Abstract

Metamaterials have received increasing attention due to their unique

electromagnetic properties. Various types of metamaterial have been proposed
with different characteristics. These unusual properties play an important role in
modern antenna design, which can provide better performance, more functions,
and more flexibility. In this work single layer of metamaterials formed as Len to
improve the impedance matching, gain, and fractional bandwidth of compact
microstrip antennas at 60 GHz band and enhancing the radiation pattern for
greater coverage.
The metamaterial inspired behavior is obtained using split ring resonators (SRR)
printed on the dielectric substrate GaAs which is located on the top of the antenna
patch. The effects of the metamaterial structure on the vertically stacked antenna
performances at 60GHz band are investigated. The results show that the gain,
directivity , bandwidth and return loss of the antenna with metamaterial
superstrate are increased at 60GHz band ,Compared with conventional patch
antenna without the metamaterial superstrate without distorting the antenna
resonance frequency. High Frequency Structure Simulator (HFSS) was used to
simulate and analysis the metamaterial substrate and antenna configurations

1
 Acknowledgments

I would like to dedicate this work to my faculty staff and students in general, my
greets and grate complements are entirely for the Electrical and Electronic
department Thatching board (Professors , Doctors, Assistants).

I must be very grateful to my project supervisor in specific (Dr. Adel Saad) for his
interesting scope of selection and guidance of the work we have done.

I also don’t want to forget thanking those thatching personal whom were very
honest and sincere with their duties throughout all the stages of my studying
carrier.

Finally I would like to pay respect to my family for their endless support and
courage they gave me always , again thank you (Ma)

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 Table of Contents

Abstract ....................................................................................................... 1
Acknowledgments ........................................................................................... 2
Table of contents............................................................................................ 3
List of Figures .............................................................................................. 5
List of abbreviations........................................................................................ 9
1. INTRODUCTION ...................................................................................... 10
1.1 Motivations ................................................................................... 10
1.2 Project organization ......................................................................... 12
2. Microstrip Patch Antenna ...................................................................... 14
2.1 Introduction ................................................................................... 14
2.2 RADIATION PATTERN ......................................................................... 14
2.2.1 Radiation Pattern Lobes ............................................................... 15
2.2.2 Field Regions ............................................................................. 16
2.3 Return Loss ....................................................................................17
2.4 VSWR .......................................................................................... 18
2.5 INPUT IMPEDANCE ............................................................................ 18
2.6 RADIATION INTENSITY ........................................................................ 19
2.7 BEAMWIDTH ................................................................................. 2019
2.8 DIRECTIVITY....................................................................................20
2.9 ANTENNA EFFICIENCY ......................................................................... 21
2.10 GAIN............................................................................................. 22
2.11 BANDWIDTH ....................................................................................23

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2.12 POLARIZATION ................................................................................. 24
2.13 Microstrip Patch Antenna ...................................................................26
2.14 Advantages and Disadvantages .............................................................28
2.15 Feeding Methods ..............................................................................29
2.16 Methods of Analysis ........................................................................ 34
2.16.1 Transmission Line Model ...............................................................35
2.17 Impedance Matching ..................................................................... 39
3. Metamaterials ..................................................................................... 42
3.1 Introduction.................................................................................. 42
3.2 Advantages ................................................................................... 43
3.3 Classification of material .................................................................. 44
3.4 Properties of Metamaterial ................................................................ 46
3.4.1 Refractive Index ........................................................................ 46
3.4.2 Backward Waves ........................................................................ 47
3.4.3 Left Handed Materials .................................................................. 47
3.5 Theory of Metamaterials .................................................................. 50
3. Types of Metamaterial ..................................................................... 52
3.6.1 Artificial Dielectrics .................................................................. 52
3.6.2 Artificial Magnetics ............................................................................... 55
3.6.3 Negative-Index Material ............................................................ 58
3.6.4 Chiral Materials ......................................................................59
3.6.5 Cloaking ............................................................................... 60
3.7 Applications of metamaterial ............................................................... 61
4. Design Microstrip Patch Antenna With Metamaterial Superstrate ................... 66
4.1 Introduction .................................................................................. 66
4.2 High Frequency Simulation Software(HFSS) ............................................. 66
4.3 LEFT-HANDED METAMATERIAL ................................................................. 66
4.3.1 Design and Simulation of Split Ring Resonator ................................... 66
4.3.2 Excitation and Boundaries in HFSS .................................................. 68
4.3.3 single unit cell SRR Simulation Result ................................................71
4.3.4 2×1 Array of SRR Simulation Result ................................................. 73

4
4.3.5 2×2 Array of SRR Simulation Result ................................................ 75
4.3.6 8×6 Array of SRR Simulation Result ................................................ 76
4.3.7 Effect of the gap width ................................................................. 78
4.3.8 Effect of the ring width Variation ..................................................... 79
4.4 MICROSTRIP PATCH ANTENNA ANALYSIS AND DESIGN .................................. 80
4.4.1 Design Specification .................................................................... 80
4.4.2 Design Procedure ........................................................................ 81
4.4.3 Simulation and Results ..................................................................84
4.5 Microstrip Antenna With Metamaterial Superstrate Design And Simulation ....... 88
4.5.1 Design Procedure....................................................................... 89
4.5.2 Results of simulation ................................................................... 89
4.6 comparison between patch antenna with and without metamaterial superstrate .. 93
5. Conclusion and Future Work....................................................................95
5.1 Conclusion......................................................................................95
5.2 future work .....................................................................................95
References................................................................................................. 96

5
 List Of Figures

Chapters Title Page

Figure 2.1 : (a) Radiation lobes and beamwidths of an antenna pattern. (b) Linear plot
of power pattern and its associated lobes and beamwidths………….16
Figure 2.2 : Field regions of an antenna…………………………………………………………………17
Figure 2.3 : return loss…………………………………………………………………………………………..18
Figure 2.4 : Three- and two-dimensional power patterns (in linear scale)……….21
Figure 2.5 : Reference terminals and losses of an antenna………………………………..23
Figure 2.6 : Bandwidth…………………………………………………………………………………………….24
Figure 2.7 : Antenna polarization……………………………………………………………………………26
Figure 2.8 : structure of a microstrip patch antenna…………………………………………..27
Figure 2.9 : Representative shapes of microstrip patch elements…………………….28
Figure 2.10 : Microstrip Line Feed……………………………………………………………………………30
Figure 2.11 : Coaxial Feed…………………………………………………………………………………………31
Figure 2.12 : Aperture coupling feed method………………………………………………………….32
Figure 2.13 : Proximity coupling feed method…………………………………………………………33
Figure 2.14 : coplanar waveguide…………………………………………………………………………….34
Figure 2.15 : Microstrip Line…………………………………………………………………………………….35
Figure 2.16 : Electric Field Lines………………………………………………………………………………35
Figure 2.17 : Top View of Antenna…………………………………………………………………………….37
Figure 2.18 : Side View of Antenna…………………………………………………………………………..37
Figure 2.19 : Current distribution on the patch surface………………………………………..39
Figure 2.20 : Voltage (V), current (I) and impedance (Z) distribution along the patch's
resonant length……………………………………………………………………………………39
Figure 3.1 : Metamaterial…………………………………………………………………………………………43

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Figure 3.2 : Classification of material on the basis of µ and ɛ…………………………….45
Figure 3.3 : Snell"s law…………………………………………………………………………………………...47
Figure 3.4 : backward wave…………………………………………………………………………………….48
Figure 3.5 : LH Material…………………………………………………………………………………………..50
Figure 3.6 : Left: left Handed System and Right: right Handed System………………52
Figure 3.7 : An Array of Cylinders, its Equivalent Circuit, and its Relative
Permittivity……………………………………………………………………………………………53
Figure 3.8 : (a) Electric Coupled Field Resonator (b) Equivalent Structure……..54
Figure 3.9 : Left: Simple View of Split Ring and Right: Split Rings in Stack………..55
Figure 3.10 : Relative Permeability Versus Frequency [1]……………………………………..55
Figure 3.11 : (a) EC- SRR (b) Equivalent Circuit ……………………………………………………..57
Figure 3.12 : Schematic Diagram of BC-SRR …………………………………………………………57
Figure 3.13 : (a) Combination of Alternating Layers of Thin Metallic Wires and Circular
Split Rings (b) S Shaped Structure …………………………………………………58
Figure 3.14 : (a) Omega Shaped Structure (b) Double H Shaped Structure…….59
Figure 3.15 : Chiral Materials…………………………………………………………..……………………..60
Figure 3.16 : Cloaking Effects…………………………………………………………..……………………..60
Figure 4.1 : Split Ring Resonator…………………………………………………………………………..67
Figure 4.2 : Spilt ring resonator in HFSS………………………………………………………………68
Figure 4.3 : PerfectH Boundary of Ring Resonator Model in HFSS.
(a)top (b)bottom………………………………………………………………………………….69
Figure 4.4 : PerfectE Boundary of Ring Resonator Model in HFSS.
(a)right (b)left……………………………………………………………………………………..70
Figure 4.5 : Port 1 of Ring Resonator Model in HFSS…………………………………………….70
Figure 4.6 : Port 2 of Ring Resonator Model in HFSS…………………………………………….71
Figure 4.7 : (a) permittivity (b) permeability (c) group delay……………………………….72
Figure 4.8 : two cells of SRR…………………………………………………………………………………….73
Figure 4.9 : (a) permittivity (b) permeability (c) group delay………………………………..74
Figure 4.10 : four cells of SRR……………………………………………………………………………………75
Figure 4.11 : (a) permittivity (b) permeability (c) group delay………………………………..76
Figure 4.12 : 8×6 array of SRR………………………………………………………………………….……….76
Figure 4.13 : (a) permittivity (b) permeability (c) group delay……………………….……….77
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Figure 4.14 : Return loss response for the ring gap variations……………………….………79
Figure 4.15 : Return loss response for the thick wire variation……………………….……..79
Figure 4.16 : Microstrip Patch Antenna………………………………………………………………….….80
Figure 4.17 : Dimensions of microstrip patch antenna…………………………………………..…81
Figure 4.18 : Microstrip Patch Antenna in HFSS…………………………………………………….84
Figure 4.19 : Return Loss (S11)………………………………………………………………………………..85
Figure 4.20 : 3D OF GAIN………………………………………………………………………………………….86
Figure 4.21 : Radiation pattern (a) in dB (b) in linear scale………………………………….87
Figure 4.22 : VSWR plot……………………………………………………………………………………………87
Figure 4.23 : magnitude of E-field…………………………………………………………………………..88
Figure 4.24 : Configuration of antenna with metamaterial superstrate………………88
Figure 4.25 : return loss(S11 )…………………………………………………………………………….89
Figure 4.26 : Radiation pattern (a) in dB) (b) in linear scale………………………………..90
Figure 4.27 : 2D dimensions of Gain (a) in linear scale (b) in dB………………………….91
Figure 4.28 : 3D dimensions of Gain……………………………………………………………………...92
Figure 4.29 : VSWR Plot…………………………………………………………………………………………..92

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 List of abbreviations

HFSS High Frequency Structure Simulator

BW Bandwidth
RL Return Loss
VSWR Voltage Standing Wave Ratio
HPBW Half Power Beamwidth
E-field Electric Field
RF Radio Frequency
RMSA Rectangular Microstrip Antenna
2-D Tow-Dimensional
3-D Three-Dimensional
SRR Split Ring Resonator
LHM Left Hand Material
RHM Right Handed Material
MMICs monolithic microwave integrated circuit

9
 Chapter 1

Introduction

10
 1. INTRODUCTION

1.1 Motivations
In the recent years, there has been rapid growth in wireless communication. With
the increasing number of users and limited bandwidth that is available, operators are
trying hard to optimize their network for larger capacity and improved quality
coverage. This surge has led the field of antenna engineering to constantly evolve
and accommodate the need for wideband, high gain, low-cost, miniaturized and
easily integrated antennas.
Microstrip antennas at 60GHz band have been experiencing a resurgence in
popularity recently as many systems have been allocated, or are proposing to use,
frequencies within this operating band. These higher frequencies and their
propagation characteristics make them an excellent choice to satisfy actual
requirements imposed by modern wireless communication systems, such as small
profile, high data rates, low cost, and short radio links. Microstrip antennas are well
known for their highly desirable physical characteristics such as planar configuration
and light weight - making them ideal for applications that require low profile
structures. These antennas can also be integrated directly with MMICs in a single
package owing to their small physical size and compatible fabrication procedure.

In particular, wireless communication in the 60GHz band, an unlicensed spectrum

cantered at 60GHz with a bandwidth exceeding 7GHz, provides a higher transmission
rate of multiple gigabits per second than other wireless techniques such as Wi-Fi
(2Mbps) and Bluetooth (11Mbps) and can even transmit uncompressed high-
definition cinema data. In addition, the signal of 60 GHz greatly attenuates over
distance due to the high oxygen absorption. Therefore, the signal cannot travel far
from the intended recipient. This feature of oxygen absorption provides many
benefits such as high security, frequency re-use and excellent interference immunity
[1, 2].

New artificial materials, such as metamaterial, are introduced to the design of antennas
for enhancing the performance and reducing the profile [3].Metamaterials are artificial

11
 materials synthesized by embedding specific inclusions, for example, periodic structures,
in the host media. Some of these materials exhibit either negative permittivity or negative
permeability. If both permittivity and permeability of such materials are negative at the
same frequency, then the composite possesses an effective negative index of refraction
for isotropic medium and is referred to as a left handed metamaterial. The name is used
because the electric field, the magnetic field and the wave vector form a left-handed
system.

These metamaterials are typically realized artificially as composite structures that are
composed of periodic metallic patterns printed on dielectric substrates. Metamaterials
have been extensively studied in the recent years, in the framework of millimeter wave
applications. Several works have been aimed towards the improvement of the
performances of antennas in the millimeter wave range of frequencies. It is noted in that
some principal properties of waves propagating in materials with negative permittivity
and negative permeability are considered and high directivity can be obtained from
conventional antenna using metamaterials [4].

In this work, the type of metamaterial antenna with high directivity is introduced for the
60GHz-band. The metamaterial is used to simulate a negative refractive index
homogeneous medium. The simulation results show that the gain, bandwidth, directivity
of the antenna with metamaterial superstrate is improved and the antenna size is
reduced.

1.2 Objectives

 Study microstrip patch antenna parameters.

 Learn how to use HFSS.
 Design and analysis of microstrip patch antenna at 60GHz band.
 study the characteristics of metamaterials, and to use that to improve the performance of
antennas.
 Design metamaterial superstrate with double split ring resonator.
 improve the characteristics of microstrip patch antenna using metamaterial superstrate.

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1.2 Project organization

This chapter has introduced the motivation behind the study of metamaterial lens antennas
and their application.

Chapter 2 : presents the basic theory of antennas and the fundamental parameters used for
evaluating antenna performance, followed by characteristics of patch antennas. This gives
an understanding of the challenges faced when designing antennas provides understanding
of the simulation software validation.

Chapter 3 : presents a review of metamaterial theory and their application.

Chapter 4 :Design Microstrip Patch Antenna With Metamaterial Superstrate

Chapter 5 : provides the conclusions of the project and recommends future research
based on this project.

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 Chapter 2

Microstrip Patch Antenna

14
 2. Microstrip Patch Antenna

2.1 Introduction
An antenna is defined by Webster’s Dictionary as “a usually metallic device (as a rod or
wire) for radiating or receiving radio waves.” The IEEE Standard Definitions of Terms for
Antennas(IEEE Std 145 – 1983) defines the antenna or aerial as “a means for radiating or
receiving radio waves.” In other words the antenna is the transitional structure between
free-space and a guiding device, The guiding device or transmission line may take the
form of a coaxial line or a hollow pipe (waveguide), and it is used to transport
electromagnetic energy from the transmitting source to the antenna, or from the antenna
to the receiver. In the former case, we have a transmitting antenna and in the latter a
receiving antenna [2].

2.2 RADIATION PATTERN

An antenna radiation pattern or antenna pattern is defined as “a mathematical function
or a graphical representation of the radiation properties of the antenna as a function of
space coordinates. In most cases, the radiation pattern is determined in the far field
region and is represented as a function of the directional coordinates. Radiation
properties include power flux density, radiation intensity, field strength, directivity, phase
or polarization.” The radiation property of most concern is the two- or three dimensional
spatial distribution of radiated energy as a function of the observer’s position along a
path or surface of constant radius [2].

2.2.1 Radiation Pattern Lobes

Various parts of a radiation pattern are referred to as lobes, which may be sub classified
into major or main, minor, side, and back lobes .A radiation lobe is a “portion of the
radiation pattern bounded by regions of relatively weak radiation intensity.”

Figure 2.1(a) demonstrates a symmetrical three dimensional polar pattern with a number
of radiation lobes. Some are of greater radiation intensity than others, but all are
classified as lobes

15
 (a)

(b)
Figure (2.1) (a) Radiation lobes and beamwidths of an antenna pattern. (b) Linear plot of power
pattern and its associated lobes and beamwidths

A major lobe (also called main beam) is defined as “the radiation lobe containing the
direction of maximum radiation.” In Figure 2.1 the major lobe is pointing in the θ=0
direction. In some antennas, such as split-beam antennas, there may exist more than one
major lobe. A minor lobe is any lobe except a major lobe. In Figure 2.1(a) and (b) all the
lobes with the exception of the major can be classified as minor lobes.
A side lobe is “a radiation lobe in any direction other than the intended lobe.” (Usually a
side lobe is adjacent to the main lobe and occupies the hemisphere in the direction of the
main beam.) Aback lobe is “a radiation lobe whose axis makes an angle of approximately
180o with respect to the beam of an antenna.” Usually it refers to a minor lobe that
occupies the hemisphere in a direction opposite to that of the major (main) lobe[2].

16
2.2.2 Field Regions
The space surrounding an antenna is usually subdivided into three regions: (a) reactive
near-field, (b) radiating near-field (Fresnel) and (c) far-field (Fraunhofer) regions as shown
in Figure 2.2.

Figure 2.2 Field regions of an antenna.

 Reactive near-field region is defined as “that portion of the near-field region

immediately surrounding the antenna wherein the reactive field predominates.” For most
antennas, the outer boundary of this region is commonly taken to exist at a distance
R<0.62(D3/λ)0.5 from the antenna surface, where λ is the wavelength and D is the largest
dimension of the antenna.

 Radiating near-field (Fresnel) region is defined as “that region of the field of an

antenna between the reactive near-field region and the far-field region wherein radiation
fields predominate and wherein the angular field distribution is dependent upon the
distance from the antenna. The inner boundary is taken to be the distance
R≥0.62(D3/λ)0.5 and the outer boundary the distance R<2D2/λ where D is the largest [2].

 Far-field (Fraunhofer) region is defined as “that region of the field of an antenna

where the angular field distribution is essentially independent of the distance from the

17
antenna[2]. If the antenna has a maximum overall dimension D, the far-field region is
commonly taken to exist at distances greater than 2D 2/λ from the antenna, λ being the
wavelength.

2.3 Return Loss

Return loss is a measure of the reflected power 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 power reflected [5]. For good impedance matching
resonant frequency must lie below -10Db. It is the returned power ratio or the return loss
RL which is given by:

𝐑 𝐋 = −𝟐𝟎𝐋𝐨𝐠 𝟏𝟎 |ᴦ| 𝐝𝐁 (𝟐. 𝟐)

For perfect matching , ᴦ=0 no power would be reflected back , whereas ᴦ=1 implies that
all incident power is reflected. For practical application ,a VSWR of 2 is acceptable and it
corresponds to a RL of -10Db

Figure 2.3 return loss

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2.4 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 [5].

2.5 INPUT IMPEDANCE

the Input impedance is defined as “the impedance presented by an antenna at its

terminals or the ratio of the voltage to current at a 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
𝐙𝐢𝐧 = 𝐑 𝐢𝐧 + 𝐣𝐗 𝐢𝐧 (𝟐. 𝟑)

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.

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2.6 RADIATION INTENSITY

Radiation intensity in a given direction is defined as “the power radiated from an antenna
per unit solid angle.” The radiation intensity is a far-field parameter, and it can be
obtained by simply multiplying the radiation density by the square of the distance. In
mathematical form it is expressed as [2].

𝐔 = 𝐫 𝟐 𝐖𝐫𝐚𝐝 (𝟐. 𝟒)

2.7 BEAMWIDTH

Associated with the pattern of an antenna is a parameter designated as beam width. The
beamwidth of a pattern is defined as the angular separation between two identical points
on opposite side of the pattern maximum. In an antenna pattern, there are a number of
beamwidths.

One of the most widely used beamwidths is the Half-Power Beamwidth(HPBW) “In a
plane containing the direction of the maximum of a beam, the angle between the two
directions in which the radiation intensity is one-half value of the beam.” This is
demonstrated in Figure 2.4. Another important beamwidth is the angular separation
between the first nulls of the pattern, and it is referred to as the First-Null
Beamwidth(FNBW). Both the HPBW and FNBW are demonstrated for the pattern in
Figure 2.4.

20
 Figure 2.4 Three- and two-dimensional power patterns (in linear scale)

2.8 DIRECTIVITY

Therefore directivity of an antenna defined as “the ratio of the radiation intensity in a

given direction from the antenna to the radiation intensity averaged over all directions.
The average radiation intensity is equal to the total power radiated by the antenna
divided by 4π. If the direction is not specified, the direction of maximum radiation
intensity is implied.” Stated more simply, the directivity of a nonisotropic source is equal
to the ratio of its radiation intensity in a given direction over that of an isotropic
source[2]. it can be written as:

𝐔 𝟒𝛑𝐔
𝐃= = (𝟐. 𝟓)
𝐔𝐨 𝐏𝐫𝐚𝐝

21
If the direction is not specified, it implies the direction of maximum radiation intensity
(maximum directivity) expressed as:

𝐔𝐦𝐚𝐱 𝟒𝛑𝐔𝐦𝐚𝐱
𝐃= = (𝟐. 𝟔)
𝐔𝐨 𝐏𝐫𝐚𝐝

Where
D=directivity (dimensionless)
D0 =maximum directivity (dimensionless)
U=radiation intensity (W/unit solid angle)
Umax=maximum radiation intensity (W/unit solid angle)
U0 =radiation intensity of isotropic source (W/unit solid angle)
Prad =total radiated power (W)

2.9 ANTENNA EFFICIENCY

Associated with an antenna are a number of efficiencies and can be defined using Figure
2.5 The total antenna efficiency (e) is used to take into account losses at the input
terminals and within the structure of the antenna. Such losses may be due, referring to
Figure 2.5(b), to

 reflections because of the mismatch between the transmission line and the
antenna.
 (I2R)losses (conduction and dielectric)

22
 (a) Antenna reference terminals

(b) Reflection conduction and dielectric loss

Figure 2.5 Reference terminals and losses of an antenna

In general, the overall efficiency can be written as

𝐞𝐨 = 𝐞𝐫 𝐞𝐜 𝐞𝐝 (𝟐. 𝟕)

where
e0 =total efficiency (dimensionless)
er =reflection(mismatch) efficiency
ec =conduction efficiency (dimensionless)
ed =dielectric efficiency (dimensionless)

2.10 GAIN

Gain of an antenna (in a given direction) is defined as “the ratio of the intensity, in a given
direction, to the radiation intensity that would be obtained if the power accepted by the
antenna were radiated isotropically. The radiation intensity corresponding to the
isotropically radiated power is equal to the power accepted (input) by the antenna
divided by 4π.”[6]. In equation form this can be expressed as:

23
 𝐆𝐨 = 𝐞𝐜𝐝 ∗ 𝐃𝐨 (𝟐. 𝟖)

2.11 BANDWIDTH

The bandwidth of an antenna is defined as “the range of frequencies within which the
performance of the antenna, with respect to some characteristic, conforms to a specified
standard.” The bandwidth can be considered to be the range of frequencies, on either
side of a canter frequency (usually the resonance frequency for a dipole), where the
antenna characteristics (such as input impedance, pattern, beamwidth, polarization, side
lobe level, gain, beam direction, radiation efficiency) are within an acceptable value of
those at the center frequency. For broadband antennas, the bandwidth is usually
expressed as the ratio of the upper-to-lower frequencies of acceptable operation [2] .

Figure 2.6 Bandwidth

24
2.12 POLARIZATION

Polarization of an antenna in a given direction is defined as “the polarization of the wave

transmitted (radiated) by the antenna. Note: When the direction is not stated, the
polarization is taken to be the polarization in the direction of maximum gain.” In practice,
polarization of the radiated energy varies with the direction from the center of the
antenna, so that different parts of the pattern may have different polarizations.
Polarization of a radiated wave is defined as “that property of an electromagnetic wave
describing the time-varying direction and relative magnitude of the electric-field vector;
specifically, the figure traced as a function of time by the extremity of the vector at a fixed
location in space, and the sense in which it is traced, as observed along the direction of
propagation.”[2].

 Linear Polarization

A time-harmonic wave is linearly polarized at a given point in space if the electric-field (or
magnetic-field) vector at that point is always oriented along the same straight line at
every instant of time. This is accomplished if the field vector (electric or magnetic)
possesses:

a. Only one component

b. Two orthogonal linear components that are in time phase or 180° (or multiples of
180°) out-of-phase.

 Circular Polarization

A time-harmonic wave is circularly polarized at a given point in space if the electric (or
magnetic) field vector at that point traces a circle as a function of time. The necessary and
sufficient conditions to accomplish this are if the field vector (electric or magnetic)
possesses all of the following:
a. The field must have two orthogonal linear components,
b. The two components must have the same magnitude,

25
c. The two components must have a time-phase difference of odd multiples of 90o

 Elliptical Polarization

A time-harmonic wave is elliptically polarized if the tip of the field vector (electric or
magnetic) traces an elliptical locus in space. At various instants of time the field vector
changes continuously with time at such a manner as to describe an elliptical locus. The
necessary and sufficient conditions to accomplish this are if the field vector (electric or
magnetic) of the following:
a. The field must have two orthogonal linear components.
b. The two components can be of the same or different magnitude.
c. (1) If the two components are not of the same magnitude, the time-phase difference
between the two components must not be 0o or multiples of 180o (because it will then
be linear).
.(2) If the two components are of the same magnitude, the time-phase difference
between the two components must not be odd multiples of 90o (because it will then be
circular).

Figure2.7 Antenna polarization

26
2.13 Microstrip Patch Antenna

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 dielectric substrate
sandwiched by a radiating patch on one side and the ground plane on the other side as
shown in Figure 2.8. The radiating patch is made of a good conductor material such as
annealed copper or gold and can take any shape possible. the radiating patch are usually
photo-etched on the dielectric substrate[6].

Figure 2.8:structure of a microstrip patch antenna

27
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 2.9 For a rectangular patch, the length L of the patch is usually 0.3333λ o< 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 2.9: Representative shapes of microstrip patch elements

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[6].

2.14 Advantages and Disadvantages

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

28
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[6]. Some of their principal advantages are given below:

A. Light weight and low volume.

B. Low profile planar configuration which can be easily made conformal to host
surface.
C. Low fabrication cost, hence can be manufactured in large quantities.
D. Supports both, linear as well as circular polarization.
E. Can be easily integrated with microwave integrated circuits (MICs).
F. Capable of dual and triple frequency operations.
G. 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:

A. Narrow bandwidth.
B. Low efficiency.
C. Low Gain.
D. Extraneous radiation from feeds and junctions .
E. Poor end fire radiator except tapered slot antennas.
F. Low power handling capacity.
G. 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

29
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.

2.15 Feeding Methods

Microstrip patch antennas can be fed using varieties of techniques. The feed-line can be
either be in direct contact or without any contact. In direct contact, the power is fed
directly to the patch using feed-line made of connecting elements like microstrip line. In
indirect contact, a coupling is done between the feed-line and the radiating patch. The
most popular feeding techniques used are microstrip line and coaxial probe which come
under direct contact schemes and again aperture coupling and proximity coupling that
come under indirect contact.

2.15.1Microstrip 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 2.10. 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.

Figure 2.10: Microstrip Line Feed

30
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[6].

2.15.2 Coaxial Feed

The Coaxial feed or probe feed is a very common technique used for feeding Microstrip
patch antennas. As seen from Figure 2.11, 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.

Figure 2.11: Coaxial Feed

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

31
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[6].

2.15.3 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 2.12. Coupling between the patch and
the feed line is made through a slot or an aperture in the ground plane.

Figure 2.12:Aperture coupling feed method

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

32
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 [6].

2.15.4 Proximity Coupled Feed

This type of feed technique is also called as the electromagnetic coupling scheme. As
shown in Figure 2.13, 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.

Figure 2.13:Proximity coupling feed method

33
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[6].

2.15.5 Coplanar waveguide feed (CPW)

In this method, the coplanar waveguide is etched on the ground plane of the patch
antenna and patch separated from ground plane by other dielectric substrate. The patch
is excited by electromagnetic coupling using a slot formed in the ground plane and
connected to the CPW feed line. The slot can be adjusted to an appropriate location
below the patch to enhance the electromagnetic coupling and to obtain a suitable input
impedance. Therefore, an antenna can be directly matched to the CPW feed as shown in
figure 2.14 .The CPW offers several advantages over conventional microstrip line such as
its lower radiation loss, reduced surface wave excitation and is easier to integrate with
other circuits.
Also , the CPW line has a uniplanar construction which implies that all of the signal line
and c millimeter wave frequencies[8].

Figure 2.14: coplanar waveguide

34
2.16 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. These give less insight as
compared to the two models mentioned above and are far more complex in nature [9].
In this transmission line model is used to calculate the initial dimensions of patch
antenna. But the simulating software, HFSS ,used in this study uses finite element method
to carry out the full wave analysis of the designed structure.

2.16.1Transmission 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
nonhomogeneous line of two dielectrics, typically the substrate and air.

Figure2.15: Microstrip Line Figure2.16: Electric Field Lines

35
Hence, as seen from Figure 2.16, 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 (ε reff )
must be obtained in order to account for the fringing and the wave propagation in the
line.
The value of εreff is slightly less than 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 2.15 above. The expression for εreff is given by Balanis as:
.

(𝛆𝐫 + 𝟏) (𝛆𝐫 − 𝟏) 𝟏𝟎𝐡 −𝟏

𝛆𝐫𝐞𝐟𝐟 = + [𝟏 + ] 𝟐 (𝟐. 𝟗)
𝟐 𝟐 𝐰

Where
𝜀𝑟𝑒𝑓𝑓 =effective dielectric constant
𝜀𝑟 =dielectric constant of substrate
ℎ =height of dielectric substrate
𝑤 =width of the patch

In order to operate in the fundamental TM10 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 TM10 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 the Figure 2.17 shown below, 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 the maximum and current is the
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.

36
 Figure 2.17: Top View of Antenna Figure 2.18: Side View of Antenna

It is seen from Figure 2.17 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 2.18), 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 [6].

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:

𝐰
(𝛆𝐫𝐞𝐟𝐟 + 𝟎. 𝟑)(
+ 𝟎. 𝟐𝟔𝟒)
∆𝐋 = 𝟎. 𝟒𝟏𝟐𝐡 𝐡 (𝟐. 𝟏𝟎)
𝐰
(𝛆𝐫𝐞𝐟𝐟 − 𝟎. 𝟐𝟓𝟖)( + 𝟎. 𝟖)
𝐡

37
Also, the effective length for a given resonance frequency f o is:

𝐜
𝐋𝐞 = (𝟐. 𝟏𝟏)
𝟐𝐟𝐨 √𝛆𝐫𝐞𝐟𝐟

Its length can be calculate using :

𝐋 = 𝐋𝐞 − 𝟐∆𝐋 (𝟐. 𝟏𝟐)

For a rectangular Microstrip patch antenna, the resonance frequency for any mn TM
mode is given by James and Hall as:

𝐜 𝐦 𝐧 𝟏
𝐟𝐨 = [( )𝟐 + ( )𝟐 ]𝟐 (𝟐. 𝟏𝟑)
𝟐√𝛆𝐫𝐞𝐟𝐟 𝐋 𝐰

Where m and n are modes along L and W respectively.

For efficient radiation, the width W is given by Bahl and Bhartia as:

𝐜
𝐰= (𝟐. 𝟏𝟒)
(𝛆 + 𝟏)
𝟐𝐟𝐨 √ 𝐫
𝟐

Now the dimensions of a patch are known. The length and width of a substrate is equal to
that of the ground plane. The length of a ground plane (Lg) and the width of a ground
plane (Wg) are calculated using the following equations.

𝐋𝐠 = 𝟔 × 𝐡 + 𝐋 (𝟐. 𝟏𝟓)
𝐖𝐠 = 𝟔 × 𝐡 + 𝐋 (𝟐. 𝟏𝟔)

38
2.17 Impedance Matching

The feed position of a patch antenna excited in its fundamental mode is typically located
in the center of the patch width direction (y axis)and somewhere along the patch
resonant length direction (x axis). The exact position along the resonant length is
determined by the electromagnetic field distribution in the patch. Looking at the current
(magnetic field) and voltage (electric field) variation along the patch, the current has a
maximum at the center and a minimum near the left and right edges, while the electric
field is zero in the center and maximum near the left and minimum near the right edges.
Keep in mind that the field distribution constantly changes in amplitude and sign. Figures
2.19 and 2.20 below clarify this:

Figure 2.19 Current distribution on the patch surface

Figure 2.20:Voltage (V), current (I) and impedance (Z) distribution along the patch's resonant
length

39
From the magnitude of the current and the voltage, we can determine that the
impedance is minimum (theoretically zero Ω) in the center of the patch and maximum
(typically a couple hundred Ω) near the edges. This means that there are two points
where the impedance is 50 Ωsomewhere along the resonant length (x) axis of the
element and this is where you would typically connect to the antenna.

If you want to connect to the edge of the patch and were looking for a specific
impedance, you could modify the width of the patch to yield the impedance you are
looking for. Increasing the width decreases the impedance.

40
 Chapter 3

Metamaterials

41
 3. Metamaterials

3.1 Introduction

Metamaterials are recently developed artificial materials. It is the only material in the
world having negative permittivity, negative permeability and negative refractive index
simultaneously [11]. Due having these three negative properties it exhibits unusual
properties compared to readily available materials. In Greek Meta means above/ after/
beyond /superior, Metamaterials are named so as these exhibit properties beyond the
properties of naturally available materials.

The history of Metamaterials started in 1967 with the visionary speculation on the
existence of “substances with simultaneously negative values of ɛ and µ [8] (fourth
quadrant of -ɛ , -µ space by the Russian physicist Viktor Veselago. In his section, Veselago
called these “substances” left-handed (LH) to express the fact that they would allow the
propagation of electromagnetic waves with the electric field, the magnetic field, and the
phase constant vectors building a left-handed triad, compared with conventional
materials where this triad is known to be right-handed.

These are artificial metallic structures that have dimensions much smaller than the
wavelength of incident radiation. It gains its properties from structure rather than
composition. It is counted as one of the, ten interesting futuristic material of the world
due to its superior properties.

Metamaterial is not a special type of material, if an array of structures of any metal will be
able to change the electric and magnetic property of the wave passing through it and
leads to negative permittivity and refractive index simultaneously, that metallic structure
can be called as metamaterial.

Metamaterials have sub-wavelength dimensions. Thus it renders high degree of

miniaturization [3] For Metamaterials, p < λg/4

Where, P-Structural average cell size

λg -Guided wavelength

42
 Figure 3.1: Metamaterial

3.2 Advantages

Negative Refractive Index Metamaterials (NRM) are the most commonly used
metamaterial configuration used currently in antenna design. Some of the advantages of
metamaterials are:

 Metamaterials used in antennas to increase performance of miniaturized

(electrically small) antenna systems
 Structure is made such that most of the wave is re-radiated after reflections.
 Used in Wireless Communication, Space Communications, GPS, Satellites, Space
Vehicle Navigation, Airplanes
 Configurations Used: Dual Positive Substrate (DPS) , Dual Negative Substrate
(DNG), Epsilon Negative Substrate (ENG), Mue Negative substrate (MNG)
 Negative Permittivity due to wire array (electric field negation)
 Negative Permeability due to SRR Array (magnetic field negation)
 Left Handed Material: Split Ring resonator (SRR)/ Complementary SRR
 Reduction of mutual coupling between elements in an antenna array

43
 Behave as high pass filter with phase advance
 Bandwidth Improvement
 Gain Miniaturization
 Higher Directivity

3.3 Classification of material

Materials can be classified on the basis of (ε , µ) in four quadrants as shown in figure 3.2.

1. The first quadrant

(ε >0, µ>0) represents right handed material (RHM).The forward Propagation of wave
takes place in the first quadrant. It is commonly used material. It follows the right hand
thumb rule for the direction of propagation of wave

2.The second quadrant

(ε< 0 and µ > 0) describes electric plasmas which support evanescent waves. It is also
called ENG (epsilon negative) material. The fourth quadrant (ε> 0 and µ < 0) also supports
evanescent, corresponding to MNG (mu negative material) µ

3.The third quadrant

(ε<0, µ<0) represents Metamaterial, also called left handed material or double negative
material(DNG).It follows the left handed rule because propagation of wave takes place in
backward direction in this medium. Due to negative µ and negative ε the refractive index
of the medium is calculated to be negative .Thus also termed as NIM (negative index
material). Electric vector E, electromagnetic vector H and wave vector k forms the left
hand triplet as shown in fig. By using the property of third quadrant, the first left handed
test

4. The fourth quadrant

For right handed system, n is positive, thus the phase velocity will be positive. Therefore,
energy and wave will travel in same direction resulting in forward wave propagation

44
 (a)

(b)

Figure 3.2: Classification of material on the basis of µ and ɛ

45
3.4 Properties of Metamaterial

It was seen that wave propagation in metamaterial was in opposite direction than the
naturally occurring materials. Materials with negative permittivity such as ferroelectrics
were available in nature but materials with negative permeability did not exist in nature.

3.4.1 Refractive Index

The refractive index, n, of a medium is defined as the ratio of the speed, C, of a wave
phenomenon such as light or sound in a reference medium to the phase speed, Vp, of the
wave in the medium.

𝐂
𝐧 = (𝟑. 𝟏)
𝐕𝐩

Metamaterials are artificial material which exhibit negative permittivity, negative

permeability and refractive index, which is not found in readily available materials.
Metamaterials have negative refractive index that is a reversal of Snell‟s law, hence called
as negative index materials. Due to negative refractive index, the group and phase
velocities of electromagnetic wave appear in opposite direction such that the direction of
propagation is reversed with respect to the energy flow direction [12]. Negative
refraction can be achieved when both μr and εr are negative, as described in the following
equation.

𝐧 = √(−𝛆𝐫 )(−𝛍𝐫 ) (𝟑. 𝟐)

𝐧 = √𝛆𝐫 (𝐞−𝐢𝛑 )𝛍𝐫 (𝐞−𝐢𝛑 ) (𝟑. 𝟑)

𝐧 = √𝛆𝐫 𝛍𝐫 (𝐞−𝐢𝛑/𝟐 )(𝐞−𝐢𝛑/𝟐 ) (𝟑. 𝟒)

𝐧 = −𝟏√𝛆𝐫 𝛍𝐫 (𝟑. 𝟓)

46
 Figure 3.3: Snell"s law

3.4.2 BACKWARD WAVES

Since the electromagnetic wave in a double negative material forms a LH triad, double
negative materials are generally referred to as LH materials. The LH triad means that
power flows away from the source (group velocity is positive) while the phase front
travels towards the source (phase velocity is negative) [3]. Therefore LH materials
support backward wave i.e. wave with antiparallel group and phase velocities. This
backward wave phenomenon can be observed in Figure 3.3 which shows the electric field
magnitude plot of an air-filled rectangular waveguide with its middle section filled with a
fictional LH material of ε = -1 and µ = -1.

47
 Figure 3.4: backward wave

3.4.3 Left Handed Materials

Electromagnetic Metamaterials are effectively homogenous artificial structures [12]

engineered to provide electromagnetic properties not readily observable in nature.
Effectively homogeneous means that scattering/diffraction is a minor/non-existent effect
in a propagating wave in a Metamaterial. Lattice constants of the Metamaterial are much
smaller than the electromagnetic wave. So what kind of unique electromagnetic
properties can Metamaterials provide? First let's define what we mean by
electromagnetic properties. Electromagnetic properties are the effect a material has on
the electric and magnetic field of a wave, which is determined by the material‟s
permittivity and permeability respectively. The four possible combinations of permittivity
and permeability are shown in figure. 3.2.As shown in the figure, when the wave incident
from air to plasmas and ferrites it gets reflected so the wave attenuates. But in case of
conventional materials and Metamaterials positive and negative refraction takes place
respectively and wave propagates [14]. Materials that reside in quadrant I, II and III are

48
known to exist in nature, however naturally occurring materials with negative
permittivity and negative permeability have not yet discovered. In 1967 Victor Veselago
speculated about the existence of such double negative materials in his paper entitled
“The electrodynamics of substances with simultaneously negative permittivity and
negative permeability”. Several fundamental phenomena [12] occurring in or in
association with LH media were predicted by Veselago:

1. Necessary frequency dispersion of the constitutive parameters

2. Reversal of Doppler effect 9

3. Reversal of Vavilov-Cerenkov radiation

4. Reversal of the boundary conditions relating the normal components of the electric
and magnetic fields at the interface between a conventional/right-handed (RH) medium
and a LH medium

5. Reversal of Snell's law

6. Subsequent negative refraction at the interface between a RH medium and an LH

medium

7. Transformation of a point source into a point image by a LH slab

8. Interchange of convergence and divergence effects in convex and concave lenses,

respectively, when the lens is made LH

9. Plasmonic expressions of the constitutive parameters in resonant-type LH

 HOW ARE LH MATERIALS REALIZED?

Early metamaterials relied on a combination of Split-ring resonators (SSRs) and

conducting wires/posts. SSRs used to generate desired relative permeability, μr for a
resonant band of frequencies [15]. Conducting posts are polarized by the electric field,
generating the desired relative permittivity, εr for all frequencies below a certain cut-off

49
frequency. As shown in figure 3.5.a) all thin wires have same radius "r‟ and are separated
by a distance "a‟ from each other.

Figure 3.5: LH MATERAIL

3.5 Theory of Metamaterials

To describe the basic properties of metamaterials, let us recall Maxwell’s equations:

𝛁 × 𝑬 = −𝒋𝝎𝝁𝑯 (𝟑. 𝟔)

𝛁 × 𝑯 = 𝒋𝝎𝜺𝑬 (𝟑. 𝟕)

where (ω) is the angular frequency.

For plane-wave electric and magnetic fields like

50
 𝐄 = 𝐄𝐨 𝐞(−𝐣𝐤𝐫+𝐢𝛚𝐭) (𝟑. 𝟖)

𝐇 = 𝐇𝐨 𝐞(−𝐣𝐤𝐫+𝐢𝛚𝐭) (𝟑. 𝟗)

where k is a wave vector, the equations (1) and (2) will become

𝐊 × 𝐄 = 𝛚𝛍𝐇 (𝟑. 𝟏𝟎)

𝐊 × 𝐇 = −𝛚𝛆𝐄 (𝟑. 𝟏𝟏)

For simultaneous positive values of ε and μ, the vectors Ε, H and k make a right
handed orthogonal system[11]. There will be forward wave propagation in this medium.

For simultaneous negative values of ε and μ, equations (5) and (6) can be rewritten as

𝑲 × 𝑬 = −𝝎|𝝁|𝑯 (𝟑. 𝟏𝟐)

𝑲 × 𝑯 = 𝝎|𝝐|𝑬 (𝟑. 𝟏𝟑)

And the vectors Ε, H and k make a left-handed orthogonal system.

Energy flow is determined by the real part of the Poynting Vector

𝟏
𝐒= 𝐑𝐞[𝐄 × 𝐇 ∗ ] (𝟑. 𝟏𝟒)
𝟐

For simultaneous change of sign of permittivity and permeability, the direction of energy
flow is not affected, therefore, the group velocity will be positive for both left -handed
and right-handed system. Refractive index is given as

𝐧 = ±√𝛆𝛍 (𝟑. 𝟏𝟒)

And phase velocity is given as

𝐜
𝐕𝐩 = (𝟑. 𝟏𝟓)
𝐧

where c is the velocity of light in vacuum.

51
For right handed system, n is positive, thus the phase velocity will be positive. Therefore,
energy and wave will travel in same direction resulting in forward wave propagation.

For left-handed system, n is negative, thus the phase velocity is negative. Hence the
direction of energy flow and the wave will be opposite resulting in backward wave
propagation [3]. Backward waves may commonly appear in non-uniform waveguides].
Figure 3.6 shows the right -handed system and left -handed system in left and right
respectively.

Figure 3.6 Left: left Handed System and Right: right Handed System

3.6 Types of Metamaterial

3.6.1 Artificial Dielectrics

Artificial dielectrics are the structures having negative permittivity but positive
permeability. An array of cylinders displays negative permittivity below plasma
frequency. Figure 3.7(a) shows an array of cylinders, its equivalent circuit and its
permittivity.

52
 (a) An array cylinders

(b) Equivalent circuit

(c) Relative permittivity versus frequency

Figure 3.7: An Array of Cylinders, its Equivalent Circuit, and its Relative Permittivity

53
where p is the distance between the axis of cylinders.

Electric coupled field resonator [13] also demonstrates negative permittivity. Figure 3.8
shows the Electric coupled field resonator and its equivalent structure .

Figure 3.8: (a) Electric Coupled Field Resonator (b) Equivalent Structure

Effective permittivity still obeys the Drude -Lorentz law and is given as

𝛚𝟐𝐩.𝐞𝐟𝐟
𝛆𝐞𝐟𝐟 = 𝟏 − (𝟑. 𝟏𝟔)
𝛚(𝛚 + 𝐢𝛄𝐞𝐟𝐟 )

where ωp.eff is the effective plasma frequency and γeff is the effective damping factor.

These are given as

𝟐𝝅𝒄𝟐
𝝎𝟐𝒑.𝒆𝒇𝒇 = 𝟐 (𝟑. 𝟏𝟕)
𝒅 𝐥𝐧(𝒑/𝒓)

And

𝛄𝐞𝐟𝐟 = 𝟎. 𝟏𝛚𝐩.𝐞𝐟𝐟 (𝟑. 𝟏𝟖)

54
3.6.2 Artificial Magnetics

Artificial magnetics are the structures having negative permeability but positive
permittivity.

Artificial magnetics exhibits negative permeability below plasma frequency. Figure 3.9
shows the simple view of split ring and split rings placed in stack.

Figure 3.9: Left: Simple View of Split Ring and Right: Split Rings in Stack

Figure 3.10 shows the relative permeability of the split rings placed in stack.

Figure 3.10: Relative Permeability Versus Frequency [1]

55
where Ɩ is the lattice spacing.

Effective permeability [9] is given as

𝐅𝛚𝟐
𝛍𝐞𝐟𝐟 =𝟏− 𝟐 (𝟑. 𝟏𝟗)
𝛚 − 𝛚𝟐𝟎 + 𝐢ᴦ𝛚

where F represents the filling ratio of split ring resonator.

𝛑𝐫 𝟐
𝐅= 𝟐 (𝟑. 𝟐𝟎)
𝐥

ω0 is the resonance frequency and is given as

𝟑𝐥𝐜 𝟐
𝛚𝟎 = √ (𝟑. 𝟐𝟏)
𝛑𝟐 𝐫 𝟑

and Г represents the damping term which is given as

𝟐
ᴦ= (𝟑. 𝟐𝟐)
𝐫𝛔𝛍𝟎

Split ring resonators(SRR) can also be classified as edge coupled SRR(EC -SRR) and broad
coupled SRR(BC -SRR).

In EC-SRR, two concentric metallic split rings are printed on a dielectric substrate[16].
When a time varying magnetic field is applied to it externally along the z-direction, the
electric current starts flowing from one ring to another through the slots between them
by the force of the cuts on each ring. The slots between the rings acts as distributed
capacitance. The EC -SRR and its equivalent circuit is shown in Figure 3.11.

56
 Figure 3.11: (a) EC- SRR (b) Equivalent Circuit

where L is the self -inductance of EC -SRR.

In BC-SRR, both metallic rings are printed on the both sides of the dielectric substrate.
Since the charge distribution in it does not form a net electric dipole, therefore, it is non
-bianisotropic. Thus it eliminates EC -SRR bianisotropy. It has smaller electrical size than
EC -SRR. Equivalent circuit of BC-SRR is same as that of EC-SRR[8]. The BC-SRR is shown in
Figure 3.12.

Figure 3.12: Schematic Diagram of BC-SRR

57
3.6.3 Negative-Index Material

Refractive index of an electromagnetic responsive material mainly depends on its

permittivity and permeability is given by equation (3.14) When either ε or μ is negative,
then refractive index will be purely imaginary resulting in evanescent waves. When both
the parameters are positive, the refractive index is positive and thus results in forward
wave propagation. When both the parameters are negative, the refractive index will be
negative resulting in backward wave propagation. The materials with simultaneous
negative permittivity and permeability are called Negative-index materials (NIM) [11].
These are also called left handed materials.

The combination of alternating layers of thin metallic wires and circular split rings, Omega
shaped, S shaped structures , Double H shaped structures etc. exhibits negative index
of refraction. Figure 3.13 shows the combination of alternating layers of thin metallic
wires and circular split rings, and S shaped structure.

Figure 3.13: (a) Combination of Alternating Layers of Thin Metallic Wires and Circular Split Rings
(b) S Shaped Structure

58
Figure 3.14 shows the omega shaped structure and Double H shaped structure

Figure 3.14: (a) Omega Shaped Structure (b) Double H Shaped Structure

3.6.4 Chiral Materials

Chiral material is comprised of particles whose mirror images cannot be superimposed. It

is different from electromagnetic metamaterials in which both ε and μ are required to be
negative for achieving negative index of refraction. But in chiral materials, either ε or μ or
both are not required to be negative. We can achieve negative refraction in chiral
materials by having strong chirality [3].

For chiral material, refractive index is

𝐧 = √𝛆𝛍 ± 𝐤 (𝟑. 𝟐𝟑)

where κ is chirality parameter. It defines the cross coupling effect between the electric
field and magnetic field when going through chiral material. Because of its chiral
asymmetry property, it reacts different for left circularly polarized and right polarized
waves [10]. Figure 3.15 shows the materials having chiral property.

59
 Figure 3.15:Chiral Materials

3.6.5 Cloaking

Metamaterials are used for making invisible cloak. Metamaterial controls the
propagation such that it can bend light around the object. If the light is not reaching at
the object, we can't see the object and it becomes invisible to us. The incident waves are
guided around the object and it is still present in its location but we can't see it. The
incident rays recover their original path at the other end. Figure 3.16 shows the examples
of cloaking[13].

Figure 3.16. Cloaking Effects

60
 3.7 Applications of metamaterial

3.7.1 Metamaterial as antenna

Metamaterial coatings have been used to enhance the radiation and matching properties
of electrically small electric and magnetic dipole antennas. Metamaterial step up the
radiated power. The newest Metamaterial antenna radiate 95% of input radio signal at
350 MHz Experimental metamaterial antenna are as small as one fifth of a wavelength.
Patch antenna with metamaterial cover have increased directivity. Flat horn antenna with
flat aperture constructed of zero index metamaterial has advantage of improved
directivity. Zero-index metamaterials can be used to achieve high directivity antennas.
Because a signal Propagating in a zero-index metamaterial will stimulate a spatially static
field structure that varies in time; the phase at any point in a zero-index metamaterial will
have the same constant value once steady state is reached. Metamaterial can enhance
the gain and reduce the return loss of a patch antenna[11].

 Applications in Patch Antenna

There are various issues while we design a patch antenna such as - compactness in size,
gain improvement, directivity enhancement, increased bandwidth, suppressed side lobes
or back lobes. Metamaterials are being used for improving the performance of
conventional patch antennas[13].

A. Directivity and Gain Enhancement

Effective permittivity can be expressed as

𝛚𝐩
ɛ𝐫𝐞𝐟𝐟 = 𝟏 − (𝟑. 𝟐𝟒)
𝛚𝟐

where ωp and ω are the plasma frequency and the frequency of the electromagnetic
wave respectively.

When resonant frequency is equal to plasma frequency, the effective permittivity will be
zero.

61
 if ω= ωp than ɛeff=0

𝒏 = √ɛ𝒓𝐞𝐟𝐟 µ𝒆𝒇𝒇 (𝟑. 𝟐𝟓)

Thus when operating at the plasma frequency, there will be zero index of refraction.
Directivity and gain can be increased by using metamaterial as antenna substrate. If a
source is embedded in a substrate with zero index of refraction, then according to Snell's
law, the exiting ray from substrate will be very close normal to the surface. Then ,all the
refracted rays will be in almost the same direction around the normal. Therefore, the
closer the operating frequency is to the plasma frequency, the better directivity can be
achieved.

B. Size Reduction

Patch antenna was loaded with planer metamaterial. The unit cell of the metamaterial
was comprised of an interdigital capacitor and a complementary split ring resonator slot
to have CRLH properties. The interdigital capacitor inserted in the patch provides series
capacitance. The SRR slot etched on the ground plane provided shunt admittance. The
series capacitance increased on increasing the interdigital finger length. It caused
decrease International Journal of Hybrid Information Technology in the half wavelength
resonance frequency, thus the size of the antenna had been reduced by 55% [10].

C. Decreased side lobe

Sense the metamaterial has negative refraction index hence it will reverse the side lobe in
to the direction of the main lobe. thus it will also cause the main lobe to increase in value
and decreases the value of the side lobe.

3.7.2 Metamaterial as Absorber

The first Metamaterial based absorber by Landy (2008) utilizes three layers, two metallic
layers and dielectric and shows a simulated absorptivity of 99% at 11.48 GHz.
Experimentally, Landy was able to achieve an absorptivity of 88% .The difference
between simulated and measured results were due to fabrication errors.

62
3.7.3 Metamaterial as superlens

Super lens uses metamaterials to go beyond the diffraction limit. Ramakrishna

(2005).showed, it has resolution capabilities that go beyond ordinary microscopes.
Conventional optical materials suffer a diffraction limit because only the propagating
components are transmitted from a light source. The non -propagating components, the
evanescent waves, are not transmitted. One way to improve the resolution is to increase
the refractive index but it is limited by the availability of high -index materials. The road
to the super lens is its aptitude to significantly enhance and recover the evanescent
waves that carry information at very small scales. No lens is yet able to completely
reconstitute all the evanescent waves emitted by an object. So the future challenge is to
design a super lens which can constitute all evanescent waves to get perfect image[13].

3.7.4 Metamaterial as cloaks

it is possible to design metamaterial "cloak" so that it guides light around some region,
rendering it invisible over a certain band of wavelengths.

The Duke team used metamaterials to make their cloaking device have gradually varying
refractive indices - from 1 on the outside of the device, decreasing to zero in the centre .
The result is that microwave light subtly bends around the device and is able to reform on
the other side, although with some detectable distortion .

Due to limitation on size ,still it's not possible to make a cloak device for operating
wavelength in visible band. Current devices work only for one wavelength but visible light
has many wavelength .

People inside a cloaked area wouldn't be able to see out because all visible light would be
bending around where they are positioned[16]. They'd be invisible, but they'd be blind,
too.

3.7.5 Metamaterial as sensor

Metamaterial opens a door for designing sensor with specified sensitivity. Metamaterials
provide tools to significantly enhance the sensitivity and resolution of sensors[9].

63
Metamaterial sensors are used in agriculture, biomedical etc. In agriculture the sensors
are based on resonant material and employ SRR to gain better sensitivity, In bio medical
wireless strain sensors are widely used, nested SRR based strain sensors have been
developed to enhance the sensitivity and described by Goran Kiti et [17] .

3.7.6 Metamaterial as Phase compensator

Metamaterial act as a phase compensator, when wave passes through a (double positive)
DPS slab having positive phase shift while DNG slab has opposite phase shift so when
wave exit from a DNG slab the total phase difference is equal to zero[14].

64
 Chapter 4

Design Microstrip Patch Antenna With

Metamaterial Superstrate

65
 4. Design Microstrip Patch Antenna With Metamaterial
Superstrate

4.1 Introduction

The Ansoft HFSS is used for the simulation, we will Design and Improve the Characteristics
of Microstrip Patch Antenna Using “Split Ring” Shaped Metamaterial Structure .The
chapter is divided into three sections, design and simulation of split ring resonator (SRR),
design and Simulation of microstrip patch antenna, and simulation microstrip patch
antenna with metamaterial.

4.2 High Frequency Simulation Software(HFSS)

HFSS is a high performance full wave electromagnetic (EM) field simulator for arbitrary 3D
volumetric passive device modeling that takes advantage of the familiar Microsoft
windows graphical user interface. It integrates simulation , visualization, solid modelling,
and automation in an easy way to learn the environment where solution to your 3D EM
problems are quickly and accurately obtained. Ansoft HFSS employs the finite element
method (FEM), adaptive meshing, and brilliant graphics to give you unparalleled
performance and insight to all of your 3D EM problems [17].

4.3 LEFT-HANDED METAMATERIAL

In this section we will design and simulate a single unit cell and multi-unit Cell of the Split
Ring Resonator.

4.3.1 Design and Simulation of Split Ring Resonator

A unit Cell of the Split Ring Resonator as shown in figure 4.1 can be simulated to operate
at a particular frequency i.e. in the operating frequency where the permeability becomes
negative. Thus boundary conditions need to be solved using Eigen functions. In the
simulation of Split Ring Resonator, we need to set the boundary conditions. The structure
of squared dual split rings resonator (SRR) on the top of gallium arsenide substrate. The

66
geometry and dimension details of squared dual split rings are shown in Figure 4.1 The
values of the geometric parameters of the ring were chosen such that the first resonant
frequency 56GHz this value was found with the different parameters constituting the
geometry of the split ring resonator. Putting the fife parameters :
thickness(c),width(b),height(l), Length(a) and gap(g) of the ring resonator.

Figure 4.1: Split Ring Resonator

The geometry parameter for the squared dual ring resonator is given below:

Thickness(c)=0.05mm
Height(l)= 0.2mm
Width(b)= 0.25mm
Length(a)=0.25mm
Gap(g)= 0.015mm
𝛆𝐫 = 𝟏𝟐. 𝟗
𝐭 = 𝟎. 𝟎𝟓
Because there are no equations for design squared dual split rings resonator, This
geometry parameter was found after changing the dimensions in the pure paper [13] to

67
obtain the dimensions of the splices running within the of 60Hz band Using the HFSS
program. Figure 4.2 below shows the simulated model of the ring resonator, in HFSS.

Figure 4.2:splt ring resonator in HFSS

The ring was enclosed in an air box because in HFSS, the background is a PEC (Perfect
Electric Conductor) and since the resonator was not to be put in a PEC during
measurement, the air box had to surround the structure so that the transmission and
reception of the EM (Electromagnetic Waves) could occur in free space. The dimension of
the air box is at least λ/4 of the lowest resonant frequency.

4.3.2 Excitation and Boundaries in HFSS

To do simulation in HFSS, boundaries and excitations had to be defined. The top and
bottom faces of the box were defined as the PerfectH (this falls on the Z-plane) while the
left and right faces were defined as the PerfectE (this falls on the Y-lane);PerfectH and
PerfectE are the boundary definitions. The PerfectH and PerfectE are orthogonal to each
other due to the principle of electromagnetic waves; PerfectH means perfect magnetic
field while PerfectE means perfect electric field. Figures 4.3 and 4.4 below show the
boundaries in HFSS.

68
 (a)

(b)
Figure 4.3:PerfectH Boundary of Ring Resonator Model in HFSS. (a)top (b)bottom

(a)

69
 (b)
Figure 4.4:PerfectE Boundary of Ring Resonator Model in HFSS.(a)right (b)left

Excitation was done by defining two wave ports; a port is a point through which a signal
or wave enters and leaves a structure. In this case, Port 1 was used as the wave entry
point while Port 2 was used as the wave exit point. Figures 4.5 and 4.6 below show the
two ports.

Figure 4.5:Port 1 of Ring Resonator Model in HFSS

70
 Figure 4.6:Port 2 of Ring Resonator Model in HFSS

In summary, the direction of wave propagation was along the x-axis, electric field was
along the y-axis while the magnetic field was along the z-axis. The solution type was set
to Driven Modal, this solution type is the one appropriate for finding the resonant
frequencies of structures in HFSS.

4.3.3 single unit cell SRR Simulation Result

After defining the proper boundaries and excitations with the appropriate solution type.
figure 4.7 are showing negative permeability , permittivity and group delay metamaterial
resonant at 56GHZ . As shown in Figure4.7, the permeability µ and the permittivity ε is
negative in narrow band frequency around the resonance frequency, outside this band
the real part of µ and ε is positive. The resonance is sufficiently strong to yield negative
permittivity. However, n is also negative at this range.

71
 (a)

(b)

(C)
Figure 4.7: (a) permittivity (b) permeability (c) group delay

72
In this context, a variation has been made in some parameters of the structure in the
substrate, varying the thick wire dimensions and the resonator gaps in order to verify the
resonance frequency and microstrip antenna behavior after that.

4.3.4 2×1 Array of SRR Simulation Result

In this section, two cells of split ring resonator are simulated with the same dimensions
and shown in Figure 4.8. In this case a new dimension has been added, the distance
between the two cells is complete and the value of this dimension is given below:
The distance interval (D)=0.2765mm

The value of this distance is chosen because it gives the best result at the frequency of
negative permittivity and permeability

Figure4.8: two cells of SRR

After the simulation of the cells in figure 4.8 negative permeability , permittivity and
group delay results are obtain at resonance frequency. Which led to the achievement of
left hand metamaterial as shown in figure 4.9

73
 (a)

(b)

(c)
Figure 4.9: (a) permittivity (b) permeability (c) group delay

74
4.3.5 2×2 Array of SRR Simulation Result

As Same method, as mentioned before, is used to obtain left hand metamaterial. The
figure 4.10 illustrates the structure of 2×2 array of SRR . The negative permeability ,
permittivity and group delay of 2×2 array of split ring Resonator has shown in Figure.
4.11.

Figure 4.10: four cells of SRR

(a)

75
 (b)

(c)
Figure 4.11: (a) permittivity (b) permeability (c) group delay

4.3.6 8×6 Array of SRR Simulation Result

Figure 4.12 shows the structure for (8 × 6) array of squared dual split rings resonator (SRR)
on the top of gallium arsenide substrate.

Figure 4.12: 8×6 array of SRR

76
Figure 4.13 show the simulated parameters of split ring resonator here we can see
negative permeability and permittivity at 61 GHz

(a)

(b)

(c)
Figure 4.13: (a) permittivity (b) permeability (c) group delay

77
Afterwards Double split rings metamaterial superstrate shown in the figure 4.12 will be
used to improve the microstrip patch antenna Characteristics such in gain, bandwidth and
directivity as well as reducing the antenna size.

4.3.7 Effect of the gap width

As the gap is reduced, the charge through it increases. Hence, the capacitance of the ring
increases and as a consequence, the resonant frequency drops down.
On the other hand, the electric field concentrates in the split gap. However, the electric
field lines in small gaps are not straight lines; they curve in response to the different
charges. Part of them propagates down in the substrate producing more loss. As the gap
be- comes larger the electric field lines between the plates will be more straight and loss
reduces [18]. Therefore the gap width should be properly optimized for good radiation
efficiency.

The simulations were carried out by the transient solver in HFSS. The boundary conditions
were set for normal incidence where the wave propagates perpendicularly to the plane of
SRRs and the electric field is parallel to the gap.

As it can be seen, the LC resonance is excited by the electric field, which couples to the
capacitance, inducing a circular current in the coil and leading to an oscillatory magnetic
dipole moment perpendicular to the SRR plane.

Figure 4.14 compares the simulated Return loss of SRR with the gap width equals to
0.015mm, 0.017mm , 0.018 mm and 0.02mm keeping the other geometric parameters,
which are described in the caption of the figure, unchanged. It can be seen that, the
resonant frequency shifts up as the gap width increases. On the other hand, the
performance of the structure seems to increase as the gap increases.

78
 Figure 4.14:Return loss response for the ring gap variations

4.3.8 Effect of the ring width Variation

This section presents the results for the width variation of the thick wire. When the
change width of the Thick Wire this results in to change the value of resonance
permittivity and permeability.

The alterations in the width dimensions of the ring reflects directly on the plasma
frequency and on the permissiveness behavior. The plasma frequency represents the
frequency limit for the permissiveness to present negative behavior[18]. On Figure 4.15 is
shown an analysis of the return loss responses in related to the width variation of the
thick wire.

XY Plot 5 HFSSDesign1 ANSOFT

-3.50E-006 Curve Info
dB(S(1,2))
Setup1 : Sw eep
-3.75E-006 o='0.002074mm'
dB(S(1,2))
Setup1 : Sw eep
o='0.002174mm'
-4.00E-006 dB(S(1,2))
Setup1 : Sw eep
o='0.002274mm'
dB(S(1,2))
dB(S(1,2))

-4.25E-006
Setup1 : Sw eep
o='0.002374mm'
dB(S(1,2))
-4.50E-006 Setup1 : Sw eep
o='0.002474mm'
dB(S(1,2))
Setup1 : Sw eep
-4.75E-006 o='0.002574mm'

-5.00E-006

-5.25E-006
55.00 57.50 60.00 62.50 65.00
Freq [GHz]

Figure4.15 - Return loss response for the thick wire variation.

79
4.4 MICROSTRIP PATCH ANTENNA ANALYSIS AND DESIGN

In this section the procedure for designing a rectangular microstrip patch antenna at
60GHz is explained. Next, a compact rectangular microstrip patch antenna is designed.
Finally, the results obtained from the simulations are demonstrated. figure 4.16 shown
the microstrip patch antenna.

Figure 4.16:microstrip patch antenna

4.4.1 Design Specification

The three essential parameters for the design of a rectangular microstrip patch antenna
are:
 Frequency of operation (𝑓𝑜): the resonant frequency of the antenna must be
selected appropriately. The resonant frequency selected for my design is 60GHz.
 Dielectric constant of the substrate (𝜀𝑟 ):the dielectric material selected for my
design is gallium arsenide has a dielectric constant of 12.9.
 Height of dielectric substrate (ℎ) :the height of the dielectric substrate is selected
as 0.25mm.
In the design of the rectangular microstrip patch antenna, the following parameters were
considered to be known:

80
o Resonant Frequency (𝒇𝒐) : 60GHz
o Dielectric Constant (𝜺𝒓 ): 12.9
o Substrate Material: gallium arsenide
o patch Material: gold
o patch thickness (𝒕) :2um
o Speed of Light : 𝟑 𝒙 𝟏𝟎𝟖 𝒎/𝒔
o Wavelength of air (𝛌𝒂𝒊𝒓 ):5mm
𝛌
o Guided Wavelength (𝛌𝒈 ): √𝜺𝒂𝒊𝒓 = 𝟏. 𝟑𝟗𝟐
𝒓

o Height of substrate(h) :0.25mm

4.4.2 Design Procedure

The gallium arsenide, whose loss tangent is 0.002, was chosen as the dielectric material
substrate.

Figure 4.17: Dimensions of microstrip patch antenna

The transmission line mode described in chapter 2 will be used to design the antenna.

Step1 :calculation of the width(W) :the width of the patch antenna is given by
equation (2.14)

81
 𝐜 𝟐
𝐖= √
𝟐𝐟𝐨 𝛜𝐫 + 𝟏

Substituting = 3 × 108 𝑚/𝑠 , 𝜀𝑟 = 12.9 , 𝑓𝑜 = 60𝐺𝐻𝑧 we get

𝟑𝟏𝟏 𝟐
𝐖= √ = 𝟎. 𝟗𝟒𝟖𝟑𝐦𝐦
𝟐 × 𝟔𝟎 × 𝟏𝟎𝟗 𝟏𝟐. 𝟗 + 𝟏

Step2 :calculation of effective dielectric constant (ɛreff) : equation (2.9) gives

the effective dielectric constant as:

𝛆𝒓 + 𝟏 𝛆𝒓 − 𝟏 𝐡 −𝟎.𝟓
𝛆𝐫𝐞𝐟𝐟 = + [𝟏 + 𝟏𝟐 ]
𝟐 𝟐 𝐰

Substituting W =0.9483mm , εr = 12.9 and h = 0.25mm we get

𝟏𝟐. 𝟗 + 𝟏 𝟏𝟐. 𝟗 − 𝟏 𝟎. 𝟐𝟓 −𝟎.𝟓

𝛆𝐫𝐞𝐟𝐟 = + [𝟏 + 𝟏𝟐 ] = 𝟗. 𝟖𝟕
𝟐 𝟐 𝟎. 𝟗𝟒𝟖𝟑

Step3 :calculation of the effective length(Leff) : equation (2.11) gives the

effective length as:

𝐜
𝐋𝐞𝐟𝐟 =
𝟐𝐟𝐨√𝛆𝒓𝒆𝒇𝒇

𝟑 × 𝟏𝟎𝟏𝟏
𝐋𝐞𝐟𝐟 = = 𝟎. 𝟕𝟗𝟔𝐦𝐦
𝟐 × 𝟔𝟎 × 𝟏𝟎𝟗 √𝟗. 𝟖𝟕

Step4 :calculation of the length extension (∆𝑳): equation (2.10) gives the
length extension as:

𝐰
(𝛆𝐫𝐞𝐟𝐟 + 𝟎. 𝟑)(
+ 𝟎. 𝟐𝟔𝟒)
∆𝐋 = 𝟎. 𝟒𝟏𝟐𝐡 𝐡
𝐰
(𝛆𝐫𝐞𝐟𝐟 − 𝟎. 𝟐𝟓𝟖)( + 𝟎. 𝟖)
𝐡

82
 𝟎. 𝟗𝟒𝟖𝟑
(𝟗. 𝟖𝟕 + 𝟎. 𝟑) ( + 𝟎 . 𝟐𝟔𝟒)
∆𝐋 = 𝟎. 𝟒𝟏𝟐 𝟎. 𝟐𝟓 𝐱𝟎. 𝟐𝟓 = 𝟎. 𝟎𝟗𝟔𝟑𝐦𝐦
𝟎. 𝟗𝟒𝟖𝟑
(𝟗. 𝟖𝟕 − 𝟎. 𝟐𝟓𝟖) ( + 𝟎. 𝟖)
𝟎. 𝟐𝟓

Step5 :calculation actual length of the patch (L): the actual length is obtained
by re-writing equation (2.12) as:

The effective length of patch antenna is equal to the one half of a wave length
within the dielectric medium. The E-fields at the edges of the patch undergo
fringing effects. As a result of these effects, effective length of the patch antenna
appears to be greater than its actual length. So, actual length of the patch antenna
λg
is usually considered as L =
2

Actual length and effective length of a patch antenna can be related as

𝐜
𝐋= − 𝟐∆𝐋 = 𝐋𝐞𝐟𝐟 − 𝟐∆𝐋
𝟐𝐟𝒐 √𝛆𝒓𝒆𝒇𝒇

Substituting Leff = 0.796mm , ∆L = 0.0963mm we get

𝐋 = 𝟎. 𝟕𝟗𝟔 − 𝟐 × 𝟎. 𝟎𝟗𝟔𝟑 = 𝟎. 𝟔𝟎𝟑𝟒𝐦𝐦

Step 6: Calculation of Inset feed Depth (𝒚𝒐 ):

The edge of the patch antenna will have high input impedance. Impedance falls
rapidly if the inset position is moved from edge of the patch towards the center.
For providing impedance matching with a 50Ω connector, a curve fit formula for
the inset feed depth (yo) is expressed as:

𝐲𝐨 = 𝟏𝟎−𝟒 [𝟎. 𝟎𝟎𝟏𝟔𝟗𝟐𝟐𝛆𝟕𝐫 + 𝟎. 𝟏𝟑𝟕𝟔𝟏𝛆𝟔𝐫 − 𝟔. 𝟏𝟕𝟖𝟑𝛆𝟓𝐫 + 𝟗𝟑. 𝟏𝟖𝟕𝛆𝟒𝐫 − 𝟔𝟖𝟐. 𝟔𝟗𝛆𝟑𝐫

𝐋
+ 𝟐𝟓𝟔𝟏. 𝟗𝛆𝟐𝐫 − 𝟒𝟎𝟒𝟑𝛆𝐫 + 𝟔𝟔𝟗𝟕]
𝟐

𝐲𝐨 = 𝟎. 𝟎𝟕𝟐𝟑𝐦𝐦

83
Step 7: Calculation of notch gap (𝒈):

Resonant frequency of patch antenna depends on the notch gap ( g). Expression
which relates notch gap and resonant frequency is given by

𝐜 𝟒. 𝟔𝟓𝐱𝟏𝟎−𝟏𝟐
𝐠= 𝐱 = 𝟒. 𝟔𝛍𝐦
√𝟐𝐱 ∈ 𝐫𝐟𝐟 𝐟

Step 8: Calculation of the ground plane dimensions (𝑳𝒈 𝒂𝒏𝒅 𝑾𝒈 ):

The transmission line model is applicable to ground planes only. However ,for
practical considerations, it is essential to have a finite ground plane. Hence, for
this design the ground plane dimensions would be given by equation (2.15)
and (2.16):

𝑳𝒈 = 𝟔𝒉 + 𝑳 = 𝟔 × 𝟎. 𝟐𝟓 + 𝟎. 𝟔𝟎𝟑𝟒 = 𝟐. 𝟏𝟎𝟑𝟒

𝑾𝒈 = 𝟔𝒉 + 𝑾 = 𝟔 × 𝟎. 𝟐𝟓 + 𝟎. 𝟗𝟒𝟖𝟑 = 𝟐. 𝟒𝟒𝟖

4.4.3 Simulation and Results

The simulation of patch antennas have been done with the help of Ansoft HFSS. The
figure4.18 show the microstrip patch antenna in HFSS.

.
Figure 4.18:microstrip patch antenna in HFSS

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 Table 4.1: Dimensions and parameters of the designed patch antenna

Parameter Length
Dielectric substrate (єr) 12.9
Thickness of substrate (h) 0.25mm
Thickness of patch and ground 2um
Patch length (L) 0.6034mm
Patch width (W) 0.9483mm
Gap width (g) 4.6um
Inset patch length (d) 0.0723mm
50Ω width (Wf) 0.18mm
50Ω distance (Lf) 0.793mm
ground plane dimensions (2.1034*2.448)mm2

Figure 4.19 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 56.2GHz .

Name X Y XY Plot 6 HFSSDesign1 ANSOFT

m10.00 56.1875 -19.2994 Curve Info

dB(S(1,1))
-2.50 Setup1 : Sw eep

-5.00

-7.50
dB(S(1,1))

-10.00 -9.9656 -9.9915

-12.50

-15.00

-17.50
m1

-20.00
40.00 45.00 50.00 55.00 60.00 65.00
Freq [GHz]
MX1: 54.9690 2.4302
MX2: 57.3992

Figure 4.19: Return Loss (S11)

85
The simulated impedance bandwidth of about 2.43 GHz (54.97-57.4 GHz) was achieved at
−10𝑑B reflection coefficient (𝑉𝑆𝑊𝑅 < 2). The reflection coefficient value that was
achieved at this resonant frequency was equal to -19.2994 dB. This reflection coefficient
value suggested that there was good matching at the frequency point below the -10dB
region.

Figure 4.20 show the antenna gain pattern and the gain of proposed antenna at 56.2GHz
is obtained as 5.6185dB. and Beamwidth at -3dB about 100 degree.

Figure 4.20: 3D OF GAIN

The radiation pattern for proposed microstrip patch antenna presented in figure 4.21.

(a)

86
 (b)

Figure 4.21: Radiation pattern (a) in dB (b) in linear scale

Figure 4.22 shows the VSWR (Voltage Standing Wave Ratio) plot for the designed
antenna. The value of the VSWR should lie between 1 and 2.

Figure 4.22: VSWR plot

Here the value for the proposed microstrip patch antenna was 1.2733 at the resonating
frequency of 56.2 GHz.

Figure 4.23 shows the distribution of electric field on the patch

87
 Figure 4.23:magnitude of E-field

4.5 Microstrip Patch Antenna With Metamaterial Superstrate Design

And Simulation
This section shows The performance of Conventional patch antenna is improved by using
Metamaterial superstrate. Figure 4.24 shows configuration of microstrip antenna with
8×6 Array Double split rings metamaterial superstrate.

Figure 4.24: Configuration of antenna with metamaterial superstrate

88
4.5.1 Design Procedure
The proposed antenna geometry and configuration is depicted in Figure 4.24, where a
three layer structure consists of a substrate, air-gap, and a superstrate of thicknesses h1,
h2, and h3,respectively. The antenna is designed to be operated at 56.2 GHz. The
antenna is composed of a (0.9486×0.575) mm2 and thickness (t=2µm) gold patch printed
on a gallium arsenide substrate that has a dielectric constant (εr1) of 12.9, a thickness
(h1) of 0.25 mm and an area of (2.2×1.65) mm2. The patch is excited by a 50-Ω probe
feed. The metamaterial superstrate is built on a 0.2 mm thick (h3) gallium arsenide
substrate with a dielectric constant (εr2) of 12.9. The superstrate is supported by foams
so that it keeps an air-gap above the substrate, The superstrate layer is about 0.4mm
above the patch antenna. The metamaterial is composed of 8×6 unit cells. Each cell has a
spacing of 0.248mm in x-direction and 0.0565mm in y-direction to the adjacent ones as
shown in Figure 4.12.

4.5.2 Results of simulation

o Return loss
The simulation results of return loss and bandwidth for the designed patch antenna with
the metamaterial superstrate lens and are shown in Figure 4.25

Figure 4.25:return loss(𝐒𝟏𝟏 )

89
 the return loss with μ negative is -53dB and The simulated impedance bandwidth of
about 3.32 GHz (54.6-57.92 GHz) was achieved at −10𝑑B reflection coefficient
(𝑉𝑆𝑊𝑅 < 2).

o Radiation Pattern

The radiation pattern for proposed microstrip patch antenna presented in figure 4.26

(a)

(b)
Figure 4.26: Radiation pattern (a) in dB) (b) in linear scale

90
o GAIN

Figures 4.27 and 4.28 shows the antenna gain pattern and the gain of proposed antenna
at 56.2GHz is obtained as 6.6224dB. and Beamwidth about 80 degree.

(a)

(b)

Figure 4.27:2D dimensions of Gain (a) in linear scale (b) in dB

91
 Figure 4.28: 3D dimensions of Gain

o VSWR
XY Plot 7 HFSSDesign1 ANSOFT
37.50 Curve Info
VSWR(1)
Setup1 : Sw eep

25.00 Name X Y
m1 56.2000 1.0046
VSWR(1)

12.50

m1

0.00
45.00 47.50 50.00 52.50 55.00 57.50 60.00 62.50 65.00
Freq [GHz]

Figure 4.29: VSWR Plot

from figure 4.29 the value of the VSWR equal 1.0046.

92
4.6 comparison between patch antenna with and without metamaterial
superstrate
In this section, we make a comparison between the conventional antenna and the
antenna using a metamaterial superstrate to illustrate the improvement in antenna
characteristics of gain, bandwidth, Directivity, Size Reduction , etc. after the use of
metamaterial superstrate. The following table shows the difference in the results
obtained previously.

Table 4.2:comparison between with and without metamaterial superstrate

antenna with metamaterial

conventional antenna
superstrate

Gain 5.6185dB 6.6224dB

Return loss -19.2994Db -53dB

BW 2.43GHz 3.32GHz

Directivity 3.57 4.54

VSWR 1.2733 1.0046

Beamwidth 100o 80o

Size(L×W) (1.0486×0.619) (0.9486×0.575)

93
 Chapter 5

Conclusion and Future Work

94
 5. Conclusion and Future Work

5.1 Conclusion

Metamaterial superstrate with double split ring was used in this work to
improve the microstrip patch antenna performance at 60 GHz band. Because
of the negative refraction index of these structures concentrate radiation
energy of the antenna patch, therefore it increases the gain of the antenna
and shapes the beam radiation pattern. Also, it help to improve bandwidth ,
return loss , directivity and reducing the size of the antenna.

5.2 future work

In future more analysis could be done on different type of antenna and how
they can be enhanced more than other antennas that are conventionally in
nature. The aim must be to find the suitable design for particular application
so that there is no spurious radiation or bandwidth wastage. A verity of such
application based antennas can be made which could reduce time-to-market
in various portable electronics devices for wider applications.

95
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