Antenna design

PROJECT REPORT

ON

ANTENNA DESIGN, SIMULATION AND
FABRICATION
This project report is submitted to VNIT in partial fulfillment of the
requirements for the degree of
“Bachelor of Technology in Electronics and Communication”

Under the guidance of
Dr. A. S. Gandhi

Submitted by
Prasanna Ramachandran, T.S.Keshav, Laxmikant Minz
Vamsikrishna Parupalli and Shaibal Chakravarty

Department of Electronics and Computer Science Engineering
Visvesvaraya National Institute of Technology
(Deemed University)
Nagpur – 440011
2006-2007

DEPARTMENT OF ELECTRONICS AND
COMPUTER SCIENCE ENGINEERING

VISVESVARAYA NATIONAL INSTITUTE OF
TECHNOLOGY, NAGPUR

CERTIFICATE
This is to certify that Mr. Prasanna Ramachandran, Mr.
T.S.Keshav, Mr. Laxmikant Minz, Mr. Vamsikrishna
Parupalli and Mr. Shaibal Chakravarty have carried out their
project work on Antenna Design, Simulation and Fabrication in
the Electronics and Computer Science Department of VNIT,
Nagpur during the year 2006-2007. Their work is approved for
submission in partial fulfillment of the requirements for the degree
of “Bachelor of Technology”.

Dr. O. G. Kakde Dr. A.S. Gandhi
Head of the Department Project Guide
Dept. of ECE, VNIT Dept. of ECE, VNIT

Date:

ACKNOWLEDGEMENTS

We would like to thank our Project Guide, Dr. A.S. Gandhi, for his
continuous support and encouragement. It was he who provided an aim and
direction to this project and constantly pushed us to work harder on it.

We would also like to thank the Communication Lab in charge, Mr.
Prashant Jaronde for providing us all hardware and software tools required
for completing this project. His assistance was invaluable.

ABSTRACT
Wireless technology is one of the main areas of research in the world of
communication systems today and a study of communication systems is
incomplete without an understanding of the operation and fabrication of
antennas. This was the main reason for our selecting a project focusing on
this field.

The field of antenna study is an extremely vast one, so, to grasp the
fundamentals we used a two pronged approach by dividing ourselves into
groups.

The first group focused on the fabrication and testing of a slotted waveguide
omni directional antenna and a biquad directional antenna.

The second group focused on the design and simulation of patch antennas
(which are widely used in cell phones today) with an emphasis on
optimization of a 1.9 GHz rectangular probe fed patch antenna. A dual band
antenna and a microstrip fed patch antenna, used in the communication lab
were also simulated.

Contents

Chapter 1 - Introduction to Antennas 1

1.1 Antenna Parameters 1

1.2 Types of Antennas 9

Chapter 2 – Hardware Aspects – Fabrication and Testing of
RF Antennas 13

2.1 Introduction 13

2.2 Slotted Waveguide Antenna 13

2.3 Biquad Antenna 16

2.4 Testing of the Antennas 20

Chapter 3 – Software Aspects – Design and Simulation of
Microstrip Patch Antennas 26

3.1 Introduction 26

3.2 Applications of Microstrip Patch Antennas 28

3.3 Advantages and Disadvantages of Patch Antennas 29

3.4 Feed Techniques 29

3.5 Methods of Analysis 34

3.6 Simulation Software – IE3D 40

3.7 Design of a Simple Rectangular Patch Antenna 41

3.8 Simulation of 1.9 GHz Patch Antenna 43

3.9 Simulation of 5GHz Patch Antenna 70

3.10 Simulation of Dual Band Patch Antennas 74

Chapter 4 – Conclusions and Scope for Improvement 85

4.1 Conclusions 85

4.2 Scope for Improvement 85

Appendix A - MATLAB Codes 86

Appendix B - Data on Equipment used for Antenna Analysis 88

References 92

________________________________________________
Chapter 1
Introduction to Antennas

Our project focuses on the hardware fabrication and software simulation of several
antennas. In order to completely understand the above it is necessary to start off by
understanding various terms associated with antennas and the various types of antennas.
This is what is covered in this introductory chapter.

1.1 Antenna parameters

An antenna is an electrical conductor or system of conductors

Transmitter - Radiates electromagnetic energy into space
Receiver - Collects electromagnetic energy from space

The IEEE definition of an antenna as given by Stutzman and Thiele is, “That part of a
transmitting or receiving system that is designed to radiate or receive electromagnetic
waves”. The major parameters associated with an antenna are defined in the following
sections.

1.1.1 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. Consider the power
density radiated by an isotropic antenna with input power P0 at a distance R which is
given by S = P0/4πR2. An isotropic antenna radiates equally in all directions, and its
radiated power density S is found by dividing the radiated power by the area of the sphere
4πR2. An isotropic radiator is considered to be 100% efficient. The gain of an actual
antenna increases the power density in the direction of the peak radiation:

Equation 1.1

Gain is achieved by directing the radiation away from other parts of the radiation sphere.
In general, gain is defined as the gain-biased pattern of the antenna.

1

Equation 1.2
1.1.2 Antenna Efficiency
The surface integral of the radiation intensity over the radiation sphere divided by the
input power P0 is a measure of the relative power radiated by the antenna, or the antenna
efficiency.

Equation 1.3
where Pr is the radiated power. Material losses in the antenna or reflected power due to
poor impedance match reduce the radiated power.

1.1.3 Effective Area
Antennas capture power from passing waves and deliver some of it to the terminals.
Given the power density of the incident wave and the effective area of the antenna, the
power delivered to the terminals is the product.

Equation 1.4

For an aperture antenna such as a horn, parabolic reflector, or flat-plate array, effective
area is physical area multiplied by aperture efficiency. In general, losses due to material,
distribution, and mismatch reduce the ratio of the effective area to the physical area.
Typical estimated aperture efficiency for a parabolic reflector is 55%. Even antennas with
infinitesimal physical areas, such as dipoles, have effective areas because they remove
power from passing waves.

1.1.4 Directivity
Directivity is a measure of the concentration of radiation in the direction of the
maximum.

Equation 1.5

Directivity and gain differ only by the efficiency, but directivity is easily estimated from
patterns. Gain—directivity times efficiency—must be measured. The average radiation
intensity can be found from a surface integral over the

2

radiation sphere of the radiation intensity divided by 4π, the area of the sphere in
steradians:

Equation 1.6

This is the radiated power divided by the area of a unit sphere. The radiation intensity
U(θ,φ) separates into a sum of co- and cross-polarization components:

Both co- and cross-polarization directivities can be defined:

Equation 1.7
Directivity can also be defined for an arbitrary direction D(θ,φ) as radiation intensity
divided by the average radiation intensity, but when the coordinate angles are not
specified, we calculate directivity at Umax.

1.1.5 Path Loss
We combine the gain of the transmitting antenna with the effective area of the receiving
antenna to determine delivered power and path loss. The power density at the receiving
antenna is given by equation 1.2 and the received power is given by equation 1.4. By
combining the two, we obtain the path loss as given below.

Equation 1.8
Antenna 1 transmits, and antenna 2 receives. If the materials in the antennas are linear
and isotropic, the transmitting and receiving patterns are identical . When we consider
antenna 2 as the transmitting antenna and antenna 1 as the receiving antenna, the path
loss is

Equation 1.9

We make quick evaluations of path loss for various units of distance R and for frequency
f in megahertz using the formula

3

where KU depends on the length units as shown in table 1.1

Table 1.1

1.1.6 Input Impedance
The input impedance of an antenna is defined as “the impedance presented by an antenna
at its terminals or the ratio of the voltage to the current at the pair of terminals or the ratio
of the appropriate components of the electric to magnetic fields at a point”. Hence the
impedance of the antenna can be written as given below.

Equation 1.10

where Zin is the antenna impedance at the terminals
Rin is the antenna resistance at the terminals
Xin is the antenna reactance at the terminals

The imaginary part, Xin of the input impedance represents the power stored in the near
field of the antenna. The resistive part, Rin of the input impedance consists of two
components, the radiation resistance Rr and the loss resistance RL. The power associated
with the radiation resistance is the power actually radiated by the antenna, while the
power dissipated in the loss resistance is lost as heat in the antenna itself due to dielectric
or conducting losses.

4

1.1.7 Antenna Factor
The engineering community uses an antenna connected to a receiver such as a spectrum
analyzer, a network analyzer, or an RF voltmeter to measure field strength E. Most of the
time these devices have a load resistor ZL that matches the antenna impedance.

The incident field strength Ei equals antenna factor AF times the received voltage Vrec.
We relate this to the antenna effective height:

Equation 1.11
−1 −1
AF has units meter but is often given as dB(m ). Sometimes, antenna factor is referred
to the open-circuit voltage and it would be one-half the value given by equation 1.11. We
assume that the antenna is aligned with the electric field; in other words, the antenna
polarization is the electric field component measured:

Equation 1.12
This measurement may be corrupted by a poor impedance match to the receiver and any
cable loss between the antenna and receiver that reduces the voltage and reduces the
calculated field strength.

1.1.8 Return Loss
It is a parameter which indicates the amount of power that is “lost” to the load and does
not return as a reflection. Hence the RL is a parameter to indicate how well the matching
between the transmitter and antenna has taken place. Simply put it is the S11 of an
antenna. A graph of s11 of an antenna vs frequency is called its return loss curve. For
optimum working such a graph must show a dip at the operating frequency and have a
minimum dB value at this frequency. This parameter was found to be of crucial
importance to our project as we sought to adjust the antenna dimensions for a fixed
operating frequency (say 1.9 GHz). A simple RL curve is shown in figure 1.1.

5

Figure 1.1 – RL curve of an antenna

1.19 Radiation Pattern
The radiation pattern of an antenna is a plot of the far-field radiation properties of an
antenna as a function of the spatial co-ordinates which are specified by the elevation
angle (θ) and the azimuth angle (φ). More specifically it is a plot of the power radiated
from an antenna per unit solid angle which is nothing but the radiation intensity. It can be
plotted as a 3D graph or as a 2D polar or Cartesian slice of this 3D graph. It is an
extremely parameter as it shows the antenna’s directivity as well as gain at various points
in space. It serves as the signature of an antenna and one look at it is often enough to
realize the antenna that produced it.

Because this parameter was so important to our software simulations we needed to
understand it completely. For this purpose we obtained the 2D polar plots of radiation
patterns for a few antennas in our lab using a ScienTech antenna trainer kit shown in
figure 1.2.

6

Figure 1.2 – ScienTech Antenna Trainer Kit

The transmitter of the kit was rotated through 360 degrees in 20 degree intervals and the
received power was measured (in µV – converted to dB) by a receiver to plot the
radiation patterns of a few antennas. A simple MATLAB code written by us to obtain the
2D Polar Plots is given in Appendix A. The main disadvantage of this trainer kit is that it
works only at 750MHz. However, it helped us to visualize the radiation patterns of some
antennas shown in the following pages.

Figure 1.3 – 2D Polar Plot for a Yagi Antenna

7

Figure 1.4 – 2D Polar Plot for a Helical Antenna

Figure 1.5 – 2D Polar Plot for a Rhombus Patch Antenna

A general 3D radiation pattern is also shown in figure 1.6

Figure 1.6 – 3D Radiation Pattern for a rectangular patch

8

1.20 Beamwidth
Beamwidth of an antenna is easily determined from its 2D radiation pattern and is also a
very important parameter. Beamwidth is the angular separation of the half-power points
of the radiated pattern. The way in which beamwidth is determined is shown in figure
1.7.

Figure 1.7 – Determination of HPBW from radiation pattern

1.2 Types of Antennas
Antennas can be classified in several ways. One way is the frequency band of operation.
Others include physical structure and electrical/electromagnetic design. Most simple,
non-directional antennas are basic dipoles or monopoles. More complex, directional
antennas consist of arrays of elements, such as dipoles, or use one active and several
passive elements, as in the Yagi antenna. New antenna technologies are being developed
that allow an antenna to rapidly change its pattern in response to changes in direction of
arrival of the received signal. These antennas and the supporting technology are called
adaptive or “smart” antennas and may be used for the higher frequency bands in the
future. A few commonly used antennas are described in the following sections.

1.2.1 Dipoles and Monopoles
The vertical dipole—or its electromagnetic equivalent, the monopole—could be
considered one of the best antennas for LMR applications. It is omni directional (in
azimuth) and, if it is a half-wavelength long, has a gain of 1.64 (or G = 2.15 dBi) in the
horizontal plane. A center-fed, vertical dipole is illustrated in figure 1.8 (a). Although this
is a simple antenna, it can be difficult to mount on a mast or vehicle. The ideal vertical
monopole is illustrated in figure 1.8 (b). It is half a dipole placed in half space, with a
perfectly conducting, infinite surface at the boundary.

9

Figure 1.8 - The vertical dipole and its electromagnetic equivalent, the vertical
monopole

A monopole over an infinite ground plane is theoretically the same (identical gain,
pattern, etc., in the half-space above the ground plane) as the dipole in free space. In
practice, a ground plane cannot be infinite, but a ground plane with a radius
approximately the same as the length of the active element, is an effective, practical
solution. The flat surface of a vehicle’s trunk or roof can act as an adequate ground plane.
Figure 1.9 shows typical monopole antennas for base-station and mobile applications.

Figure 1.9 - Typical monopole antennas for (a) base-station applications and (b)
mobile applications

1.2.2 Corner Reflector
An antenna comprised of one or more dipole elements in front of a corner reflector,
called the corner-reflector antenna, is illustrated in figure 1.10.

10

Figure 1.10 - Corner-reflector antennas

This antenna has moderately high gain, but its most important pattern feature is that the
forward (main beam) gain is much higher than the gain in the opposite direction. This is
called the front-to-back ratio and is evident from its radiation pattern shown in figure
1.11.

Figure 1.11 - A corner-reflector antenna horizontal-plane pattern

1.2.3 Yagi Antenna
Another antenna design that uses passive elements is the Yagi antenna. This antenna,
illustrated in figure 1.12, is inexpensive and effective. It can be constructed with one or
more (usually one or two) reflector elements and one or more (usually two or more)
director elements. Figure 1.1.3 shows a Yagi antenna with one reflector, a folded-dipole
active element, and seven directors, mounted for horizontal polarization.

11

Figure 1.12 - The Yagi antenna — (a) three elements and (b) multiple
elements

Figure 1.13 - A typical Yagi antenna

Figure 1.14 is the typical radiation pattern obtained for a three element (one reflector, one
active element, and one director) Yagi antenna. Generally, the more elements a Yagi has,
the higher the gain, and the narrower the beamwidth. This antenna can be mounted to
support either horizontal or vertical polarization and is often used for point-to-point
applications, as between a base station and repeater-station sites.

Figure 1.14 - A Yagi antenna horizontal plane pattern

12

Chapter 2
Hardware Aspects - Fabrication and Testing of RF
Antennas

2.1 Introduction
For the project we constructed two RF antennas and tested them in our lab.
The antennas that we constructed were: 1) Slotted Waveguide Antenna. (Omni
directional)
2) Biquad antenna. (Directional)
Working central frequency of these antennas is 2.4GHz. 2.4GHz comes under the
unlicensed wireless band usually used in WLAN.

2.1.1 Significance of 2.4 GHz
Since 1986, FCC rules have provided for unlicensed spread-spectrum operation in the
915 MHz (902–928 MHz), 2.4 GHz (2400–2483.5 MHz), and 5.7 GHz (5725–5850
MHz) bands. But a vast number of RF devices currently operate in the 2.4 GHz band
(like microwave ovens, cordless telephones, medical devices etc.). Recently there has
been proliferation of "Wi-Fi" hotspots and wireless computers permitting undeterred
internet access by the public and RF identification (RFID) technology.

2.2 Slotted Waveguide Antenna

2.2.1 Introduction
Slotted waveguides are resonant antennas and have a relatively narrow operating
frequency range. A slotted waveguide is a waveguide that is used as an antenna in
microwave radar applications. Prior to its use in surface search radar, such systems used a
parabolic segment reflector.

A slotted waveguide has no reflector but emits directly through the slots. The spacing of
the slots is critical and is a multiple of the wavelength used for transmission and
reception. The antenna's vertical focus is usually enhanced by the application of a
microwave lens attached to the front of the antenna. As this, like the companion slotted
waveguide, is a one-dimensional device, it too may be made relatively cheaply as
compared to a parabolic reflector and feed horn. In a related application, so-called leaky
waveguides are also used in the determination of railcar positions in certain rapid transit
applications. They are primarily used to determine the precise position of a train when it
is being brought to a halt at a station, so that the doorway positions will align correctly
with queuing points on the platform or with a second set of safety doors should such be
provided.

13

2.2.2 Working
A waveguide is a very low loss transmission line. It allows propagation of signals to a
number of smaller antennas (slots). The signal is coupled into the waveguide with a
simple coaxial probe and as it travels along the guide it traverses the slots. Each of these
slots allows a little of the energy to radiate. The slots are in a linear array pattern, and the
total of all the radiated signals adds up to a very significant power gain over a small range
of angles close to the horizon. In other words, the waveguide antenna transmits almost all
of its energy at the horizon, usually exactly where we want it to go. Its exceptional
directivity in the elevation plane gives it quite high power gain. Additionally, unlike
vertical co-linear antennas, the slotted waveguide transmits its energy using horizontal
polarization, the best type for distance transmission.

2.2.3 Construction

Figure – 2.1 – A Slotted Waveguide Antenna

The components we used to construct this antenna are given below
i) 1m RG-213U cable (coaxial cable)
ii) N connectors (BNC-female)
iii) Plastic casing

Each sector of the antenna needs to be a 1/2 wavelength long multiplied by the velocity
factor of the cable. The velocity factor of RG-213 is 0.66. If a different cable (such as
LMR-400) is used then the velocity factor of that cable needs to be determined and all the
dimensions will need to be recalculated.
V * C 0.66 * 299792458
1/2 wavelength = ------- = ---------------------- = 0.0405m = 40.5mm Equation 2.1
2*F 2 * 2441000000

V = Velocity Factor of RG213 = 0.66
C = Velocity of light = 299792458 m/s
F = Frequency of Signal = 2441000000 Hz (middle of the 2.4GHz range)

14

The 1/4 wave element is not adjusted by the velocity factor, as it is in the open, so it
works out at just 31mm long giving a total antenna length of 355mm + fly-lead. Each
sector consists of a short length of RG-213 cable, with the central core sticking out each
end. When building the antenna, the exact length of each piece of RG-213 is not that
important, it is the overall length of each sector that counts.

Figure -2.2 – Sectors of the antenna

We found that cutting the cable to 37mm with 6mm of core sticking out each end, got
enough overlap to easily solder the segments together. If 1mm is allowed for the width of
the hacksaw when cutting the sectors apart, it means that 37 +6 +6 +1 = 50mm of cable
was required for each sector. For making 8sectors + ¼wave section, 420 mm of cable
length for the antenna + cable for the fly lead was required, as illustrated by figure - 2.2.

For making the first segment with the monopole, the sheath, shielding and central
insulator of length 31mm was stripped with out damaging the inner conductor which
would act as monopole. Leaving 43mm from the star of monopole i.e. 77mm from the
monopole’s tip the coaxial cable was completely cut. Then leaving 6mm from the other
end, sheath, shielding, and central insulator were removed leaving the inner conductor
exposed so that it could be connected to other segments.

The other seven segments of the antenna were symmetrical and of 50mm length. So,
seven 50mm segments were cut from the coaxial cable. For each segment 6mm of sheath,
shielding and central insulator were removed leaving the central conductor for connecting
it to other segments. After making all the segments, all eight sectors were checked round
the end to make sure that none of the shielding was touching the central cable, as odd
strands can get left.

A gentle V shaped cut was made with a knife, at each end of the sectors, to expose the
shielding, which is where the central core of the next sector would be soldered. This was
done to all sectors which had to be soldered, including the fly-lead part.

15

Figure – 2.3 – V cut at sector ends

V cuts at each end of the sector lined up; otherwise, when the antenna is soldered
together, the whole thing will be twisted all around. All the eight segments and the fly
lead were soldered taking care that the wire would not get twisted.

Once the antenna was ready, it was tested with a multimeter to check if the connections
were correct. The center of the fly lead should form a circuit to the 1/4 wave section, and
the shield of the fly lead to the shield of the top section. The antenna was now tested to
ensure that there were no crossed connections, by ensuring there was no circuit between
the center of the fly lead and the shielding of the top sector and no circuit between the 1/4
wave section and the shielding of the flyleaf. The slotted waveguide antenna that we
constructed is shown below.

Figure – 2.4 – Slotted Waveguide Antenna Constructed

2.3 Biquad Antenna

2.3.1 Introduction

A biquad antenna is a wide band antenna. These antennas are fairly directive, cheap and
simple to make. A Biquad is nothing but two single turn loop antennas forming an array
where each one is a driven component. The array improves the directivity and bandwidth
.The working of a biquad is the same as a folded dipole antenna. It generates the same
radiation pattern as a dipole with more directivity and bandwidth. A biquad antenna can
be considered as a modified form of a folded dipole antenna. More specifically its
elements come under the category of small loop single turn antennas.

16

2.3.2 Working

A small loop is the dual of an ideal dipole. Pattern and radiation resistance of a loop are
insensitive to the loop shape and depend only on the loop area. Radiation from a small
loop is highest in the plane of loop and zero along its axis. As the perimeter of a loop
antenna becomes a sizeable fraction of a wavelength, the current amplitude and phase
will vary over the wire extent. So, a loop antenna with a perimeter that is of the order of
half-wavelength or larger will display performance variation with loop size and shape.

The biquad antenna that we made is a combination of two one wavelength square loop
antennas.

Figure – 2.5 - Square loop

It has one quarter wavelength sides. For one wavelength perimeter it is reasonable to
assume that current distribution is sinusoidal and continuous around the loop.

2.3.3 Construction

The components we used to construct the antenna were

i) 123x123mm square section of blank PCB
ii) 50mm length of 1/2" copper pipe
iii) Short length of CNT-400 or LMR-400 low loss coax (~300mm long)
iv) 250mm of 2.5mm2 copper wire (approx 1.5mm diameter)
v) N connector

We cut a square piece of blank printed circuit board, 123x123mm. 50mm section of
copper pipe was taken and filed both ends smooth. Using sandpaper the copper pipe was
polished up including the inside of the copper pipe, to ensure a good connection with the
coax braid. A notch was cut into one end of the copper pipe, removing approx 2mm from
half the circumference.

17

Figure – 2.6 – Copper Pipe

A hole was drilled in the centre of the blank PCB so that the copper pipe was a tight fit in
the hole. We drilled a small hole and then widened it using file for making it precisely fit
for inserting the copper pipe.

Figure – 2.7 – Square PCB used for construction

Copper pipe was inserted into the hole, with the notched end on the copper side of the
blank PCB. The copper pipe protruded approx 16mm through the hole, measured on the
copper side of the PCB. The copper pipe was soldered to the PCB to ensure better
electrical connectivity. It is not possible to solder the two elements with normal 25W
solder gun. We used a high power solder to connect these two elements.

244 mm of copper wire was taken and is bent in as shown in the figure. All the bents are
of 90 degrees.

18

Figure – 2.8 – Biquad Antenna Loop

The element was now attached to the reflector. Only the two "ends" of the copper wire
were to be attached to the copper pipe - the centre of the copper wire must not touch the
copper pipe (hence the notch which was cut into the end of the copper pipe). Assembling
everything as mentioned, our antenna looked as shown below.

.

Figure 2.9 – Biquad Loop Constructed

For feeding antenna we stripped approx 30mm of the outer sheath from the end of the
coaxial cable. The braid was folded back over the outer sheath the centre conductor was
trimmed, so that about 4mm protruded. The outer braid was to be shorted to reflector
(ground plane).

Figure – 2.10 – Stripping of Sheath

We inserted the braid into the copper pipe, so that the end of the centre conductor lined
up with the extreme end of the copper pipe, and we then soldered the centre of the
element to it, ensuring the centre of the element was not in contact with the copper pipe.
At this stage we had completely constructed the biquad antenna shown below.

19

Figure 2.11 – Biquad Antenna Constructed

2.4 Testing of the Antennas

For testing our antennas we used the equipment available in our lab. Equipment like
network analyzer, spectrum analyzer and signal generator, which are recent additions to
our lab, were studied and then used to determine s11 (insertion loss), transmitting power,
received power etc. Details about these equipment are available in Appendix B. We first
found out insertion loss parameter of each antenna using network analyzer. Then we
determined the receiving power of antennas using one as a transmitter and the other as a
receiver.

2.4.1 S11 parameter

s11 gives us the insertion loss of antennas. Insertion loss is proportional to the ratio of
reflected to the input power of the antenna. Antennas generally radiate efficiently for
particular range of frequencies. At these frequencies the radiated power should be almost
equal to input power, i.e., reflected power should very small. So the expected plot of s11
for an antenna would be a flat line through out the frequency scale with deep dip in the
operating frequency range.

20

2.4.2 S11 Curve of the Slotted Waveguide Antenna

The S11 curve of the slotted waveguide antenna obtained using vector analyzer is shown
in figure 2.12.

Figure – 2.12 – S11 curve obtained for the Slotted Waveguide Antenna

The dip is the central operating frequency of the antenna. The operating frequency of the
antenna was found to be 2.3 GHz. The s11 measured at this frequency was -45 dB.

For the antenna we got more than one dip. The reason for this was that our antenna, being
an array of slots, was radiating at different frequencies which were very close by.

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2.4.3 S11 Curve of the Biquad Antenna

The S11 vs frequency curve of the biquad antenna obtained using a vector analyzer is
shown in figure 2.13.

Figure – 2.13 – S11 Curve obtained for the Biquad Antenna

The dip indicates the central operating frequency of the antenna. The operating frequency
of the antenna was found to be 2.34 GHz. s11 measured at this frequency was -38 dB.

2.4.4 Problems faced during Testing

We have used BNC connectors for feeding the signal to the antennas. But these
connectors were found to be very unreliable for s11 measurement using network analyzer.
Even a slight movement in the antenna or the connectors had a significant effect on the
results. The s11 measurement which we made could only give us the frequency of
operation. For proper measurement of s11, SMA connectors are highly recommended.
These connectors are very rugged and results obtained with these connectors are very
reliable.

22

We were also unable to obtain the radiation patterns of the constructed antennas. The
theoretical radiation patterns, though, are shown in the following figures.

Figure – 2.14 – 2D Radiation Pattern of a Slotted Antenna

Figure – 2.15 – 2D Radiation Pattern (Polar Plot) of a Biquad Antenna

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Figure – 2.16 – Orientation and 3D Radiation Pattern of a Biquad Antenna

2.4.5 Power Measurement Arrangement

For power measurement we made an arrangement where one of the antennas was made a
transmitter and the antenna, a receiver. The arrangement is as shown below:

Figure – 2.17 – Arrangement for determining power received

24

Here the slotted waveguide omni-directional antenna is acting as probe antenna so it was
our transmitter and the biquad antenna is acted as a receiver.

We fed a continuous signal of different frequency and power to the transmitting antenna
from the signal generator (can be seen in the diagram) and on other end we connected the
biquad antenna to the spectrum analyzer through a coaxial cable.). On the receiver end
we traced out the received signal frequency and power. We found that when a signal of
2.4GHz with a power level of 10 dBm was fed there was a signal of same frequency with
lower power level (near -30 dBm received). We even interchanged the setup (i.e. biquad
was made transmitter and slotted waveguide antenna was made receiver) and performed
our testing. Power received in this case, at same frequency and power level, was bit lower
nearly -35 dBm. The values displayed by the signal generator and the receiver (spectrum
analyzer) for first the case are shown in the following figures.

Figure – 2.18– Signal Generator Display

Figure – 2.19– Spectrum Analyzer Display

25

Chapter 3
Software Aspects – Design and Simulation of
Micrsostrip Patch Antennas

The software simulations of our project focused on designing and testing of patch
antennas using software called IE3D (described later on in this chapter). Before the
software results are presented the theory behind patch antennas is elucidated.

3.1 Introduction
Microstrip antennas are planar resonant cavities that leak from their edges and radiate.
Printed circuit techniques can be used to etch the antennas on soft substrates to produce
low-cost and repeatable antennas in a low profile. The antennas fabricated on compliant
substrates withstand tremendous shock and vibration environments. Manufacturers for
mobile communication base stations often fabricate these antennas directly in sheet metal
and mount them on dielectric posts or foam in a variety of ways to eliminate the cost of
substrates and etching. This also eliminates the problem of radiation from surface waves
excited in a thick dielectric substrate used to increase bandwidth.

In its most basic form, a Microstrip patch antenna consists of a radiating patch on one
side of a dielectric substrate which has a ground plane on the other side as shown in
Figure 3.1. The patch is generally made of conducting material such as copper or gold
and can take any possible shape. The radiating patch and the feed lines are usually photo
etched on the dielectric substrate. Arrays of antennas can be photoetched on the substrate,
along with their feeding networks. Microstrip circuits make a wide variety of antennas
possible through the use of the simple photoetching techniques.

Figure -3.1 – A Typical Microstrip Patch Antenna

26

In order to simplify analysis and performance prediction, the patch is generally square,
rectangular, circular, triangular, elliptical or some other common shape as shown in
Figure 2. For a rectangular patch, the length L of the patch is usually 0.3333λo < L <
0.5λo, where λo is the free-space wavelength. The patch is selected to be very thin such
that t << λo (where t is the patch thickness). The height h of the dielectric substrate is
usually 0.003 λo ≤ h ≤ 0.05 λo . The dielectric constant of the substrate (εr) is typically in
the range 2.2≤ εr≤12.

Figure -3.2 – Typical patch shapes

A patch radiates from fringing fields around its edges. The situation is shown in figure
3.3. Impedance match occurs when a patch resonates as a resonant cavity. When
matched, the antenna achieves peak efficiency. A normal transmission line radiates little
power because the fringing fields are matched by nearby counteracting fields. Power
radiates from open circuits and from discontinuities such as corners, but the amount
depends on the radiation conductance load to the line relative to the patches. Without
proper matching, little power radiates. The edges of a patch appear as slots whose
excitations depend on the internal fields of the cavity. A general analysis of an arbitrarily
shaped patch considers the patch to be a resonant cavity with metal (electric) walls of the
patch and the ground plane and magnetic or impedance walls around the edges.

For good antenna performance, a thick dielectric substrate having a low dielectric
constant is desirable since this provides better efficiency, larger bandwidth and better
radiation. However, such a configuration leads to a larger antenna size. In order to design
a compact Microstrip patch antenna, higher dielectric constants must be used which are
less efficient and result in narrower bandwidth. Hence a compromise must be reached
between antenna dimensions and antenna performance.

27

Figure – 3.3 – Fringing Fields in Patch Antennas

3.2 Applications of Microstrip Patch Antennas
Microstrip patch antennas are increasing in popularity for use in wireless applications due
to their low-profile structure. Therefore they are extremely compatible for embedded
antennas in handheld wireless devices such as cellular phones, pagers etc. The telemetry
and communication antennas on missiles need to be thin and conformal and are often
microstrip patch antennas. Another area where they have been used successfully is in
satellite communication.

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3.3 Advantages and Disadvantages of Patch Antennas
Some of their principal advantages of microstrip patch antennas are given below:
• Light weight and low volume.
• Low profile planar configuration which can be easily made conformal to host surface.
• Low fabrication cost, hence can be manufactured in large quantities.
• Supports both, linear as well as circular polarization.
• Can be easily integrated with microwave integrated circuits (MICs).
• Capable of dual and triple frequency operations.
• Mechanically robust when mounted on rigid surfaces.

Microstrip patch antennas suffer from a number of disadvantages as compared to
conventional antennas. Some of their major disadvantages are given below:
• Narrow bandwidth
• Low efficiency
• Low Gain
• Extraneous radiation from feeds and junctions
• Poor end fire radiator except tapered slot antennas
• Low power handling capacity.
• Surface wave excitation

Microstrip patch antennas have a very high antenna quality factor (Q). Q represents the
losses associated with the antenna and a large Q leads to narrow bandwidth and low
efficiency. Q can be reduced by increasing the thickness of the dielectric substrate. But as
the thickness increases, an increasing fraction of the total power delivered by the source
goes into a surface wave. This surface wave contribution can be counted as an unwanted
power loss since it is ultimately scattered at the dielectric bends and causes degradation
of the antenna characteristics. However, surface waves can be minimized by use of
photonic bandgap structure. Other problems such as low gain and low power handling
capacity can be overcome by using an array configuration for the elements.

3.4 Feed Techniques
Microstrip patch antennas can be fed by a variety of methods. These methods can be
classified into two categories- contacting and non-contacting. In the contacting method,
the RF power is fed directly to the radiating patch using a connecting element such as a
microstrip line. In the non-contacting scheme, electromagnetic field coupling is done to
transfer power between the microstrip line and the radiating patch. The four most popular
feed techniques used are the microstrip line, coaxial probe (both contacting schemes),
aperture coupling and proximity coupling (both non-contacting schemes).

3.4.1 Microstrip Line Feed
In this type of feed technique, a conducting strip is connected directly to the edge of the
microstrip patch as shown in Figure 3.4. The conducting strip is smaller in width as
compared to the patch and this kind of feed arrangement has the advantage that the feed
can be etched on the same substrate to provide a planar structure.

29

Figure – 3.4 - Microstrip Line Feed

The purpose of the inset cut in the patch is to match the impedance of the feed line to the
patch without the need for any additional matching element. This is achieved by properly
controlling the inset position. Hence this is an easy feeding scheme, since it provides ease
of fabrication and simplicity in modeling as well as impedance matching. However as the
thickness of the dielectric substrate being used, increases, surface waves and spurious
feed radiation also increases, which hampers the bandwidth of the antenna. The feed
radiation also leads to undesired cross polarized radiation.

3.4.2 Coaxial Feed
The Coaxial feed or probe feed is a very common technique used for feeding Microstrip
patch antennas. As seen from Figure 3.5, the inner conductor of the coaxial connector
extends through the dielectric and is soldered to the radiating patch, while the outer
conductor is connected to the ground plane.

The main advantage of this type of feeding scheme is that the feed can be placed at any
desired location inside the patch in order to match with its input impedance. This feed
method is easy to fabricate and has low spurious radiation. However, its major
disadvantage is that it provides narrow bandwidth and is difficult to model since a hole
has to be drilled in the substrate and the connector protrudes outside the ground plane,
thus not making it completely planar for thick substrates (h > 0.02λo). Also, for thicker
substrates, the increased probe length makes the input impedance more inductive, leading
to matching problems. It is seen above that for a thick dielectric substrate, which provides
broad bandwidth, the microstrip line feed and the coaxial feed suffer from numerous
disadvantages. The non-contacting feed techniques discussed below, solve these
problems.

30

Figure – 3.5 – Coaxial Feed

3.4.3 Aperture Coupled Feed
In this type of feed technique, the radiating patch and the microstrip feed line are
separated by the ground plane as shown in Figure 3.6. Coupling between the patch and
the feed line is made through a slot or an aperture in the ground plane.

The coupling aperture is usually centered under the patch, leading to lower cross
polarization due to symmetry of the configuration. The amount of coupling from the feed
line to the patch is determined by the shape, size and location of the aperture. Since the
ground plane separates the patch and the feed line, spurious radiation is minimized.
Generally, a high dielectric material is used for the bottom substrate and a thick, low
dielectric constant material is used for the top substrate to optimize radiation from the
patch. The major disadvantage of this feed technique is that it is difficult to fabricate due
to multiple layers, which also increases the antenna thickness. This feeding scheme also
provides narrow bandwidth.

31

Figure – 3.6 – Aperture Feed

3.4.4 Proximity Coupled Feed
This type of feed technique is also called as the electromagnetic coupling scheme. As
shown in Figure 3.7, two dielectric substrates are used such that the feed line is between
the two substrates and the radiating patch is on top of the upper substrate. The main
advantage of this feed technique is that it eliminates spurious feed radiation and provides
very high bandwidth (as high as 13%), due to overall increase in the thickness of the
microstrip patch antenna. This scheme also provides choices between two different
dielectric media, one for the patch and one for the feed line to optimize the individual
performances.

Matching can be achieved by controlling the length of the feed line and the width-to-line
ratio of the patch. The major disadvantage of this feed scheme is that it is difficult to
fabricate because of the two dielectric layers which need proper alignment. Also, there is
an increase in the overall thickness of the antenna.

Table 3.1 summarizes the characteristics of the different feed techniques.

32

Figure – 3.7 – Proximity Coupled Feed

Table – 3.1 – Comparison of different Feed Methods

It is to be noted that in our project simulations we have used microstrip feed and co-axial
feed techniques.

33

3.5 Methods of Analysis
The most popular models for the analysis of Microstrip patch antennas are the
transmission line model, cavity model, and full wave model (which include primarily
integral equations/Moment Method). The transmission line model is the simplest of all
and it gives good physical insight but it is less accurate. The cavity model is more
accurate and gives good physical insight but is complex in nature. The full wave models
are extremely accurate, versatile and can treat single elements, finite and infinite arrays,
stacked elements, arbitrary shaped elements and coupling.

It must be noted that our project is centered on the transmission line model and uses all of
the empirical equations this model is based on for simulations. The cavity model is not at
the centre of our project and is hence explained very briefly. The method of moments is
explained in detail as it is used by several field solvers (such as IE3D) for simulations.

3.5.1 Transmission Line Model
This model represents the microstrip antenna by two slots of width W and height h,
separated by a transmission line of length L. The microstrip is essentially a non
homogeneous line of two dielectrics, typically the substrate and air. Figure 3.8 illustrates
this.

Figure – 3.8 – Microstrip Line

As seen from Figure 3.9, most of the electric field lines reside in the substrate and parts
of some lines in air. As a result, this transmission line cannot support pure transverse
electric- magnetic (TEM) mode of transmission, since the phase velocities would be
different in the air and the substrate. Instead, the dominant mode of propagation would be
the quasi-TEM mode. Hence, an effective dielectric constant (εreff) must be obtained in
order to account for the fringing and the wave propagation in the line.

34

Figure – 3.9 – Electric Field Lines

The value of εreff is slightly less then εr because the fringing fields around the periphery of
the patch are not confined in the dielectric substrate but are also spread in the air as
shown in Figure 9. The expression for εreff is given as:

εreff= (εreff + 1)/2 + (εreff - 1)/2[1+12h/W]-1/2 Equation 3.1

Where εreff = Effective dielectric constant
εr = Dielectric constant of substrate
h = Height of dielectric substrate
W = Width of the patch

Figure - 3.10 – Microstrip Patch Antenna

35

Figure 3.10 shows a rectangular microstrip patch antenna of length L, width W resting on
a substrate of height h. The co-ordinate axis is selected such that the length is along the x
direction, width is along the y direction and the height is along the z direction. In order to
operate in the fundamental TM mode, the length of the patch must be slightly less than λ /
2 where λ is the wavelength in the dielectric medium and is equal to λo/√(εreff) where λo is
the free space wavelength. The TM mode implies that the field varies one λ / 2 cycle
along the length, and there is no variation along the width of the patch. In figure 3.11 the
microstrip patch antenna is represented by two slots, separated by a transmission line of
length L and open circuited at both the ends. Along the width of the patch, the voltage is
maximum and current is minimum due to the open ends. The fields at the edges can be
resolved into normal and tangential components with respect to the ground plane.

Figure – 3.11 – Top View of Antenna

It is seen from figure 3.12 that the normal components of the electric field at the two
edges along the width are in opposite directions and thus out of phase since the patch is
λ/2 long and hence they cancel each other in the broadside direction. The tangential
components (seen in figure 11), which are in phase, means that the resulting fields
combine to give maximum radiated field normal to the surface of the structure. Hence the
edges along the width can be represented as two radiating slots, which are λ / 2 apart and
excited in phase and radiating in the half space above the ground plane.

36

Figure – 3.12 – Side View of Antenna

The fringing fields along the width can be modeled as radiating slots and electrically the
patch of the microstrip antenna looks greater than its physical dimensions. The
dimensions of the patch along its length have now been extended on each end by a
distance ΔL, which is given empirically by as:

ΔL=0.412h(εreff + 0.3)(W/h + 0.264)/((εreff - 0.258)(W/h + 0.8)) Equation 3.2

The effective length of the patch Leff now becomes:

Leff=L+2 ΔL Equation 3.3

For a given resonance frequency fo, the effective length is given by as:

Leff=c/(2fo√(εreff) Equation 3.4
For a rectangular Microstrip patch antenna, the resonance frequency for any TM mode is
given as:

fo= c/(2√(εreff)[(m/L)2+(n/W)2]1/2 Equation 3.5

Where m and n are modes along L and W respectively. For efficient radiation, the width
W is given as:

W= c/(2fo√((εr+1)/2)) Equation 3.6

37

3.5.2 Cavity Model
Although the transmission line model discussed in the previous section is easy to use, it
has some inherent disadvantages. Specifically, it is useful for patches of rectangular
design and it ignores field variations along the radiating edges. These disadvantages can
be overcome by using the cavity model. In this model, the interior region of the dielectric
substrate is modeled as a cavity bounded by electric walls on the top and bottom. The
basis for this assumption is the following observations for thin substrates (h<<λ).

1)Since the substrate is thin, the fields in the interior region do not vary much in the z
direction, i.e. normal to the patch.

2)The electric field is z directed only, and the magnetic field has only the transverse
components Hx and Hy in the region bounded by the patch metallization and the ground
plane. This observation provides for the electric walls at the top and the bottom.

3.5.3 Full Wave Solutions-Method of Moments
One of the methods, that provide the full wave analysis for the microstrip patch antenna,
is the Method of Moments. In this method, the surface currents are used to model the
microstrip patch and the volume polarization currents are used to model the fields in the
dielectric slab. It as been shown by Newman and Tulyathan how an integral equation is
obtained for these unknown currents and using the Method of Moments, these electric
field integral equations are converted into matrix equations which can then be solved by
various techniques of algebra to provide the result. A brief overview of the method of
moments is given below.

The basic form of the equation to be solved by the method of moments is:

F(g) = h Equation 3.7

where F is a known linear operator, g is an unknown function, and h is the source or
excitation function. The aim here is to find g, when F and h are known. The unknown
function g can be expanded as a linear combination of N terms to give:

Equation 3.8
where an is an unknown constant and gn is a known function usually called a basis or
expansion function. Substituting equation 2 in 1 and using the linearity property of the
operator F, we can write:

Equation 3.9

The basis functions gn must be selected in such a way, that each F(gn) in the above
equation can be calculated. The unknown constants an cannot be determined directly
because there are N unknowns, but only one equation. One method of finding these

38

constants is the method of weighted residuals. In this method, a set of trial solutions is
established with one or more variable parameters. The residuals are a measure of the
difference between the trial solution and the true solution. The variable parameters are
selected in a way which guarantees a best fit of the trial functions based on the
minimization of the residuals.

From the antenna theory point of view, we can write the Electric field integral equation as

E=fe(J) Equation 3.10

where E is the known incident electric field.
J is the unknown induced current.
fe is the linear operator.

The first step in the moment method solution process would be to expand J as a finite
sum of basis function given as:

Equation 3.11

where bi is the ith basis function and Ji is an unknown coefficient. The second step
involves the defining of a set of M linearly independent weighting functions, wj. Taking
the inner product on both sides and substituting equation 3.5 in equation 3.4 we get:

Equation 3.12
Where j=1,2….M

In matrix form we get [Zij][J]=[Ej] Equation 3.13

Where Zij=<wjfe(bi)>
Ej=<wj,H>
J is the current vector containing the unknown quantities.

The vector E contains the known incident field quantities and the terms of the Z matrix
are functions of geometry. The unknown coefficients of the induced current are the terms
of the J vector. Using any of the algebraic schemes mentioned earlier, these equations can
be solved to give the current and then the other parameters such as the scattered electric
and magnetic fields can be calculated directly from the induced currents. IE3D is a
powerful simulation software that uses the method of moments. It is an efficient field
solver and this is why we used it for carrying out all our patch antenna simulations. The
following section describes IE3D’s uses and merits.

39

3.6 Simulation Software – IE3D
The software used to perform all simulations is Zealand Inc’s IE3D. IE3D is a full-wave
electromagnetic simulator based on the method of moments. It analyzes 3D and
multilayer structures of general shapes. It has been widely used in the design of MICs,
RFICs, patch antennas, wire antennas, and other RF/wireless antennas. It can be used to
calculate and plot the S parameters, VSWR, current distributions as well as the radiation
patterns. Some of IE3D’s features are

1) Can model true 3D metallic structures in multiple dielectric layers in open, closed or
periodic boundary
2) High efficiency, high accuracy and low cost electromagnetic simulation tool on PCs
with windows based graphic interface
3) Automatic generation of non-uniform mesh with rectangular and triangular cells
4) Can model structures with finite ground planes and differential feed structures
5) Accurate modeling of true 3D metallic structures and metal thickness
6) Efficient matrix solvers
7) 3D and 2D display of current distribution, radiation patterns and near field.

For our purposes it is a very powerful tool as it allows for ease of design and accurate
simulation results. The results obtained for each patch were 2D view of patch, 3D view of
patch, RL curve, Directivity, gain, beam width and other such parameters, true 3D
radiation pattern, mapped 3D radiation pattern and 2D polar radiation pattern. These
terms are defined below.

True 3D Radiation Pattern- It is the pattern in the actual 3D space. The size of the pattern
from the origin represents how strong the field at a specific (theta, phi) angle.

Mapped 3D Radiation Pattern - It is the pattern with the theta angle mapped to the radius
of a cylindrical coordinate system. The radius in the cylindrical system represents value
of the theta angle.

2D Polar Radiation Pattern - A polar pattern is basically a cut on the True 3D pattern at a
specific phi angle.

2D Cartesian Radiation Pattern - A Cartesian pattern is basically a cut on the Mapped 3D
pattern at a specific phi angle.

For our project IE3D was very useful as it ensured ease of patch design and
comprehensive simulation results. This was the reason for the slowness of IE3D
compared to other software like Sonnet. Typically IE3D took around 100s to generate a
frequency point (we mostly used 20 such points for generation of all curves etc) and in
some cases even 600s (10 min) depending on the patch dimensions, frequency range,
degree of meshing etc. Sonnet on the other hand was slightly faster taking around 50s per
frequency point for simple simulations but it only displayed the return loss curve while
IE3D was used to determine 3D radiation patterns etc. This is why all simulations were
carried out using IE3D only. The simulation results follow.

40

3.7 Design of a Simple Rectangular Patch Antenna
The software part of our project revolved around determination of the radiation pattern
and return loss curve (s11 vs frequency) of several simple rectangular patch antennas.
From the transmission line model of rectangular patch antennas it is clear that the three
essential parameters for the design of a rectangular Microstrip Patch Antenna
are:
1) Frequency of operation (fo): The resonant frequency of the antenna must be selected
appropriately.
2) Dielectric constant of the substrate (εr): A substrate with a high dielectric constant
reduces the dimensions of the antenna.
3) Height of dielectric substrate (h): For the microstrip patch antenna to be used in certain
applications (such as cell phones) it is essential that it is not bulky and to ensure this the
height of the dielectric substrate can’t be more than a few mm.

The effect of all the above 3 factors and the position of feed point on antenna
performance was studied by simulating several rectangular patch antennas. The basic
patch chosen for this purpose is shown in figure 3.13.

Figure – 3.13 – Top View of the rectangular patch

41

This patch is intended for cell phone applications and hence its frequency of operation
was chosen to be 1.9 GHz (GSM frequency band). Its parameters are

fo=1.9GHz
εr=11.9
h=1.5 mm

Using the above parameters and the equations of the transmission line model we obtain

W=31.1mm
εreff=10.7871
Leff=24 mm
ΔL=0.63455 mm
L=22.8 mm

The transmission line model is applicable to infinite ground planes only. However, for
practical considerations, it is essential to have a finite ground plane. It has been shown
that similar results for finite and infinite ground plane can be obtained if the size of the
ground plane is greater than the patch dimensions by approximately six times the
substrate thickness all around the periphery. Hence, for this design, the ground plane
dimensions would be given as:

Lg=6h+L=31.8 mm
Wg=6h+W=40.1 mm

A simple MATLAB program that we used to perform these calculations is given in
Appendix A.

A coaxial probe type feed is to be used in this design. As shown in Figure 3.13, the center
of the patch is taken as the origin and the feed point location is given by the co-ordinates
(Xf ,Yf) from the origin. The feed point must be located at that point on the patch, where
the input impedance is 50 ohms for the resonant frequency. Hence, a trial and error
method is used to locate the feed point. For different locations of the feed point, the
return loss (RL) is compared and that feed point is selected where the R.L is most
negative. There exists a point along the length of the patch where the RL is minimum.
Hence in this design, Yf was kept constant at zero and only Xf was be varied to locate the
optimum feed point.

42

Figure – 3.14 (a) 3D view of radiation pattern for cellular phone orientation in the
YZ plane (b) 3D view of radiation pattern for cellular phone orientation in the XZ
plane

The first set of simulation results show the effect of feed point on the return loss curve
and radiation pattern. When the microstrip patch antenna designed would be placed into a
cellular phone, its orientation would be such that the z axis would be parallel to the
surface of the earth. Figure 3.14 shows the 3D radiation pattern plots for this scenario.
From the figure it became clear to us that the back lobe protruding into the cell phone had
to be made as small as possible and the main lobe had to be expanded to ensure better
transmission. To ensure this we varied h and εr until this occurred. In the process the
effect of these parameters on patch dimensions, RL curve and radiation pattern was
studied. These simulation results for this patch and 2 other patches are presented later in
this report. First an introduction to the software used for the simulations is presented.

3.8 Simulation of a 1.9 GHz Patch Antenna
3.8.1 Introduction
One of the antennas that we simulated was the 1.9 GHz patch antenna. 1.9 GHz antenna
is a commonly used frequency, used predominantly in GSM phones in United States. Our
objective was to design a probe fed patch antenna that resonates at 1.9 GHz and then vary
the parameters of the antenna such that the working of the patch is optimized. We divided
the simulations into three basic groups-

1) Firstly, we varied the feed point of the patch. The gain of the antenna varies greatly as
we vary the feed point. We get best gain when the probe is located at the 50 Ohm
impedance line. In this case the return loss curve dips the maximum. Since there is no
specific way of finding this line, we vary the feed point and try to get the best gain by
trial and error.

2) We tried to ensure that the entire radiation due to the patch is in one direction. This is
primarily because of the growing concern that cell phone signals are detrimental to
human health. Hence we tried to design a patch such that the entire signal propagates

43

away from the user. This was achieved by varying the thickness of the patch. The catch
here is that the patch cannot be made too thick, or it cannot be used in a cell phone
3) We also varied the permittivity of the dielectric and observed its effects on the
performance of the patch.

All the patches were deigned with help of equations given previously. The simulation
results for the patches are given in the following pages.

3.8.2 Effect of variation of probe feed on the patch
The centre of the patch is located at (0,0). The probe was fed at (2,0), (3,0), (4,0), (5,0),
and (6,0) and its effect on various parameters of the patch, primarily, on the return loss
curve was observed. Basic dimensions of the patch calculated were as follows.

Length of ground plane = 31.8 mm
Width of ground plane = 40.1 mm
Length of the patch = 22.8 mm
Width of the patch = 31.1 mm
Permittivity of substrate = 11.9
Height of substrate = 1.5 mm
Frequency = 1.9 GHz

Figure – 3.15 - The meshed patch designed in IE3D to resonate at 1.9GHz
In this case the probe is located at (2,0)

The above figure shows one of the patches simulated. A new patch was created for as the
probe feed point was varied. A comparison of the results obtained in each case follows.

44

3.8.2.1 Return Loss Curves

Figure – 3.16 – Return Loss curve for different feed points

As it can be seen from the above set of curves, we get best results when the probe is
located (3,0), since the power reflected is minimum then.

45

3.8.2.2 Other Frequency Properties
Frequency : 1.91053 (GHz)
Incident Power : 0.01 (W)
Input Power : 0.00139718 (W)
Radiated Power : 0.000572898 (W)
Average Radiated Power : 4.55898e-005 (W/s)
Radiation Efficiency : 41.0038%
Antenna Efficiency : 5.72898%
Conjugate Match Efficiency: 20.5019%
Total Field Properties :
Gain : -9.11385 dBi
Directivity : 3.30538 dBi
Maximum : at (0, 90) deg.
3dB Beam Width : (96.6573, 156.222) deg.
Conjugate Match Gain : -3.57668 dBi

Table – 3.2 - Probe feed at (2,0) and f=1.9GHz

Input Power : 0.00151214 (W)
Gain : -8.73455 dBi
3dB Beam Width : (96.6001, 156.159) deg.


46

Input Power : 0.00200064 (W)
Gain : -7.42624 dBi
3dB Beam Width : (96.8584, 153.967) deg.


Input Power : 0.00207797 (W)
Gain : -7.22921 dBi
3dB Beam Width : (96.9764, 153.532) deg.


47

Input Power : 0.00175946 (W)
Gain : -7.95669 dBi
3dB Beam Width : (97.0207, 153.505) deg.


As can be seen from the above tables, other parameters such as gain, directivity and 3dB
beamwidth are nearly the same as we vary the feed points.

3.8.2.3 True 3D patterns

Figure – 3.17 - Probe feed at (2,0)

48



49



50

3.8.2.4 Mapped 3D Patterns



51



52

As seen from above figures, the shape of the true 3D pattern and the mapped 3D pattern
remain almost invariant as the feed point is varied. The 2D polar plot obtained for probe
feed at (2,0) is shown in figure 3.26. Like the 3D pattern remained invariant, the 2D
pattern for probe feed at other points also remained almost invariant, and hence has not
been shown.

3.8.2.5 2D Polar Plot (Radiation Pattern)

Figure – 3.26 – 2D Polar Plot for different frequencies and angle (φ) for feed point
at (2,0)

53

3.8.3 Effect of variation of height of the patch on the patch
characteristics
The height of the patch, or in other words the thickness of the substrate was varied, and
its effect on the various parameters of the patch antenna was observed. The primary
objective of these simulations was to ensure, bulk of the signal propagates in a single
direction. It was expected, that as the substrate is made thicker, the signal propagating
through the substrate would reduce. Three set of simulations were performed.

With substrate height= 0.5mm
With substrate height= 2mm
With substrate height= 10mm

The results obtained follow.

The dimension of the patches simulated are as follows

Frequency = 1.9 GHz

Height of substrate = 2 mm
Frequency = 1.9 GHz

Height of substrate = 10 mm
Frequency = 1.9 GHz

Figure – 3.27 shows the meshed patches

54

a) h=0.5mm b) h=2 mm c)h=10 mm

Figure – 3.27 – Meshed patches for different values of h

The simulation results for all three cases follow.

3.8.3.1 True 3D patterns

Figure – 3.28 - For substrate height = 0.5mm

55

Figure – 3.29 - For substrate height = 2mm

Figure – 3.30 - For substrate height = 10mm

56

As expected, as the height is increased, the signal propagated through the substrate
reduces. This fact becomes clearer from the mapped 3D patterns shown in the following
figures.

3.8.3.2 Mapped 3D patterns

Figure – 3.31 - For Substrate height = 0.5 mm

57

Figure – 3.32 - For Substrate height = 2 mm

Figure – 3.33 - For Substrate height = 10 mm

58

It can be seen that as the height of the substrate is increased, the gain in dBi in backward
direction decreases. Hence, the expected objective was achieved. The effect of variation
of height on other parameters is given in the following pages.


Figure – 3.34 – RL curve for substrate height = 0.5 mm

Figure – 3.35 – RL curve for Substrate height = 2 mm

59

Figure – 3.36 - RL curve for Substrate height = 10 mm

The return loss curve is seen to improve initially and then deteriorate as height is
increased.


Input Power : 0.000849249 (W)
Radiated Power : 9.09267e-005 (W)
Gain : -17.7599 dBi
3dB Beam Width : (89.5577, 184.065) deg.

Table – 3.7 - For height= 0.5mm at frequency=1.9GHz

60

Input Power : 0.00628805 (W)
Average Radiated Power : 0.000286295 (W/s)
Gain : -0.696194 dBi
3dB Beam Width : (99.771, 129.61) deg.

Table – 3.8 - For height= 0.5mm at frequency =1.9GHz

Input Power : 0.00325512 (W)
Gain : 0.127792 dBi
3dB Beam Width : (95.0533, 112.184) deg.
Conjugate Match Gain : 1.99182 dBi

Table – 3.9 - For height= 10mm at frequency =1.9GHz

As seen from the above figures, the radiation efficiency and the gain increase
significantly, while other parameters vary slightly, as the height is increased

61

3.8.4 Effect of variation of permittivity of the substrate on the patch
We observed the effect of variation of permittivity of the substrate on the characteristics
of the patch. We performed two sets of simulations.

1) With substrate permittivity =2.2
2) With substrate permittivity =15
We coupled these simulations with simulations done at substrate permittivity=11.9
(given previously) to analyze the effect of variation permittivity on the substrate. The
patch dimensions for the two permittivity values of the substrate are given below.

Frequency = 1.9 GHz

Width of the patch = 31 .1 mm
Frequency = 1.9 GHz

Permittivity of substrate = 15
Frequency = 1.9 GHz

The figures of the meshed patches are given below followed by the simulation results.

62

a) Permittivity=2.2 b) Permittivity=11.9 c) Permittivity=15

Figure – 3.37 – Meshed patches for varying dielectric constant


Figure – 3.38 – RL curve for permittivity = 2.2

63

Figure – 3.39 – RL curve for permittivity = 11.9

Figure – 3.40 – RL curve for permittivity = 15

It was observed from the return loss curves that the best performance was obtained at
permittivity=11.9 because for this value s11 at the operating frequency was minimum.

64

3.8.4.2 True 3D Patterns

Figure – 3.41 - Permittivity = 2.2

Figure – 3.42 - Permittivity = 11.9

65

Figure – 3.43 - Permittivity = 15

As permittivity increases, it was observed that the radiation through the substrate
(backward direction) increased. This can also be observed from the Mapped 3D pattern.
It is also clear that changes in h and permittivity have the opposite effect on the true and
mapped 3D radiation patterns.

3.8.4.3 Mapped 3D Patterns

Figure – 3.44 - Permittivity= 2.2

66

Figure – 3.45 - Permittivity= 11.9

Figure – 3.46 - Permittivity= 15

67


Input Power : 0.000185371 (W)
Gain : -13.8382 dBi
3dB Beam Width : (44.3396, 102.652) deg.
Conjugate Match Gain : 0.471063 dBi

Table – 3.10 - Permittivity = 2.2

Input Power : 0.00200064 (W)
Gain : -7.42624 dBi
3dB Beam Width : (96.8584, 153.967) deg.

Table – 3.11 - Permittivity = 11.9

68

Input Power : 0.00427509 (W)
Gain : -3.72241 dBi
3dB Beam Width : (116.149, 122.209) deg.

Table – 3.12 - Permittivity = 15

It was observed that for a given frequency the antenna efficiency decreased and the gain
increased, as permittivity was increased.

3.8.5 Conclusions based on simulation results
Based on our simulation results we were able to clearly see the effect of changing h and εr
on antenna dimensions and performance. These results are presented in a lucid manner in
table 3.13 assuming a fixed frequency of operation.

Parameter Lg (Length of Wg (Width of L (Length of W (Width of
Variation ground plane) ground plane) metal patch) metal patch)

h increased Increases Increases Decreases Remains
Constant

h decreased Decreases Decreases Increases Remains
Constant

εr increased Decreases Decreases Decreases Decreases

εr decreased Increases Increases Increases Increases

Table – 3.13 – Effect of variation of h and εr on patch dimensions

69

3.9 Simulation of a 5GHz Patch Antenna

3.9.1 Introduction
One of the experiments in our RF laboratory course required us to obtain the s11 curve of
a microstrip fed patch antenna. We decided to simulate this antenna, so that students will
have not only the s11 curve of the antenna, but also its radiation patterns and other
parameters such as its directivity, which will help them understand the working of the
patch better. The dimensions of the patch and a figure of the meshed patch are given
below.

Frequency = 5 GHz
Width of microstrip = 1.836 mm
Length of microstrip = 30.45 mm

Figure – 3.47 – Meshed Patch

The simulation results follow

70

3.9.2 True 3D Pattern

Figure – 3.48 – True 3D Radiation Pattern of the 5 GHz Patch

3.9.3 Mapped 3D Pattern

Figure – 3.49 – Mapped 3D Radiation Pattern of the 5 GHz Patch

71

3.9.4 2D Polar Plot

Figure – 3.50 – Polar plot for the antenna for three values of φ at f=2.5GHz and
f=6GHz

3.9.5 Other Frequency Properties

Input Power : 0.00520864 (W)
Gain : -3.03168 dBi
3dB Beam Width : (56.8323, 183.477) deg.

Table 3.14 – Other parameters for the 5 GHz antenna

72

3.9.6 Return Loss Curve

Figure – 3.51 – RL curve for the patch antenna

It can be seen from the return loss curve that the antenna resonates at 3.5GHz. However,
this value differs from the expected value of 5GHz. Reasons for the deviation could be
that we didn’t have all the dimensions of the patch, and data on type of material used for
metal and dielectric. Since, we had to manually measure some dimensions, this is a cause
for the errors. Another reason is that when we are actually testing the patch, we do so by
placing it on a metallic jig. The jig, should act as a ground. When we are doing the
simulations, we do not consider the effect of the jig. This too could have brought about
the variation.

73

3.10 Simulation of Dual Band Patch antennas
3.10.1 Antenna 1

3.10.1.1 Introduction
The following patch antenna is a dual band antenna that uses two rectangular patches
with bridges connecting them. It shows two minima in its return loss curve unlike all
simple patches that only show one such point. The first dual band we simulated was
composed of two rectangular patches, which configure 2.4 and 5.5GHz connected to each
other using 4-briges. Bridges have a role of connection of each rectangular patch to
operate antenna in dual frequency band. In addition, bridges have a role of tuning the
frequency bands by changing bridge width. It has an advantage on conversion of
frequency band by simply changing the bridge width (BW). The configuration of the
patch is shown in figure 52 (a and b).

(a) (b)

Figure – 52 – Configuration of the dual band patch

74

The dimensions of the patch are as follows

Ground plane Lg = Wg = 40 mm (Square ground plane)
Outer Patch L = W = w2 = 28 mm (Square outer patch)
Inner Patch L = W = w1 = 13 mm (Square inner patch)
Frequency = 2.4 GHz (due to outer patch)
= 5.5 GHz (due to inner patch)
Bridge width = 2 mm

Variation of Bridge Width (BW) affects the frequency of operation thus changing the
return loss curve of the antenna, however the simulation of such antennas took nearly
four hours to complete so this variation in RL curve due to changes in BW could not
be studied by us and only the effect of BW = 2 mm was considered. Location of
feeding point (F) is determined by input impedance. It is located at 2.5mm with gap
(G) between the nearest edge of inner patch and feeding point. The simulation results
follow.

Figure – 3.53 – Meshed dual band patch antenna 1

75

3.10.2 True 3D Radiation Pattern

The true 3D radiation pattern obtained after simulation is shown in figure 54.

Figure – 3.54 – True 3D Radiation Pattern for dual band antenna 1

3.10.3 Mapped 3D Radiation Pattern

The mapped 3D radiation pattern obtained after simulation is shown in figure 55.

Figure – 3.55 – Mapped 3D Radiation Pattern for dual band antenna 1

76

3.10.4 2D Polar plot

The 2D polar plot obtained after the simulation is shown in figure 56. It has been
plotted for only three frequencies (2 GHz, 3.67 GHz and 5.9 GHz) for three values of
φ (0, 90 and 170 degrees).

Figure – 3.56 – 2D Polar Plot for dual band antenna 1

77


Incident Power: 0.01 (W)
Input Power: 0.000356354 (W)
Radiated Power: 0.000255574 (W)
Average Radiated Power: 2.03379e-005 (W/s)
Radiation Efficiency: 71.719%
Antenna Efficiency: 2.55574%
Total Field Properties:
Gain: -11.5476 dBi
Directivity: 4.37724 dBi
Maximum: at (5, 90) deg.
3dB Beam Width: (56.0092, 117.71) deg.
Conjugate Match Gain: -0.0767216 dBi
Theta Field Properties:
Gain: -11.5477 dBi
3dB Beam Width: (9.98227, 56.0093) deg.
Table – 3.15 – Frequency properties of antenna 1 at 2.27857 GHz

Frequency: 5.34286 (GHz)
Input Power: 0.000785845 (W)
Average Radiated Power: 4.46886e-005 (W/s)
Gain: -8.28596 dBi
3dB Beam Width: (51.5497, 95.0348) deg.
Gain: -9.33806 dBi
3dB Beam Width: (46.5382, 89.8729) deg.


78


Figure – 3.57 – Return Loss Curve of dual band patch antenna 1

From the return loss curve it is clear that the simulated results match with those
theoretically predicted and the antenna does have operating frequencies at 2.4 GHz
and 5.5 GHz.

3.10.2 Antenna 2

3.10.2.1 Introduction
We constructed a new dual band antenna with different patch dimensions to observe
the shift in operating frequencies caused due to this. It was our intention to construct a
patch with operating frequencies at 0.9 GHz and 1.9 GHz (the GSM frequencies used
in India and the U.S) so that a theoretical cell phone patch antenna that could be used
at two different frequencies could be constructed. By increasing the patch dimensions
we were able to lower both operating frequencies, as shown by the simulation results.
However, we were unable to lower them to the required values again due to the large
simulation time required and trial and error involved. We also noticed that though the
theory behind our efforts was correct the resulting patch would be of very large size
(greater than 10cm by 10 cm) which wouldn’t be practical for a cell phone.
Nevertheless, the results for a dual band antenna that operates at 2.3 GHz and 4.6
GHz are presented in the following pages.

79

The dimensions of the patch are as follows

Ground plane Lg = Wg = 77 mm (Square ground plane)
Outer Patch L = W = w2 = 56 mm (Square outer patch)
Inner Patch L = W = w1 = 42 mm (Square inner patch)
Frequency = 2.3 GHz (due to outer patch)
= 4.6 GHz (due to inner patch)
Bridge width = 2 mm

Figure – 3.58 - Meshed dual band patch antenna 2

80

3.10.2.2 True 3D Radiation Pattern

The true 3D radiation pattern obtained after simulation is shown in figure 3.59.

Figure – 3.59 – True 3D Radiation Pattern for Dual Band Antenna 2

3.10.2.3 Mapped 3D Radiation Pattern

The mapped 3D radiation pattern obtained after simulation is shown in figure 3.60.

Figure – 3.60 – Mapped 3D Radiation Pattern for Dual Band Antenna 2

81

3.10.2.4 2D Polar plot

The 2D polar plot obtained after the simulation is shown in figure 3.61. It has been
plotted for only three frequencies (0.3 GHz, 5.014 GHz and 5.407 GHz) for three
values of φ (0, 90 and 170 degrees).

Figure – 3.61 – 2D Polar Plot for Dual Band Antenna 2

82


Input Power: 0.00757225 (W)
Average Radiated Power: 0.000421428 (W/s)
Gain: 3.92592 dBi
3dB Beam Width: (88.0808, 91.6176) deg.
Conjugate Match Gain: 2.12338 dBi
Gain: 3.92485 dBi
3dB Beam Width: (0, 0) deg.
Table – 3.17 – Frequency properties of antenna 2at 2.26429 GHz

Input Power: 0.0090008 (W)
Average Radiated Power: 0.000593984 (W/s)
Gain: 3.74383 dBi
3dB Beam Width: (48.3662, 121.301) deg.
Gain: 2.54818 dBi
3dB Beam Width: (44.816, 95.3565) deg.


83


Figure – 3.62 – Return Loss Curve of dual band patch antenna 2

From the return loss curve it is clear that the antenna has operating frequencies at 2.4
GHz and 5.5 GHz.

84

Chapter 4
Conclusions and Scope for Improvement

4.1 Conclusions

Upon the conclusion of our project we made the following assessment of our
work:

The overall working of antennas was understood. The major parameters
(such as Return Loss curves, Radiation Patterns, Directivity and Beamwidth)
that affect design and applications were studied and their implications
understood. The constructed slotted waveguide and biquad antennas
operated at the desired frequency and power levels. Several patch antennas
were simulated (using IE3D) and the desired level of optimization was
obtained. It was concluded that the hardware and software results we
obtained matched the theoretically predicted results.

4.2 Scope for Improvement

There were some areas we felt we did not address. They were

• The experimental radiation patterns of the constructed antennas could
not be obtained and compared with the theoretical patterns
• Though we were able to simulate several patch antennas, we were
unable to fabricate one and compare the practical and simulated
results.
• A more complete study of different field solvers and simulators (such
as Sonnet, AWR, HFSS etc) could not be made. We were only able to
focus on IE3D.

85

Appendix A
MATLAB Codes
Code 1: 2D Radiation Pattern Generator

clc;

n=input('Enter step size');

q=1;

for i=0:n:360

x(q)= input(‘Enter power in micro volts’);

if (x(q)<=0)

x(q)=1;

end

v(q)=20*log10(x(q));

t(q)=i*pi/180;

q=q+1;

end

v(length(v))=v(1);

figure(1)

polar(t,v,’red’);

86

Code 2: Patch Antenna Dimensions Calculator

function Antcal()

%This function is to be used to calculate the different parameters of a rectangular patch
antenna

clc;

fo=input('Enter frequency of operation (fo) in Hz');

Er=input('Enter Dielectric constant (Er)');

h=input('Enter height of substrate (h) in m');

W=(3*10^8)/(2*fo*sqrt((Er+1)/2))

Eref=(Er+1)/2+((Er-1)/2)/(sqrt(1+12*h/W))

Lef=(3*10^8)/(2*fo*sqrt(Eref))

dL=((0.412*h)*(Eref+0.3)*(W/h+0.264))/((Eref-0.258)*(W/h+0.8))

L=Lef-2*dL

Lg=6*h+L

Wg=6*h+W

end

87

Appendix B
Data on Equipment used for Antenna Analysis
Network Analyzer

Today, when we refer to the things that network analyzers measure, we speak mostly
about devices and components. The examples of the types of devices that can be tested
with network analyzers are given in Figure 1. They include both passive and active
devices (and some that have attributes of both). Many of these devices need to be
characterized for both linear and nonlinear behavior. It is not possible to completely
characterize all of these devices with just one piece of test equipment.

Figure 1 – Devices that can be tested by a Network Analyzer

Network analyzers are used to measure components, devices, circuits, and sub-
assemblies. They contain both a source and multiple receivers, and generally display
ratioed amplitude and phase information (frequency or power sweeps). A network

88

analyzer is always looking at a known signal (in terms of frequency), since it is a
stimulus response system. With network analyzers, it is harder to get an (accurate) trace
on the display, but very easy to interpret the results. With vector-error correction,
network analyzers provide much higher measurement accuracy than spectrum analyzers.

Figure – 2 – Generalized Block Diagram of a Network Analyzer

The generalized block diagram of a network analyzer (figure 2), shows the major signal-
processing sections. In order to measure the incident, reflected and transmitted signal,
four sections are required:

1) Source for stimulus

2) Signal-separation devices

3) Receivers that down convert and detect the signals

4) Processor/display for calculating and reviewing the results

89

Spectrum Analyzer

At the most basic level, a spectrum analyzer can be described as a frequency-selective,
peak-responding voltmeter calibrated to display the rms value of a sine wave. It is
important to understand that the spectrum analyzer is not a power meter, even though it
can be used to display power directly. As long as we know some value of a sine wave and
know the resistance across which we measure this value, we can calibrate our voltmeter
to indicate power. With the advent of digital technology, modern spectrum analyzers
have been given many more capabilities. In this note, we shall describe the basic
spectrum analyzer as well as the many additional capabilities made possible using digital
technology and digital signal processing.

Spectrum analyzers are most often used to measure signal characteristics such as carrier
level, sidebands, harmonics, phase noise, etc., on unknown signals. They are most
commonly configured as a single channel receiver, without a source. Because of the
flexibility needed to analyze signals, spectrum analyzers have a much wider range of IF
bandwidths available than most network analyzers. Spectrum analyzers are often used
with external sources for nonlinear stimulus/response testing. When combined with a
tracking generator, spectrum analyzers can be used for scalar component testing. With
spectrum analyzers, it is easy to get a trace on the display, but interpreting the results can
be much more difficult than with a network analyzer.

Figure – 3 – Block Diagram of a Spectrum Analyzer

Referring to the block diagram of a spectrum analyzer we see that an input signal passes
through an attenuator, then through a low-pass filter (later we shall see why the filter is
here) to a mixer, where it mixes with a signal from the local oscillator (LO). Because the
mixer is a non-linear device, its output includes not only the two original signals, but also
their harmonics and the sums and differences of the original frequencies and their
harmonics. If any of the mixed signals falls within the pass band of the intermediate-
frequency (IF) filter, it is further processed (amplified and perhaps compressed on a
logarithmic scale). It is essentially rectified by the envelope detector, digitized, and
displayed. A ramp generator creates the horizontal movement across the display from left

90

to right. The ramp also tunes the LO so that its frequency change is in proportion to the
ramp voltage.

A simple comparison of network and spectrum analyzers that sums up their functions is
shown in figure 4.

Figure – 4 – Comparison of Network and Spectrum Analyzers

91

References
Books

Modern Antenna Design by Thomas Milligan (2nd edn – Thomas Wiley and Sons)

Antenna Theory and Design by Robert S. Elliot (Wiley Publications)

Antennas for all Applications by John Krauss (Third edition TMH)

Electromagnetic Waves and Radiating Systems – Edward C. Jordan and Keith G.
Balmain (2nd edn – PHI Publishers)

Research Papers

A Dual band antenna for WLAN applications by double rectangular patch with 4 bridges
– Chang Won Jung and Franco De Flaviis

Design and analysis of an Electrically Steerable Microstrip Antenna for Ground to Air
Use – Johan Lagerqvist

A High-Performance Dual Frequency Microstrip Antenna for GPS
Luigi Boccia, Giandomenico Amendola and Giuseppe Di Massa

Analysis and Design of Equilateral Triangle Microstrip Patch Antenna with Microstrip
Feed – V. Sarala and V. M. Pandharipande

Websites

www.ingecom.ch

www.zealand.com

www.wikipedia.com

www.howstuffworks.com

www.sonnetsoftware.com

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