Team 4: Adam Winterstrom
Cheng-yu Chang
Thuan Dinh
EE175WS00-4
June 14,2000
Quarter Wavelength Microstrip
Antenna for Communication
between Vehicles
Final Report
Technical Advisor: Alex Balandin
Project Advisor: Barry Todd
1
Table of Contents
Executive Summary………………………………………………………………..3
Keywords……………………………………………………………………………3
Introduction………………………………………………………………………….4-6
Problem Statement…………………………………………………………………6
Possible Solutions…………………………………………………………………..7-8
Solution……………………………………………………………………………….9-13
Engineering Analysis………………………………………………………………..14-15
Discussion of Results………………………………………………………………..16-25
Conclusions and Recommendations……………………………………………….22-23
References……………………………………………………………………………25-26
Appendix………………………………………………………………………………26-46
2
Executive Summary:
A low profile, omni-directional, car-mounted antenna that can withstand harsh road and
weather conditions is needed for communication between vehicles at 469.2 MHz. A new
state-of-the-art printed circuit antenna is proposed that can actually be integrated into the
vehicle body during production and become invisible. This low cost antenna is only 8 x 10
centimeters in area and less than a half centimeter thick. A standard BNC connector is
used for easy receiver connection with coaxial cable.
The microstrip antenna, made of common copper plated FR4 substrate, was modeled and
designed using transmission-line analysis [3]. The normally half-wavelength patch antenna
was modified using copper-shorting pins to cut the size of the antenna in half, making it a
quarter-wavelength patch antenna. The antenna was tested in a large grass field using a
MOTOROLA transmitter passing a 469.2Mhz signal to an ICOM communications receiver (ICR8500). The small antenna (10x10x.41 cm) under test exhibited an omni-directional far-field
radiation pattern in the H-plane with only a +/- 2.5 dB variations. The over-all gain of the
antenna was -12dB over an isotropic radiator.
Keywords:

Microstrip

Patch

Resonator

Quarter-wave

Small antenna

Omni microstrip antenna (OMA)

Dielectric substrate

Omni-directional

Transmission line model
3

Conformal

Low profile

Electrically short antenna

Strip line

Shorting pins

Probe-fed

Printed circuit antenna

Low-gain-antenna
Introduction:
Summary of the problem
There is a consumer demand for a small, omni-directional, low profile, antenna
that needs to be able to with stand off-road vehicle use; in other words virtually any
imaginable environment. Especially important is the durability since it will encounter very
high vibration levels and lots of scrapping from trees and bushes. Since the antenna
application is for short-range (less than 1km) communication between vehicles, a narrow
bandwidth (around 10MHz), low gain and mediocre efficiency can be tolerated.
History of the Problem
Presently CB radios (28Mhz) are being used for off-road vehicles. The antennas for these
radios are very long and unattractive. They have a tendency to get pulled off or bent by
low hanging trees and garage doors. At a higher frequency of 469.2 MHz a microstrip
antenna can be used. This type of antenna is very low profile, conformal, and rugged,
which makes it attractive for off-road applications. So far the only microstrip antennas
used for vehicles (that we have knowledge of) is a conformal antenna that was used on
armored vehicles for military satellite communication [2].
History of Microstrip Antennas
Microstrip lines were first proposed in 1952 but it wasn’t until 1974 that microstrip
antennas got a lot of attention and began being used for military applications. So far
these antennas have mainly been used on aircraft, missiles, and rockets. Just recently
they have been expanded to commercial areas such as mobile satellite communications,
the direct broadcast satellite (DBS), and the global positioning system (GPS) [1].
Motivation and Goals
Coming into this project we knew virtually nothing about antennas except that
they were used in wireless communication. We wanted to know more about the field of
antenna engineering. How they related to what we had been learning in the University,
how they worked, why there were so many different types of antennas, and why the
shapes and sizes of antennas varied so much. Our goal was to be able to design, build
and understand simple antennas for various applications.
We learned the importance of antennas in a Webster’s dictionary definition;
antenna- one of the sensory appendages on the heads of insects and most other
anthropoids. That definition says it all, just as our senses; hearing, seeing, feeling,
smelling, and tasting, are important to us so is the antenna important to wireless
communication. Without the antennas wireless communication would not be possible.
A Forecast of Results
We believe our design will meet all of the desired specs needed for the vehicle
antennas. We expect the customer and consumer will be pleased with the outcome, and
a demand for microstrip antennas in other consumer markets will result. Although
efficiency and bandwidth test cannot be performed due to a lack in testing equipment, an
accurate estimation will be calculated.
What the Reader Will Find in the Report.
This document provides the detailed design, testing results and analysis of a
small (10x10cm) quarter-wave antenna. The antenna was designed slightly above the
specification size but it is predicted that a production model could be manufactured at
8x10 cm with better results if an alternate substrate is used.
The contents of this report include: an overview of microstrip antenna design
parameters including the function of each component, the design of four patch antennas
(one designed to meet the specs and the others used for comparison and analysis);
detailed test procedures including drawings of the test set-up; test results of the far field E
and H planes; polar plots of the E and H planes that show the gain of the antenna
5
compared to a reference dipole antenna; a discussion of how to improve the prototype;
solution methods and derivations; computer programs and printouts with descriptions;
hardware details; and a bibliography.
Problem Statement:
One of the hottest vehicles on the market today is the Sports Utility Vehicle
(SUV), these vehicles are built for off-road, rugged terrain. Though they are made for
hard-core four-wheel drive use, it is not smart to go four-wheel driving alone. Most people
go in teams that way when someone gets stuck or breaks a part they have other people
who can get them UN-stuck or tow them if necessary. Communication between cars is
necessary; this is why most 4-wheelers have Citizens Band (CB) radios. The problem
with these radios is their conversation can be heard by anyone who wants to listen, and
require very long wire antennas. These antennas are often bent or ripped of the vehicles
when going through tight spots with low hanging branches from trees and bushes. This
has created a demand for a new antenna. The four wheelers need a small, Omnidirectional, small range, low profile, economical, rugged, efficient, and easy to
mount antenna. It should have a gain of at least 1db, a rather narrow bandwidth,
and operate in some frequency higher than 28MHz but less than 2GHz.
6
Possible Solutions:
The problem is for a mobile, Omni-directional, small range, low profile, rugged,
efficient, inexpensive, easy to mount antenna, that has a gain of 1db and operates in the
specified frequency range. With these factors in mind, we first looked at many of the
different types of antennas that exist. Then we threw out all of the ones that could not
possibly work because of certain factors such as being too big, too directive, and too
expensive. Then, we narrowed our possible solutions down to the three antennas that we
felt could meet our specifications with the best results and lowest cost (This process can
be seen on our analysis of possible solutions). The antennas that we considered are:

A reduced height helical whip antenna, which would be approximately 2" in length
have a flexible shaft, and would be damage resistant and fully weatherized.

A phasing coil whip antenna, which would create great efficiency at a low cost by
essentially creating two antennas.

A microstrip antenna, which would be very small, low profile, could be conformed to the
shape of the car and would be the cheapest to manufacture. Any one of these solutions
would be a great choice and it would be impossible to argue one of them as the best
choice since it really depends on consumer's preference. However, we choose to go with
the microstrip antenna.
7
Solution
Feasibility Mounting
Cost
Arrow
Dyn.
Very
good
Directivity
Good
Flexible
Bad
Highly
directive
Comment
Microstrip
Antenna
Very
possible
Very
Definitely
easy,
very low
could be
cost
attach to
anywhere
Slot Antenna
Very
Possible
Not easy
Horn Antenna
Very
Possible
Very hard Expensive
Too big
Wire Antenna
Very
Possible
Easy
Very low
cost
Ok
Omni
directional
Short
Very common
and practical.
Not challenging
Too long for
specs
Dipole
Antenna
Very
Possible
Easy
Low cost
Ok
omnidirectional
Short
Possibility,
Not challenging
Too long for
specs
Helices
Antenna
Possible
need to
be
mounted
to PCB
Very low
cost
Bad
Highly
directive
Need omnidirectional
Short
Parabolic
Reflector
Possible
Very hard
Too
and not expansive
practical
Very
Bad
Highly
directive
Long
Narrow
Bandwidth,
Rugged
construction.
Not enough
work
Not practical
Too big
Phase Coil
Antenna
Possible
Very easy Low cost
and most
common
Very
Good
Reduce
Height helical
whip
Very
Possible
Very easy Very low
cost
Very
Good
Low cost
Flexible
Time
Possible Low weight, low
to Finish
profile with
with
conformability,
Time
and low
limit
manufacturing
cost
Possible Low gain, not
to Finish
practical,
with
require to input
Time
slot in the car
limit
Long
Very directive,
not good for
omni-directional
OmniPossible
practical
directional to Finish choice, but too
with
common. We
Time
want a new
limit
design
OmniPossible Omni-direction,
directional to Finish Flexible shaft,
with
looks good for
Time
this problem
limit
Table 1
This table shows various different types of antennas and eliminates ones that would not be
suitable for the problem at hand. The most suitable antennas are Microstrip,Phase Coil, Reduced whip
8
Solution:
Fig. 1
Basic Model of Microstrip Antenna. Shows the fringing
electric fields at the two ends due to the dicontinuites of
the patch
Overview of the Design Solution
The solution chosen for this problem is a rectangular quarter-wave microstrip
patch antenna that can be mounted to any side of a vehicle depending on user
preference. The Microstrip patch is modeled as a transmission line that radiates from its
ends Fig1. The antenna is fed with a coaxial cable via a BNC connector. A small ground
plane gives the antenna its omnidirectional pattern in the H-plane. The structure of the
patch antenna is very simple. The complexity in design comes in the equations modeling
the antenna (see Apendix E). Once the antenna is modeled it is easy to change the
various parameters to get the desired characteristics.
The characteristics of the rectangular patch antenna that can be adjusted or
changed to achieve the desired specifications are: length of patch, width of patch,
thickness of the patch, height of substrate, dielectric constant of the substrate, loss
9
tangent of the substrate, feed type, feed point, conductivity of patch, and the size of the
ground plane. The important properties of interest that the features above control are:
impedance, resonant frequency, bandwidth, efficiency, beamwidth, directivity, gain, and
polarization.
Impedance and Resonant Frequency
The input impedance of any antenna is very important. For maximum efficiency
the input impedance must match the feed-line impedance, which is 50ohms in most
cases.
When the length of the antenna is approximately a half-wavelength the
impedance of the antenna becomes entirely real. Since the wavelength is directly related
to the frequency (E.1) the patch is said to be at resonant at this frequency [1]. The
impedance of a half -wave microstrip patch is zero in the center of the patch and
becomes maximum at the edges of the patch length. Therefore impedance matching can
easily be accomplished by insetting the feed point of the patch at the point of desired
impedance (E.5). The feed inset can be done in several ways; the two most common
methods are microstrip fed and probe fed patches. Probe fed patches tend to produce
less cross-polarization at the feed point making them more efficient [8].
Bandwidth
The major limitation to microstrip antennas are there narrow bandwidths [10].
The bandwidth is defined as the frequency range over a certain Voltage Standing Wave
Ratio (VSWR) (E.8). Since the bandwidth is a function of the tolerable mismatch, it can
very depending upon the application.
For our application a VSWR of 2.5:1 will be
tolerated. The VSWR was not mentioned in the original specifications, but it is one of the
most important parameters in antenna design. The bandwidth of a patch is increased by
increasing the size of the antenna. The length of the patch is determined by the resonant
frequency and dielectric constant (E.4). Since the frequency is usually predetermined,
using a substrate of lower dielectric constant would be the only way to increase the
10
length and consequently the bandwidth. Of course from E.22 there is also the width and
height of the patch that can be increased for better bandwidth. In fact when designing a
microstrip patch you always want the width to be as wide as possible, the thickness as
thick as possible (without exciting higher-order modes E.7) and the dielectric constant
and loss tangent as low as possible [3]. If the Bandwidth is still not large enough a
multilayer patch also known as multi-band patch can be constructed. Multi-layered
patches are discussed in detail in [1,] and [14].
Efficiency
The total efficiency of the antenna (E.20) is affected by the resistively of the
patch, loss tangent, height, width and the feed matching network. To get the most
radiation efficiency out of your antenna you want the lowest loss tangent and the lowest
receptivity that is available in materials [3]. You also want the width and height as large
as possible. The over-all efficiency of your antenna is very much depending on the feed
matching network. In fact most of the efficiency in microstrip antennas is lost in the feed
network [1]. One of the on-going researches in patch antennas is impedance-matching
technique for increasing bandwidth and efficiency [10].
Beamwidth, directivity, and Gain
Microstrip antennas are low-gain antennas. This is due to the wide beamwidth of
the antennas. The beamwidth is what characterizes the directivity an antenna [1].
Microstrip radiation patterns are slow functions of the patch dimensions and substrate
properties. The factors that effect the patterns are the patch width, substrate dielectric
constant, and, to a lesser degree substrate height. The antenna polarization is linear with
the E-field parallel the patch length. Therefore the E-field lies along the length while the
H-plane is parallel to the width [1]. The wider the width the more narrow the beamwidth in
H-plane (E.12). The H-plane radiation is a result of fringing fields at the two edges along
the length. As the width increases the edges get further apart. The radiation from these
fields adds up to produce a far-field pattern with a maximum broadside to the patch [1].
The same thing happens for the E-field, but the E-field is changed by varying the
11
dielectric constant (E.11). Most microstrip patch patterns have the same general shape if
you assume an infinite ground plane and no higher order modes are excited (E.7). Of
course there is no such thing as an infinite ground plane, and other factors such as ridges
and bumps will play a roll in the actual pattern. For finite ground plane patches the energy
that radiates along the ground plane can be scattered in many directions by the edges. It
then combines with the direct radiation from the patch [1]. For very small ground planes
(less than a wavelength), ripples are introduced into the pattern over a wide range of
angles and a lot of radiation spills onto the backside of the ground plane. The effect of a
finite ground plane is presented in [5] where a good agreement between theory and
measurement was predicted using Geometrical Theory of Diffraction.
Quarter-wave Microstrip
The above discussion applies for both half-wave and quarter-wave patches with
a few small exceptions. A quarter-wave patch is possible since the electric field under the
patch is oriented vertically between the patch and ground plane and has an approximate
co sinusoidal variation with the maximum values at the edges and the center being zero
[1]. Since the electric fields are zero at the center a short circuit can be placed at the
center, and the basic operation will not be affected. These patches are used insinuations
where there is not enough room for a full sized patch. These patches also have a broader
E-plane pattern since the patch now only has one radiating edge along the length. Being
smaller than the normal patch, the short-circuited patch bandwidth is only about 80% of
that of the half-wave patch [1]. The short circuit can be accomplished using shorting pins
that connect the radiating patch and ground plane. The size and number of pins is
determined by E.9. This equation also shows that pins have some effect on the patch
length.
Designing the Prototype
From the above discussion it is clear that to get the most out of your design at a
particular frequency the patch should be as wide as possible, substrate as thick as
possible, and dielectric constant and loss tangent as low as possible. However in our
12
case the antenna element is constrained to be mounted within a small volume and yet
the antenna gain is desired to be as high as possible. This case calls for compromises to
be made within the bounds of the design while maximizing the bandwidth and efficiency.
The biggest challenge in this problem is the 10x8 cm size constraint and the 1dB
gain requirement. We were not able to design a half-wave patch to meet the size
specification so our first compromise was to design a quarter-wave patch. The next
compromise was the choice of FR4 substrate. We choose to use FR4 substrate because
of its availability and the short time schedule we were under. Although the FR4 dielectric
constant (er=4.7) was suitable for our needs the loss tangent (loss=. 01) was not. We
expected a very low efficiency (E.20) in our prototype but we knew that it could be greatly
improved in production by using a substrate of lower loss tangent that is available from
various companies. With the dielectric constant and loss tangent chosen the only other
parameters that we could vary were the width and thickness.
Using the equations and concepts discussed in the design solution a quarterwave patch using shorting pins was designed. The equations were implemented in a
Matlab program (Appendix F) that was organized in a systematic fashion to help the user
design a patch antenna to meet certain size constraints. To insure that the antenna would
not excite higher order modes, our thickness was limited to E.7. The width of the
prototype is the maximum width 8cm if the ground plane is trimmed. Trimming the ground
plane would not have much effect on the radiation pattern of the already very small
ground plane. The feed point of the antenna was determined from E.5
13
Engineering Analysis:
Fig. 2
This block diagram describes our approach to designing and
implementing a microstrip antenna to meet the specs of the problem.
Antenna Design (Pre-Software Stage)

Basic Antenna parameters [1].

Microstrip special parameters (substrate dielectric constant and loss tangent, patch
shape and dimensions, substrate height, conductor conductivity, feed location, input
acceptable “vswr” for Bandwidth calculation) [3].
Antenna Design (Software Stage)

Microstrip antenna parameter equations [3] .

Write programs to implement equations and plot results.

Make sure programs meet spec requirements

Mechanical Design using Protel.
Antenna Design (Hardware)

Prototype fabrication of Mechanical design
Antenna Testing

Test antenna using test procedures
14

Record all data and plot results.

Record all unacceptable errors
Antenna Final Design

Revise software to account for error

Fabricate revised design if there is time.

Test new design (continue until results are exceptable).
Fig. 3 The picture below shows all of the components of a quarter-wave microstrip patch.
The feed method shown is slightly different than our prototype. This picture actually
shows how we feed the larger ground plane antennas in Appendix C. Notice the three
layers of substrate used to achieve a thicker patch. There is shorting pins that are
soldered to the patch and ground plane. The center conducting wire of the BNC connector
is connected to the patch and the nut used fasten BNC connector is used for the ground
connection.
GROUND PLANE
PATCH
NUTS
SHORTING PIN
BNC
FR4 SUBSTRATE
15
Discussion of Results: evaluation of Design
Prototype Relative to the Production Model
The size of the prototype (10 x 10 x 0.41 cm) is slightly larger than the production
model (10 x 8 x 0.41). For production the shorting-pins and probe-feed could actually be
etched, adding to the efficiency of the antenna. The original model also uses three layers
of substrate to achieve a thickness of .41cm, during production a single thick layer should
be used to reduce the losses due to the glue used to hold the substrate together. Also
during production a cover-layer can be placed over the patch for added protection. For
the prototype FR4 substrate (er=4.7, loss tangent = .01) was used because of the
availability and cost. For large-scale production it is suggested that a substrate of lower
loss tangent be used. A good alternative would be RO3006 (e r=6.15, loss tangent =.
0013) from Rogers Corporation (See appendix G). Although the dielectric constant is
slightly larger, the loss tangent is much smaller than that of FR4. This change would
actually decrease the length of the antenna by approximately 1 centimeter and increase
the efficiency by 30%. The increase in substrate cost would be a small price to pay for
the added efficiency. Depending on the receiving device being used for communication, a
different connector may be used instead of a BNC-Female.
If all of the changes above are incorporated into the production models a significant
increase in efficiency would be made, and the antenna gain would begin to approach
zero.
16
Table 2. Below are the prototype characteristics using FR4 and the changes that would
result from using RO3006. The dimensions were calculated using the Matlab program in
Appendix F.
Parameters
FR4
RO3006
Dielectric Constant
4.7
6.15
Loss Tangent
0.01
0.0013
Patch width (cm)
8.2
8.2
Patch Length (cm)
7.654
6.15
Patch thickness (cm)
0.0035
0.0035
Antenna Length (cm)
10
8
Antenna width (cm)
10
10
Antenna thickness (cm)
0.41
0.41
Efficiency (%)
52.7
81.22
Bandwidth (MHz)
7.86
4.47
Results
Fig 4 The polar plot below shows the measured E and H plane radiation patterns that resulted from the
prototype antenna. Notice how close the H-plane pattern is to an Omni-directional pattern. This is the
result of a very small ground plane. See Appendix D for an analysis of the effects of a small ground plane.
The null that results in the E-plane is also an expected result due to a small ground plane [5]. Both planes
have there maximum gains in the front broadside to the patch at around zero degrees. The numbers on the
plot correspond to the difference between the minimum and maximum gain, not the actual gain. The
maximum gain in the plot is –12dB.
17
18
Table 3. This table shows the gain of the prototype over an isotropic radiator (reference dipole).
The maximum gain of –12 dB in the H-plane corresponds to the maximum point in Fig 4, and the
minimum gain of –37 in the E-plane corresponds to the Minimum point in Fig.4.
Degree
0
E-plane Gain db
-17
H-plane Gain db
-12
10
-17
-12
20
-17
-12
30
-17
-12
40
-17
-12
50
-16
-12
60
-16
-12
70
-16
-13
80
-16
-13
90
-15
-13
100
-15
-13
110
-15
-14
120
-15
-14
130
-15
-16
140
-15
-16
150
-15
-16
160
-18
-16
170
-18
-17
180
-21
-17
190
-23
-17
200
-28
-17
210
-37
-17
220
-31
-17
230
-22
-17
240
-20
-17
250
-18
-17
260
-18
-16
270
-18
-16
280
-18
-16
290
-19
-16
300
-19
-15
310
-19
-15
320
-19
-15
330
-18
-15
340
-18
-14
350
-18
-14
19
360
-17
-13
Strengths and Weaknesses
The strengths of this antenna are its durability, small size, low profile,
conformability and low cost. The small size and low profile make the antenna
aesthetically pleasing to consumers. Being conformable would also allow car
manufactures to implement the antennas into their automobiles body structure making
them invisible and less prone to vandalism or damage from off-road use. The durability
of the antennas makes them suitable for extreme situations, including vibrations, wind,
rain, snow, and temperature. All this features are at a very low cost.
The antenna does have its weaknesses however. The small bandwidth and low
efficiency of the antenna are not desired features. Although the bandwidth can be
increased if needed, it will consequently increase the thickness of the antenna. The
original specifications for problem don’t indicate a specific efficiency, but it is always
desired to have as much efficiency as possible.
Table 4. Prototype Comparison to specifications
Specs
Theoretical
Prototype
Frequency
469.2 MHz
469.2 MHz
469.2 MHz
Pattern
Omni
Broad beamwidth Omni
Dimensions
10x8x5 cm
10x10x.41 cm
10x10x.41
weight
.5 kg max
*******
0.091 Kg
mounting
Adhesive
*******
Adhesive
Range
1km
*******
*******
impedance
50 ohms
50 ohms
*******
Bandwidth
10 MHz
7.65 MHz
*******
Gain
1.0 dB
********
~12dB
20
Temp
-32 to 110
********
Yes
Wind Survival
150 mph
********
Yes
Humidity
95%
********
Yes
Connection
Comp. W/ Receiver
********
BNC
Radiation Efficiency
Non spec
52.7%
********
VSWR
Non spec
2.5:1
********
Patch Q
Non spec
59.68
********
Specifications not met by prototype
Their where two specifications that we did not meet with our prototype: size and gain.
Their where also three specifications that we were not able to measure: range, input
impedance and bandwidth. Three other parameters that where not motioned in the
original specifications but are very important in any antenna design are also not
measured: Overall efficiency, the total patch Q, and VSWR.
Of the two specifications that where not met only one is unattainable. The size is
not a problem and it was already mentioned that by trimming the edges or by using a
different substrate, RO3006, our size would meet the specs. The gain however is not a
realistic parameter. The only way to get a gain above 0dB for a microstrip patch antenna
is to construct an array of antennas [12]. This would type of antenna would not meet our
size specs. We can improve our gain though, so that it would approach zero dB, by
increasing the efficiency of the antenna, which can be accomplished by using a more
efficient substrate (RO3006).
The three specifications that we were not able to measure: range, input
impedance, and bandwidth, can all be calculated theoretically using the equations in
Appendix A. The range was not calculated because it depends on the power being
transmitted by the transmitter, which we do not know. The input impedance and
bandwidth where calculated and are shown in table 4. The input impedance was attained
21
by insetting the feed point at the point of 50 ohms (E..5). The bandwidth was calculated
to be only 7.65 MHz (when VSWR = 2.5) and even lower 4.4 MHz if RO3006 substrate is
used. This is not a problem though because the bandwidth can be increased by
constructing a multi-layered patch [1]. We did not attempt to do this with the prototype
because we did not have the equipment to measure the bandwidth.
The overall efficiency, the total patch Q and the VSWR are all very important
antenna design parameters that where left out of the original specifications because of
our lack of antenna knowledge at the beginning of this design project. We later defined
the VSWR to be 2.5:1. We where able to calculate the efficiency and Q-factor values
theoretically using the equations in Appendix E, but we where not able to measure the
actual values because of a lack of testing equipment. It can be seen in table 4 that our
efficiency is very low (52.7%) but table 3 shows that if we use RO3006 substrate we can
increase our efficiency by almost 30%.
If all these changes are incorporated into a production model the only
specification that could not be met is the gain of 1db. However a gain of 1db is not
needed for this application nor would be possible with our solution.
Conclusions and Recommendations
This new antenna may have a profound affect to the sport of off-road driving. With an
antenna designed specially for their passion, off-roaders now have a long awaited
alternative to the unpleasant CB antennas at a low cost. The next step is a compact, low
cost receiving and transmitting device for 469.2 MHz that would allow for the switch to the
new antenna.
At this point the new microstrip antenna has only been built on an FR4 dielectric
substrate at the frequency of 469.2 MHz. This is actually a low frequency when it comes
to microstrip antennas. Usually microstrip antennas are built for frequencies in the GHz
range due to the large size considerations at low frequencies. The results of the FR4
substrate were mediocre and it was suggested that a different substrate, RO3006, be
22
used for better efficiency. There is however another alternative that we would have liked
to pursue had we had the time that involves the use of a Ferrite substrate. The
ferromagnetic substrates in [6] and [7] posses both dielectric and magnetic properties
adding to the complexity of analysis but reducing the size of the patch by a factor of 3
and increasing the bandwidth by over 2 percent (a typical patch has a 1% bandwidth).
The goals of this project were achieved. We all learned a lot about antennas and how to
design them for different applications. We understand the importance of antennas in the
field of engineering. Although our antenna was not as elaborate or as efficient as we had
dreamed from the beginning, it was a groundbreaking point for us and for UCR. We are
proud to have laid the foundation for antenna research at UCR and we hope that it will
continue in the following years with larger and more complex projects.
Recommendations for Future Antenna Projects
Although the University was very generous in providing us with expensive equipment, we
were still very limited to what we could test. It is our suggestion that the University invest
even more into test equipment to provide the following: A variable frequency transmitter
so that bandwidth characteristics and resonant frequency can be tested, and A VSWR
meter (The allowable VSWR of an antenna is one of the most important design
parameters),
Equipment Setup Procedure:
1. Connect 12V DC Battery to Receiver.
2. Once the Transmitter has power, it continuously sends out a signal of 469.2 MHz.
3. Place the Transmitter on a step latter to reduce interference.
4. Connect Receiver with 12V DC Battery and press power button.
5. Set the frequency to 469.2 MHz on the Transmitter.
6. Connect the output end of Attenuator to the Receiver.
23
7. Record the internal attenuator settings of the receiver.
8. Connect input end of Attenuator to RG58 cable.
9. Connect RG58 cable to the antenna under test.
10. Mount the antenna to the angle varying testing apparatus.
11. Separate the transmitter and receiver approximately 50 feet apart.
12. Ready to test.
Fig 5. Test equipment set up.
L
Test Procedure:
1. Align the test antenna to read 0degrees on the protractor, when the antennas zero
degree point is pointed directly at the transmitter (Broadside for Microstrip antennas).
2. Continuously adjust the Attenuator until it reads your chosen reference point on the
receiver’s analog meter (we used 5dB as our reference point).
24
3. Record the attenuator readings at every 10-degree turn of the antenna (Use smaller
steps for better-defined pattern).
4. Actual gain will be the reference antenna readings subtracted from the antenna
under test.
5. Measure both the E and H planes.
6. All testing people should duck below the height of antenna.
7. Do more than one trial and average out all the trials for best results.
Note. It helps to have at least two people to do the measurements. One person
adjusts the Attenuator and reads the receiver, and the other person adjusting the
antenna.
For best results a large wide-open field should be used.
References:
[1]
Robert A. Sainati, “CAD of Microstrip Antennas for Wireless Appliccations,” 1996
[2]
K. Fjuimoto, A. Henderson, K. Hirasawa, J. R. James, “Small Antennas, “ 1995, pp. 242.
[3]
A. D. Krall, J. M. McCorkle, John F. Scarzello, A. M. Syeles, “The omni microstrip
antenna: A new small antenna,” IEEE Trans. Antenna and Propagation, vol. AP-27, No.
4, pp. 85-853, November 1979.
[4]
J. Watkins, “Radiation loss from open circuited dielectric Resonators,” IEEE Trans.
Microwave Theory Tech., pp. 637-639, Oct. 1973.
[5]
John Huang, “The finite ground plane effect on the micrstrip antenna radiation patterns,”
IEEE Trans. Antenna and Propagation, vol. AP-31, No. 4, pp. 649-653, July 1983.
[6]
Srin. Das, Santosh K. Chowdhury, “Rectangular microstrip Antenna on a Ferrite
Substrate,” IEEE Trans. Antenna and propagation, vol. AP-30, No. 3, pp. 499-502, May
1982.
[7]
Robert A. Pucel, Daniel J. Masse, “Microstrip Propagation on Magnetic Substrates,”
IEEE Trans. Microwave Theory and Tech., vol. MTT-20, No. 5, pp. 305-307, May 1972.
[8]
Jian-Xiong Zheng, David C. Chang, “End-Correction Network of a Coaxial probe for
Microstrip Patch Antennas, “ IEEE Trans. Antenna and Propagation, vol. 39, No 1, pp.
115-119, Jan. 1991.
[9]
David R. Jackson, Nicolasos G. Alexopoulos, “Gain Enhancement Method for Printed
Circuit Antennas,” IEEE Trans. Antenna and Propagation, vol. AP-33, No. 9, pp. 977-987,
Sep. 1985.
25
[10]
Hugo F. Pues, Antonine R. Van De Capelle, “An Impedance-Matching Technique for
Increasing the Bandwidth of Microstrip Antenna,” IEEE Trans. Antenna and Propagation,
vol. 37, No. 11, pp. 1345-1349, Nov. 1989.
[11]
John Q. Howell, “Microstrip Antenna,” IEEE Trans. Antenna and propagation, pp. 90-93,
Jan. 1976.
[12]
W. S. Gregorwich, “An Electronically Despun Array Flush-Mounted on a Cylindrical
Spacecraft,” IEEE Trans. Antenna and Propagation, vol. AP-22, No. 1, pp. 71-73, Jan.
1974.
[13]
Robert E. Munson, “Conformal Microstrip Antennas and Microstrip Phased Arrays,” IEEE
Trans. Antenna and Propagation, pp. 74-79, Jan. 1974.
[14]
Savacina, J., “Analysis of Multilayer Microstrip Lines by a Conformal Mapping Method,”
IEEE Trans. On Microwave Theory and Techniques, Vol. 40, No. 11, Nov. 1992, pp.
2116.
Appendix:
Appendix A: Definitions
Antenna: "That part of a transmitting or receiving system which is designed to radiate or
to receive electromagnetic waves". An antenna can also be viewed as a transitional
structure (transducer) between free-space and a transmission line (such as a coaxial
line). An important property of an antenna is the ability to focus and shape the radiated
power in space e.g.: it enhances the power in some wanted directions and suppresses
the power in other directions.
Antenna directivity: The directivity of an antenna is given by the ratio of the maximum
radiation intensity (power per unit solid angle) to the average radiation intensity
(averaged over a sphere). The directivity of any source, other than isotropic, is always
greater than unity.
Antenna efficiency: The total antenna efficiency accounts for the following losses: (1)
reflection because of mismatch between the feeding transmission line and the antenna
and (2) the conductor and dielectric losses.
Antenna gain: The maximum gain of an antenna is simply defined as the product of the
directivity by efficiency. If the efficiency is not 100 percent, the gain is less than the
directivity. When the reference is a loss less isotropic antenna, the gain is expressed in
26
dBi. When the reference is a half wave dipole antenna, the gain is expressed in dBd (1
dBd = 2.15 dBi).
Antenna pattern: The antenna pattern is a graphical representation in three dimensions
of the radiation of the antenna as a function of angular direction. Antenna radiation
performance is usually measured and recorded in two orthogonal principal planes (such
as E-Plane and H-plane or vertical and horizontal planes). The pattern is usually plotted
either in polar or rectangular coordinates. The pattern of most base station antennas
contains a main lobe and several minor lobes, termed side lobes. A side lobe occurring in
space in the direction opposite to the main lobe is called back lobe. Normalized pattern:
Normalizing the power/field with respect to its maximum value yields a normalized
power/field pattern with a maximum value of unity (or 0 dB).
Antenna polarization: "In a specified direction from an antenna and at a point in its far
field, is the polarization of the (locally) plane wave which is used to represent the radiated
wave at that point". "At any point in the far-field of an antenna the radiated wave can be
represented by a plane wave whose electric field strength is the same as that of the wave
and whose direction of propagation is in the radial direction from the antenna. As the
radial distance approaches infinity, the radius of curvature of the radiated wave's phase
front also approaches infinity and thus in any specified direction the wave appears locally
a plane wave". In practice, polarization of the radiated energy varies with the direction
from the center of the antenna so that different parts of the pattern and different side
lobes sometimes have different polarization. The polarization of a radiated wave can be
linear or elliptical (with circular being a special case).
E-plane: "For a linearly polarized antenna, the plane containing the electric field vector
and the direction of maximum radiation". For base station antenna, the E-plane usually
coincides with the vertical plane.
Effective radiated power (ERP): "In a given direction, the relative gain of a transmitting
antenna with respect to the maximum directivity of a half-wave dipole multiplied by the
net power accepted by the antenna from the connected transmitter".
27
Far-field region: "That region of the field of an antenna where the angular field
distribution is essentially independent of the distance from a specified point in the
antenna region". The radiation pattern is measured in the far field.
Frequency bandwidth: "The range of frequencies within which the performance of the
antenna, with respect to some characteristics, conforms to a specified standard". VSWR
of an antenna is the main bandwidth limiting factor.
Gain pattern: Normalizing the power/field to that of a reference antenna yields a gain
pattern. When the reference is an isotropic antenna, the gain is expressed in dBi. When
the reference is a half-wave dipole in free space, the gain is expressed in dBd.
H-plane: "For a linearly polarized antenna, the plane containing the magnetic field vector
and the direction of maximum radiation". For base station antenna, the H-plane usually
coincides with the horizontal plane.
Half-power beamwidth: " In a radiation pattern cut containing the direction of the maximum of a
lobe, the angle between the two directions in which the radiation intensity is one-half the
maximum value".
Half-power beamwidth is also commonly referred to as the 3-dB beamwidth.
Input impedance: " The impedance presented by an antenna at its terminals". The input
impedance is a complex function of frequency with real and imaginary parts. The input
impedance is graphically displayed using a Smith chart.
Isotropic radiator: "A hypothetical, loss less antenna having equal radiation intensity in
all direction". For based station antenna, the gain in dBi is referenced to that of an
isotropic antenna (which is 0 dB).
Radiation efficiency: "The ratio of the total power radiated by an antenna to the net
power accepted by the antenna from the connected transmitter".
Reflection coefficient: The ratio of the voltages corresponding to the reflected and
incident waves at the antenna's input terminal (normalized to some impedance Z0). The
28
return loss is related to the input impedance Zin and the characteristic impedance Z0 of
the connecting feed line by: Gin = (Zin - Z0) / (Zin+Z0).
Microstrip antenna: "An antenna which consists of a thin metallic conductor bonded to a
thin grounded dielectric substrate". An example of such antennas is the microstrip patch.
Omnidirectional antenna: "An antenna having an essentially non-directional pattern in a
given plane of the antenna and a directional pattern in any orthogonal plane". For base
station antennas, the omnidirectional plane is the horizontal plane.
Voltage standing wave ratio (VSWR): The ratio of the maximum/minimum values of
standing wave pattern along a transmission line to which a load is connected. VSWR
value ranges from 1 (matched load) to infinity for a short or an open load. For most base
station antennas the maximum acceptable value of VSWR is 1.5. VSWR is related to the
reflection coefficient Gin by: VSWR= (1+|Gin|)/(1-| Gin |).
Appendix B: Yagi Antenna Result
Angle
Gain (dB)
10
46
20
Gain -
Gain -
Angle
Gain (dB)
15
190
31
0
46
15
200
28
-3
30
40
9
210
21
-10
40
33
2
220
13
-18
50
28
-3
230
26
-5
60
31
0
240
28
-3
70
31
0
250
27
-4
80
32
1
260
34
3
90
26
-5
270
33
2
100
32
1
280
21
-10
110
33
2
290
31
0
120
25
-6
300
25
-6
130
21
-10
310
32
1
140
23
-8
320
31
0
Reference
29
Reference
150
20
-11
330
34
3
160
21
-10
340
40
9
170
28
-3
350
45
14
180
30
-1
360
46
15
Appendix C: Microstrip Antenna Dimensions
30
This is a half-wavelength microstrip antenna with
a very small ground-plane (less than wavelength),
using FR4 substrate. It was designed, built and
tested so its radiation pattern could be compared
to a quarter-wavelength patch with a very small
ground plane. The results of the test can be seen
in Appendix B.
It was feed with a BNC connector the same way
as the prototype.
This patch was only 1/3 the height of the
prototype.
31
This prototype quarter-wavelength microstrip antenna with a very small ground-plane (less than
wavelength) is using FR4 substrate. All the dimension in this drawing in “mil”, and the dimension in the
report is in “cm”. The conversion between these units are “1 inch = 2.54 cm, 1 inch = 1000 mil”. The
feed point radius shown is the radius of BNC connector. The actual hole in the top patch is made as small
as possible so that the center pin of the connector can be soldered to the patch. The ground pin is soldered
to the ground plane. The BNC connector used for this antenna was mounted the bottom of the ground
plane using adhesive.
32
This is a half-wavelength microstrip antenna with a large ground-plane, and using FR4 as substrate. It
was designed, built and tested so its radiation pattern could be compared to the antennas that have a
very small ground plane. The result is shown in Appendix B.
33
This is a quarter-wavelength microstrip antenna with a large ground-plane, and using FR4 as substrate. It
was designed, built and tested so its radiation pattern could be compared to the antennas that have a very
small ground plane. The result is shown in Appendix B.
34
Appendix D: Ground Plane Radiation Analysis
This section shows the results of four different microstrip antennas that where built and tested. There are two quarter
wave patches (one with very small ground plane and one with a larger ground plane) that where designed using the
program in Appendix F. There are also two half wave patches (a very small and a lager ground plane antenna) that
where designed using a program included in [1]. Both of these antennas are considered small ground plane antennas
but it can be seen from the drawings in Appendix C that two of the antennas have larger ground planes. To be
considered a large ground plane it needs to be around 3 times the wavelength. The results of a small ground plane
antenna can be accurately predicted using the Geometrical theory of diffraction [5]. We did not attempt to calculate the
predicted patterns for this report because of the time constraint.
Table D.1 Patch antenna gains over an isotropic radiator (reference dipole antenna)
Angle
½ Wavelength
¼ Wavelength
½ Wavelength
¼ Wavelength
With
With
With
With
Large Ground
Large Ground
Small Ground
Small Ground
Gain (dB)
Gain (dB)
Gain (dB)
Gain (dB)
E | H
E | H
E | H
E
| H
0
-25 | -13
-26 | -13
-16 | -12
-17 | -12
10
-27 | -13
-26 | -13
-18 | -12
-17 | -12
20
-28 | -13
-27 | -14
-18 | -12
-17 | -12
30
-28 | -14
-28 | -14
-17 | -12
-17 | -12
40
-29 | -15
-29 | -15
-17 | -12
-17 | -12
50
-30 | -16
-30 | -16
-16 | -13
-16 | -12
60
-35 | -17
-31 | -18
-18 | -13
-16 | -12
70
-36 | -18
-36 | -19
-17 | -13
-16 | -13
80
-38 | -19
-38 | -20
-17 | -13
-16 | -13
90
-41 | -21
-41 | -21
-18 | -13
-15 | -13
100
-42 | -22
-42 | -23
-19 | -13
-15 | -13
110
-42 | -24
-42 | -24
-20 | -14
-15 | -14
120
-42 | -26
-42 | -25
-23 | -15
-15 | -14
130
-40 | -27
-40 | -26
-24 | -16
-15 | -16
35
140
-40 | -27
-40 | -26
-25 | -16
-15 | -16
150
-40 | -27
-38 | -26
-30 | -16
-15 | -16
160
-41 | -27
-38 | -26
-31 | -17
-18 | -16
170
-42 | -28
-39 | -26
-35 | -17
-18 | -17
180
-43 | -28
-40 | -26
-37 | -17
-21 | -17
190
-46 | -29
-44 | -27
-45 | -17
-23 | -17
200
-43 | -30
-51 | -26
-42 | -17
-28 | -17
210
-41 | -31
-51 | -28
-40 | -17
-37 | -17
220
-36 | -30
-43 | -28
-38 | -16
-31 | -17
230
-34 | -28
-40 | -28
-30 | -16
-22 | -17
240
-31 | -26
-36 | -27
-27 | -16
-20 | -17
250
-30 | -23
-35 | -27
-23 | -16
-18 | -17
260
-30 | -22
-34 | -25
-20 | -16
-18 | -16
270
-26 | -20
-33 | -23
-19 | -16
-18 | -16
280
-26 | -18
-32 | -21
-20 | -16
-18 | -16
290
-26 | -16
-31 | -20
-18 | -16
-19 | -16
300
-25 | -16
-30 | -18
-17 | -15
-19 | -15
310
-25 | -15
-30 | -17
-19 | -15
-19 | -15
320
-25 | -15
-30 | -15
-17 | -14
-19 | -15
330
-25 | -14
-26 | -14
-18 | -14
-18 | -15
340
-25 | -13
-26 | -13
-17 | -14
-18 | -14
350
-25 | -13
-26 | -13
-16 | -14
-18 | -14
360
-25 | -13
-26 | -13
-16 | -13
-17 | -13
*Note the plots below do not show the actual gain but rather the difference between the maximum
and minimum gain. The actual gain of the antennas can be obtained from Table D.1.
36
Figure D.1
This plot compares the E-plane patterns of the prototype antenna (very
small ground) to a quarter-wave patch with a larger ground plane. It is clear that the
larger ground plane antenna had a lower overall gain. This was not expected but we
believe the reason for it is due to the different feed method used. Besides the over all
gain this plot gives us some good insight. Notice that the larger ground plane antenna
has a narrower beamwidth, this is because less radiation is allowed to spill to the backside of the ground plane The smaller the ground plane gets the more radiation spills to
the back-side of the antenna creating an almost omni directional antenna.
Figure D2
This plot compares the H-plane pattern s of the quarter and Half-wave patches with
larger ground palnes. Notice that the two plots are almost Identical. This is because the
width of the quarter and half-wave patch remains the same so the distances between the
two radiating edges of the H-plane remain the same and a simular pattern results.
Figure D3.
This plot the E-planes of the half-wave and quarter-wave larger ground plane antennas.
Since in a quarter-wave patch there is only one radiating edge in the E-plane because of
the short circuit, we expect the quarter-wave antenna to have a broader beamwidth than
the Half wave. In reality however there is radiation coming from the shorted-side and the
result is a pattern that is very simular to the half-wave pathc.
Figure D4 and Dd
These two plots show the E and H planes of the the quarter and half-wave patches with
very small ground planes. It can be seen tha t H-planes are almost Identical for both and
the E-plane of the quarter-wave is broader than the half-wave which is what is expexted.
37
38
39
Appendix E: Equations for Analysis of the Quarter-wave Resonator
These equations came from [1], [2] and [3].
Wavelength in free space
E1
o 
c
f
Where c is the speed of light and f is the resonant frequency.
The microstrip wavelength is given by
E2
g 
o
e'r

g
 length of quarter - wave patch
4
g
2
 length of 1/2 wavepatch
BM 
VSWR  1
Q  VSWR
 360d ' 
er 

2
R  t sin 
 ohms
d  0


0


2 P
0 t GG
P rec 
4r 2 t r
0.3c
h
2f e
u r
SWR  1
BW 
Q
SWR
total
2
2
l
1   a 
2 r  0.601 a 

ln

4





a 2   2r 
a2
2 

4
 k h 

sin  0  cos 
 2 

E V

0 k h
 0  cos( )
 2 


 k W 

sin  0  cos 
 2 

E V

0  k 40
W
 0  cos( )
 2 


er’ is the effective dielectric constant, which is related to er the dielectric constant by
E3
 1

1

h
2
e 'r  e r  1  e r  1  1  10

2







Where  and h are the width and height (or thickness) of the patch.
As an antenna, the g/4 shorted resonator will lose energy to three main sinks: The radiation into
space, the resistive loss of the conductive currents flowing in the metal strips, and the dielectric
loss of the displacement currents through the substrate.
Conductor loss Qc is given by
E4
Qc 
1580  Z 0    e 'r
1


 o   f  p 2
Z0 is the characteristic impedance of the feed, and p is the receptivity of the resonator conductor
(ohms-m)
E5
Z0 
120h






0.0724   
e r  1  1.735 e 
r
h




 0.836







120h
e r     A
The dielectric loss Qd is given by
E6
Qd 
e 'r
q e r tan 
Where tan is the loss tangent of the dielectric substrate and q is given by
E7
q















1
1
2
1
1
h 2
1  10











 


 
















We obtain a term for the over all loss material by combining (4) and (6) to give us
E8
Q41M 
Qc Qd
Qc  Qd
The radiation from the microstrip resonator QR is given by
E9
Z 0 e 'r
QR 
2300







h

0







2
The fractional power radiated by the antenna is the antenna efficiency:
E10
n
QM
QM  QR

1
0.5 0.5
q e r 0.5 tan   0 2 e 'r
p
0
1

19.2[ A]hm
210h 2 
The total Q governs the bandwidth (BW).
E11
QT 
QM QR
QM  QR

f
BM
Therefore the fractional bandwidth is
E12














BM
1
1 2300 h


f
QT Z 0 e 'r  0






2






 0 fp
e
 Z 0 q r tan  
'
1580 e 'r
er






0.5 






From this equation it can be seen that decreasing the values of tan and p (which increase
efficiency) will decrease the bandwidth.
Since the bandwidth and efficiency are both functions of common factors we see that
E13
BM
1
n 
f
QR
This is also known as the figure of merit.
In any design (13) along with (2) should be considered. Equation (1) allows the antenna to be
small by increasing e, but from (13) this will simultaneously decrease the figure of merit.
E14
E   j  I m 

1
e j k 0 r

 120 k 0 h  cos  x   1  e j cos / E eff
r

E eff
Eeff- dielectric constant
h-height of substrate
42





E15
E  j  I m 

1
e j k 0 r

 120 k 0 h  cos   sin   x   1  e j cos / E eff
r

E eff
Appendix F: Computer Programs and Sample Radiation Patterns
%Quater wavelength patch program.
%Calculates demensions and feed point for a rectangular quarterwave
%short circuited patch.
%Calculates efficiency, Bandwidth, Quality Factor
clear all
Er=input('Enter dielectric constant: ');
loss=input('dielectric loss tangent: ');
w=input('Enter patch width(cm): ');
t=input('Enter thickness of the substrate (cm): ');
Fr=input('Enter operation frequency (MHz): ');
%unit conversions
w=w*10^-2;
t=t*10^-2;
Fr=Fr*10^6;
%Ee = effective dielectric constant.
Ee=.5*(Er+1+(Er-1)*(1+10*t/w)^(-.5));
%wl = wavelenght in the substrate
wavelength=3*10^8/Fr
WAVELENGTHinFREESPACE=wavelength*10^2
wl=wavelength/(Ee^.5);
WAVELENGTHinSUBSTRTE=wl*10^2
%Calculating Length of 1/4-patch
lb=(3*10^8/(4*Fr*sqrt(Ee))) - (0*w);
lb1=lb*10^2;
patchlength=lb1
%Z=6*t;
%Z1=Z*10^2
%la=L-(lb + (2*Z));
%la1=la*10^2
ue=1;
A=(1+1.735*Er^(-.0724)*(w/t)^(-.836))
input('is 1<[A]<2 if not equation is not valid');
Z0=120*pi*t/(sqrt(Er)*w*A);
q=.5*(1+1/(1+10*(t/w)^.5));
p=1.72*10^-8; %resistivity of the resonator conductor (ohms-m)
%BW = bandwidth (VSWR=2.5)
BW=((1/Z0)*((2300*pi/Ee)*(t/wavelength)^2 + (Z0*q*Er/Ee)*loss +
(wavelength/(1580*w))*(Fr*p/Ee)^.5))*Fr;
43





VSWR=2.5
Bandwidth=BW
%QT=Total quality factor
QT=Fr/BW;
qualityFactor=QT
Rd=input('Enter input impedence (ohms): ');
%Rd=4/pi*(Fr/BW)*Z0*(sin(2*pi*d*sqrt(Ee*ue)/(3*10^8/Fr)))^2
d=(wavelength/(2*pi*sqrt(Ee)))*asin(sqrt(Rd*pi*BW/(4*Fr*Z0)));
DISTANCEfromSHORT=d*10^2
efficiency =
1/((1+(q*sqrt(Er)*loss*wavelength^2/(19.2*A*t*w)))+(sqrt(Ee)*sqrt
(p)*wavelength^(5/2)/(210*pi*t^2*w)))
%Equations checking the above calculations
Qc=1580*Z0*w*sqrt(Ee)/(wavelength*(Fr*p)^.5);
Qd=Ee/(q*Er*loss);
QM=Qc*Qd/(Qc+Qd);
QR=Z0*Ee/(2300*pi*(t/wavelength)^2);
QT2=QM*QR/(QM+QR);
VSWR=2.5;
BW2=(VSWR-1)/(QT2*sqrt(VSWR));
44
Appendix G: Bibliography
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Willey & Sons, Inc., 1997.
Iskander, Magdy F., “Electromagnetic Fields and Waves,” Prentice-Hall, Inc
., 1992.
“Technology Sampler,” Printed Circuit Antenna Design, Fabrication, and Metrology
http://oracle.mtac.pittedu/WWW/html/printed_circuit_antenna.html
Antennas Techniques & Concepts
http://www.imst.de/antenna/producs/a-desi.html
RO3003, 3006, 3010 High Frequency Laminates
http://www.rogers-corp.com/mwu/ordinfo.htm
“IEEE Standard Definitions of Terms for
http://www.cssantenna.com/technical/notes.html.
Antennas,
IEEE
Std
145-1983,”
IEEE Standards board “IEEE Standard Test Procedures for Antennas” The Institute of
Electrical and Electronics Engineers, Inc 1979.
Robert A. Sainati, “CAD of Microstrip Antennas for Wireless Appliccations,” 1996, pp. 55,
62.
K. Fjuimoto, A. Henderson, K. Hirasawa, J. R. James, “Small Antennas, “ 1995, pp. 242.
A. D. Krall, J. M. McCorkle, John F. Scarzello, A. M. Syeles, “The omni microstrip
antenna: A new small antenna,” IEEE Trans. Antenna and Propagation, vol. AP-27, No.
4, pp. 85-853, November 1979.
J. Watkins, “Radiation loss from open circuited dielectric Resonators,” IEEE Trans.
Microwave Theory Tech., pp. 637-639, Oct. 1973.
John Huang, “The finite ground plane effect on the micrstrip antenna radiation patterns,”
IEEE Trans. Antenna and Propagation, vol. AP-31, No. 4, pp. 649-653, July 1983.
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45
David R. Jackson, Nicolasos G. Alexopoulos, “Gain Enhancement Method for Printed
Circuit Antennas,” IEEE Trans. Antenna and Propagation, vol. AP-33, No. 9, pp. 977-987,
Sep. 1985.
Hugo F. Pues, Antonine R. Van De Capelle, “An Impedance-Matching Technique for
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John Q. Howell, “Microstrip Antenna,” IEEE Trans. Antenna and propagation, pp. 90-93,
Jan. 1976.
W. S. Gregorwich, “An Electronically Despun Array Flush-Mounted on a Cylindrical
Spacecraft,” IEEE Trans. Antenna and Propagation, vol. AP-22, No. 1, pp. 71-73, Jan.
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Robert E. Munson, “Conformal Microstrip Antennas and Microstrip Phased Arrays,” IEEE
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Savacina, J., “Analysis of Multilayer Microstrip Lines by a Conformal Mapping Method,”
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2116.
46