable. The function of a coax cable is to transfer
radio frequency power from one point to another. In doing so, in the ideal world, the same amount
of power should exit from the remote end of the coax as centers it. However in the real world this
is not so, and some power is lost along the length of the RF cable, and loss power reaches the
remote end than enters the RF cables.
The power loss caused by coaxial cable is referred as attenuation. It is defined in terms of decibels
per unit length, and at a given frequency. Obviously the power the coax cable, the greater the loss,
but it is also found that the loss is frequency dependent, broadly rising the frequency, although the
actual level of the loss is not linearly dependent upon the frequency. For virtually all applications
the minimum level of the loss is required. The power is lost in variety ways:

Resistive loss

Dielectric loss

Radioactive loss
Of all these forms of loss, the radiated loss is generally the least important as only a very small
amount of power is generally radiated from the cable. Accordingly most of the focus on reducing
loss is placed onto the conductive and dielectric losses.
I.
Resistive loss: Resistive losses within the coax cable arise from the resistance of the
conductors and the current flowing in the conductor’s results in heat being dissipated. The
actual area through which the current flows in the conductor is limited by the skin effect, which
becomes progressively more apparent as the frequency rises. To help overcome this multistranded conductors are often used. To reduce the level of loss due in the coax cable, the
conductive area must be increased and this results in low loss coax cables being made larger.
However it is found that the resistive losses increase as the square root of the frequency.
16
II.
Dielectric loss: The dielectric loss represent another of the major losses arising in most coax
cables. Again the power lost as dielectric loss is dissipated as heat. It is found that the dielectric
loss is independent of the size of the RF cable, but it does increase linearly with frequency.
This means that resistive losses normally dominate at lower frequencies. However as resistive
losses increase as the square root of frequency, and dielectric losses increase linearly, the
dielectric losses dominate at higher frequencies.
III.
Radiated loss: Radiation loss occurs in two wire lines since the fields from one line do not
completed cancel out those from the other line. If the conductors form a tight electromagnetic
system with the outer conductor have a thickness greater than 5 times the skin depth then
radiation is negligible. If outer conductor is a loose braid, it will result in radiation. Special
types of coax with multiple braids, or a solid outer conductor have no measureable radiation
losses.
The radiated loss of a coax cable is normally much less than the resistive and dielectric losses.
However some very cheap coax cables may have a very poor outer braid and in these cases it may
represent a noticeable element of the loss.
2.2.3 Power rating specification
Although for low level signal applications the power rating is unlikely to be important, where
higher power levels are being carried, this specification can be an issue. Normally the limiting
factor arises from the heat loss within the cable. If the power in the RF cable is to be pulsed, then
it is necessary to check that the operating voltage is not exceeded.
2.2.4 Velocity factor specification
The velocity factor specifications of a coaxial cable is the speed at which the signal travels within
the cable compared to the speed of the signal (i.e. speed of light) in a vacuum.
In some instances, the velocity factor specification for the coax cable may be of importance. For
many areas where the coax is simply being used for feeding signals from one point to another, it
17
will not be important. For applications where the phase of the signal is of importance, the velocity
factor needs to be known.
The velocity factor specification is quoted as a figure which is less than "1". It cannot go above
unity otherwise signals would be travelling faster than the speed of light.
It is found that cables have very similar velocity factor figures. This is because the dielectric
between the two conductors governs the velocity factor. Cables using a solid polyethylene
dielectric will have a velocity factor around 0.66, and those using foam polyethylene will have
velocity factor figures ranging from about 0.80 to 0.88.
2.2.5 Capacitance specification
For some applications the capacitance specification of the coax cable will be important. As can be
imagined, there is a capacitance between the inner and outer conductors of the cable, and this is
proportional to the length of cable used as well as the dielectric constant and the inner and outer
conductor diameters.
2.2.6 Maximum voltage
In some applications the voltage may rise to high levels. At some voltage it is possible the cable
may break down, causing damage to the cable itself. Voltages can arise as a result of high levels
of standing waves and high power levels. Checks should be made, before selecting a particular
type of coax that it will be able to withstand the level of voltage anticipated.
2.2.7 Coax mechanical dimensions specification
The mechanical dimensions specification of the coax is important for a variety of reasons. The
dimensions of different coax cables are obviously often different. Larger diameter coax cables
often tend to have lower loss levels and higher power ratings.
As cable size may be important to ensure that it fits apertures etc. this may be an issue. However
one of the major reasons to know the size is to ensure that correct terminating connectors can be
used. As connectors need to have the correct dimensions to ensure the cable will fit with the
18
connector correctly, it is necessary to know the dimensions of cable. Often connectors will be made
specifically for a popular size of cable.
2.2.8 Common dielectric materials
PE-Solid Polyethylene: supports low temperature applications.
FPE-Foamed Polyethylene: Provides lower attenuation and capacitance than solid PE.
Air Spaced: supports a lower dielectric constant than Polyethylene while allowing for small
diameter cable size.
The function of the dielectric material in the coaxial cable is to maintain the spacing between the
shield and the center conductor. Because this material is not a perfect insulator, a certain amount
of signal energy is dissipated in the dielectric material itself. Lower-loss cables are achieved by
using dielectric materials with better insulating properties. The most common dielectric material
is polyethylene, it has a good electrical properties, and it is cheap and flexible. Therefore, it is a
material of choice for insulation of coax cable. Polyethylene has lower dielectric losses than PVC
and is sensitive to moisture under voltage stress (i.e. for high voltages only). The ideal dielectric
material does not exhibit electrical conductivity when an electric field is applied. In practice, all
dielectrics do have some conductivity, which generally increases with increase in temperature and
applied field. If the applied field is increased to some critical magnitude, the material abruptly
becomes conducting, a large current flows (often accompanied by a visible spark), and local
destruction occurs to an extent dependent upon the amount of energy which the source supplies to
the low-conductivity path.
This critical field depends on the geometry of the specimen, the shape and material of the
electrodes, the nature of the medium surrounding the dielectric, the time variation of the applied
field, and other factors. Temperature instability can occur because of the heat generated through
conductivity or dielectric losses, causing thermal breakdown. A breakdown can be brought about
by a variety of different causes, sometimes with a number of them acting simultaneously.
Nevertheless, under carefully specified and controlled experimental conditions, it is possible to
measure critical field which is dependent only on the inherent insulating properties of the material
itself in those conditions. This field is called the intrinsic electric strength of the dielectric.
19
CHAPTER THREE
System Modeling
3.1 Equivalent Circuit of the Coaxial Cable
Generally, like any transmission line, the coaxial cable has these four parameters; capacitance,
resistance, conductance and inductance. The equivalent circuit of coaxial cable shown in fig. 3.1
Figure 3.1.The electrical model of coaxial transmission line
Coaxial cables from the transmission line perspective can have a valuable electrical influence on
a test setup. Coaxial cables are considered as lossy elements, and assigned lumped capacitance
and/or inductance, although the electrical effects of a coaxial cable can be much more complex
than a single capacitance value.
In this research, the examination of how the electrical performance of a coaxial cable has made,
notably loss and distributed capacitance/inductance can affect the integrity of a signal and the
differences of dielectrics can change those values and finally the performance of the cable. The
coaxial cable circuit contains:
Shunt capacitance: it is the capability of the coaxial to carry a charge. It is measured per unit
length (Farad perimeter).
2𝜋𝜖
𝐶 = ln (𝐷/𝑑) ………………….. (1)
20
Series resistance: ohms per meter. The resistance per unit length is just the resistance of the inner
conductor and the shield at low frequencies. At higher frequencies, skin effect increases the
effective resistance by confining the conduction to a thin layer of each conductor. To calculate this
resistance it is given by:
𝑅=
1
2𝜋
1
1
∗ (𝑑 + 𝐷) ∗ (𝜋𝑓𝜇 ⁄𝜎) 1/2…………… (2)
In addition to the losses of the series resistance, in coaxial cable where the high frequencies exist,
the effect of dielectric loss becomes significant. Dielectric loss is caused when the insulating
material inside the transmission line absorbs energy from the alternating electric field and causes
a high heat.
Shunt conductance: Generally in coaxial cables, the shunt conductance is very small because
dielectrics with good properties are used (low dielectric constant). At high frequencies, a
dielectric can have a significant resistive loss.
2𝜋𝜎
𝐺 = 𝑙𝑛 (𝐷/𝑑) …………… (3)
Series inductance: to represent or simulate the magnetic field around the wires, self-inductance
is represented bay series inductor (Henries per unit length) it is given by
𝜇
𝐷
𝐿 = (2𝜋) ∗ 𝑙𝑛 (𝑑 ) ……………….. (4)
Characteristic impedance: This is the total opposition or resistance to the flow of electrical
energy within the cable. It is a complex value defined by the cable’s resistance, capacitance,
inductance, and conductance, and is the equivalent value of these items combined.
(𝑅+𝑗𝐿)
𝑍 = ( (𝐺+𝑗𝐶) )1/2 …………… (5)
Where,
d: Outside diameter of inner conductor
D: Inside diameter of the shield
μ: Magnetic permeability of dielectric medium
ϵ: Dielectric permittivity of the dielectric medium
σ: Conductivity of the inner conductor
21
3.2 Dielectric Losses
Dielectric loss is due to the electric absorbing energy as it is polarized in each direction. It occurs
when the conductance is non-zero. Dielectrics have losses increase when increasing the voltage on
the conductors. As shown in Fig, 3.2. The dielectric losses also increase with the frequency since
the shunt conductance increase approximately linearly with frequency. The dielectric loss
represents another of the major losses arising in most coaxial cables. The power lost as dielectric
loss is dissipated as heat and it increases with frequency. The Power electrical losses result from
the generation of heat in the center conductor; braid shield, and the dielectric.
The loss is mainly a function of the kind of dielectric (insulator) used between the center conductor
and the shield. It is a loss of energy that goes into heating a dielectric material in varying electric
field. To calculate the cable, capacitor:
𝑊𝑑 = 𝜔 𝐶 𝑉𝑜2 𝑡𝑎𝑛𝛿 ………………………… (6)
𝜀
𝐷
𝐶 = [18 ∗ 𝑙𝑛 (𝑑𝑐 )] ∗ 10−9 (𝐹/𝑚) …………. (7)
Where,
dc: Diameter of conductor, mm
D: External diameter of insulation, mm
C: Cable capacitance per unit length, F.m-1
Vo: Cable rated voltage to earth, V
Wd: Dielectric loss per unit length, W.m-1
Tan δ: Loss factor for insulation
εr: Dielectric relative permittivity
ω: Angular frequency (2πf)
22
Figure 3.2. Attenuation constant in coaxial cable
3.3 The Electrical Model of Coaxial Cable and simulation
The coaxial transmission line with many different dielectrics has been tested in Mat lab to show
the effect of the different dielectric in the coaxial cable. By applying all the equation in the
theoretical calculation in the Mat lab code to test the performance of the dielectric and display it.
The Air has been tested as a dielectric, and it has good performance, but because of mechanical
limitations it cannot be practically used. Every dielectric has different properties which means
different attenuation constant.
23
TABLE 3.1
Relative permittivity of the tested dielectrics
Di-electric
𝜀𝑟
1
Air
1
2
Polyimide
3.4
3
Polyethylene
2.25
4
Teflon
2.1
The specifications are:
•6 MHz propagation wave
•Outside diameter of inner conductor (d= 0.45)
•Inside diameter of the shield (D = 1.47)
•Conductor conductivity = 5.8 ∗ 𝑒 7
1
•Propagation constant equation (𝛾): 𝛾 = ((𝑅 + 𝐽𝑤𝐿)(𝐺 + 𝐽𝑤𝐶))2 ………… (8)
Hence Mat lab codes has been built by using the equations (1-8)
24
CHAPTER FOUR
Simulation Result and Discussion
4.1 Simulation Result
The quality of the coaxial cable directly depends upon the characteristic impedance. The main
consideration is this impedance value should match both at the transmitting and receiving end of
the transmission line. The impedance characteristic gets less with the frequency increases,
Polyamide has the lowest impedance, but polyethylene is more used material a dielectric since it
is cheaper. Coaxial cable has losses (Attenuation). The term is “Attenuation", and it is measured
in decibels per meter. One dB is roughly 25%, but it is on a logarithmic scale. The image above
demonstrates how is the polyamide have less attenuation than the sleep of these tested dielectrics.
It delivers the best performance whether at higher or lower frequency bandwidths.
TABLE 4.1
MATLAB RESULTS OF AIR AS A DIELECTRIC
Air (εr = 1)
Coaxial Parameters
1
Shunt conductance (S/m)
5.3078e-16
2
Shunt capacitance (F/m)
4.6931e-11
3
Series inductance (H/m)
2.3675e-07
4
Series resistance (ohm/m)
5
9.3354
Gamma
0.0657+125.664i
6
Alpha α (Np/m)
0.065718
7
Beta β (rad /m)
25.6637
8
Characteristic impedance (ohms)
71.026-0.03714i
25
TABLE 4.2
MATLAB RESULT OF POLYIMIDE AS A DIELECTRIC
Polyimide(εr = 3.4)
Coaxial parameters
1
Shunt conductance (S/m)
5.3078e-16
2
Shunt capacitance (F/m)
1.5957e-10
3
Series inductance (H/m)
2.3675e-07
4
Series resistance (ohm/m)
5
9.3354
Gamma
0.1212+231.71i
6
Alpha α (Np/m)
0.12118
7
Beta β (rad /m)
231.7125
8
Characteristic impedance (ohms)
38.52-0.0201i
TABLE 4.3
MATLAB RESULT OF POLYETHYLENE AS A DIELECTRIC
Coaxial parameters
Polyethylene
(εr=2.25)
1
Shunt conductance (S/m)
5.3078e-16
2
Shunt capacitance (F/m)
1.0559e-10
3
Series inductance (H/m)
2.3675e-07
4
Series resistance (ohm/m)
5
9.3354
Gamma
0.0986+188.495i
6
Alpha α (Np/m)
0.098577
7
Beta β (rad /m)
188.4956
8
Characteristic impedance (ohms)
47.351-0.02476i
26
TABLE 4.4
MATLAB RESULT OF TEFLON AS A DIELECTRIC
Coaxial parameters
Teflon
(εr=2.1)
1
Shunt conductance (S/m)
5.3078e-16
2
Shunt capacitance (F/m)
9.8555e-11
3
Series inductance (H/m)
2.3675e-07
4
Series resistance (ohm/m)
5
Gamma
6
Alpha α (Np/m)
7
Beta β (rad /m)
182.104
8
Characteristic impedance (ohms)
53.351-0.02476i
9.3354
0.0952+182.104i
0.095234
4.2 Discussion
4.2.1 Characteristic Impedance
The characteristic impedance is affected by relative permittivity (εr) for a homogeneous dielectric
can be approximately computed by using electrical modeling n the coaxial cable and make a Mat
lab simulation to clarify the behavior of this impedance along the frequency band.
Characteristic impedance determines the amount of power transfer and attenuation effect along the
coaxial cable transmission line, it also controls the amount of traveling, reflected and standing
waves. The equality of the coaxial cable directly depends upon the characteristic impedance. The
27
main consideration is this impedance value should match both at the transmitting and receiving
end of the transmission line.
2.6
air er=1
polymide er=3.4
polyethylene er=2.25
Teflon er=2.1
2.4
2.2
Frequency (Ghz)
2
1.8
1.6
1.4
1.2
1
0.8
200
250
300
350
400
450
500
characteristic impedance (ohms)
550
600
650
Figure 4.1 Characteristic impedance Vs. frequency
Fig.4.1. shows that the impedance characteristic gets less with the frequency increases, the
impedance for the frequency bandwidth 0.9-1.8 GHz is relatively high when the frequency goes
high to the thousands of gigahertz like satellite applications the impedance should be around (50100) ohm. Polyamide has the lowest impedance, but polyethylene is more used material a
dielectric since it is cheaper.
4.2.2 Attenuation
The coaxial cable has a solid copper inner conductor of radius a = 1mm and a copper outer
conductor of inner radius b. The outer conductor is much thicker than a skin depth. The dielectrics
28
have different εr and the frequency 1 GHz. Letting the ratio outer to the inner diameter (b/a) vary
from 1.5 to 10, generate a plot of the attenuation (in dB/m) versus the line impedance. Using the
lossless assumption to calculate impedance. In fig. 4.2. Attenuation Vs. Characteristic impedance
for Air, Teflon, polyamide and polyethylene is shown.
1
air er=1
polyimide er=3.4
polyethylene er=2.25
Teflon er=2.1
0.9
attenuation (dB/m)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
20
40
60
80
100
characteristic impedance (ohms)
120
140
Figure 4.2 Attenuation of different dielectrics
Coaxial cable has losses (Attenuation). The term is “Attenuation", and it is measured in decibels
per meter. One dB is roughly 25%, but it is on a logarithmic scale. The image above
demonstrates how is the polyamide have less attenuation than the rest of these tested dielectrics.
It delivers the best performance whether at higher or lower frequency bandwidths. Of all figures
of loss in coaxial cable, the radiation loss is generally the least important as only a real minuscule
amount of force is generally radiated from the transmission line. Consequently, most of the
focus on reducing loss is put onto the skin effect and dielectric losses. Since the resistor of the
conductors and power is squandered in the dielectric which used for insulating the conductors,
transmission line losses are affected to a lesser degree by the fabric utilized as the cable
dielectric.
29
CHAPTET FIVE
CONCLUSION AND FUTURE WORK
5.1 Conclusion
The mathematical analysis of the coaxial transmission line with four dielectrics mediums is
represented based on mat lab software for the Air, Teflon, polyamide and polyethylene. A detailed
analysis has been to establish the essence of the dielectrics of the electrical model parameters,
characteristic impedance and attenuation. This simulation software program experimentally
depicts the operation of the coaxial transmission line with different dielectric mediums. The work
has proven that the performance of the polyimide has better results than the Air, polyethylene and
Teflon and it give less attenuation, practically the polyethylene has wider using because of its
cheap price and easy to be made.
5.2 Future Work
We recommended that there is no one solution forever. Any person should develop its core
competency with the dynamic changing environment continuously. It should update them with the
ongoing environment. The recommendation and solution are based on the key problems of this
semester project.
The recommendations for the future work includes:
I.
Implementation of other versions of Di-electrical material in order to meet different
design requirements can improve this work.
II.
III.
Hardware Implementation of the coaxial cable scheme
Additional MATLAB functions can be created to process various types of applications
that randomly generated signals,
30
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[4] RadimZajíˇcek and Jan Vrba, "Broadband Complex Permittivity Determination for Biomedical
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32
Appendix
Math-code 1
% mat lab code of characteristic impedance Vs frequency.
//Clear all
clc
c=0.3e9;
er =1;%relative permitivity for air
uu =c/sqrt(er);
a=4.30;
b=2.150;
fc = (uu/ (2*.0254*a));
flo =1.7e9/sqrt(er);
fhi=2.6e9/sqrt(er);
N=100;
df= (fhi-flo)/N;
f=flo: df: fhi;
A= sqrt (1-(fc./f).^2);
ZTE= (120*pi/sqrt(er))./A;
fG= f./1e9;
plot(ZTE,fG,'K')
hold on
c=0.3e9;
er =3.4;%relative permitivity for polymide
uu =c/sqrt(er);
a=4.30;
b=2.150;
fc = (uu/ (2*.0254*a));
flo =1.7e9/sqrt(er);
fhi=2.6e9/sqrt(er);
N=100;
df= (fhi-flo)/N;
f=flo: df: fhi;
A= sqrt (1-(fc./f).^2);
ZTE= (120*pi/sqrt(er))./A;
fG= f./1e9;
plot(ZTE,fG,'g')
hold on
c=0.3e9;
er =2.25;%relative permitivity for polyethylene
uu =c/sqrt(er);
a=4.30;
b=2.150;
fc = (uu/ (2*.0254*a));
flo =1.7e9/sqrt(er);
fhi=2.6e9/sqrt(er);
N=100;
df= (fhi-flo)/N;
33
f=flo: df: fhi;
A= sqrt (1-(fc./f).^2);
ZTE= (120*pi/sqrt(er))./A;
fG= f./1e9;
plot(ZTE,fG,'b')
hold on
c=0.3e9;
er =2.1;%relative permitivity for poly Teflon
uu =c/sqrt(er);
a=4.30;
b=2.150;
fc = (uu/ (2*.0254*a));
flo =1.7e9/sqrt(er);
fhi=2.6e9/sqrt(er);
N=100;
df= (fhi-flo)/N;
f=flo: df: fhi;
A= sqrt (1-(fc./f).^2);
ZTE= (120*pi/sqrt(er))./A;
fG= f./1e9;
plot(ZTE,fG,'r')
xlabel('characteristic impedance (ohms)')
ylabel ('Frequency (Ghz)')
legend('air er=1','polymide er=3.4','polyethylene er=2.25','Teflon
er=2.1')
hold on
grid on
34
Math-code 2
% MATLAB code of attenuation of different di-electrics
% plot of alpha Vs Zo for a particular coax
//Clear all
clc
% some constant values
muo=pi*4e-7;
eo=8.854e-12;
a=1;
er =1;%relative permitivity for air
sigd=0.0002;
sigc=5.8e7;
f=1e9;
%Perform calculations
b=1.5:.1:10;
B=2*pi*sigd./log (b./a);
C=2*pi*er*eo./log (b./a);
L=muo*log (b./a)/ (2*pi);
Rs=sqrt (pi*f*muo/sigc);
R= (1000*((1./a) + (1./b))*Rs)/ (2*pi);
w=2*pi*f;
RL=R+1i*w*L;
GC=B+1i*w*C;
Gamma=sqrt (RL.*GC);
Zo=abs(sqrt (RL./GC));
alpha=real (Gamma);
loss=exp (-2*alpha*1);
lossdB=-10*log10 (loss);
plot(Zo, lossdB, 'b');
% some constant values
muo=pi*4e-7;
eo=8.854e-12;
a=1;
er =3.4;%relative permitivity for polyimide
sigd=0.0002;
sigc=5.8e7;
f=1e9;
%Perform calculations
b=1.5:.1:10;
B=2*pi*sigd./log (b./a);
C=2*pi*er*eo./log (b./a);
L=muo*log (b./a)/ (2*pi);
Rs=sqrt (pi*f*muo/sigc);
R= (1000*((1./a) + (1./b))*Rs)/ (2*pi);
w=2*pi*f; RL=R+1i*w*L;
GC=B+1i*w*C;
Gamma=sqrt (RL.*GC);
Zo=abs (sqrt (RL./GC));
alpha=real (Gamma);
loss=exp (-2*alpha*1);
lossdB=-10*log10 (loss);
35
plot(Zo, lossdB, 'k');
hold on
% some constant values
muo=pi*4e-7;
eo=8.854e-12;
a=1;
er =2.25;%relative permitivity for polyethylene
sigd=0.0002;
sigc=5.8e7;
f=1e9;
%Perform calculations
b=1.5:.1:10;
G=2*pi*sigd./log (b./a);
C=2*pi*er*eo./log (b./a);
L=muo*log (b./a)/ (2*pi);
Rs=sqrt (pi*f*muo/sigc);
R= (1000*((1./a) + (1./b))*Rs)/ (2*pi);
w=2*pi*f; RL=R+1i*w*L;
GC=B+1i*w*C;
Gamma=sqrt (RL.*GC);
Zo=abs (sqrt (RL./GC));
alpha=real (Gamma);
loss=exp (-2*alpha*1);
lossdB=-10*log10 (loss);
plot(Zo, lossdB, 'g');
hold on
% some constant values
muo=pi*4e-7;
eo=8.854e-12;
a=1;
er =2.1;%relative permitivity for Teflon
sigd=0.0002;
sigc=5.8e7;
f=1e9;
%Perform calculations
b=1.5:.1:10;
G=2*pi*sigd./log (b./a);
C=2*pi*er*eo./log (b./a);
L=muo*log (b./a)/ (2*pi);
Rs=sqrt (pi*f*muo/sigc);
R= (1000*((1./a) + (1./b))*Rs)/ (2*pi);
w=2*pi*f; RL=R+1i*w*L;
GC=B+1i*w*C;
Gamma=sqrt (RL.*GC);
Zo=abs (sqrt (RL./GC));
alpha=real (Gamma);
loss=exp (-2*alpha*1);
lossdB=-10*log10 (loss);
plot(Zo, lossdB, 'r');
xlabel('characteristic impedance (ohms)')
ylabel ('attenuation (dB/m)')
legend('air er=1','polyimide er=3.4','polyethylene er=2.25','Teflon
er=2.1');
hold on
grid on
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