UNIVERSITY OF NAIROBI
FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING
PROJECT INDEX: PRJ 18
PATCH ANTENNA ARRAY FOR THE 2.4 GHz ISM BAND
By
Waihenya Peter Ndung’u
F17/28805/2009
Supervisor: Dr. Wlifred N. Mwema
Examiner: Prof. H Ouma
A Project submitted in partial fulfillment of the requirements for the award of the degree
Of
Bachelor of Science in ELECTRICAL AND INFORMATION ENGINEERING of the Univeristy of
Nairobi
Submitted on: April 24th, 2015
DECLARATION OF ORIGINALITY
Declaration Form for Students UNIVERSITY OF NAIROBI Declaration of Originality Form This
form must be completed and signed for all works submitted to the University for examination.
Name of Student: WAIHENYA PETER NDUNG’U
Registration Number: F17/28805/2009
College: COLLEGE OF ARCHITECTURE AND ENGINEERING
Faculty/School/Institute: ENGINEERING
Department: ELECTRICAL AND INFORMATION ENGINEERING
Course Name: FINAL YEAR PROJECT
Title of the work: DESIGN OF A PATCH ANTENNA ARRAY FOR THE 2.4GHz ISM BAND
DECLARATION
1. I understand what Plagiarism is and I am aware of the University’s policy in this regard
2. I declare that this project is my original work and has not been submitted elsewhere
for examination, award of a degree or publication. Where other people’s work or my
own work has been used, this has properly been acknowledged and referenced in
accordance with the University of Nairobi’s requirements. 3. I have not sought or used
the services of any professional agencies to produce this work 4. I have not allowed,
and shall not allow anyone to copy my work with the intention of passing it off as
his/her own work 5. I understand that any false claim in respect of this work shall
result in disciplinary action, in accordance with University Plagiarism Policy.
Signature
Date 24/04/2015
2
DEDICATION
This project is dedicated to my loving parents Dr. and Mrs. Waihenya for their utmost support and
encouragement throughout my education life and especially when I was undertaking my BSc. Electrical
and Electronics Engineering degree.
3
AKNOWLEDGEMENT
I would like to express my heartfelt gratitude to Dr Wilfred Mwema of the department of Electrical and
Information Engineering, University of Nairobi for his critical guidance as my project supervisor. I would
also like to sincerely thank my family and classmates for their support. May God bless you.
4
ABSTRACT
In this study, a coaxial fed patch antenna array for application in the 2.4GHz ISM band was
implemented using the Ansoft HFSS software. Standard formulas were used to calculate
different parameters of the antenna. These were just used as a basis of design as some
parameters varied considerably during simulation. A good extent of the antenna design was
hence done through trial and error. The proposed antenna was designed to work at 2.44GHz
frequency band. A fractional bandwidth of 2.62%, which was not close to the desired 10% and a
reflection coefficient of -18.2131dB were attained. This may have been brought about by poor
impedance matching and a high level of spurious feed radiation and surface waves. A way of
improving the bandwidth would have been to use proximity coupling feeding method which
offers the highest bandwidth (as high as 13%) and is somewhat easy to model and has low
spurious radiation. However, its fabrication would have been more difficult. A directivity of
8.53dB was achieved. This was a fairly high though directivity increase could have been studied
through use of different substrate material and thickness.
5
LIST OF FIGURES
Figure 2.1 Antenna measurement co-ordinate system………………………………………………………………….……...12
Figure 2.2 Microstrip antenna and coordinate system…………………………………………………………………..…….16
Figure 2.3 Microstrip line and its electric field lines, and effective dielectric constant…………………...……..17
Figure 2.4 Physical and effective lengths of rectangular microstrip patch…………………………………..…………18
Figure 2.5 Feed arrangements for microstrip patch arrays…………………………………………………………..……….20
Figure 3.1 Configuration for compensated right-angled bends……………………………………………………..……….23
Figure 3.2 Characteristics of the step width junction discontinuity………………………………………………….…...24
Figure 3.3 T-junction discontinuity compensation and minimization of the effect……………………………..….24
Figure 3.4 4 element patch antenna HFSS model………………………………………………………………………………....27
Figure 3.5 4-element patch antenna PCB layout with dimensions……………………………………………………......27
Figure 3.6 Implemented 4-element patch antenna array……………………………………………………………….……..28
Figure 3.7 ground plane of the patch array…………………………………………………………………………………….……..29
Figure 3.8 N male to sma female cable………………………………………………………………………………………….…......29
Figure 4.1 Return loss 𝑆11 obtained for the patch array…………………………………………………………………….…..31
Figure 4.2 Simulated E-Plane (phi=90°, theta varying) ………………………………………………………………………....32
Figure 4.3 Simulated H-plane (theta=90°, phi varying)………………………………………………………………………....32
Figure 4.4 3D radiation pattern…………………………………………………………………………………………………………....33
Figure 4.5 E-Plane and H-Plane patterns in rectangular coordinates …………………………………………………....34
Figure 4.6 VSWR plot…………………………………………………………………………………………………………………………....35
Figure 4.7 Smith chart of the proposed patch antenna………………………………………………………………………....36
Figure A1.4 Rectangular microstrip patch and its equivalent circuit transmission-line model………………..40
Figure A1.5 Recessed microstrip- line feed……………………………………………………………………………………………43
6
LIST OF TABLES
Table 4.1 Variation of antenna parameters with changes in dimensions……………………………………………....30
Table 4.2 Variation of resonance frequency with changes in patch feed length………………………………….…34
Table 4.3 HFSS Antenna Parameters in HFSS…………………………………………………………………………………………37
7
TABLE OF CONTENTS
DECLARATION OF ORIGINALITY……………………………………………………………………………………………………………….2
DEDICATION…………………………………………………………………………………………………………………………………………....3
AKNOWLEDGEMENT………………………………………………………………………………………………………………………………..4
ABSTRACT…………………………………………………………………………………………………………………………………………..……5
LIST OF FIGURES………………………………………………………………………………………………………………………………………6
LIST OF TABLES………………………………………………………………………………………………………………………………………..7
CHAPTER 1: INTRODUCTION…………………………………………………………………………………………………………………10
CHAPTER 2: LITERATURE REVIEW…………………………………………………………………………………………………………11
Fundamental Specifications of Antennas ……………………………………………………………………………………………..11
Microstrip Antennas………………………………………………………………………………………………………………………………14
Basic Characteristics…………………………………………………………………………………………………………………..………….15
Transmission Line Model Analysis for a Rectangular Patch…………………………………………………………………….16
Arrays and Feed Networks………………………………………………………………………………………………………………....…19
CHAPTER 3: THE DESIGN METHODOLOGY………………………………………………………………………………………….…21
Design Procedure………………………………………………………………………………………………………………………………..…21
Ground Plane……………………………………………………………………………………………………………………………………..….22
Microstrip Discontinuities………………………………………………………………………………………………………………………23
Main Beam Direction…………………………………..…………………………………………………………………………………………25
Matching of Microstrip Lines to the Source……………………………………………………..…………………………………….25
Quarter Wave Transformer……………………………………………………………………………………………………………………25
Simulation…………………………………………………………………………………………….……………………………………………….27
Fabrication………………………………………………………………………………………….…………………………………………………28
CHAPTER 4: HFSS SIMULATION RESULTS AND ANALYSIS……………….……………………………………………………..30
Variation of Patch Length and Width……………………………………………………………………………………………………..30
8
Reflection Coefficient……………………………………………………………………………………………………………………………..31
Radiation Pattern…………………………………………………………………………………………………………………………………..32
Inset Feed Position…………………………………………………………………………………………………………………………………34
VSWR Plot………………………………………………………………………………………………………………………………………………35
Smith Chart……………………………………………………………………………………………………………………………………………36
Ground Plane………………………………………………………………………………………………………………………………………...36
H plane Inter-Element Separation….……………………………………………………………………………………………………...37
E Plane Inter-Element Separation………………………………..…………………………………………………………………………37
CHAPTER 5: CONCLUSION…………………………………………….……………………………………………………………………….39
APPENDICES…………………………………………………………………………………………………………….……………………………40
Appendix A……………………………………………………………………………………………………….……………………………………40
Conductance…………………………………………………………………………………………………….………….………………………..40
Resonant Input Resistance……………………………………………………………………………………………………..………………41
Appendix B…………………………………………………………………………………………………………………………………………….45
Matlab Code for calculation of the insed feed position where the input impedance is 50 Ohms…………….45
Matlab code for calculation for the width of the 50 ohm line……………………………………………………………..….45
REFERENCES………………………………………………………………………………………………………………………………………….47
9
CHAPTER 1: INTRODUCTION
An antenna is a transducer between a guided wave and a radiated wave, or vice versa. The
structure that "guides" the energy to the antenna is most evident as a coaxial cable attached
to the antenna. A patch antenna is a type of radio antenna with a low profile, which can be
mounted on a flat surface. It consists of a flat sheet of metal, usually copper, mounted on a
larger sheet of metal called a ground plane. A patch array antenna is, in general, some
arrangement of multiple patch antennas that are all driven by the same source. Frequently, this
arrangement consists of patches arranged in orderly rows and columns (a rectangular array).
The reason for these types of arrangements is higher gain. Higher gain commonly implies a
narrower beamwidth and that is, indeed, the case with patch arrays.
This report presents the design and analysis of patch network antenna array for the 2.4GHz ISM
band which is largely license exempt and can be accessed freely for example bluetooth. The
antenna will be designed with an aim of achieving high directivity and at least a 10% fractional
bandwidth. The antenna will have a center frequency of 2.44 which is almost the same as the
given ISM band center frequency. It was so chosen so as to have a bandwidth whose range is
falls within the 2.4 Ghz band. The work presented here is the continuation or enhancement of
the 2013 final year patch antenna array project where a basic 4 element patch antenna array
was designed without much emphasis on the gain, directivity or bandwidth.
The report consists of five chapters. After the introduction, the necessary theoretical
background is presented in the second chapter. Then a chapter describing the design and all the
steps and choices made for the patch antenna array follows. An Analysis of the simulated
results together with discussions is done in chapter four. The conclusion, which includes a short
summary of the design achievements, is presented in chapter five.
10
CHAPTER 2: LITERATURE REVIEW
An antenna is generally a bidirectional device, that is, the power through the antenna can flow
in both directions, coupling electromagnetic energy from the transmitter to free space and
from free space to the receiver, and hence it works as a transmitting as well as a receiving
device. Transmission lines are used to transfer electromagnetic energy from one point to
another within a circuit and this mode of energy transfer is generally known as guided wave
propagation. An antenna can be thought of as a mode transformer which transforms a guidedwave field distribution into a radiated-wave field distribution. It can also be thought of as a
mode transformer which transforms a radiated-wave field distribution into a guided-wave field
distribution (since the two waves may have different impedances, it may also be thought of as
an impedance transformer) [8].
Fundamental Specifications of Antennas
Lobes
Any given antenna pattern has portions of the pattern that are called lobes. A lobe can be a
main lobe, a side lobe or a back lobe and these descriptions refer to that portion of the antenna
pattern in which the lobe appears. In general, a lobe is any part of the pattern that is
surrounded by regions of weaker radiation. So a lobe is any part of the pattern that sticks out
[15].
Radiation Pattern
Radiation pattern is graphical representation of the relative field strength transmitted from or
received by the antenna. It is measurement of radiation around the antenna. Antenna radiation
patterns are taken at one frequency, one polarization and one plane cut. The patterns are
usually presented in polar or rectilinear form with a dB strength scale. It is important to state
that an antenna radiates energy in all directions, at least to some extent, so the antenna
pattern is actually three-dimensional. It is common, however, to describe this 3D pattern with
two planar patterns, called the principal plane patterns. These principal plane patterns can be
obtained by making two slices through the 3D pattern through the maximum value of the
pattern or by direct measurement. It is these principal plane patterns that are commonly
referred to as the antenna patterns [14, 15].
11
Azimuth and Elevation Plane (E and H plane)
Characterizing an antenna's radiation properties with two principal plane patterns works quite
well for antennas that have well-behaved patterns, that is, not much information is lost when
only two planes are shown. Figure 2.1 shows a possible coordinate system used for making such
antenna measurements [15].
Figure 2.1 Antenna measurement co-ordinate system
The term azimuth is commonly found in reference to "the horizon" or "the horizontal" whereas
the term elevation commonly refers to "the vertical". When used to describe antenna patterns,
these terms assume that the antenna is mounted (or measured) in the orientation in which it
will be used. In Figure 2.1, the 𝑥𝑦-plane (𝜃 = 90°) is the azimuth plane (E-plane). The azimuth
plane pattern is measured when the measurement is made traversing the entire 𝑥𝑦-plane
around the antenna under test. The elevation plane (H-plane) is then a plane orthogonal to the
𝑥𝑦-plane, say the 𝑦𝑧-plane (Φ = 90°). The elevation plane pattern is made traversing the entire
𝑦𝑧-plane around the antenna under test [15].
The Poynting vector describes both the direction of propagation and the power density of the
electromagnetic wave. It is found from the vector cross product of the electric and magnetic
fields and is denoted S:
𝑆 = 𝐸 × 𝐻∗
𝑤/𝑚2
(2 − 1)
Root mean square (RMS) values are used to express the magnitude of the fields. 𝐻 ∗ is the
complex conjugate of the magnetic field phasor. The magnetic field is proportional to the
electric field in the far field. The constant of proportion is η, the impedance of free space (η
=376.73):
12
|𝐸|2
|𝑆| = 𝑆 =
𝜂
𝑤/𝑚2
(2 − 2)
Because the Poynting vector is the vector product of the two fields, it is orthogonal to both
fields and the triplet defines a right-handed coordinate system: (E, H, S) [6].
Return Loss
Return loss is a measure of the reflected energy from a transmitted signal. It is a logarithmic
ratio measured in dB (decibel) that compares the power reflected by the antenna to the power
that is fed into the antenna from the transmission line. The larger the value of return loss the
less is the energy reflected. For good impedance matching resonant frequency must lie below
−10 𝑑𝐵. [14] .
Bandwidth
Bandwidth is defined as the range between upper cut-off frequency (𝑓𝑈 ) at -10 dB and lower
cut-off (𝑓𝐿 ) frequency at -10 dB. Bandwidth indicates range of frequency for which an antenna
provides satisfactory operation [14].
3-dB Beamwidth
Also known as the Half Power Beamwidth (HPBW) is typically defined for each of the principle
planes. The 3-dB beamwidth in each plane is defined as the angle between the points in the
main lobe that are down from the maximum gain by 3dB. This is the point where the magnitude
of the radiation pattern decreases by 50% (or -3 dB) from the peak of the main beam [14, 15].
VSWR
VSWR stands for Voltage Standing Wave Ratio. The parameter VSWR is a measure that
numerically describes how well the antenna is impedance matched to the radio or transmission
line it is connected to. The smaller the VSWR the better the antenna matched to the
transmission line and the more the power delivered to the antenna. For the perfect matching
VSWR = 1, there is no reflection and return loss. In the real system it is very hard to achieve a
perfect match, so it is defined that having VSWR < 2 is still good matching system [14].
Directivity
Directivity of an antenna is a measure of the concentration of the radiated power in a particular
direction [14]. If the antenna had 100% radiation efficiency, all directivity would be converted
to gain. Typical half wave patches have efficiencies well above 90% [13].
13
Antenna Gain
Gain is a measure of the ability of the antenna to direct the input power into radiation in a
particular direction and is measured at the peak radiation intensity [6].It is standard practice to
use an isotropic radiator as the reference antenna in this definition. An isotropic radiator is a
hypothetical lossless antenna that radiates its energy equally in all directions. This means that
the gain of an isotropic radiator is G=1 (or 0 dB). It is customary to use the unit dBi (decibels
relative to an isotropic radiator) for gain with respect to an isotropic radiator [15].
Polarization
The Polarization of an antenna is the polarization of the wave radiated by the antenna in the far
field [8]. Polarization is a property of waves that can oscillate with more than one direction
[16].The plane in which the electric field varies is also known as the polarization plane. For
optimum system performance, transmit and receive antennas must have the same polarization
[13].
Front-to-back ratio
The front-to-back (F/B) ratio is used a figure of merit that attempts to describe the level of
radiation from the back of a directional antenna. Basically, it is the ratio of the peak gain in the
forward direction to the gain 180-degrees behind the peak. On a dB scale, it is just the
difference between the peak gain in the forward direction and the gain 180-degrees behind the
peak [15].
Microstrip Antennas
Microstrip antennas are also referred to as patch antennas. They are low profile, conformable
to planar and non-planar surfaces, simple and inexpensive to manufacture using modern
printed-circuit technology, mechanically robust when mounted on rigid surfaces, compatible
with MMIC designs and when the particular patch shape and mode are selected, they are very
versatile in terms of resonant frequency, polarization, pattern and impedance [1].
Major operational disadvantages of microstrip antennas are their low efficiency, low power,
high Q (sometimes in excess of 100), poor polarization purity, poor scan performance, spurious
feed radiation and very narrow frequency bandwidth, which is typically only a fraction of a
percent or at most a few percent. There are methods, however, such as increasing the height of
the substrate that can be used to extend the efficiency (to as large as 90 percent if surface
waves are not included) and bandwidth (up to about 35 percent). However, as the height
increases, surface waves are introduced which usually are not desirable because they extract
14
power from the total available for direct radiation (space waves). The surface waves travel
within the substrate and they are scattered at bends and surface discontinuities, such as the
truncation of the dielectric and ground plane, and degrade the antenna pattern and
polarization characteristics [1].
Basic Characteristics
Microstrip antennas, as shown in Figure 2.2, consist of a very thin (t ≪ λ0 , where λ0 is the
free-space wavelength) metallic strip (patch) placed a small fraction of a wavelength (h≪ λ0 ,
usually 0.003λ0 ≤ h≤0.05λ0 ) above a ground plane. The microstrip patch is designed so its
pattern maximum is normal to the patch (broadside radiator). This is accomplished by properly
choosing the mode (field configuration) of excitation beneath the patch. End-fire radiation can
also be accomplished by judicious mode selection. For a rectangular patch, the length L of the
element is usually λ0 /3 <L<λ0 /2. The strip (patch) and the ground plane are separated by a
dielectric sheet (referred to as the substrate). There are numerous substrates that can be used
for the design of microstrip antennas, and their dielectric constants are usually in the range of
2.2≤𝜀𝑟 ≤12. The ones that are most desirable for good antenna performance are thick
substrates whose dielectric constant is in the lower end of the range because they provide
better efficiency, larger bandwidth, loosely bound fields for radiation into space, but at the
expense of larger element size [1].
The radiating elements and the feed lines are usually photo-etched on the dielectric substrate.
The radiating patch may be square, rectangular, thin strip (dipole), circular, elliptical, triangular,
or any other configuration. Square, rectangular, dipole (strip), and circular are the most
common because of ease of analysis and fabrication, and their attractive radiation
characteristics, especially low cross-polarization radiation [1].
15
Figure 2.2 Microstrip antenna and coordinate system
There are many configurations that can be used to feed microstrip antennas. The four most
popular methods are the microstrip line, coaxial probe, aperture coupling, and proximity
coupling. The microstrip-line feed is easy to fabricate, simple to match by controlling the inset
position and rather simple to model. However as the substrate thickness increases, surface
waves and spurious feed radiation increase, which for practical designs limit the bandwidth [1].
There are various methods of analysis for microstrip antennas with the most popular models
being the transmission-line, cavity, and full wave models (which include primarily integral
equations/Moment Method). The transmission-line model is the easiest of all, it gives good
physical insight, but is less accurate and it is more difficult to model coupling [1].
Transmission–Line Model Analysis for a Rectangular Patch
Fringing Effects
Because the dimensions of the patch are finite along the length and width, the fields at the
edges of the patch undergo fringing. This is illustrated along the length in Figures 2.2(a, b) for
the two radiating slots of the microstrip antenna. The same applies along the width. The
amount of fringing is a function of the dimensions of the patch and the height of the substrate.
For the principal E-plane (𝑥𝑦-plane) fringing is a function of the ratio of the length of the patch L
to the height h of the substrate (L/h) and the dielectric constant 𝜀𝑟 of the substrate. Since for
microstrip antennas L/h≫1, fringing is reduced; however, it must be taken into account
16
because it influences the resonant frequency of the antenna. The same applies for the width.
For a microstrip line shown in Figure 2.3(a), typical electric field lines are shown in Figure 2.3(b).
This is a nonhomogeneous line of two dielectrics; typically the substrate and air. As can be seen,
most of the electric field lines reside in the substrate and parts of some lines exist in air. As
W/h≫1 and 𝜀𝑟 ≫ 1, the electric field lines concentrate mostly in the substrate. Fringing in this
case makes the microstrip line look wider electrically compared to its physical dimensions.
Since some of the waves travel in the substrate and some in air, an effective dielectric constant
𝜀𝑟𝑒𝑓𝑓 is introduced to account for fringing and the wave propagation in the line [1].
Figure 2.3 Microstrip line and its electric field lines, and effective dielectric constant
The effective dielectric constant is defined as the dielectric constant of the uniform dielectric
material so that the line of Figure 2.3(c) has identical electrical characteristics, particularly
propagation constant, as the actual line of Figure 2.2(a).
Effective Length, Resonant Frequency, and Effective Width
Because of the fringing effects, electrically the patch of the microstrip antenna looks greater
than its physical dimensions. For the principal E-plane (𝑥𝑦 plane), this is demonstrated in Figure
2.4(a) where the dimensions of the patch along its length have been extended on each end by a
distance ∆𝐿, which is a function of the effective dielectric constant 𝜀𝑟𝑒𝑓𝑓 and the width-to
height ratio (w/h) [1].
17
Figure 2.4 Physical and effective lengths of rectangular microstrip patch
Since the length of the patch has been extended by ∆𝐿 on each side, the effective length of the
patch is now (L=𝜆/2 for for dominant 𝑇𝑀010 mode with no fringing)
𝐿𝑒𝑓𝑓 = 𝐿 + 2∆𝐿
(2 − 4)
For the dominant 𝑇𝑀010 mode, the resonant frequency of the microstrip antenna is a function
of its length. Usually given by
(𝑓𝑟 )010 =
1
2𝐿√𝜀𝑟 √𝜇0 𝜀0
=
𝑣0
2𝐿√𝜀𝑟
(2 − 5)
where 𝑣0 is the speed of light in free-space. Since (2-5) does not account for fringing, it must be
modified to include edge effects and should be computed using
(𝑓𝑟𝑐 )010 =
1
2𝐿𝑒𝑓𝑓 √𝜀𝑟𝑒𝑓𝑓 √𝜇0 𝜀0
𝑣0
=𝑞
2𝐿√𝜀𝑟
=
1
2(𝐿 + 2∆𝐿)√𝜀𝑟𝐸𝐹𝐹 √𝜇0 𝜀0
=𝑞
1
2𝐿√𝜀𝑟 √𝜇0 𝜀0
(2 − 6)
where
𝑞=
(𝑓𝑟𝑐 )010
(𝑓𝑟 )010
(2 − 7)
18
The 𝑞 factor is referred to as the 𝑓𝑟𝑖𝑛𝑔𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 (length reduction factor). As the substrate
height increases, fringing also increases and leads to larger separation between the radiating
edges and lower resonant frequencies [1].
Arrays and Feed Networks
Usually the radiation pattern of a single element is relatively wide, and each element provides
low values of directivity (gain). In many applications it is necessary to design antennas with very
directive characteristics (very high gains) to meet the demands of long distance communication.
This can only be accomplished by increasing the electrical size of the antenna. Enlarging the
dimensions of single elements often leads to more directive characteristics. Another way to
enlarge the dimensions of the antenna, without necessarily increasing the size of the individual
elements, is to form an assembly of radiating elements in an electrical and geometrical
configuration. This new antenna, formed by multielements which are driven by the same
source, is referred to as an array. In most cases, the elements of an array are identical. This is
not necessary, but it is often convenient, simpler, and more practical [1].l
The total field of the array is determined by the vector addition of the fields radiated by the
individual elements. This assumes that the current in each element is the same as that of the
isolated element (neglecting coupling). This is usually not the case and depends on the
separation between the elements. To provide very directive patterns, it is necessary that the
fields from the elements of the array interfere constructively (add) in the desired directions and
interfere destructively (cancel each other) in the remaining space. Ideally this can be
accomplished, but practically it is only approached. In an array of identical elements, there are
at least five controls that can be used to shape the overall pattern of the antenna [1]. These
are:
1. The geometrical configuration of the overall array (linear, circular, rectangular,
spherical, etc.)
2. The relative displacement between the elements
3. The excitation amplitude of the individual elements
4. The excitation phase of the individual elements
5. The relative pattern of the individual elements
Arrays are very versatile and are used, among other things, to synthesize a required pattern
that cannot be achieved with a single element. In addition, they are used to scan the beam of
an antenna system, increase the directivity, and perform various other functions which would
be difficult with any one single element. The elements can be fed by a single line or by multiple
lines in a feed network arrangement. The first is referred to as a series-feed network while the
19
second is referred to as a corporate-feed network. The corporate-feed network is used to
provide power splits of 2𝑛 (i.e., n=2, 4, 8, 16, 32, etc.). This is accomplished by using either
tapered lines, or using quarter-wavelength impedance transformers [1].
Figure 2.5 Feed arrangements for microstrip patch arrays
Corporate-fed arrays are general and versatile. With this method the designer has more
control of the feed of each element (amplitude and phase) and it is ideal for scanning phased
arrays, multi-beam arrays, or shaped-beam arrays. The phase of each element can be
controlled using phase shifters while the amplitude can be adjusted using either amplifiers or
attenuators [1].
Those who have been designing and testing microstrip arrays indicate that radiation from the
feed line, using either a series or corporate-feed network, is a serious problem that limits the
cross-polarization and side lobe level of the arrays [38]. Both cross-polarization and side lobe
levels can be improved by isolating the feed network from the radiating face of the array. This
can be accomplished using either probe feeds or aperture coupling [1].
In microstrip arrays, as in any other array, mutual coupling between elements can introduce
scan-blindness which limits, for a certain maximum reflection coefficient, the angular volume
over which the arrays can be scanned. For microstrip antennas, this scan limitation is strongly
influenced by surface waves within the substrate. This scan angular volume can be extended by
eliminating surface waves. One way to do this is to use cavities in conjunction with microstrip
elements. It has been shown that the presence of cavities, either circular or rectangular, can
have a pronounced enhancement in the E-plane scan volume, especially for thicker substrates.
The H-plane scan volume is not strongly enhanced. However the shape of the cavity, circular or
rectangular, does not strongly influence the results [1].
20
CHAPTER 3: THE DESIGN METHODOLOGY
A rectangular patch was chosen as the basis of the design because of its ease of fabrication and
analysis. The microstrip line was used as the feeding method as it is easy to fabricate, simple to
match by controlling the inset feed position and rather simple to model. The antenna was
designed to work in the 2.4GHz ISM band which has a frequency range of 2.4-2.5GHz, a center
frequency of 2.450GHz, a bandwidth of 100MHz and is freely available worldwide. Some
applications in the 2.4GHz ISM band include the home microwave oven, sulphur lamps,
communication applications such as wireless LANs, bluetooth and radio control equipment such
as low power remote control of toys [3].
Design Procedure
The FR4 Glass Epoxy, whose loss tangent is 0.002, was chosen as the dielectric material
substrate.
To commence the design procedure assumes, specific information had to be included: dielectric
constant of the substrate (𝜀𝑟 ), the resonant frequency (𝑓𝑟 ) and the height of the substrate, ℎ.
𝜀𝑟 = 4.3 , 𝑓𝑟 = 2.44𝐺𝐻𝑧, ℎ = 1.6𝑚𝑚
For an efficient radiator, the practical width that leads to good radiation efficiencies is
𝑊=
1
2
𝑣𝑜
2
√
√
=
2𝑓𝑟 √𝜇𝑜 𝜀𝑜 𝜀𝑟 + 1 2𝑓𝑟 𝜀𝑟 + 1
(3 − 1)
= 37.58𝑚𝑚
where 𝑣𝑜 is the free-space velocity of light.
The initial values (at low frequencies) of the effective dielectric constant are referred to as the
static values, and they were calculated as
𝑊/ℎ > 1
𝜀𝑟𝑒𝑓𝑓=
𝜖𝑟 + 1 𝜀𝑟 − 1
ℎ 1
+
[1 + 12 ]−2
2
2
𝑊
= 3.99
21
(3 − 2)
A very popular and practical approximate relation was then used to find the normalized
extension of the length as
𝑊
(𝜀𝑟𝑒𝑓𝑓 + 0.3)( + 0.264)
∆𝐿
ℎ
= 0.412
𝑊
ℎ
(𝜀𝑟𝑒𝑓𝑓 − 0.258)( + 0.8)
ℎ
(3 − 3)
∆𝐿 = 0.741𝑚𝑚
The actual length of the patch was determined by solving 𝐿 as,
𝐿=
1
2𝑓𝑟 √𝜀𝑟𝑒𝑓𝑓 √𝜇𝑜 𝜀𝑜
− 2∆𝐿
(3 − 4)
= 29.15𝑚𝑚
For efficient transfer of power from a transmission line to the patch antenna, the input
impedance of the patch antenna needed to be matched to the characteristic impedance of the
transmission line. It was observed that impedance seen by a transmission line attached to the
radiating edge was very high, and also the impedance (ratio of voltage to current) decreased as
one moved towards the center of the patch. Therefore, depending on the characteristic
impedance of the transmission line, an appropriate point on the patch was chosen through
calculation as the feed point [8].
In order to access the appropriate impedance point on the patch, a recess was created in the
patch. The recess or inset feed was used to improve the impedance matching between the
patch and the feed line. The inset feed position, where the input impedance was 50 ohms and
the lengths and widths for the microstrip feeds were calculated using the matlab code in
appendix B. A FDTD-Finite Difference Time Domain- analysis shows that the inset disturbs the
transmission line or cavity model and increases the impedance variation with distance
compared to a coaxial probe feed given a patch resonant length L and feed position 𝑦𝑜 from the
center. Transmission line analysis method was applied as it gives a good insight. However, it is
more difficult to model coupling as well as less accurate [1, 6, 8].
Ground Plane
As part of the antenna, the ground plane should be infinite in size as for a monopole antenna
but in reality this is not easy to apply besides a small size of ground plane is desired. In practice,
it has been found that the microstrip impedance with finite ground plane width (𝑍𝑜 ) is
22
practically equal to the impedance value with infinite width ground plane (𝑍𝑖 ) , if the ground
width 𝑊𝑔 is at least greater than 3*W. The radiation of a microstrip antenna is generated by the
fringing field between the patch and the ground plane, the minimum size of the ground plane is
therefore related to the thickness of the dielectric substrate.[9, 11].
The size of the ground plane was chosen as 114𝑚𝑚 𝑙𝑒𝑛𝑔𝑡ℎ 𝑏𝑦 148𝑚𝑚 𝑤𝑖𝑑𝑡ℎ .
Microstrip Discontinuities
Surface waves are electromagnetic waves that propagate on the dielectric interface layer of the
microstrip. The propagation modes of surface waves are practically TE and TM. Surface waves
are generally at any discontinuity of the microstrip. Once generated, they travel and radiate,
coupling with other microstrip of the circuit, decreasing isolation between different networks
and signal attenuation. Surface waves are a cause of crosstalk, coupling, and attenuation in a
multi-microstrip circuit. For this reason surface waves are always an undesired phenomenon
[9].
A discontinuity in a microstrip is caused by an abrupt change in geometry of the strip
conductor, and electric and magnetic field distributions are modified near the discontinuity.
The altered electric field distribution gives rise to a change in capacitance, and the changed
magnetic field distribution to a change in inductance.
a) Bends
Four 90° bends were encountered in the design. This brought about excess capacitance
at the square corners making the characteristic impedance value to be lower than that
of the uniform connecting lines. A bend of this angle doesn’t work well above a few GHz
due to a high VSWR. The same holds true for bends with angles greater than 90°
Compensation for the microstrip corner bend was made by the use of decreased
capacitance technique. Since experiments on various bends have proven that a
decrease in the input reflection coefficients can be achieved if the corner is chamfered
(mitered), the following configuration was applied
Figure 3.1 Configuration for compensated right-angled bends; W is the width of the line
23
Therefore,
1.8 × 2.62 = 4.716𝑚𝑚
b) Step Width Junction
This discontinuity was found at the 𝜆⁄4 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟𝑠. The effect of the fringing
capacitance associated with the wider line of the step discontinuity is similar to an
increase in the length of that line
Figure 3.2 Characteristics of the step width junction discontinuity
In terms of distributed elements, the discontinuity capacitance C has the effect of an
increase in length of the wide line w1, and an equal decrease in length of the narrow
line w2. To compensate for the excess capacitance, the wider line w1 was made to be
electrically longer by a length of 9.26mm.
c) T-Junction
These discontinuities were found in the patch antenna array as branch –lines. The TJunctions were easily compensated for by simply adjusting the lengths of the different
lines. The offset in the main line is usually very small, and the main effect is on the
length of the stub
Figure 3.3 T-junction discontinuity compensation and minimization of the effect
𝑤1 = 12 = 2.62𝑚𝑚 ;
0.7𝑤1 = 0.7 × 2.62 = 1.834𝑚𝑚
24
Main Beam Direction:
For the 4-element array of figure 3.4, the main beam was directed broadside to the array by
ensuring there was no input phase difference from element to element. To implement an even
number of in-phase patch elements, the feed network needed to be carefully designed. The
distance from the 50-ohm SMA source to each patch element needed to be identical or
multiples of λ. Unequal line lengths would have produced phase shifts, which would yield fixed
beams that would be scanned away from the broadside. A quarter-wave transformer was used
to match the 100-ohm line to a 50-ohm line. The 100-ohm microstrip line was fed using a 50ohm SMA. In the design of an effective in-phase radiator, the distance between the patch
elements needed to be optimized to yield a peak gain. The antenna-array chapter in Antenna
Theory by Balanis provided insight on the optimum antenna separation distance. The author
identified a separation distance of 𝜆/2 as providing the optimal gain. In the design, this
separation was used as 31.33mm [2, 4].
Matching of Microstrip Lines to the Source
The characteristic impedance of a transmission line of the microstrip feed patch was designed
with respect to the source impedance. The characteristic impedance 𝑍𝑜 of the transmission line
from the source with respect to the source impedance 𝑍𝑠 was
𝑍𝑜 = 𝑛. 𝑍𝑠
(3 − 5)
𝑍𝑜 = 2 × 50 = 100 𝑂ℎ𝑚𝑠
Where the factor 𝑛 was the number of twigs emanating from the node connected to the
source. The inner conductor of the coax was soldered to the 100-ohm microstrip line, and the
outer conductor connected to the ground plane. Since the coax fed two 100-ohm microstrip
lines in parallel, no mismatch occurred at this input as the parallel combination of the two
microstrip lines was equal to 50-ohm [4, 10].
Quarter-wave Transformer:
For the input impedance of a transmission line of length L with a characteristic impedance 𝑍𝑜
and connected to a load with impedance 𝑍𝐴 :
𝑍𝑖𝑛 (−𝐿) = 𝑍𝑜 [
𝑍𝐴 + 𝑗𝑍𝑜 tan(𝛽𝐿)
]
𝑍𝑜 + 𝑗𝑍𝐴 tan(𝛽𝐿)
25
(3 − 6)
When the length of the transformer is a quarter wavelength;
𝜆
𝑍𝑜2
𝑍𝑖𝑛 (𝐿 = ) =
4
𝑍𝐴
(3 − 7)
The above states that by using a quarter-wavelength of a transmission line, the impedance of
the load 𝑍𝐴 can be transformed by the above equation.
Hence by using a transmission line with a characteristic impedance of 50-ohms, the 50 ohm
inset feed line was matched to
𝑍𝑜 = √50 ∗ 50
(3 − 8)
= 50 𝑜ℎ𝑚𝑠
Where 𝑍𝑜 = Characteristic impedance of the quarter-wavelength transformer
This ensured that no power would be reflected back to the SMA feed point as it tried to deliver
power to the antenna [5].
The length of the quarter wavelength transformer was calculated as
𝐿=
𝜆
𝜆0
=
4 4√𝜀𝑟𝑒𝑓𝑓
(3 − 9)
= 15.39𝑚𝑚
Where 𝜆 = Effective wavelength
𝜆𝑜 = Free space wavelength
Simulation
The antenna array was designed using the Ansoft HFSS 13.0 software. HFSS is a 3D full wave
electromagnetic field simulator. It uses the finite element method together with adaptive
meshing to solve the wave equations. If a 3D model has been made, HFSS sets up the mesh
automatically. HFSS computes S-parameters, can calculate and plot both the near and far field
radiation and compute important antenna parameters such as gain and radiation efficiency.
This software was used to vary the sizes of the patches, microstrip feed lines and ground plane
in order to come up with the desired results [12]. Figure 3.4 illustrates the HFSS antenna
model.
26
Figure 3.4 4 element patch antenna HFSS model
H-Plane
E-Plane
Figure 3.5 4-element patch antenna PCB layout with dimensions
27
Fabrication
As per the HFSS designs, masks for fabrication of the microstrip antenna and the ground plane
were designed using AutoCAD. The mask images were then transferred to transparent films
before being photoengraved to a double sided PCB by exposure to UV light for 60 seconds. The
PCB was then suspended in Sodium Hydroxide developer for a minute to develop photoresist. It
was washed after which chemical etching done using a solution of iron chloride to create the
patch antenna. The etched copper pattern was rinsed in water and again exposed to UV light
for a minute. It was immersed in the developer to remove the photoresist and finally cleaned
with water. After air drying, an RF RP-SMA connector (through-hole, Jack (male pin) right angle
PCB mount connector) with solder post was soldered at the center of the PCB from the
backside. An RG58/U cable was used to connect to the SMA connector. The other end of the
cable was terminated to an N male connector. This was to be used as the connector to a
spectrum analyzer [7].
Figure 3.6 Implemented 4-element patch antenna array
28
Figure 3.7 ground plane of the patch array
Figure 3.8 N male to sma female cable
29
CHAPTER 4: HFSS SIMULATION RESULTS AND
ANALYSIS
Variation of Patch Length and Width
Dimensions calculated in the design procedure were used to create the 4 element array patch
antenna. The antenna, however, did not produce acceptable results. In order to shift the 𝑆11
minima towards the desired center frequency of 2.4GHz, the length and width of the patch
were shortened as follows
Table 4.1 Variation of antenna parameters with changes in dimensions
Length(mm)
38.47
34.47
30.47
30.47
30.47
Width(mm)
29.85
29.85
28.66
26.85
23.85
Resonance Frequency(GHz)
2.27
2.33
2.45
2.56
2.87
Peak Directivity(dB)
7.34
7.78
8.30
7.84
7.34
A length of 30.47mm and width of 28.66mm were selected as the 𝑆11 minima operated at the
center frequency. It was observed that a decrease in width increased the resonance frequency.
This is due to the increase in ∆𝐿 and 𝜀𝑟𝑒𝑓𝑓 . The input impedance at resonance also increased
because the radiation from the radiating edges decreases, which increases the radiation
resistance. The bandwidth of the antenna decreases. There is a decrease in the directivity,
efficiency, and hence gain, resulting from a decrease in the effective aperture of the antenna.
Effective aperture (also known as effective area) is the area over which the antenna collects
energy from the incident wave and delivers it to the receiver load [8, 17].
30
Reflection Coefficient and Bandwidth
Figure 4.1 shows the reflection coefficient [𝑆11] of the proposed antenna in dB. 𝑆11 gives the
reflection coefficient at the inset feed position where the input to the microstrip patch antenna
was applied. It should be less than -10dB for an acceptable operation. It shows that the
proposed antenna had a frequency of resonance of 2.44GHz [18].
Figure 4.1 Return loss 𝑆11 obtained for the patch array
The simulated impedance bandwidth of about 63.3MHz (2.4721-2.4088 GHz) was achieved at
−10𝑑𝐵 reflection coefficient (VSWR≤2). The reflection coefficient value that was achieved at
this resonant frequency was equal to -18.2131 dB. This reflection coefficient value suggested
that there was good matching at the frequency point below the -10dB region [18].
The fractional bandwidth achieved for the antenna was
𝑓𝑈 − 𝑓𝐿
2.4721 − 2.4088
𝐵𝑊 =
× 100% =
= 2.62%
𝑓𝐶
2.44045
(4 − 1)
where
𝑓𝐶 =
𝑓𝑈 + 𝑓𝐿
2
𝑓𝐶 , 𝑓𝑈 and 𝑓𝐿 are the center, upper and lower cutoff frequencies respectively.
31
(4 − 2)
Radiation Pattern
Figure 4.2 Simulated E-Plane (phi=90°, theta varying)
Figure 4.3 Simulated H-plane (theta=90°, phi varying)
The radiation patterns in the E-plane and H-plane of the patch antenna array at 2.44GHz for
𝑦𝑜 = 10.545𝑚𝑚 are shown in Figure 4.2 and Figure 4.3 above. They are also referred to as the
32
azimuth plane and elevation plane pattern respectively. The coplanar components in the E and
H planes are 𝐸𝜃 in the Φ = 0° and 𝐸Φ in Φ = 90° planes.
Figure 4.4 shows the simulated 3-D radiation pattern with gain of 5.2235 dB for proposed
antenna configuration at 2.44GHz. .
Figure 4.4 3D radiation pattern
The strongest energy was radiated outward, in the 𝑦𝑧-plane, at the widths of the patch
elements and at an angle of 36°. It was observed that the antenna had an azimuth plane
beamwidth of about 57° and an elevation plane beamwidth of 41° as indicated on the patterns
in figures 4.2 and figure 4.3 by the blue lines. These lines were drawn where the gain was down
from the peak by -3dB. The beamwidths were the total angular width between the two 3dB
points on the curves. [15].
The azimuth and elevation patterns were derived by simply slicing through the 3D radiation
pattern. For the azimuth plane pattern, slicing was done through the 𝑥𝑧 plane at 𝑦 = 0, while
for the elevation plane the slicing was done through the 𝑦𝑧 plane at 𝑥 = 0.
33
Figure 4.5 E-Plane and H-Plane patterns in rectangular coordinates
The Figure 4.5 shows that the antenna had two main lobes which were 180° out of phase with
each other. It was used to determine the half-power beamwidths for the radiation patterns as
the peaks and 3 dB points below them could easily be picked.
Inset Feed Position
Initially, the length of the inset feed position was calculated as 𝑦𝑜 = 14.15𝑚𝑚 from the edge of
the antenna. The slot width was chosen as 3.62mm which was 1mm greater than that of the
microstrip feed. An increase in the width of the slot brought about an increase in the resonance
frequency. The microstrip feed going into the patch element was 15.67mm in length which is
equal to 𝜆⁄4 wavelength. The resulting resonance frequency was below the desired value
hence the length had to be increased as shown below
Table 4.2 Variation of resonance frequency with changes in patch feed length
Length of Feed(mm)
15.67
18.67
20.67
25.67
Resonance Frequency(GHz)
1.77
2.26
2.29
3.29
34
The feed length of 18.67mm was chosen for analysis as it was closer to the center frequency
and also not too long.
Changing of the inset feed position 𝑦𝑜 affected the resonance frequency of the patch antenna.
The longer the length, the lesser the resonance frequency became and vice versa. Lesser
directivity, gain as well as magnitude of the 𝑆11 parameter were realized when a longer length
was used.
VSWR Plot
Figure 4.6 shows the VSWR (Voltage Standing Wave Ratio) plot for the designed antenna. The
value of the VSWR should lie between 1 and 2. SWR is used as an efficiency measure for
transmission lines, electrical cables that conduct radio frequency signals, used for purposes
such as connecting radio transmitters and receivers with their antennas, and distributing cable
television signals [18].
Figure 4.6 VSWR plot
Here the value for the proposed microstrip patch antenna was 1.2801 at the resonating
frequency of 2.44GHz.
35
Smith Chart
Figure 4.7 Smith chart of the proposed patch antenna
The smith chart is a graphical representation of the normalized characteristic impedance. It
provides the information about the impedance match of the radiating patch. The smith chart
for the designed patch antenna array showed an input impedance of 51.73+12.47i ohms at
resonant frequency 2.44GHz. The magnitude of the input impedance was 53.21 which showed
that accurate machine was not achieved. This was due to shifting of the inset feed position
away from the center of the patch element which was done in order to improve the directivity,
gain and return coefficient of the antenna.
Ground Plane
For a finite ground plane, the resonance frequency of the antenna was almost the same but the
input impedance was slightly higher than that of the infinite ground. It was observed that an
increase in the dimensions of the ground plane increased the resonance frequency and
magnitude of the 𝑆11 parameter. There was an increase in the directivity and hence gain.
36
H Plane Inter-element Separation
From the variation of the spacing between the patch elements in the H-plane, it was observed
that as the spacing was increased, the magnitude of the return loss 𝑆11 as well as the directivity
of the antenna decreased. This meant that the gain decreased. The resonance frequency,
radiated power and efficiency however increased. A separation of 𝜆⁄2 was chosen for the
simulation as it gave the optimal gain.
E plane Inter-element separation
An increase in the E-plane separation gave similar results to that of the H-plane. However, a
separation of 𝜆⁄2 could not be achieved because of the orientation of the patch elements as
well as the different lengths of the microstrip feeds.
Table 4.2 HFSS Antenna Parameters in HFSS
The table 4.2 shows a summary of the antenna parameters from the HFSS software. The
software did not give the antenna parameters summary in decibels as shown. The directivity D
37
and efficiency 𝜂 were 7.1273 and 46.7%, which gave a gain G (=𝜂D) of the antenna as 3.32. The
front to back ratio was 242.9, implying that there was a difference of about 23.85 dB between
the peak gain in the forward direction and the gain 180-degrees behind the peak. This is
evidence of presence of back lobes from the radiation [15].
38
CHAPTER 5: CONCLUSION
A 4 element, microstrip fed patch antenna array of rectangular shaped radiating elements was
successfully designed and implemented using the FR4 Epoxy Glass substrate. Through analysis
with the Ansoft HFSS simulation software, it was observed that the antenna worked in the
2.4GHz ISM band by having a resonance frequency of 2.44GHz, and had a fractional bandwidth
of 2.26% and a directivity of 8.53dB . The patch antenna array was coaxially fed through a 50
ohm cable with a 50 ohm sma-connector. Impedance matching was done well though not
accurately. The maximum achievable gain by the antenna was 5.2235 dB.
Time did not allow for more analysis to be done through different design simulations and
testing of the prototype. This was caused by the lack of the necessary testing equipment and
environment like the spectrum analyzer and anechoic chamber which is a room designed to
completely absorb reflections of either sound or electromagnetic wave [1].
39
APPENDICES
Appendix A
Conductance
Each radiating slot is represented by a parallel equivalent admittance Y (with conductance G
and susceptance B). This is shown in FigureA1. 4.
Figure A1.4 Rectangular microstrip patch and its equivalent circuit transmission-line model
The slots are labeled as #1 and #2. The equivalent admittance of slot #1, based on an
infinitely wide, infinite slot, is given by
𝑌1 = 𝐺1 + 𝑗𝐵1
(𝐴1)
Where for a slot of finite width W
𝐺1 =
𝐵1 =
𝑊
1
(𝑘𝑜 ℎ)2 ]
[1 −
120𝜆𝑜
24
𝑊
[1 − 0.636𝑙𝑛(𝑘𝑜 ℎ)]
120𝜆𝑜
ℎ
1
<
𝜆𝑜 10
ℎ
1
<
𝜆𝑜 10
(𝐴2)
(𝐴3)
Since slot #2 is identical to slot #1, its equivalent admittance is
𝑌2 = 𝑌1 , 𝐺2 = 𝐺1 ,
𝐵2 = 𝐵1
(𝐴4)
In general, the conductance is defined as
𝐺1 =
2𝑃𝑟𝑎𝑑
|𝑣𝑜 |2
(𝐴5)
The radiated power is written as
40
𝑃𝑟𝑎𝑑
𝑘𝑜 𝑊
|𝑣𝑜 |2 𝜋 sin( 2 𝑐𝑜𝑠𝜃) 2
=
∫ [
] 𝑠𝑖𝑛3 𝜃𝑑𝜃
2𝜋𝜂𝑜 0
𝑐𝑜𝑠𝜃
(𝐴6)
Therefore, the conductance of (1-10) can be expressed as
𝐺1 =
𝐼1
120𝜋 2
(𝐴7)
Where
2
𝑘𝑜 𝑊
sin( 2 𝑐𝑜𝑠𝜃
𝐼1 = ∫ [
]
𝑐𝑜𝑠𝜃
0
𝜋
= −2 + cos(𝑋) + 𝑋𝑆𝑖 (𝑋) +
sin(𝑋)
𝑋
𝑋 = 𝑘𝑜 𝑊
(𝐴8)
(𝐴9)
Asymptotic values of (1-12) and (1-12a) are
𝐺1 =
1 𝑊 2
( )
90 𝜆0
1 𝑊
( )
{ 120 𝜆𝑜
𝑊 ≪ 𝜆𝑜
(𝐴10)
𝑊 ≫ 𝜆𝑜
Resonant Input Resistance
The total admittance at slot #1 (input impedance) is obtained by transferring the admittance of
slot #2 from the output terminals to the input terminals using the admittance transformation
equation of transmission lines. Ideally the two slots should be separated by λ/2 where λ is the
wavelength in the dielectric (substrate). However, because of fringing the length of the patch is
electrically longer than the actual length. Therefore the actual separation of the two slots is
slightly less than λ/2. If the reduction in length is properly chosen (typically 0.48𝜆 < 𝐿 <
0.49𝜆), the transformed admittance of slot #2 becomes
̌2 + 𝑗𝐵
̌2 = 𝐺1 − 𝑗𝐵1
𝑌̃2 = 𝐺
(𝐴11)
̌2 = 𝐺1
𝐺
(𝐴12)
Or
41
̌2 = −𝐵1
𝐵
(𝐴13)
Therefore the total resonant input admittance is real and is given by
𝑌𝑖𝑛 = 𝑌1 + 𝑌̌2 = 2𝐺1
(𝐴14)
Since the total input admittance is real, the resonant input impedance is also real, or
𝑍𝑖𝑛 =
1
1
= 𝑅𝑖𝑛 =
𝑌𝑖𝑛
2𝐺1
(𝐴15)
The resonant input resistance, as given by (A15), does not take into account mutual effects
between the slots. This can be accomplished by modifying (A15) to
𝑅𝑖𝑛 =
1
2(𝐺1 ± 𝐺12 )
(𝐴16)
Where the plus (+) sign is used for modes with odd (antisymmetric) resonant voltage
distribution beneath the patch and between the slots while the minus (-) sign is used for modes
with even (symmetric) resonant voltage distribution. The mutual conductance is defined, in
terms of the far-zone fields, as
𝐺12 =
1
𝑅𝑒∬𝑠 𝑬1 × 𝑯∗2 . 𝑑𝒔
|𝑉0 |2
(𝐴17)
Where 𝑬1 is the electric field radiated by slot #1, 𝑯2 is the magnetic field radiated by slot #2, 𝑉𝑜
is the voltage across the slot, and the integration is done over a sphere of large radius. It can be
shown that 𝐺12 can be calculated using
2
𝑘𝑜 𝑊
sin
(
𝑐𝑜𝑠𝜃
1
2
=
∫ [
] 𝐽𝑜 (𝑘𝑜 𝐿𝑠𝑖𝑛𝜃)𝑠𝑖𝑛3 𝜃𝑑𝜃
2
120𝜋 0
𝑐𝑜𝑠𝜃
𝜋
𝐺12
(𝐴18)
Where 𝐽𝑜 is the Bessel function of the first kind of order zero.
As shown by above the input resistance is not strongly dependent upon the substrate height h.
In fact for very small values of h, such that 𝑘𝑜 ℎ ≪ 1, the input resistance is not dependent on h.
Modal-expansion analysis also reveals that the input resistance is not strongly influenced by the
substrate height h. It is apparent that the resonant input resistance can be decreased by
increasing the width W of the patch. This is acceptable as long as the ratio of W/L does not
exceed 2 because the aperture efficiency of a single patch begins to drop, as W/L increases
beyond 2. The resonant input resistance, as calculated by (1-17), is referenced at slot #1.
42
However, it has been shown that the resonant input resistance can be changed by using an
inset feed, recessed a distance 𝑦𝑜 from slot #1, as shown in Figure A1.5.
Figure A1.5 Recessed microstrip- line feed
This technique can be used effectively to match the patch antenna using a microstrip-line feed
whose characteristic impedance is given by
60
𝑍𝑐 =
√𝜀𝑟𝑒𝑓𝑓
𝑙𝑛 [
8ℎ 𝑊𝑜
+ ],
𝑊𝑜 4ℎ
120𝜋
𝑊𝑜
≤ 1 (𝐴19 − 𝐴)
ℎ
𝑊𝑜
𝑊𝑜
{√𝜀𝑟𝑒𝑓𝑓 [ ℎ + 1.393 + 0.667ln( ℎ + 1.444)]
,
𝑊𝑜
>1
ℎ
(𝐴19 − 𝐵)
Where 𝑊𝑜 is the width of the microstrip line, as shown in Figure A1. 5. Using modal-expansion
analysis, the input resistance for the inset feed is given approximately by
𝑅𝑖𝑛 (𝑦 = 𝑦𝑜 ) =
1
𝜋
𝐺12 + 𝐵12
𝜋
𝐵1
2𝜋
2
2
[𝑐𝑜𝑠 ( 𝑦𝑜 ) +
𝑠𝑖𝑛
(
𝑦
)
−
𝑠𝑖𝑛
(
𝑦 )]
𝑜
2(𝐺1 ± 𝐺12 )
𝐿
𝑌𝑐2
𝐿
𝑌𝑐
𝐿 𝑜
(𝐴20)
Where 𝑌𝑐 = 1⁄𝑍𝑐 . Since for most practical microstrips 𝐺1 /𝑌𝑐 ≪ 1 and 𝐵1 /𝑌𝑐 ≪ 1, (1-20)
reduces to
𝑅𝑖𝑛 (𝑦 = 𝑦𝑜 ) =
1
𝜋
𝑐𝑜𝑠 2 ( 𝑦𝑜 )
2(𝐺1 ± 𝐺12 )
𝐿
𝜋
= 𝑅𝑖𝑛 (𝑦 = 0)𝑐𝑜𝑠 2 ( 𝑦𝑜 )
𝐿
(𝐴21)
The values obtained using (A20) agree fairly well with experimental data. However, the inset
feed introduces a physical notch, which in turn introduces a junction capacitance. The physical
notch and its corresponding junction capacitance influence slightly the resonance frequency,
which typically may vary by about 1%. It is apparent from (A20A) that the maximum value
43
occurs at the edge of the slot (𝑦𝑜 = 0) where the voltage is maximum and the current is
minimum; typical values are in the 150–300 ohms. The minimum value (zero) occurs at the
center of the patch (𝑦𝑜 = 𝐿/2) where the voltage is zero and the current is maximum. As the
inset feed point moves from the edge toward the center of the patch the resonant input
impedance decreases monotonically and reaches zero at the center. When the value of the
inset feed point approaches the center of the patch (𝑦0 = 𝐿/2), the 𝑐𝑜𝑠 2 (
𝜋𝑦𝑜
𝐿
) function varies
very rapidly; therefore the input resistance also changes rapidly with the position of the feed
point. To maintain very accurate values, a close tolerance must be preserved.
44
Appendix B
Matlab Code for calculation of the insed feed position where the input impedance is 50 Ohms
≫er=4.3; %dielectric constant
f=2.44e9; %frequency in Hz
h=1.6; %substrate thickness in mm
la=(3e9/f)*1000;
k=(2*pi)/la;
w=30.47; %width of the patch in mm
l=29.28; %length of the patch in mm
x=k*w;
i1=-2+cos(x)+(x*sinint(x))+(sin(x)/x);
g1=i1/(120*pi*pi); %conductance
%jb=besselj(0,(k.*l.*sin(th)));
a=@(th)(((sin((x./2).*cos(th))./cos(th)).^2).*(besselj(0,k.*l.*sin(th)))).*(sin(th)).^3;
a1=quad(a,0,pi);
g12=a1/(120*pi*pi); %in siemens
r_in=1/(2*(g1+g12));
inset=(l/pi)*(acos(sqrt(50/r_in))) %inset feed point distance in mm
inset =
14.2961
Matlab code for calculation of antenna dimensions
er=4.2; %er=input('Enter the di-electric constant:')
f=2.44*10^9; %f=input('Enter the frequency (GHz):')
h=0.16*10; %h=input('Enter the substrate thickness (in mil)')
wid=(3e8/(sqrt((er+1)/2)*2*f))*1000 %width of patch in mm
e_eff=((er+1)/2)+ (((er-1)/2)* (1+((12*h)/wid))^-0.5) %Effective dielectric constant
l_eff=(3e8/(2*f*sqrt(e_eff)))*1000 %Effective Length
del_l=(((e_eff+0.3)*((wid/h)+0.264))/((e_eff-0.258)*((wid/h)+0.8)))*(0.412*h) %Normalized extension of
length
L=l_eff-(2*del_l) %Actual length of Patch
45
wid =
38.1254
e_eff =
3.9048
l_eff =
31.1100
del_l =
0.7435
L=
29.6230
Matlab code for calculation for the width of the 50 ohm line
>> solve [x/1.6+0.667*ln((x/1.6)+1.444)]=2.3868
ans =
2.6182207203339794813467175866412
46
REFERENCES
[1] Constantine A. Balanis Antenna Theory, Analysis and Design, 3rd Edition, John Wiley & Sons,
Inc., 2005
[2] John Hermann, Zach Dyals, and Angel Arcia, “Analysis and Design of ISM-Band Patch
Antenna Array”, ECE 4370: 5.8GHz High-Directivity Antenna, 2012, Group 3, pp. 1-13
[3] http://en.m.wikipedia.org/wiki/ISM_band
[4] Design of Microstrip Patch Antenna using FR4 substrate
http://just.edu.jo/~nihad/files/mat/591/report.pdf
[5] http://www.antenna-theory.com/tutorial/txline/transmission5.php
[6] Thomas A. Milligan Modern Antenna Design, 2nd Edition, John Wiley & Sons, Inc., 2005
[7] Deepak Sood,Gurpal Singh, Chander Charu Tripathi, Suresh Chander Sood & Pawan Joshi,
“Design, fabrication and characterization of microstrip square patch antenna array for X-band
applications”, Indian Journal of Pure & Applied Physics, 2008, Vol. 46, pp. 593-597
[8] A.R. Harish, M.Sachidananda, Antennas and Wave Propagation, 4th Edition, Oxford
University Press, 2007
[9] Iulan Rosu, “Microstrip, Stripline, and CPW Design”, YO3DAC/ VA3IUL,
http://www.qsl.net/va3iul
[10] John R. Ojha and Marc Peters, “Patch Antennas and Microstrip Lines, Micrrowave and
Millimeter Wave Technologies Modern UWB antennas and equipment”, Igor Mini(Ed.), 2010,
ISBN 978-953-7619-67-1, In-Tech DOI: 10.5772/9016.
[11] Yi Huang, Kevin Boyle, Antennas From Theory to Practice, John Wiley and Sons, Ltd,
Publication, 2008
[12] Fredrick Gulbrandsen, “Design of an X-band Phased Array Patch Antenna”, 2013,
Norwegian University of Science and Technology, Department of Electronics and
Telecommunications http://www.diva-portal.org/smash/get/diva2:646810/FULLTEXT01.pdf
[13] D. Orban and G.J.K.Moernaut, “The Basics of Patch Antennas, Updated”, RF Globalnet
Newsletter, 2009
http://rfglobalnet.com/doc/technical-article-the-basics-of-patch-antenna-0001
47
[14] Ruchi Kadwane, Vinaya Gohokar, “Design and Characteristics Investigation of Multiband
Microstrip Patch Antenna for Wireless Application”, International Journal of Emerging
Engineering Reserch and Technology, 2014, Vol. 2, Issue 3, pp. 61-66
[15] http://www.cisco.com/c/en/us/products/collateral/wireless/aironet-antennasaccessories/prod_white_paper0900aecd806a1a3e.html
[16] http://en.m.wikipedia.org/wiki/Polarization_(waves)
[17] Girish Kumar, K.P. Ray, Broadband Microstrip Antennas, Artech House, Inc.,2003
[18] Jaswinder Kaur, Rajesh Khanna, “Co-axial Fed Rectangular Microstrip Patch Antenna for 5.2
Ghz WLAN A pplication”, Universal Journal of Electrical and Electronic Engineering, 2013, Vol. 1,
Issue 3, pp 94-98
48