Circular shape proximity feed microstrip antenna

“CIRCULAR SHAPE PROXIMITY FEED
MICROSTRIP ANTENNA”
A DISSERTATION
Submitted in partial fulfillment of the requirements
For the award of degree of
MASTER OF TECHNOLOGY
In
MICROWAVE AND MILLIMETER ENGINEERING
Submitted to
RAJIV GANDHI PROUDYOGIKI VISHWAVIDYALAYA,
BHOPAL - 462036 [M.P] INDIA
Submitted by
AMITESH RAIKWAR
[Enrollment No - 0104EC09MT01]
Under the supervision of
Asst. Prof. SHABAHAT HASAN
Department of Electronics & Communication Engineering
RKDF INSTITUTE OF SCIENCE & TECHNOLOGY,
BHOPAL - 462047 [M.P] INDIA
SESSION:-2009-2011

RKDF Institute of Science & Technology, Bhopal (M.P.)
CERTIFICATE
This is to certify that the work embodies in this Thesis Dissertation entitled as
“CIRCULAR SHAPE PROXIMITY FEED MICROSTRIP ANTENNA”
being submitted by Mr. AMITESH RAIKWAR [Enrollment No-
0104EC09MT01] in partial fulfillment of the requirement for the award of
Master of Technology in “Microwave and Millimeter Engineering” to Rajiv
Gandhi Proudyogiki Vishwavidyalaya, Bhopal - 462036 (M.P.) India during the
academic year 2009-2011 is a record of bonafide piece of work, carried out by
him under my supervision and guidance in the Department of Electronics &
Communication Engineering RKDF Institute of Science & Technology,
Bhopal-462047 (M.P.) India.
Under the Guidance of Approved by
Asst. Prof. SHABAHAT HASAN
Department of Electronics &
Communication
Asst. Prof. ABHISHEK CHOUBEY
Head of Department (EC)
Department of Electronics &
Communication
Forwarded by :
Prof. K. K. PURANIK
Director

CERTIFICATE OF APPROVAL
The Dissertation entitled “CIRCULAR SHAPE PROXIMITY FEED
MICROSTRIP ANTENNA” being submitted by Mr. AMITESH
RAIKWAR [Enrollment No-0104EC09MT01] has been examined by us and
is hereby approved for the award of degree of “Master of Technology” in
“MICROWAVE AND MILLIMETER ENGINEERING”, for which it has
been submitted. It is understood that by this approval the undersign do not
necessarily endorse or approve any statement made, opinion expressed or
conclusion drawn therein, but approve the dissertation only for the purpose for
which it has been submitted.
(Internal Examiner) (External Examiner)

DECLARATION
I AMITESH RAIKWAR, a student of Master of Technology in
“MICROWAVE AND MILLIMETER ENGINEERING” session 2009-
2011 RKDF Institute of Science & Technology, Bhopal (M.P.) India here by
informed that the work presented in this dissertation entitled “CIRCULAR
SHAPE PROXIMITY FEED MICROSTRIP ANTENNA” is the outcome of
my own work, is bonafide and correct to the best of my knowledge. And this
work has been carried out taking care of Engineering Ethics. The work
presented does not infringe any patented work and has not been submitted to
any other University or anywhere else for the award of any degree or any
professional diploma
AMITESH RAIKWAR
Enrollment No - 0104EC09MT01

ACKNOWLEDGMENT
Human Society Survives on mutual dependences and support. I had experienced
deeply as I undertook this work, so I would like to thank everyone who had of
immense help and encouragement in various ways both directly and indirectly.
Behind every achievement of a student the valuable encouragement & guidance
of his/her teacher’s lies, without as a student could never know the beauty &
fruit of hard work. So I make an effort to acknowledge my esteemed guide Asst.
Prof. Shabahat Hasan and Asst. Prof. Abhishek Choubey, Head of
Department, Electronics & Communication Engineering, RKDF IST,
Bhopal (M.P.) India whose excellent & constant supervision has helped in
steering the present work through to its completion.
I express my heartfelt gratitude & sincere thanks to Dr. Namrata Jain
Academic Dean, RKDF IST, Bhopal (M.P.) India for her valuable inspiration
& encouragement that helps me to complete thesis work.
I wish to acknowledge & express my deep sense of gratitude to Prof. K. K.
Puranik, Director, RKDF IST, Bhopal (M.P.) India for his recommendation
& for inspiring me in completion of thesis.
I am deeply grateful to Dr. G. D. Singh, Managing Director, RKDF IST,
Bhopal (M.P.) India for his constant encouragement & providing me resources
from college.
AMITESH RAIKWAR
Enrollment No - 0104EC09MT01

i
ABSTRACT
In this thesis two different circular shaped proximity feed antenna are undertaken, both in the
area of compact RF/microwave circuits design. The first design involves the design of a
Circular shaped radiating patch antenna with Semicircular ground plane and ring of circles. A
study of several circular shaped microstrip antennas reported in the past has been carried out.
In this research, a method of reducing the size of a printed slot-ring antenna for dual band
applications is proposed. The reduction in size is achieved by introducing proximity feed
technology with circular shaped feed line.
The minimum axial ratio of 0.3 dB is obtained at 1.27 GHz, which is the operating frequency
of the antenna. The size of the proposed antenna is reduced by about 50% compared to a
conventional Circular Polarization slot-ring antenna and it displays a Circular Polarization
bandwidth of about 2.5%. The simulated results are presented, and they are in good
agreement. The small size of the antenna makes it very suitable for use in modern
RF/microwave wireless systems which require compact, low cost, and high performance
circuits. Moreover, its Circular Polarization behavior makes it more applicable for
applications such as satellite communications.
The second geometry in the thesis involves the design of a compact circular microstrip
Antenna using semicircular ground plane attached on both sides of a square geometry. The
measured dual frequency band with center frequency is 3.0 GHz. The Antenna demonstrates
about 21% bandwidth with antenna gain of 1.8 dB in the radiation band, a return loss of less
than -10 dB is achieved in this work. The simulated results are in good agreement. The
proposed antenna is very reliable for use in modern wireless systems which require dual band
geometries having compact size, low insertion loss, high selectivity, and good antenna gain.

ii
TABLE OF CONTENTS
Title Page No.
ABSTRACT i
TABLE OF CONTENTS ii
LIST OF FIGURES v
LIST OF TABLES viii
LIST OF SYMBOLS ix
CHAPTER 1
INTRODUCTION AND OVERVIEW
1.1 Introduction 1
1.2 Aim and Objective 2
1.3 Motivation 2
1.4 Outline of the Thesis 3
CHAPTER 2
LITERATURE SURVEY AND PROBLEM FORMULATION
2.1 Literature Survey 4
2.2 Problem Formulation 6
CHAPTER 3
MICROSTRIP ANTENNA
3.1 Introduction 8
3.2 Fundamental Parameters of Antennas. 8
3.3 Types of Antenna 8
3.4 Radiation Mechanism 9
3.5 Microstrip Antenna 9
3.5.1 Introduction 9
3.5.2 Features of the Microstrip Antenna 10
3.5.3 Advantages and Disadvantages 12
3.5.3.1 Advantages 12
3.5.3.2 Disadvantages 12
3.5.4 Excitation Techniques of Microstrip Antennas 13
3.5.4.1 Microstrip (Offset Microstrip) line feed 13
3.5.4.2 Coaxial or Probe Feed 14
3.5.4.3 Aperture Coupled Feed 15

iii
3.5.4.4 Proximity-Coupled Feed 17
3.5.5 Methods of Analysis 19
3.5.5.1 Transmission Line Model 20
3.5.5.2. Cavity Model 26
3.5.6 Circular patch 28
3.5.7 Circular Polarization 39
3.5.7.1 Single feed circularly polarized microstrip antenna 40
3.5.7.2 Dual feed circularly polarized microstrip antenna 41
3.5.7.3 Circular Polarization Synchronous Rotation 42
3.5.8. Characteristics of the Circular Patch Antenna 48
3.5.8.1 Geometry and Coordinate Systems 48
3.5.8.2 Characteristics of Normal Modes 48
3.5.8.2.1 Internal Fields 48
3.5.8.2.2 Resonant Frequencies 50
3.5.8.2.3 Radiation Fields 50
3.5.8.3 Coaxial Feed Circular Patch 51
3.5.8.3.1 Internal and Radiation Fields 51
3.5.8.3.2 Losses and Q 52
3.5.8.3.3 Input Impedance 53
3.5.8.4 Circularly Polarized Microstrip Antennas 53
3.5.8.4.1 Dual-orthogonal feed circularly polarized microstrip
antennas. 54
3.5.8.4.1.1 The Quadrature (90 º) Hybrid. 55
3.5.8.4.2 Singly Fed Circularly Polarized Microstrip Antennas. 56
3.5.8.4.2.1 Sequential Rotation Feeding Technique 56
CHAPTER 4
DESIGNING OF MICROSTRIP ANTENNA
4.1 Design and analysis of dual band Microstrip Antenna. 58
4.1.1 Circular Microstrip Antenna Basic Properties. 58
4.1.2 Flow chart of the designing of a circular shaped microstrip antenna. 60
4.2 Design of Microstrip patch antennas 61
4.2.1 Design Specifications 61
4.2.2 Design Procedure (PSO/IE3D). 61

iv
4.2.3 Simulation Setup and Results 61
4.2.3.1 Simulation of a Patch Antenna using IE3D. 61
CHAPTER 5
RESULT AND DISCUSSION
5.1 Simulated structures 69
5.1.1 A Proximity feed Dual Band Circular shaped antenna with Semicircular
ground plane. 69
5.1.2. Circular shape, Dual band proximity feed UWB antenna. 76
CHAPTER 6
CONCLUSION & FUTURE SCOPE
6.1 Conclusion 83
6.2 Future scope 83
REFERENCES 85
PUBLICATIONS 90

v
LIST OF FIGURES
Fig: 3.1 Shows the top and side views of a rectangular microstrip antenna. 10
Fig: 3.2 Shows other shapes of microstrip antennas 10
Fig: 3.3 Shows other shapes of microstrip antennas. 11
Fig: 3.4 Structure of Circular Patch Antenna. 11
Fig: 3.5 Microstrip line feed. 14
Fig: 3.6(a) Coaxial feed. 15
Fig: 3.6(b) Coaxial or Probe Feed. 15
Fig: 3.7(a) Aperture coupled feed. 17
Fig: 3.7(b) Aperture coupled microstrip rectangular antenna. 17
Fig: 3.8(a) Proximity coupling for underneath the patch . 18
Fig: 3.8(b) Proximity coupled feed. 18
Fig: 3.9 The Equivalent Circuits 18
Fig: 3.10(a) Microstrip Line, 20
Fig: 3.10(b) Electric Field Lines 20
Fig: 3.11(a) Top View of Antenna, 21
Fig: 3.11(b) Side View of Antenna 21
Fig: 3.12 Substrate dimensions 25
Fig: 3.13(a) Recessed Microstrip-line feed , 25
Fig: 3.13(b) Normalized input resistance 25
Fig: 3.14(a) Charge distribution and current density creation on the microstrip patch 27
Fig: 3.34(b) Rectangular design 27
Fig: 3.15 Circular Patch co-ordinate. 29
Fig: 3.16(a) E-Plane. 31
Fig: 3.16(b) H-Plane 31
Fig: 3.17(a) Conductance 32
Fig: 3.17(b) Directivity 32
Fig: 3.18 Quality factor 33
Fig: 3.19 Radiation Efficiency 34
Fig: 3.20 Input Impedance 34
Fig: 3.21 Patch Relative Positioning. 35
Fig: 3.22 Patch Coupling. 35
Fig: 3.23 Patch mutual conductance. 36

vi
Fig: 3.24 Square and rectangular combination 36
Fig: 3.25(a) Circular geometry 36
Fig: 3.25(b) Circular geometry 36
Fig: 3.26(a) Circular Patch: Patterns, 37
Fig: 3.26 (b) E-H Plane in circular patch 38
Fig: 3.26(c) E-H Plane in circular patch 38
Fig: 3.27 Single feed circularly polarized microstrip antenna 40
Fig: 3.28 Co-ordinate system in square patch(a) and (b) 40
Fig: 3.29 (a) Patch with slot. 41
Fig: 3.29(b) Patch with truncated corners. 41
Fig: 3.30 Examples for dual fed Circularly Polarized patches [24] 41
Fig: 3.31 Phase shift realized with delay line 41
Fig: 3.32 Phase shift realized with 900
hybrids (branch line coupler) 42
Fig: 3.33 Circular Polarization Synchronous Rotation 42
Fig: 3.34(a) Square patch driven at adjacent sides through power divider. 42
Fig: 3.34(b) Square patch driven at adjacent sides through A 90 hybrid. 42
Fig: 3.34(c) Circular patch fed with Coax. 43
Fig: 3.34(d) Circular patch feed arrangement. 43
Fig: 3.34(e) Single feed for nearly square patch. 43
Fig: 3.35(a) Single feed for Left-hand circular (LHC) 43
Fig: 3.35(b) Single feed for Right-hand circular (RHC) 43
Fig: 3.36(a) Right-Hand Circular 45
Fig: 3.36(b) Left hand circular 45
Fig: 3.37(a) Trimmed square (L=W) Feed Points: 1 or 3, 45
Fig: 3.37(b ) Elliptical with tabs 45
Fig: 3.38(a) Series Feed 45
Fig: 3.38(b) Corporate (parallel) feed 45
Fig: 3.38(c) Tapered Impedance Feed Matching Transformer 45
Fig: 3.38(d) λ/4 Impedance Feed Matching Transformer 45
Fig: 3.39 Planar Array of circular patches 46
Fig: 3.40 Conventional & Cavity-Backed 46
Fig: 3.41 Broadside Reflection Co-efficient 47
Fig: 3.42 Disc Sector 47

vii
Fig: 3.43 Ring sector 47
Fig: 3.44 Circular ring 47
Fig: 3.45 Geometry of a circular patch antenna 49
Fig: 3.46 Top view of a coaxial fed circular patch 52
Fig: 3.47 Dual feed in a circular microstrip antenna 54
Fig: 3.48 Geometry of a Branch-Line Coupler 55
Fig: 3.49 Aperture and phase of orthogonal modes in single point feed circularly
polarized microstrip patch. 56
Fig: 3.50 Arrangement of elements for two test arrays 57
Fig: 3.50(a) Conventional array 57
Fig: 3.50(b) Sequential array 57
Fig: 3.51 Measured axial ratio vs Frequency 57
Fig: 4.1 Microstrip patch antenna designed using IE3D. 61
Fig: 4.2 Simulation procedure 68
Fig: 5.1 Antenna design 69
Fig: 5.2 Simulation steps for A Proximity feed Dual Band Circular shaped antenna
with Semicircular ground Plane. 75
Fig: 5.3(a) Front View of Antenna 76
Fig: 5.3(b) Back View of Antenna 76
Fig: 5.4 Simulation steps for Circular shape, Dual band proximity feed UWB antenna
81

viii
LIST OF TABLES
Table 3.1 Below summarizes the characteristics of the different feed techniques 19
Table 3.2 General characteristics of Power Divider Networks 55
Table 4.1 First four Bessel function zeros used with equation. 59

ix
LIST OF SYMBOLS
mm - millimeter.
dB - decibel.
Hz - hertz.
d - diameter.
h - height.
L - length.
W - width.
Γ - reflection coefficient.
Z0 - characteristic impedance.
λο - free-space wavelength.
εr- - dielectric constant of the substrate.
t - patch thickness.
C - speed of light 3x 10-8
m.
fr - the resonant frequency (in Hz),
P - the total power radiated by the isotropic antenna
dΩ - solid angle differential in spherical coordinates
- radiation intensity.
- radiation intensity average.
- total radiated power.
- radiation power density.
 - the antenna efficiency.
D - directivity.
- total antenna efficiency (dimensionless)
- reflection efficiency = ( ) (dimensionless)
- conduction efficiency (dimensionless)
- dielectric efficiency (dimensionless)
- antenna input impedance.
- characteristic impedance of transmission line.
VSWR - voltage standing wave ratio =
- antenna radiation efficiency, which is used to relate the gain and directivity.

x
- radiation intensity
P ( , ∅) - the power radiated per unit solid angle in the direction ( , ∅).
- the total radiated power.
- the half-angle of the cone
- maximum frequency.
- minimum frequency range.
- center frequency.
Q - the quality factor,
- the reflected voltage.
- the incident voltage.
- antenna impedance at terminals (ohms)
- antenna resistance at terminals (ohms)
- antenna reactance at terminals (ohms)
- radiation resistance of the antenna
- loss resistance of the antenna
I - the intensity supplied by a generator connected
- the open circuit voltage at the antenna terminals.
“ ” - the reflection coefficient,
- polarization efficiency.
- vector effective length.
- incident electric field
- open-circuit voltage generated at antenna terminals by incident wave.
- incident electric field.
- vector effective length.
- effective area (aperture) (m2
)
- power delivered to load (W)
Wi - power density of incident wave (W/m2
)
Aem - maximum effective area =
- power supplied by the source
- the power reflected.
- load impedance.
- characteristic impedance.

xi
- brightness temperature (K)
- emissivity (dimensionless)
- molecular (physical) temperature (K)
- antenna temperature
- thermal efficiency of antenna
K - Boltz Mann’s constant (1.38X10-23
J/K)
- system noise power (W)
- antenna noise temperature, K
- effective dielectric constant.
W - width of the patch
Leff - the effective length of the patch
- E- field radiated by slot #1
- H- field radiated by slot #2
- voltage across the slot.
- total Q.
- Q due to radiation (space wave)
- Q due to conduction (ohmic) losses.
- Q due to dielectric losses.
- Q due to surface waves.
- power radiated into space by circular patch.
- the Bessel function of the first kind of order n and
- the Bessel function of the second kind of order n.
- the derivative of with respect to the argument

CHAPTER 1
INTRODUCTION AND
OVERVIEW

1
CHAPTER 1
Introduction and Overview
1.1 Introduction
In this thesis, a collection of concepts and technologies were utilized to develop the antenna
under study. Furthermore, the goal of this thesis is to develop an antenna with certain antenna
reconfiguration properties such as beam scanning, radiation pattern, and polarization. In
addition, the developed antenna must be without phase shifters, antenna array configuration as
well as minimized antenna elements. In order to meet these design specifications, research has
been extensively done on these topics. It has been demonstrated in literature that the control of
multiple modes in a single antenna can achieve radiated pattern reconfiguration, and polarization
reconfiguration by using microstrip technology.
In a typical wireless communication system increasing the gain of antennas used for
transmission increases the wireless coverage range, decreases errors, increases achievable bit
rates and decreases the battery consumption of wireless communication devices. One of the
main factors in increasing this gain is matching the polarization of the transmitting and receiving
antenna. To achieve this polarization matching the transmitter and the receiver should have the
same axial ratio, spatial orientation and the same sense of polarization. In mobile and portable
wireless application where wireless devices frequently change their location and orientation it is
nearly impossible to constantly match the spatial orientation of the devices. Circularly polarized
antennas could be matched in wide range of orientations because the radiated waves oscillate in
a circle that is perpendicular to the direction of propagation [1-3].
Microstrip antenna technology began its rapid development in the late 1970s. By the early 1980s
basic microstrip antenna elements and arrays were fairly well establish in term of design and
modeling [4]. In the last decades printed antennas have been largely studied due to their
advantages over other radiating systems, such as light weight, reduced size, low cost,
conformability and possibility of integration with active devices.
Microstrip patch antennas on a thin dielectric substrate inherently attracted the interest of
researchers because of its many above listed advantages but this technique also have some
disadvantage like narrow impedance bandwidth. To overcome this disadvantage proximity feed

2
technique is preferred by many researchers. The circular geometry drew the attention of MPA
researchers as it is smaller than other patch geometries [5].
Many wireless service providers have discussed the adoption of polarization diversity and
frequency diversity schemes in place of space diversity approach to take advantage of the
limited frequency spectra available for communication. Due to the rapid development in the
field of satellite and wireless communication there has been a great demand for low cost
minimal weight, compact low profile antennas that are capable of maintaining high performance
over a large spectrum of frequencies. Through the years, microstrip antenna structures are the
most common option used to realize millimeter wave monolithic integrated circuits for
microwave, radar and communication purposes. Compact microstrip antennas capable of dual
polarized radiation are very suitable for applications in wireless communication systems that
demand frequency reuse and polarization diversity.
1.2 Aim and Objective
The aim of the project is to design and fabricate a dual frequency and dual polarized microstrip
patch antenna. The proposed thesis provides an in-depth explanation of antenna pattern
measurement techniques used to determine the performance of dual polarized antennas and of
some antenna characteristics that are unique to antennas used in a polarization diversity scheme.
The performance comparison is based on radiation pattern, bandwidth, return loss, VSWR and
gain. The slit length, slit width, distance of the slit from the edge of the patch, feed point and the
cross slot parameters are varied in order to obtain optimum results.
1.3 Motivation
Use of conventional microstrip antennas is limited because of their poor gain, low bandwidth
and polarization purity. There has been a lot of research in the past decade in this area. These
techniques include use of cross slots and sorting pins, increasing the thickness of the patch, use
of circular and triangular patches with proper slits and antenna arrays. Various feeding
techniques are also extensively studied to overcome these limitations. Our work was primarily
focused on dual band and dual frequency operation of microstrip patch antennas. Dual frequency
operation of the antenna has become a necessity for many applications in recent wireless
communication systems. Antennas having dual polarization can be used to obtain polarization
diversity.

3
1.4 Outline of the Thesis
The outline of this thesis is as follows: -
Chapter 1. Introduction
It is the present chapter, which provides a brief introduction, motivation and overall project
objectives.
Chapter 2. Literature Survey and Problem Formulation
Chapter 3. Basic Parameters
This chapter explains the basic concepts used throughout the project for the design of the
antenna. This chapter explains the concepts of microstrip technology used for the design of the
antenna. It presents the basic theory of MPAs, including the basic structures, feeding techniques
and characteristics of the MPA. Then the advantages and disadvantages of the antenna are
discussed and the methods of analysis used for the MPA design. Finally the performance
parameters to compare the various antenna structures have been discussed. The calculations
needed to find the dimensions of the conventional MPA using transmission line model are
presented in this chapter.
Chapter 4. Design & Result Analysis
This chapter details the design process, including the construction and measurements of the
antennas. It outlines the various methods to obtain dual band and dual polarization in compact
MPAs are discussed. Gain and bandwidth enhancement techniques are also discussed in brief.
Discusses in detail the patch proposed for dual band dual frequency application. The simulation
results for this antenna has been discussed. Then the performance of the antenna has been
studied by comparing return loss, radiation pattern, VSWR, gain, bandwidth and axial ratio.
Chapter 5. Conclusion & Future scope
Presents the concluding remarks, with scope for further research work. Conclusions and
Guidelines for Future Work. This section presents the conclusions of the project. It also
proposes future lines to enhance the behaviour of the antenna.

CHAPTER 2
LITERATURE SURVEY
AND
PROBLEM FORMULATION

4
CHAPTER 2
Literature Survey and Problem Formulation
2.1 Literature Survey.
Circular Patch Antenna with Enhanced Bandwidth using Narrow Rectangular Slit for Wi-
Max Application published by Ramesh Kumar, Gian Chand, Monish Gupta, Dinesh Kumar
Gupta, discussed Since the inception of Microstrip Patch antenna constant efforts are being
made to modify the overall performance of this class of antenna field .Although the microstrip
antenna has some of shortcoming till this date such as low gain, narrow operating bandwidth,
poor radiation efficiency, yet it has been one the most suitable candidate for modern wireless
communication technology. This paper focus on the bandwidth enhancement of microstrip
circular patch antenna by introducing a narrow rectangular slit of length 12 mm and width 0.6
mm and thickness 0.2 mm on the conventional circular patch. The proposed antenna is excited
through the microstrip feed line technique and the antenna design and the parametric studies has
been executed using An soft’s HFSS (High Frequency Structure Simulator). The antenna
resonate at two frequencies 2.7 GHz and 5.4 GHz having gain1.215 dBi & 5.37 dBi at respective
frequency, these bands cover the lower and upper band of Wi-Max application.
A Dual Band Fractal Circular Microstrip Patch Antenna for C-band Applications given by
Nitasha Bisht and Pradeep Kumar proposes the design of a circular patch antenna with fractals
for C-band applications. The designed antenna has been fed with L probe feeding technique. The
proposed circular patch antenna with fractals produces a dual band operation for the C-band
applications. The designed model is simulated using CST microwave studio software based
upon infinite difference time domain method. The simulated results for various parameters like
return loss, radiation pattern etc have been presented. The designed antenna operates for dual
band at 6.6 GHz and 7.5 GHz with increase in Gain and Bandwidth. Such type of antennas is
useful in Telecommunication, Wi-Fi, Satellite communication, Radar, Commercial and Military
application.
Broadband Microstrip Patch Antenna written by Mohammad Tariqul Islam, Mohammed
Nazmus Shakib, Norbahiah Misran, Tiang Sew Sun had explained that the enhancing bandwidth
and size reduction mechanism that improves the performance of a conventional microstrip patch
antenna on a relatively thin substrate (about 0.01λ0), is presented in this research. The design

5
adopts contemporary techniques; L-probe feeding, inverted patch structure with air-filled
dielectric, and slotted patch. The composite effect of integrating these techniques and by
introducing the novel slotted patch, offer a low profile, broadband, high gain, and compact
antenna element. The simulated impedance bandwidth of the proposed antenna is about 22%.
The proposed patch has a compact dimension of 0.544λ0× 0.275λ0 (where λ0 is the guided
wavelength of the centre operating frequency). The design is suitable for array applications with
respect to a given frequency of 1.84-2.29 GHz.
Circular Microstrip Patch Array Antenna for C-Band Altimeter System designed by
Asghar Keshtkar, Ahmad Keshtkar, and A. R. Dastkhosh was the practical and experimental
results obtained from the design, construction, and test of an array of circular microstrip
elements. The aim of this antenna construction was to obtain a gain of 12 dB, an acceptable
pattern, and a reasonable value of SWR for altimeter system application. In this paper, the cavity
model was applied to analyse the patch and a proper combination of ordinary formulas;
HPHFSS software and Microwave Office software were used. The array includes four circular
elements with equal sizes and equal spacing and was planed on a substrate. The method of
analysis, design, and development of this antenna array is explained completely here. The
antenna is simulated and is completely analyzed by commercial HPHFSS software. Microwave
Office 2006 software has been used to initially simulate and find the optimum design and
results. Comparison between practical results and the results obtained from the simulation shows
that we reached our goals by a great degree of validity.
A Dual Polarized Aperture Coupled Circular Patch Antenna Using a C-Shaped Coupling
Slot by S. K. Padhi, N. C. Karmakar, Sr., C. L. Law, and S. Aditya, explained that the design
and development of a dual linearly polarized aperture coupled circular microstrip patch antenna
at C-band are presented. The antenna uses a novel configuration of symmetric and asymmetric
coupling slots. Variations in isolation between orthogonal feed lines and antenna axial ratio with
the position of coupling slots are studied and broadband isolation and axial ratio are achieved.
The prototype antenna yields 7.6 dBi peak gain, 70 3-dB beam width, 25 dB cross-polarization
levels and an isolation better than 28 dB between the two ports. With an external quadrature
hybrid coupler connected to the two orthogonal feed lines, the antenna yields 3-dB axial ratio
bandwidth of more than 30% at 5.8 GHz.
Circular Patch Microstrip Array Antenna for KU-band by T.F. Lai, Wan Nor Liza Mahadi,
Norhayatisoin presented a circular patch microstrip array antenna operate in KU-band (10.9

6
GHz–17.25 GHz). The proposed circular patch array antenna will be in light weight, flexible,
slim and compact unit compare with current antenna used in KU-band. The paper also presents
the detail steps of designing the circular patch microstrip array antenna. An advance Design
System (ADS) software is used to compute the gain, power, radiation pattern, and S11 of the
antenna. The proposed Circular patch microstrip array antenna basically is a phased array
consisting of ‘n’ elements (circular patch antennas) arranged in a rectangular grid. The size of
each element is determined by the operating frequency. The incident wave from satellite arrives
at the plane of the antenna with equal phase across the surface of the array. Each ‘n’ element
receives a small amount of power in phase with the others. There are feed network connects
each element to the microstrip lines with an equal length, thus the signals reaching the circular
patches are all combined in phase and the voltages add up. The significant difference of the
circular patch array antenna is not come in the phase across the surface but in the magnitude
distribution.
2.2 Problem Formulation
The most commonly used Microstrip patch antennas are rectangular and circular patch antennas.
These patch antennas are used as simple and for the widest and most demanding applications.
Dual characteristics, circular polarizations, dual frequency operation, frequency agility, broad
band width, feed line flexibility, beam scanning can be easily obtained from these patch
antennas here we are proposing the design of a Circular microstrip patch antenna having return
loss S11 less than -10 dB for a whole range of frequency used for 3G network.
For patch design, it is assumed that the dielectric constant of the substrate (εr), the resonant
frequency (fr in Hz), and the height of the substrate h (in cm) are known.
A first-order approximation to the solution for a is to find ae and to substitute it into ae and a in
the logarithmic function. This will lead to
 … (2.2.1)
Where,
Above given Equation does not take into consideration the fringing effect. Since fringing makes
the patch electrically larger, the effective radius of patch is used and is given by
 … (2.2.2)

7
Hence, the resonant frequency for the dominant TM110 is given by
 … (2.2.3)
The design of microstrip antenna will be done as follows:
fr= 1.9 GHz.
h = 0.16 cm.
εr= 2.32.
For a coaxial feed, matching the antenna impedance to the transmission line impedance can be
accomplished simply by putting the feed at the proper location. Some formulas have been
suggested for computing the input impedance in the resonance state. Typically with very thin
substrates, the feed resistance is very smaller than resonance resistance, but in thick substrates,
the feed resistance is not negligible and should be considered in impedance matching
determining the resonance frequency. In general, the input impedance is complex, and it
includes both a resonant part and a non-resonant part which is usually reactive. Both the real and
imaginary parts of the impedance vary as a function of frequency. Ideally, both the resistance
and reactance exhibit symmetrically about the resonant frequency and the reactance at resonance
is equal to the average of sum of its maximum value (which is positive) and its minimum value
(which is negative). In the proposed work we will try to get the return loss less than -10 dB for
the whole range of frequencies used for 3G network (i.e. 1.7 GHz to 2.2 GHz). For achieve the
desired goal we can change shape of ground plane and use different type of fractals.

8
CHAPTER 3
Microstrip Antenna
3.1 Introduction
An antenna is a part of a transmitting or receiving system, designed specifically to radiate or
receive electromagnetic waves [17].The antenna is a passive linear reciprocal device that can
convert electromagnetic radiation into electric current and vice-versa, so it is a transitional
structure between the free space and a guiding device. [18]
3.2 Fundamental Parameters of Antennas.
1. Radiation Pattern.
2. Radiation Power Density.
3. Radiation Intensity.
4. Beamwidth.
5. Directivity.
6. Polarization.
7. Input Impedance.
8. Gain.
9. Beam Efficiency.
10. Bandwidth
11. Antenna Temperature
12. Antenna Efficiency & Antenna Radiation Efficiency.
13. Antenna Vector Effective Length, Equivalent Areas and Maximum Effective area.
14. Friss Transmission Equation and Radar Range Equation.
3.3 Types of Antenna
1. Wire Antenna.
a. Dipole. b. Circular (square) loop. c. Helix.
2. Aperture antennas.
a. Pyramidal Antennas. b. Conical horn. c. Rectangular waveguide.
3. Microstrip Antennas.
a. Rectangular b. Circular.

9
4. Array Antennas.
a. Yagi-uda Array. b. Aperture Array. c. Microstrip Patch Array.
d. Slotted – Waveguide Array.
5. Reflector Antennas.
a. Parabolic reflector with front feed.
b. Parabolic Reflector with Casse grain Feed.
c. Corner Reflector.
6. Lens Antennas.
a. Lens with Index of n>1. b. Lens with Index of n<1.
3.4 Radiation Mechanism.
1. Single wire.
2. Two Wires.
3. Dipole.
3.5 Microstrip Antenna
3.5.1 Introduction
The microstrip antenna concept was first proposed by Deschamps in 1953. However this
concept was undeveloped until 1970 when the revolution in electronic circuit miniaturization
and large-scale integration helped to build practical antennas. The antennas developed by
Munson were used as low-profile flush-mounted antennas on rockets and missiles, this work
showed that microstrip antenna was a practical concept for use in many systems problems. [22].
The microstrip antennas have many unique and attractive advantages, such as it slow profile,
light weight, small volume, and ease of fabrication using printed-circuit technology that led to
the design of several configurations for various applications. Nowadays with increasing
requirements for personal and mobile communications, the demand for smaller and low-profile
antennas has brought the microstrip antennas to the forefront, because they are being use not
only in military applications but also in commercial areas such as mobile satellite
communications, terrestrial cellular communications, direct broadcast satellite (DBS) system,
global positioning system (GPS), remote sensing, and hyperthermia. [22, 23 and 24].
In this chapter, we are going to discuss some of the microstrip antenna’s technical features, its
advantages and disadvantages, considerations of the substrate material, feeding techniques,
polarization behaviours and bandwidth characteristics. “Microstrip (Patch) Antenna is a metallic
strip or patch mounted on a dielectric layer (substrate) which is supported by a ground plane.

10
3.5.2 Features of the Microstrip Antenna
A microstrip antenna, in its simplest form, consists of a radiating patch on one side of a
dielectric substrate and a ground plane on the other side.
Fig: 3.1 Shows the top and side views of a rectangular microstrip antenna [24].
The radiating patch can be designed with a variety of shapes such as: square, circular, triangular,
semicircular, sectoral, and annular ring shapes; but rectangular and circular configurations are
the most commonly used configuration because of ease of analysis and fabrication.
The radiating patch is normally made of a thin copper foil, or is copper-foil plated with gold or
nickel because they are corrosion resistive metals. A microstrip antenna generally consists of a
dielectric substrate sandwiched between a radiating patch on the top and a ground plane on the
other side as shown in Figure 3.4. The patch is generally made of conducting material such as
copper or gold and can take any possible shape. The radiating patch and the feed lines are
usually photo etched on the dielectric substrate.
For simplicity of analysis, the patch is generally square, rectangular, circular, triangular, and
elliptical or some other common shape. For a rectangular patch, the length of the patch is
usually in the range of 0.3333 0< < 0.5 0, where 0 is the free space wavelength. The patch is
selected to be very thin such that << 0 (where is the patch thickness). The height h of the
substrate is usually 0.003 0 ≤ h ≤ 0.05 0. The dielectric constant of the substrate is typically
in the range 2.2 ≤ ≤ 12 [3] .The substrate panel is used to maintain the required precision
spacing between the patch and its ground, to give mechanical support for the radiating patch,
and it has a thickness in the range of 0.01–0.05 free-space wavelength (λ0).
Fig: 3.2 Shows other shapes of microstrip antennas [24].
Semicircular Annular ring Square ring

11
Fig: 3.3 Shows other shapes of microstrip antennas [24].
Fig: 3.4 Structure of Circular Patch Antenna
It is also often used with high dielectric-constant material to load the patch and reduce its size.
For large array application, the substrate material should be low in insertion loss with a loss
tangent of less than 0.005. We can separate the substrate materials into three categories, in
accordance with their dielectric constant:
1. Having a relative dielectric constant :
This type of material can be polystyrene foam, air.
Material consisting mostly of fibber glass reinforced Teflon.
The material can consist of ceramic, quartz, or alumina.
We can also find materials with a much larger than 10, but a high dielectric constant can lead
to a significant reduction in the radiation efficiency of the antenna. For good performance of the
antenna (typically for broadband applications), it is best to use a thicker substrate, whose

12
dielectric constant is in the lower range and have small losses, but the thicker substrate will
provide a low efficiency and lower dielectric constant will have an impact on a larger antenna.
So compensation should be made between the dimensions of the antenna and the antenna
performance.
3.5.3 Advantages and Disadvantages
The microstrip antenna has proved to be an excellent radiator for many applications because of
its several advantages, but it also has some disadvantages; however some of them can be
overcome using new techniques of feeding, configuration of the patch, etc. Microstrip antennas
are used as embedded antennas in handheld wireless devices such as cellular phones, and also
employed in Satellite communications.
3.5.3.1 Advantages
Some of their advantages are given below:
 They are light in weight and take up little volume because their low profile.
 They can be made conformal to the host surface.
 Low fabrication cost, hence can be manufactured in large quantities.
 They are easier to integrate with other microstrip circuits on the same substrate.
 They support both, linear as well as circular polarization.
 They can be made compact for use in personal mobile communication and hand held
devices.
 They allow multiple-frequency operation, because you can use stacked patches.
 Mechanically robust when mounted on rigid surfaces.
 Can be easily integrated with microwave integrated circuits.
 Capable of dual and triple frequency operations.
3.5.3.2 Disadvantages
Microstrip patch antennas suffer from more drawbacks as compared to conventional antennas.
Some of their disadvantages are given below:
 Narrow bandwidth.
 Lower power gain.
 Lower power handling capability.
 Polarization impurity.
 Surface wave excitation.
 Extraneous radiation from feeds and junctions.

13
 Poor end fire radiator except tapered slot antennas.
 Low efficiency and Gain.
 Large size (physical) at VHF and possibly UHF bands.
3.5.4 Excitation Techniques of Microstrip Antennas
The feeding method or excitation technique is an important design parameter because it
influences to the input impedance, the polarization characteristic and the antenna efficiency. As
the feeding method influences to the input impedance, is often used for purposes of impedance
matching. We can excite or feed a microstrip antenna directly or indirectly. A microstrip antenna
is feed directly using a connecting element such as the use of a coaxial probe or by a microstrip
line, when it is excited indirectly, there is no direct metallic contact between the feed line and
radiating patch, and it could be using proximity coupling or by aperture coupling [24].
Microstrip patch antennas can be fed by a variety of methods. These methods can be classified
into two categories- contacting and non-contacting. In the contacting method, the RF power is
fed directly to the radiating patch using a connecting element such as a microstrip line. In the
non-contacting scheme, electromagnetic field coupling is done to transfer power between the
microstrip line and the radiating patch. The four most popular feed techniques used are the
microstrip line, coaxial probe (both contacting schemes), aperture coupling and proximity
coupling (both non-contacting schemes).
3.5.4.1 Microstrip (Offset Microstrip) line feed
A microstrip patch excited by microstrip transmission line feed is shown in Figure 3.5, as we
can see the microstrip line is connected directly to the edge of the microstrip patch; the edge
impedance should be matched with the impedance of the feed line for maximum power transfer.
A method of impedance matching between the feed line and radiating patch is achieved by
introducing a single or multi-section quarter-wavelength transformers. This feed arrangement
has the advantage that the feed can be etched on the same substrate to provide a planar structure,
so they are easy to fabricate.
The conducting strip is smaller in width as compared to the patch; however in the millimetre-
wave range, the size of the feed line is comparable to the patch size, leading to increased
undesired radiation. The disadvantage is the radiation from the feed line, which leads to an
increase in the cross-polar level. In this type of feed technique, a conducting strip is connected
directly to the edge of the microstrip patch as shown in figure 3.5. The conducting strip is
smaller in width as compared to the patch. This kind of feed arrangement has the advantage that
the feed can be etched on the same substrate to provide a planar structure.

14
Fig: (a) Fig: (b)
Fig: 3.5 Microstrip Line Feed]
Properties:
 Easy to Fabricate.
 Simple to match by controlling the inset feed position.
 Low spurious radiation (≈ -20dB)
 Narrow Bandwidth (2-5%).
 As the substrate height increases, the surface waves and spurious feed radiation increases.
3.5.4.2 Coaxial or Probe Feed
As shown in Figure 3.6, the centre conductor of the coaxial connector extends through the
substrate and then is soldered to the radiating patch, while the outer conductor is connected to
the ground plane. The main advantage of this type of feeding scheme is that the feed can be
placed at any desired location inside the patch in order to match with its input impedance (to
achieve impedance matching).
This feed method is easy to fabricate and has low spurious radiation. The main disadvantage of a
coaxial feed antenna is the requirement of drilling a hole in the substrate to reach the bottom part
of the patch. Other disadvantages are that the connector protrudes outside the bottom ground
plane, so that it is not completely planar and include narrow bandwidth.
The coaxial feed or probe feed is one of the most common techniques used for feeding
microstrip patch antennas. As seen from figure 3.6 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.
However, its major disadvantage is that it provides narrow bandwidth and is difficult to model
since a hole has to be drilled into the substrate. Also, for thicker substrates, the increased probe
length makes the input impedance more inductive, leading to matching problems.

15
Fig: (a) Figure (b)
Fig: 3.6(a) Coaxial feed, (b) Coaxial or Probe Feed [24]
By using a thick dielectric substrate to improve the bandwidth, the microstrip line feed and the
coaxial feed suffer from numerous disadvantages such as spurious feed radiation and matching
problem. The non-contacting feed techniques which have been discussed, solve these problems.
Properties:
 Easy to Fabricate and Match.
 Low spurious radiation (-30 dB).
 Simple to match by controlling the position
 Narrow Bandwidth (1-3%).
 More difficult to model, especially for thick substrates (h>λ0/50).
3.5.4.3 Aperture Coupled Feed
This is an indirect method of feeding the patch. In this type of feeding technique, the ground
plane separates the radiating patch and the microstrip feed line. The coupling between the
radiation patch and the feed line is made through an opening slot or an aperture in the ground
plane. Figure 3-7 illustrates an aperture coupled microstrip rectangular antenna. The coupling
aperture is usually centred 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. The slot aperture can be either resonant or non resonant.
The resonant slot provides another resonance in addition to the patch resonance thereby
increasing the bandwidth, but at the expense of back radiation.

16
An advantage of this feeding technique is that the radiator is shielded from the feed structure by
the ground plane; another advantage is the freedom of selecting two different substrates to get an
optimum antenna performance (one for the feed line and another for the radiating patch). The
use of a thick substrate or stacked parasitic patches allows the patch to achieve wide bandwidth
[23]. In this study we are going to use this feed technique for all the antennas that were going to
simulate and build, because it can provide low cross-polarization levels, more freedom in
impedance-matching design and it does not have direct contact between the feed circuit and the
radiating elements, hence it allows an independent optimization of these parts of the antenna.
In aperture coupling as shown in figure 3.7 the radiating microstrip patch element is etched on
the top of the antenna substrate, and the microstrip feed line is etched on the bottom of the feed
substrate in order to obtain aperture coupling. The thickness and dielectric constants of these two
substrates may thus be chosen independently to optimize the distinct electrical functions of
radiation and circuitry. The coupling aperture is usually centered under the patch, leading to
lower cross-polarization due to symmetry of the configuration. The amount of coupling from the
feed line to the patch is determined by the shape, size and location of the aperture. Since the
ground plane separates the patch and the feed line, spurious radiation is minimized.
Generally, a high dielectric material is used for bottom substrate and a thick, low dielectric
constant material is used for the top substrate to optimize radiation from the patch. This type of
feeding technique can give very high bandwidth of about 21%. Also the effect of spurious
radiation is very less as compared to other feed techniques. The major disadvantage of this feed
technique is that it is difficult to fabricate due to multiple layers, which also increases the
antenna thickness.
Properties:
 Easier to model.
 Moderate spurious radiation (≈ -20 dB below ground plane).
 Ground plane between substrates isolates the feed from the radiating element and minimizes
interference.
 Independent optimization of the feed and radiating elements.
 Most difficult to fabricate.
 Low Bandwidth (1-4%).
 Typically high dielectric material is used for bottom substrate, and thick & low dielectric
constant for top.

17
 Feed – line width, slot size and position, and electrical parameters of substrates can optimize
design and match.
Fig: (a) Fig: (b)
Fig: 3.7(a) Aperture coupled feed , (b) Aperture coupled microstrip rectangular antenna [24]
3.5.4.4 Proximity-Coupled Feed.
This method uses electromagnetic coupling between the feed line and the radiating patch, which
are printed on the same or separate substrates. The feed line can be placed underneath the patch,
or can also be placed in parallel and very close to the edge of a patch but always avoiding any
soldering connection.
Figure 3.8 shows a proximity coupled rectangular patch antenna. The advantage of this coupling
is that it yields the largest bandwidth compared to other coupling methods due to overall
increase in the thickness of the microstrip patch antenna; it is easy to model and has a low
spurious radiation. The disadvantage is that it is more difficult to fabricate.
This type of feed technique is also called as the electromagnetic coupling scheme. As shown in
figure 3.8, 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 of about 13%, due to increase in the electrical 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.

18
Fig: (a) Fig: (b)
Fig: 3.8(a) Proximity coupling for underneath the patch [23], (b) Proximity coupled feed
The major disadvantage of this feed scheme is that it is difficult to fabricate because of the two
dielectric layers that need proper alignment. Also, there is an increase in the overall thickness of
the antenna.
Properties:
 Largest bandwidth (as high as 13%).
 Easier to model.
 Low spurious radiation.
 More difficult to fabricate.
 Length of feeding stub and width-to-line ratio of patch can control match.
Fig: 3.9 The Equivalent Circuits

19
Table 3.1 below summarizes the characteristics of the different feed techniques.
Characteristics Coaxial
Probe
Feed
(Non planar)
Radiating
Edge
Coupled
(Coplanar)
Non radiating
Edge
Coupled
(Coplanar)
Gap
Coupled
(Coplanar)
Inset
Feed
(Coplanar)
Proximity
Coupled
(Planar)
Aperture
Coupled
(Planar)
CPW Feed
(Planar)
Spurious
Feed
Radiation
More Less Less More More More More Less
Polarization
Purity
Poor Good Poor Poor Poor Poor Excellent Good
Fabrication
Ease
Solder
Reqd.
Easy Easy Easy Easy
Alignment
Reqd.
Alignment
Reqd.
Alignment
Reqd.
Reliability Poor Better Better Better Better Good Good Good
Impedance
Matching
Easy Poor Easy Easy Easy Easy Easy Easy
BW (at
matching)
2-5% 9-12% 2-5% 2-5% 2-5% 13%(30) 21%(33) 3%(39,40)
3.5.5 Methods of Analysis
The analytic models for microstrip antenna allow the designer to predict the antenna
characteristics, such as input impedance, resonant frequency, band width, radiation patterns and
efficiency. We can divide these methods into two groups [24]. The preferred 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).
3.5.5.1. The transmission line model.
3.5.5.2. Cavity model.
3.5.5.3. Full-wave model
a. Integral Equation (MoM).
b. Modal.
c. Finite Difference time domain.
d. Finite elements. & others.
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.
In the first group, we have:
 The transmission line model;
 The cavity model;
 The multipart network model (MNM).

20
These methods are based on equivalent magnetic current distribution around the patch edges.
The transmission line model is the simplest of all; the cavity model is more accurate and
complex. All methods provide a good physical insight of the basic antenna performance.
In the second group, we have:
 The method of moments (MoM);
 The finite-element method (FEM);
 The spectral domain technique (SDT);
 The finite-difference time domain (FDTD) method.
These methods are based on the electric current distribution on the patch conductor and the
ground plane. These models provide more accurate results, but they are also more complicated
to analyze. The simulating software used in this study is "Advanced Design System"; it is based
in the method of moments, so we are going to give a brief review into the method of moments.
The method of moments uses the surface currents to model the microstrip patch; and the volume
polarization currents in the dielectric piece are used to model the fields in the dielectric piece.
An integral equation is formulated for each of the unknown currents on the microstrip patch, the
feed lines and their images in the ground plane. Integral equations are then transformed into
algebraic equations that can be easily solved using a computer.
The moment method, is considered very accurate because it takes into account the fringing fields
outside the physical boundary of the two-dimensional patch and includes the effects of mutual
coupling between two surface current elements as well as the surface wave effect in the
dielectric, thus providing a more exact solution [24].
3.5.5.1 Transmission Line Model
This model represents the microstrip antenna by two slots of width and height h, separated by
a transmission line of length . The microstrip is essentially a non-homogeneous line of two
dielectrics, typically the substrate and air.
Fig: (a) Fig: (b)
Fig: 3.10 (a) Microstrip Line, (b) Electric Field Lines

21
Hence, as seen from Figure 3.10(b), 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 ( ) must be obtained in order to account for the
fringing and the wave propagation in the line. The value of is slightly less than because
the fringing fields around the periphery of the patch are not confined in the dielectric substrate
but are also spread in air.
The expression for reff W/h >1 is given by [1] as:
 … (3.5.5.1.1)
Where,
= Effective dielectric constant.
= Dielectric constant of substrate.
h = Height of dielectric substrate
= Width of the patch.
Also
 … (3.5.5.1.2)
In the Figure 3.11(a) shown below, the microstrip patch antenna is represented by two slots,
separated by a transmission line of length and open circuited at both the ends. Along the width
of the patch, the voltage is a maximum and the current is a minimum due to open ends. The
fields at the edges can be resolved into normal and tangential components with respect to the
ground plane.
Fig: (a) Fig: (b)
Fig: 3.11 (a) Top View of Antenna, (b) Side View of Antenna

22
It is seen from Figure 3.11 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 3.11), which are in phase, means that the resulting fields combine to give maximum
radiated field normal to the surface of the structure. Hence the edges along the width can be
represented as two radiating slots, which are λ/2 apart and excited in phase and radiating in the
half space above the ground plane. 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 a:
 … (3.5.5.1.3)
The effective length of the patch Leff now becomes:
 … (3.5.5.1.4)
For a given resonance frequency , the effective length is given by [9] as:
 … ( 3.5.5.1.5)
 … (3.5.5.1.6)
Where,
g = fringe factor (length reduction factor)
The resonant frequency with no fringing is given by
 … (3.5.5.1.7)
 …(3.5.5.1.8)
Because of fringing, the effective distance between the radiating edges seems longer than L by
an amount of at each edge. This causes the actual resonant frequency to be slightly less than
fro by a factor q. Thus
 … (3.5.5.1.9)
 … (3.5.5.1.10)

23
This factor q has been determined using modal-expansion techniques, and by solving a
transcendental equation it can be plotted vs. the substrate thickness . These values are shown
in the figure that follows for = 1, 1.33, 1.66 and 2 . The fringing effect
increases with the increasing substrate thickness. This leads to larger effective distances between
the radiating edges and an approximate linear decrease (vs. thickness) of the resonant frequency.
Slot Admittance : Each radiating aperture is modelled as a narrow slot of width and height
radiating into half space.
Conductance: is the voltage across the centre of the slot . We can define a conductance such
that when placed across the centre of the slot will dissipate the same power as the radiated by the
slot. Thus,
 … (3.5.5.1.11)
 … (3.5.5.1.12)
 … (3.5.5.1.13)
 … (3.5.5.1.14)
Where,
Input Admittance :The slight reduction from is necessary to account for the fringing at the
radiating edges. If the reduction of L from is properly choosen (choosing properly the length
reduction factor q), the transformed admittance of slot #2 becomes
 … (3.5.5.1.15)
In order for the patch to have a broadside pattern it is desired to excite the slots 1800
out-of-
phase. This is accomplished by choosing the length L slightly less than .
Typically:
 … (3.5.5.1.16)
 … (3.5.5.1.17)
 … (3.5.5.1.18)

24
 … (3.5.5.1.19)
 … (3.5.5.1.20)
Taking into account coupling:
 … (3.5.5.1.21)
Where,
+ is used with odd (ant symmetric) resonant voltage distribution beneath the patch and
between the slot.
-is used with even (symmetric) resonant voltage distribution beneath the patch and
between the slot.
 … (3.5.5.1.22)
Where,
= E- field radiated by slot #1
= H- field radiated by slot #2
= voltage across the slot.
 … (3.5.5.1.23)
The resonant input resistance can be decreased by increasing the width W of the patch. This is
acceptable as long as the ratio W/L does not exceed 2 because the aperture efficiency of a single
patch begins to drop, as W/L increases beyond 2. When the radiating edges are separated by
half-wavelength (in the substrate), the transmission line model yields for W/L=5 and
W= an input resonant resistance of about 120 ohms. Modal analysis reveals that the
resonant resistance is not strongly influenced by the substrate height (except for square patches
with h/λ0<<1). Also it is observed that the resonant input resistance is not very strongly
influenced by the substrate height, except for thin substrates for nearly square patches (W/L ≈ 1)
where the resistance values fall rapidly with decreasing small substrate height.
Characteristic Impedance/Admittance
 … (3.5.5.1.24)
 … (3.5.5.1.25)
 … (3.5.5.1.26)
 … (3.5.5.1.27)

25
 … (3.5.5.1.28)
 … (3.5.5.1.29)
 … (3.5.5.1.30)
Fig: 3.12 Substrate Dimensions
Assuming constant field along directions parallel to the radiating edges, the characteristic
admittance is given by
 … (3.5.5.1.31)
Where,
is large (low characteristic impedance line ).
A better approximation for the characteristic impedance is (for Wo/h >1)
 … (3.5.5.1.32)
Inset Feed-Point Impedance
Fig : (a) Fig : (b)
Fig: 3.13 (a) Recessed Microstrip-line feed , (b) Normalized input resistance
Using the modal-expansion analysis, it has been shown that the inset-feed-point impedance is
given by
 … (3.5.5.1.33)

26
As the inset feed-point distance increases, the resonant input resistance decreases. Infact, at
, the input resistance vanishes. This feeding mechanism can be very useful for
matching patches to lines with small values of characteristics impedance on the order of 50
ohms.
For G1 <<Yc, B1<<Yc :
 … (3.5.5.1.34)
 … (3.5.5.1.35)
Where,
+ for odd voltage distribution
- For even voltage distribution.
As the values of y0 approach L/2, the function varies rapidly. Therefore as the
feeding point approaches the centre of the patch, the input resistance changes rapidly with the
position of the feeding point. In order to maintain very accurate values, a close tolerance must be
maintained.
3.5.5.2. Cavity Model
The cavity model helps to give insight into the radiation mechanism of an antenna, since it
provides a mathematical solution for the electric and magnetic fields of a microstrip antenna. It
does so by using a dielectrically loaded cavity to represent the antenna. This technique models
the substrate material, but it assumes that the material is truncated at the edges of the patch. The
patch and ground plane are represented with perfect electric conductors and the edges of the
substrate are modeled with perfectly conducting magnetic walls.
Consider figure 3.14 shown. When the microstrip patch is provided power, a charge distribution
is seen on the upper and lower surfaces of the patch and at the bottom of the ground plane. This
charge distribution is controlled by two mechanisms ─ an attractive mechanism and a repulsive
mechanism. The attractive mechanism is between the opposite charges on the bottom side of the
patch and the ground plane, which helps in keeping the charge concentration intact at the bottom
of the patch. The repulsive mechanism is between the like charges on the bottom surface of the
patch, which causes pushing of some charges from the bottom, to the top of the patch. As a
result of this charge movement, currents flow at the top and bottom surface of the patch.

27
Fig: (a) Fig: (b)
Fig: 3.14 (a) Charge distribution and current density creation on the microstrip patch, (b)Rectangular design
The cavity model assumes that the height to width ratio (i.e. height of substrate and width of the
patch) is very small and as a result of this the attractive mechanism dominates and causes most
of the charge concentration and the current to be below the patch surface. Much less current
would flow on the top surface of the patch and as the height to width ratio further decreases, the
current on the top surface of the patch would be almost equal to zero, which would not allow the
creation of any tangential magnetic field components to the patch edges. Hence, the four
sidewalls could be modeled as perfectly magnetic conducting surfaces. However, in practice, a
finite width to height ratio would be there and this would not make the tangential magnetic
fields to be completely zero, but they being very small, the side walls could be approximated to
be perfectly magnetic conducting [5].
Since the walls of the cavity, as well as the material within it are lossless, the cavity would not
radiate and its input impedance would be purely reactive. Hence, in order to account for
radiation and a loss mechanism, one must introduce a radiation resistance RR and a loss
resistance RL. A lossy cavity would now represent an antenna and the loss is taken into account
by the effective loss tangent δeff which is given as:
 δ … (3.5.5.2.1)
Thus, the above equation describes the total effective loss tangent for the microstrip patch
antenna.Therefore, we only need to consider modes inside the cavity. Now, we can write an
expression for the electric and magnetic fields within the cavity in terms of the vector potential
Az [2]:
 … (3.5.5.2.2)
 … (3.5.5.2.3)

28
 … (3.5.5.2.4)
 … (3.5.5.2.5)
 … (3.5.5.2.6)
 … (3.5.5.2.7)
Since the vector potential must satisfy the homogeneous wave equation, we can use separation
of variables to write the following general solution. Hence we obtain a solution for the electric
and magnetic fields inside the cavity as given below.
 ... (3.5.5.2.8)
 … (3.5.5.2.9)
      cos cos cosx z
z mnp x y z
K K
E j A K x K y K z
w 
  … (3.5.5.2.10)
      cos sin cos
y
x mnp x y z
K
H A K x K y K z

  … (3.5.5.2.11)
      sin cos cosx
y mnp x y z
K
H A K x K y K z

  … (3.5.5.2.12)
 0 … ( 3.5.5.2.13)
Here,
Where m = n = p ≠ 0 & is the amplitude constant.
3.5.6 Circular patch
TMz
 … (3.5.6.1)
 … (3.5.6.2)
 … (3.5.6.3)
 … (3.5.6.4)

29
 … (3.5.6.5)
 0 … (3.5.6.6)
Fig: 3.15 Circular Patch co-ordinate.
Boundary Conditions:
 … (3.5.6.7)
 … (3.5.6.8)
 … (3.5.6.9)
:
 … (3.5.6.10)

… (3.5.6.11)
 … (3.5.6.12)
m=0,1,2…
Hence :
Where,
m=1,n=1 :
m=2, n=1 :

30
m=0, n=1 :
m=3, n=1 :
 … (3.5.6.13)
First 4 are:
:
 … (3.5.6.14)
Resonant Frequency:
modes
 = … (3.5.6.15)
 … (3.5.6.16)
a/h>>1
 … (3.5.6.17)
 … (3.5.6.18)
 … (3.5.6.19)
Also if given: Given: , h, : modes
Radius a of a patch is given by
 … (3.5.6.20)
Where
h in cm
Equivalent Current Densities
modes:
 … (3.5.6.21)
 … (3.5.6.22)
 … (3.5.6.23)

31
 … (3.5.6.24)
 … (3.5.6.25)

 … (3.5.6.26)
Far- Zone Fields
 … (3.5.6.27)
 … (3.5.6.28)
 … (3.5.6.29)
Where
Fig: 3.16 (a) E-Plane. (b) H-Plane
(Ø=00
, 1800
) h=0.1588 cm , f0= 10GHz,a=0.525 ,
ae=0.598 cm , = 0.1 cm, =2.2
Fig: (a)
(f=900
,2700
) h=0.1588 cm , f0= 10GHz,a=0.525 ,
ae=0.598 cm , = 0.1 cm, =2.2
Fig: (b)

32
E-Plane (
 … (3.5.6.30)
 … (3.5.6.31)
H-Plane (
 … (3.5.6.32)
 … (3.5.6.33)
Conductance
 … (3.5.6.34)
 … (3.5.6.35)
 … (3.5.6.36)
Fig: (a) Fig: (b)
Fig:3.17 (a) Conductance and (b) Directivity
Directivity (Do)
 … (3.5.6.37)
Resonant Input Resistance
 … (3.5.6.38)
 … (3.5.6.39)
Where,

33
Quality Factor
 … (3.5.6.40)
Where,
= Total Q.
= Q due to radiation (space wave)
= Q due to conduction (ohmic) losses.
= Q due to dielectric losses.
= Q due to surface waves.
Fig: 3.18 Quality factor
Bandwidth (fractional):
 … (3.5.6.41)
Modified form that takes into account Impedance Matching
 … (3.5.6.42)
Bandwidth (constant fr)
BW ~Volume ~ Area * Height
~ Width * Length * Height
BW ~

34
Radiation Efficiency
 … (3.5.6.43)
 … (3.5.6.44)
Fig: 3.19 Radiation Efficiency
Input Impedance:
Fig: 3.20 Input Impedance

35
Coupling:
Fig 3.21: Patch Relative Positioning
Fig: 3.22 Patch Coupling
E-Plane

2
0
12 0 0 00
0 0 0
sin cos
1 2
sin3 2 2 sin 2 sin 2 sin
cos
k W
Y Y L Y L
J J JG



      
     
   
                        
          
    
 
… (3.5.6.45)
H-Planes

… (3.5.6.46)
Where
z = centre-to-centre separations of slots.

36
Fig 3.23: Patch mutual conductance
Fig: 3.24 square and rectangular combination
Circular Patch: Resonance Frequency
Fig: (a) Fig: (b)
Fig: 3.25 (a) and (b) circular geometry
From separation of variables:
 … (3.5.6.47)

37
Where,
= Bessel functions of first kind order.
 … (3.5.6.48)
 … (3.5.6.49)
 … (3.5.6.50)
(nth root of Bessel function)
 … (3.5.6.51)
Dominant mode: TM11
 … (3.5.6.52)
 … (3.5.6.53)
Fringing extension :
 … (3.5.6.54)
 … (3.5.6.55)
“Long/Shen Formula”:
 … (3.5.6.56)
Or
 … (3.5.6.57)
Circular Patch: Patterns
(Based on Magnetic Current Model)
Fig: (a)

38
Fig: (b) Fig: (c)
Fig: 3.26 (a) Circular Patch: Patterns , and (b) & (c) E-H Plane in circular patch
In fig., origin is at the centre of the patch.
The probe is on the X axis.
In the patch cavity:
 … (3.5.6.58)
(The edge voltage has a maximum of one volt)

0
… (3.5.6.59)

0
… (3.5.6.60)
Where,
Circular Patch: Input Resistance
 … (3.5.6.61)
 … (3.5.6.62)
Where,
= radiation efficiency.
0

39
= power radiated into space by circular patch with maximum edge voltage of
one volt.
CAD Formula:

0
… (3.5.6.63)
Where,
3.5.7 Circular Polarization
Nowadays circular polarization is very important in the antenna design industry, it eliminates the
importance of antenna orientation in the plane perpendicular to the propagation direction, it
gives much more flexibility to the angle between transmitting & receiving antennas, also it
enhances weather penetration and mobility [17, 22]. It is used in a bunch of commercial and
militarily applications. However it is difficult to build good circularly polarized antenna [2]. For
circular polarization to be generated in microstrip antenna two modes equal in magnitude and 90
out of phase are required [23-24]. Microstrip antenna on its own doesn’t generate circular
polarization; subsequently some changes should be done to the patch antenna to be able to
generate the circular polarization [25]. The circular microstrip patch antenna's lowest mode is
the TM11, the next higher order mode is the TM21 which can be driven to produce circularly
polarized radiation. Circularly polarized microstrip antennas can be classified according to the
number of feeding points required to produce circularly polarized waves. The most commonly
used feeding techniques in circular polarization generation are dual feed and single feed [24].

40
3.5.7.1 Single feed circularly polarized microstrip antenna
Single feed microstrip antennas are simple, easy to manufacture, low cost and compact in
structure as shown in Figure 3-27. It eliminates the use of complex hybrid polarizer, which is
very complicated to be used in antenna array [24, 28]. Single feed circularly polarized microstrip
antennas are considered to be one of the simplest antennas that can produce circular polarization
[7]. In order to achieve circular polarization using only single feed two degenerate modes should
be excited with equal amplitude and 90° difference. Since basic shapes microstrip antenna
produce linear polarization there must be some changes in the patch design to produce circular
polarization. Perturbation segments are used to split the field into two orthogonal modes with
equal magnitude and 90° phase shift. Therefore the circular polarization requirements are met.
Fig: 3.27 Single feed circularly polarized microstrip antenna
The dimensions of the perturbation segments should be tuned until it reaches an optimum value
at the design frequency [24, 27, 29-30].The feed is on the diagonal. The patch is nearly (but not
exactly) square.
 … (3.5.7.1)
Basic principle: the two modes are excited with equal amplitude, but with a 45o
phase.
Design equations:
 … (3.5.7.2)
 … (3.5.7.3)
The resonance frequency (Rin is maximum) is the optimum Circularly Polarized frequency.
(SWR < 2).
Fig: (a) Fig: (b)
Fig: 3.28 Co-ordinate system in square patch (a) and (b)

41
 … (3.5.7.4)
At resonance:
 … (3.5.7.5)
Where and are the resonant input resistances of the two LP (x and y) modes, for the same
feed position as in the Circularly Polarized patch.
Note: Diagonal modes are used as degenerate modes.
Figure: (a) Figure: (b)
Fig: 3.29 (a) Patch with slot, (b) Patch with truncated corners
3.5.7.2 Dual feed circularly polarized microstrip antenna
As 90° phase shift between the fields in the microstrip antenna is a perquisite for having circular
polarization, dual feed is an easy way to generate circular polarization in microstrip antenna.
The two feed points are choosen perpendicular to each other as shown in Figure 3-30. With the
help of external polarizer the microstrip patch antenna is fed by equal in magnitude and
orthogonal feed. Dual feed can be carried out using quadrature hybrid, ring hybrid, Wilkinson
power divider, T-junction power splitter or two coaxial feeds with physical phase shift 90° [26-
17].
Fig: 3.30 Examples for dual fed Fig: 3.31 Phase shift realized with delay line
Circularly Polarized patches [24]

42
Fig: 3.32 Phase shift realized with 900
hybrids (branch line coupler)
3.5.7.3 Circular Polarization Synchronous Rotation
Elements are rotated in space and fed with phase shifts.
Fig: 3.33 Circular Polarization Synchronous Rotation
Because of symmetry, radiation from higher-order modes (or probes) tends to be reduced,
resulting in good cross-polarization.
Circular polarization can be studied with following points:
1. 2 components of E-field orthogonal to each other and ┴ to direction of travel.
2. Equal amplitudes.
3. Time-phase difference has to be odd multiples of 900
.
Fig: (a)
Fig: (b)

43
Fig: (c) Fig: (d)
Fig: (e)
Fig: 3.34 :(a) square patch driven at adjacent sides through power divider , (b) square patch driven at adjacent sides
through A 900
hybrid (c) Circular patch fed with Coax (d) Single feed for nearly square patch (e) Circular patch
feed arrangement for and higher modes
 … (3.5.7.6)
 … (3.5.7.7)
Where
Fig(a) Fig: (b)
Fig: 3.35 (a) Single feed for Left-hand circular (LHC), (b) Single feed for Right-hand circular (RHC)

44
If the feed point (y’, z’) is selected along the diagonal so that
 … (3.5.7.8)
Then the axial ratio at broadside of Ey to the Ez is
 … (3.5.7.9)
To achieve circular polarization, the magnitude of the axial ratio must be unity while the phase
must be ±900
. Two phasers representing the numerator and denominator are of equal magnitude
and 900
out of phase.This can occur when
 … (3.5.7.10)
And the operating frequency is selected at the midpoint between the resonant frequencies of
and modes.The previous condition is satisfied when
 … (3.5.7.11)
Based on this for L & W
 … (3.5.7.12)
 … (3.5.7.13)
Where f0 is the centre frequency.
Circular polarization can also be achieved by the feeding the element off the main diagonal. To
achieve this
 … (3.5.7.14)
 … (3.5.7.15)
Other practical ways of achieving nearly circular polarization. For square patches, this can be
achieved by cutting very thin slots as shown in the next two figures.

45
Fig: (a) Fig: (b)
Fig: 3.36(a)Right-Hand Circular, (b)Left hand circular
Alternate ways to achieve nearly circular polarization.
1. Trim opposite corners of a square patch.
2. Make match slightly elliptical or add tabs.
Fig:(a)
Fig: (b)
Fig: 3.37 :(a) Trimmed square (L=W) Feed Points: 1 or 3 , (b) Elliptical with tabs
Arrays & Feed Networks
Fig: (a) Fig: (b)
Fig: (c) Fig: (d)
Fig: 3.38 : (a) Series Feed, (b) Corporate (parallel) feed, (c) Tapered Impedance Feed Matching Transformer, and
(d) λ/4 Impedance Feed Matching Transformer

46
Scan Blindness
Fig: 3.39 Planar Array of circular patches.
Broadside Reflection Co-efficient
 … (3.5.7.16)
Where
= Input Impedance when main beam is scanned toward
= Input Impedance when main beam is broadside.
Fig: 3.40 Conventional & Cavity-Backed

47
Fig: 3.41 Broadside Reflection Co-efficient
Other Geometries Resonant Frequencies:
Fig: 3.42 Disc Sector
 … (3.5.7.17)
Where,
m = q (π/ , q=0, 1, 2, ...
n=1.2.3, …
Fig: 3.43 Ring sector Fig: 3.44 Circular ring

48
 … (3.5.7.18)
 … (3.5.7.19)
Where,
, g = 0, 1, 2, …
n=1, 2, 3, …
Circular Ring
 … (3.5.7.20)
 … (3.5.7.21)
Where,
0,1,2, … , n = 1, 2, 3, …
3.5.8. Characteristics of the Circular Patch Antenna
3.5.8.1 Geometry and Coordinate Systems
The circular patch antenna is extensively used in practice. The geometry is shown in Fig. 3.45. It
is characterized by the radius (a), the substrate thickness (t) and its relative permittivity (εr).
Spherical coordinate system is used to describe a field point P(r, θ, φ) while cylindrical
coordinate system is used to describe a source point P’
(ρ,  , z).
3.5.8.2 Characteristics of Normal Modes
3.5.8.2.1 Internal Fields
The normal modes refer to the source free fields which can exist in the region between the patch
and the ground plane. This region is modeled as a cavity bounded by electric walls on the top
and bottom and magnetic walls on the sides. As discussed , under the assumption that the
thickness is much less than the wavelength, the electric field has only a vertical component Ez
which is independent of z and satisfies the homogeneous equation
 … (3.5.8.2.1.1)
and the boundary condition on the side walls of the cavity. In cylindrical coordinates,
Eqn. reads
 … (3.5.8.2.1.2)
Due to the assumption of the cavity model, .Using the method of the separation of
variables, we let
 … (3.5.8.2.1.3)

49
Equation becomes
 … (3.5.8.2.1.4)
Since the right hand side depends on  only and the left hand side depends on ρ only, we have
the following equations for the functions Q and P:
 … (3.5.8.2.1.5)
 … (3.5.8.2.1.6)
The solution for Q is
 …(3.5.8.2.1.7)
Where,
n is an integer since Q must be periodic with period 2π.
The solution for P is
 … (3.5.8.2.1.8)
Where,
is the Bessel function of the first kind of order n and is the Bessel function of the
second kind of order n.
Since fields are finite at ρ = 0, = 0.
Thus
 … (3.5.8.2.1.9)
Fig: 3.45 Geometry of a circular patch antenna.

50
From Maxwell’s equations, we obtain
 … (3.5.8.2.1.10)
 … (3.5.8.2.1.11)
Where,
is the derivative of with respect to the argument .
Applying the magnetic wall boundary condition, we have
 … (3.5.8.2.1.12)
Let the roots of be . Then the eigen values of , denoted by , are:
 … (3.5.8.2.1.13)
3.5.8.2.2 Resonant Frequencies
The resonant frequency of a mode is
 … (3.5.8.2.2.1)
The first five values of are:
(n,m) (1,1) (2,1) (0,2) (3,1) (1,2)
1.841 3.054 3.832 4.201 5.331
Equation , which is based on the perfect magnetic wall assumption, yields resonant frequencies
which differ from measurements by about 20%. To take into account the effect of fringing field,
an effective radius was introduced. This was obtained by considering the radius of an ideal
circular parallel plate capacitor which would yield the same static capacitance after fringing is
taken into account. A detailed calculation yields the formula [1, 2]
 … (3.5.8.2.2.2)
Using , the resonant frequency formula becomes
 … (3.5.8.2.2.3)
Equation yields theoretical resonant frequencies which are within 2.5% of measured values.
3.5.8.2.3 Radiation Fields
The surface magnetic current density on the side walls of the cavity is given by
 … (3.5.8.2.2.4)

51
Since is expressed in cylindrical coordinates, it has to be transformed to spherical coordinates
before deriving the far fields (radiation fields) :
 … (3.5.8.2.2.5)
In our problem, .
The electric vector potential is
 … (3.5.8.2.2.6)
where integration is over the area of the fictitious magnetic side wall.
The far fields are given by
 0 … (3.5.8.2.2.7)
 0 … (3.5.8.2.2.8)
Where,
After lengthy manipulation, we arrived at the result:

… (3.5.8.2.2.11)

… (3.5.8.2.2.12)
3.5.8.3 Coaxial Feed Circular Patch
3.5.8.3.1 Internal and Radiation Fields
Figure 3.46 shows a coaxial feed at a distance d from the centre of the patch of radius a. The
feed is modeled by a z-directed current ribbon of some effective angular width 2w. Hence
 … (3.5.8.3.1.1)
Where

52
The effective arc width 2wd is a parameter chosen such that good agreement between the
theoretical and experimental impedances are obtained. Usually, it is several times the diameter
of the inner conductor. Using the formulas, the fields under the circular cavity are found to be
given by:
 … (3.5.8.3.1.2)
Where
 … (3.5.8.3.1.3)
 … (3.5.8.3.1.4)
The fields in the far zone (radiation fields) are evaluated to be

… (3.5.8.3.1.5)

… (3.5.8.3.1.6)
Fig: 3.46 Top view of a coaxial fed circular patch.
3.5.8.3.2 Losses and Q
Based on the resonance approximation, the dielectric, copper, and radiation losses and the total
energy stored when the excitation frequency is near the resonant frequency of mode (n,m) are
given by
 … (3.5.8.3.2.1)

53
 … (3.5.8.3.2.2)
 … (3.5.8.3.2.3)
 … (3.5.8.3.2.4)
where σ is the conductivity of the patch and the ground plane, and
The total Q factor
 … (3.5.8.3.2.5)
The effective loss tangent and the effective wave number in the substrate are given by
 … (3.5.8.3.2.6)
 … (3.5.8.3.2.7)
3.5.8.3.3 Input Impedance
The input impedance
 … (3.5.8.3.2.8)
Where
After evaluating the integrals, we obtain

… (3.5.8.3.2.9)
In the above equation for Z, the effective wave number keff has replaced kd and the effective loss
tangent has been utilized.
3.5.8.4 Circularly Polarized Microstrip Antennas
In our study we are going to build a microstrip antenna that it is going to work with circular
polarization, this kind of antennas is widely used as efficient radiators in satellite

54
communications because of the advantages that can provide us. The most important of these
advantages is that the orientation of the transmitting antenna and receiving antenna orientation
need not necessarily be the same, so this allows the designer to have more freedom to design the
transmission and reception system. With the use of circular polarized antennas, the system can
tolerate changes in the polarization of the signal, these changes may be caused by the
reflectivity, absorption, multipath, inclement weather and line of sight problems; conditions that
(most of the time) can affect the polarization of a transmitted wave.
Hence, circular polarized antennas give us a higher probability of a successful link because they
can transmit and receive signals on all planes. In an antenna, circular polarization can be
achieved through a single feed or using two feeds in the same patch. In an antenna array, we can
generate circular polarization by the sequential rotation of the feeders.
3.5.8.4.1 Dual-orthogonal feed circularly polarized microstrip antennas.
The most common and direct way to generate a circular polarization is through the use of a dual-
feed technique. The two orthogonal modes required for the generation of circular polarization
can be simultaneously excited using two feeds at orthogonal positions that are fed by 1∟0° and
1∟90° as shown in Figure 3.47.
When we are designing a microstrip antenna, first we have to match it to the feed lines, this
process can be achieved by an appropriately electing of the feed locations or through the use of
impedance transformers. Another technique is using a power divider circuit, which provides
there quired amplitude and phase excitations.
Figure 3.47 Dual feed in a circular microstrip antenna [24].
Some of them, which have been successfully employed in a feed network of a circular
polarization patch, are:
 The 180-Degree Hybrid
 The Wilkinson Power Divider

55
 The T-Junction Power Divider
 The Quadrature Hybrid
3.5.8.4.1.1 The Quadrature (90 º) Hybrid
It is also known as Branch-line hybrid. The quadrature hybrids are 3dB directional couplers with
90° phase difference in the outputs through and coupled arms. Its basic operation is : The input
signal at port 1 is equally split in amplitude at the output ports 2 and 3 with a 90 degrees shift
phase between these outputs. Because of this shift phase, any reflections from the patch tend to
cancel at the output port 1 so that the match remains accepted [22]. The port 4, it is the isolated
port because no power is coupled to that port. However, the combined mismatch at port 4 should
be absorbed by a matched load to prevent potential power division degradation of the hybrid
which, otherwise, can affect axial ratio performance. The type of 3dB coupler that it has been
designed for this project is as shown in Figure .
Fig: 3.48 Geometry of a Branch-Line Coupler. [26]
The Table 3.2 shows some features about the Power Divider Networks, and it can explain why
we decide to use the Quadrature Hybrid for our case of study.
Table 3-2 General characteristics of Power Divider Networks. [27]
Output Port
900
Phase shift Isolation Input Match Change of CP
T-junction divider No*
No Yes↑
No
Wilkinson divider No*
Yes Yes↑
No
Quadrature Hybrid Yes Yes Yes Yes, by switching input and isolate ports.
Ring Hybrid No*
Yes Yes↑
Yes↑
by switching input and isolate ports.
*
Requires a quarter-wavelength of line extension in one output arm to generate phase shift.
↑
With a quarter-wavelength of line extension in one output arm in place.
We can mention that the main features are that we do not need to add any other device to get the
900
phase shift and neither for the input match; besides it give us an easy way to change the
sense of circular polarization. These features led us to use less material and build a smaller and
lighter antenna.

56
3.5.8.4.2 Singly Feed Circularly Polarized Microstrip Antennas
A singly – feed circular polarization may be regarded as one of the simplest radiators for
exciting circular polarization and is very helpful in situations where the space do not allow to
accommodate dual-orthogonal feeds with a power divider network. This technique generally
radiates linear polarization; but in our study case we want to achieve a circular polarization, so
we are going to talk of some techniques used to achieve this goal.
Circular polarization can be accomplished by inserting a pair of symmetric perturbation
elements at the boundary of a square or circular patch, in this case a pair of truncated corners
[22].In our study, for the design and development of one of the antennas, we are going to
employ this technique to enhance the axial ratio bandwidth of the antenna.
Fig: 3.49 Aperture and phase of orthogonal modes in single point feed circularly polarized microstrip patch [22]
Other simple and common techniques to generate circular polarization are cutting a diagonal slot
in the square or circular patch, or using a nearly square patch (also can be a nearly circle) on the
diagonal, this produces two resonance modes corresponding to lengths W and L (where W/L =
[1.01 - 1.10] in the case of a square patch), this two modes are spatially orthogonal, have equal
magnitude and are in phase quadrature. The circular polarization is obtained at a frequency that
is between the resonance frequencies of these two modes. [24]
3.5.8.4.2.1 Sequential Rotation Feeding Technique
One disadvantage we have with a single – feed microstrip antenna is that it give us a narrow
impedance and axial ratio bandwidths; but we can increased them by using a sequentially rotated
array configuration. [22 , 24, 28,29].To get a circular polarized wave, the antenna elements are

57
physically rotated relative to each other and the feed phase is individually adjusted to each
element to compensate for the rotation. It has been mathematically demonstrated in reference
[22], that the sequential array radiates perfect circular polarized wave independently of the
polarization of the elements, I mean that the elements could be circularly or linearly polarized
[24,28]; but we will have better results using circularly polarized elements. Another feature of
the sequential array is that can greatly reduce the cross polarization, even at off-centre
frequency, hence we can get a wideband circularly polarized microstrip array. Figure shows two
8-element arrays. One is a conventional and the other is sequential array.
We can see from the graphs that in the conventional array, there is no rotation of the Circular
Polarization elements and all elements are fed with equal amplitude and 0 degrees phase
difference; but in the sequential array the elements are rotated and feed with equal amplitude but
with a phase difference equal to the angle of rotation. Figures show the axial ratio and VSWR of
these arrays.
Fig: (a) Fig :(b)
Fig: 3.50 Arrangement of elements for two test arrays [22] (a) Conventional array, (b) Sequential array
Fig: 3.51 Measured axial ratio vs Frequency [22]
From figure, we can see that the sequential array has more wideband characteristics of
polarization and impedance than the conventional array.

CHAPTER 4
DESIGNING OF
MICROSTRIPANTENNA

58
CHAPTER 4
Designing of Microstrip Antenna
4.1 Design and analysis of dual band Microstrip Antenna
4.1.1 Circular Microstrip Antenna Basic Properties
The circular microstrip antenna offers a number of radiation pattern options not readily
implemented using a rectangular patch. The fundamental mode of the circular microstrip patch
antenna is the TM11. This mode produces a radiation pattern that is very similar to the lowest
order mode of a rectangular microstrip antenna. The next higher order mode is the TM21, which
can be driven to produce circularly polarized radiation with a monopole-type pattern. This is
followed in frequency by the TM02 mode, which radiates a monopole pattern with linear
polarization. In the late 1970s, liquid crystals were used to experimentally map the electric field
of the driven modes surrounding a circular microstrip antenna and optimize them.
The circular metallic patch has a radius a and a driving point located at r at an angle φ measured
from the xˆ axis. As with the rectangular microstrip antenna, the patch is spaced a distance h
from a ground plane. A substrate of εr separates the patch and the ground plane. An analysis of
the circular microstrip antenna, which is very useful for engineering purposes, has been
undertaken by Derneryd and will be utilized here. The electric field under the circular microstrip
antenna is described by:
 … (4.1.1.1)
The circular microstrip antenna is a metal disk of radius a and has a driving point location at r
which makes an angle φ with the xˆ axis. The thickness of the substrate is h, where h << λ0,
which has a relative dielectric constant of εr.
 … (4.1.1.2)
 … (4.1.1.3)
where k is the propagation constant in the dielectric which has a dielectric constant ε = ε0εr. Jn is
the Bessel function of the first kind of order n. J´n is the derivative of the Bessel function with
respect to its argument, ω is the angular frequency (ω = 2πf). The open circuited edge condition
requires that J´n (ka) = 0. For each mode of a circular microstrip antenna there is an associated
radius which is dependent on the zeros of the derivative of the Bessel function. Bessel functions
in this analysis are analogous to sine and cosine functions in rectangular coordinates. E0 is the

59
value of the electric field at the edge of the patch across the gap.
Table 4-1 first four Bessel function zeros used with equation (4.1.1.4).
Anm TMnm
1.84118 1,1
3.05424 2,1
3.83171 0,2
4.20119 3,1
The resonant frequency, fnm, for each TM mode of a circular microstrip antenna is given by:
 …(4.1.1.4)
Where Anm is the mth
zero of the derivative of the Bessel function of order n. The constant c is
the speed of light in free space and aeff is the effective radius of the patch. A list of the first four
Bessel function zeros used with equation (4.1.1.4) are presented in Table 4-1. (In the case of a
rectangular microstrip antenna, the modes are designated by TMmn, where m is related to x and n
is related to y. The modes for a circular microstrip antenna were introduced as TMnm, where n is
related to φ and m is related to r (often designated ρ).
The reversal of indices can be a source of confusion. aeff is the effective radius of the circular
patch, which is given by
 … (4.1.1.5)
Where , a/h>>1
where a is the physical radius of the antenna.
Equations can be combined to produce:
 … (4.1.1.6)
The form of equation is
 a = f (a) … (4.1.1.7)
Which can be solved using fixed point iteration to compute a design radius given a desired value
of Anm from Table 4-1, which determines the mode TMnm, and given the desired resonant
frequency fnm at which the antenna is to operate.
An initial approximation for the radius a0 to begin the iteration is
 … (4.1.1.8)
The initial value a0 is placed into the right-hand side of equation (4.1.1.6) to produce a value for
a. This value is designated a1, then is placed into the right hand side to produce a second, more
refined value for a designated a2, and so on. Experience indicates that no more than five
iterations are required to produce a stable solution.

60
4.1.2 Flow chart of the designing of a circular shaped microstrip antenna:-
4.2 Design of Microstrip patch antennas
In this chapter, the procedure for designing a microstrip patch antenna is explained. Next, a
compact rectangular microstrip patch antenna is designed for use in cellular phones. Finally, the
results obtained from the simulations are demonstrated.
4.2.1 Design Specifications
The three essential parameters for the design of a Circular Microstrip Patch Antenna:
 Frequency of operation (fo): The resonant frequency of the antenna must be selected
appropriately.
 Dielectric constant of the substrate (εr).
 Height of dielectric substrate (h).
Start
Calculation of dimensions
of proposed geometry
Simulation of Geometry
through IE3D software and
calculation of return loss
S11
If return loss is less than -
10 dB at 2 different
frequencies in desired
frequency range.
END
If return loss is not less than -10
dB at 2 different frequencies in
desired frequency range.

61
4.2.2 Design Procedure (PSO/IE3D)
Fig: 4.1 Microstrip patch antenna designed using IE3D
4.2.3 Simulation Setup and Results
The software used to model and simulate the Microstrip patch antenna is Zeland Inc’s IE3D.
IE3D is a full-wave electromagnetic simulator based on the method of moments. It analyses 3D
and multilayer structures of general shapes. It has been widely used in the design of MICs,
RFICs, patch antennas, wire antennas, and other RF/wireless antennas. It can be used to
calculate and plot the S11 parameters, VSWR, current distributions as well as the radiation
patterns.
4.2.3.1 Simulation of a Patch Antenna using IE3D.
In this brief tutorial, we use IE3D to simulate a microstrip-fed, patch antenna. In this tutorial we
are not concerned about the design of this antenna and we will focus our attention on using IE3D
to simulate the structure and obtain its parameters. The tutorial is organized in a number of
steps, which must be followed in sequence to obtain best results.
1. Run Zeland Program Manager. You will see a layout similar to that shown in Figure
4.2(a).
2. Run MGRID by clicking on the MGRID button shown in Figure 4.2(a). MGRID is the
main interface of IE3D, in which you can draw the layout of the circuit to be simulated.
Notice that all the fields are empty.

62
3. Run MGRID by clicking on the MGRID button shown in Figure 4.2(a). MGRID is the
main interface of IE3D, in which you can draw the layout of the circuit to be simulated.
Notice that all the fields are empty.
Fig: 4.2 (a) Zeland Program Manager.
3. Click the new button as shown in Figure 4.2(b).
4. The basic parameter definition window pops up. You should see something similar to
Figure 4.2(c). In this window you can define basic parameters of the simulation such as the
dielectric constant of different layers, the units and layout dimensions, and metal types
among other parameters. In “Substrate Layer” section note that two layers are
automatically defined. At z=0, the program automatically places an infinite ground plane
(note the material conductivity at z= 0) and a second layer is defined at infinity with the
dielectric constant of 1.
Fig: 4.2(b) Main view of MGRID

63
Fig: 4.2(c) Basic parameter definition.
5. In the basic parameter definition window, click on “New Dielectric Layer” button as is
shown in Figure 4.2(c). You will see a window similar to the one shown in Figure 4.2(d).
Enter the basic dielectric parameters in this window:
Fig: 4.2(d) defining the parameters of the antenna substrate

64
Fig: 4.2(e) Layout view of the problem after the definition of the dielectric layers
6. The next step is to draw the antenna and the layout.
Fig: 4.2(f) Window space for designing.

65
Fig: 4.2 (g). Design formed.
7. After designing, the next step is to run the simulation. However, before that, let us first
mesh the structure; this mesh is used in the Method of Moment (MoM) calculation. Press
the “Display Meshing” button. The “Automatic Meshing Parameters” menu pops up. This
menu is shown in Fig 4.2 (h).
Fig: 4.2 (h). Meshing window.

66
Fig: 4.2(i). Meshing window (continued)
In this menu, you have to specify the highest frequency that the structure will be simulated.
The number of cells/wavelength determines the density of the mesh. In method of moment
simulations, you should not use fewer than 10 cells per wavelength. The higher the number
of cells per wavelength, the higher the accuracy of the simulation. However, increasing the
number of cells increases the total simulation time and the memory required for simulating
the structure. In many simulations using 20 to 30 cells per wavelength should provide
enough accuracy. However, this cannot usually be generalized and is different in each
problem; press OK, a new window pops up that shows the statistics of the mesh as in fig
4.2(i); press OK again and the structure will be meshed.
8. Now it is time to simulate the structure. Press the “Run Simulation” button. The simulation
setup window pops up. Here you can specify the simulation frequency points as well as the
basic parameters of the mesh. Click on Enter button in the Frequency parameters field.
Fig: 4.2 (j) Design after applying run simulation

67
Fig: 4.2(k) simulation set-up
Fig: 4.2 (l) Simulation set-up (continued)

68
Fig: 4.2(m) Electromagnetic simulation and optimization engine
Fig: 4.2 Simulation Procedure
9. Press OK and the structure will be simulated. The simulation progress window shows the
progress of the simulation. It will only take a couple of seconds for the simulation to finish.
After the simulation is completed, IE3D automatically invoked MODUA and shows the S
parameters of the simulated structure. MODUA is a separate program that comes with the
IE3D package. This program is used to post process the S-parameters of the simulated
structure.

CHAPTER 5
RESULT AND DISCUSSION

Circular shape proximity feed microstrip antenna

Circular shape proximity feed microstrip antenna

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