Project Report

CHAPTER 1

INTRODUCTION TOANTENNA

1.1. HISTORY

The first radio antenna were built by Henrich Hertz, a professor at Technical institute in Karlsruhe, Germany. In 1886, he assembled apparatus we would now described as a complete radio system operating at meter wavelength with an end loop dipole as the transmitter and resonant square loop antenna as receiver. Guglielmo Marconi of Cologne, Italy went on to adding running circuits, big antenna and ground system for longer wavelength, and was able.to signal over large distances. In mid-December 1901, he startled the world by receiving signal at St. Johns, Newfoundland, from a transmitting station he had constructed at Likening in Cornwall, England.

1.2. INTRODUCTION “An antenna (or aerial) is a transducer designed to transmit or receive electromagnetic waves.”

In other words, an antenna converts electromagnetic energy into electric currentsor vice versa. An antenna is considered as a region of transition between a transmission line and space. Antennas radiate/couple/concentrate/direct electromagnetic energy in the desired direction. An antenna may be anisotropic (non directional) or anisotropic(directional). While choosing an antenna, many electric, mechanical and structural aspects are to be taken into account. Still high efficiency and high gain are the basics requirements for transmitting antenna, whereas low side lobe and large SNR are the key selection criteria for receiving antenna. . Antennas are used in systems such as radio and television broadcasting, point-to-point radio communication, wireless LAN, cell phones, radar, and spacecraft communication. Antennas are most commonly employed in air or outer space, but can also be operated under water or even through soil and rock at certain frequencies for short distances. The transmitter antenna produces an electromegnetic energy caused by alternating current flowing through it while in reciever antenna, opposite is happened, an electromagnetic energy from another sources causes induction of alternating induction current. The current and voltage distribution on a half-wave Hertz antenna is shown in fig.1.1 A wire is cut into half and is connected to the high frequency alternating current generator so that the frequency of the generator is each half of wire is one-quarter wavelength of the output. A law of physics states that like charges repel each other. Consequently, electrons will flow away from the negative terminal as far as possible while the positive terminal will attract electrons. View B of Fig.1.1 shows the direction and distribution of electron flow. The distribution curve shows that most current flows in the center and none flows at the ends.

1 | P a g e

Fig.1.1 Current and Voltage distribution on an antenna

The current distribution over the antenna is always the same, regardless of how much or how little current is flowing. However, current at any given point on the antenna will vary directly with the amount of voltage that the generator develops. One-quarter cycle after the electrons begin to flow, the generator develops it; minimum voltage and the current decreases to zero. At that moment, the condition shown in view C of Fig1.1 will exist. Although no current is flowing, a minimum number of electrons are at the left end of the line and a minimum number are at the right end. The charge distribution along the wire varies as the voltage of the generator varies (view C).

1.3.PARAMETER

1.3.A. Radiation pattern

Radiation pattern of an antenna is the graphical representation of the distribution of power as a function of direction angles from the antenna.

2 | P a g e

It is defined for large distance from the antenna,where the spatial (angular) distribution of the radiated power does not depend on the distance from the radiation source.

It is independent on the power flow direction: it isthe same when the antenna is used to transmit and when it is used to receive radiowaves.

It is usually different for different frequencies and different polarizations of radio wave radiated/ received.

i) Isotropic pattern

In this pattern the energy by the antenna is radiated uniformly in all direction. Its radiation pattern is represented by a sphere whose center coincides with the location of the isotropic radiator.

i) Directional antenna pattern

Directional antenna are those antennas which radiates much more power in a particular or desired direction.

ii) Omnidirectional antenna pattern

An antenna, which has a non-directional pattern in a plane–It, is usually directional in other planes. An Omnidirectional pattern is then a special type of directional pattern.

Fig.1.2 Omnidirectional antenna radiation pattern

iii)Principal patterns

Principal patterns are the 2-D patterns of linearly polarized antennas, measured in 2 planes

1. The E-plane: a plane parallel to the E vector and containing the direction of maximum radiation,

3 | P a g e

2. The H-plane: a plane parallel to the H vector, orthogonal to the E-plane, and containing the direction of maximum radiation Property.

Fig1.3 Principal E & H plane patterns for a pyramidal horn antenna

Radiation Pattern lobes

iv) Radiation Pattern lobes:Pattern lobe is a portion of the radiation pattern with a local maximum Lobes are classified as: major, minor, side lobes, back lobes.

Fig.1.4 Radiation pattern lobe of a directional antenna

4 | P a g e

Fig1.5 Linear plot of power pattern and its associated lobes and beamwidths

1.3.B. Directivity

Directivity is the characteristics of an antenna which allow it to transmit or receive the signal in or from particular direction.Reception of the signal at the reciever antenna can be improved by the directional antenna. Horizontal half-wave antennas accept radio signals from all directions, with the strongest reception being received in a line perpendicular to the antenna (broadside), and the weakest reception being received from the direction of the antenna's ends. Directional antenna radiates much more energy in the desired direction and reduces much energy from the undesired direction.

1.3.C. Gain

Gain is defined as the increase in signal strength as signal is processed by the antenna for a given incident angle. Gain can also be defined as

“ The ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions. “Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi).

G ≈ η (4π/λ2)Ap …..(1.1)where

η – efficiency of the antenna

5 | P a g e

λ – wavelength in metersAp – the physical area of the aperture in m2

1.3.D.Beamwidth

Beamwidth is that frequency range over which antenna operates.

i) Half-power beamwidth (HPBW)It is the angle between two vectors from the pattern’s origin to the points of the major lobe where the radiation intensity is half of its maximum.

i) First-null beamwidth (FNBW) It is the angle between two vectors, originating at the pattern’s origin and tangent to the main beam at its base.

FNBW≈ 2(HPBW) …..(1.2)

1.3.E. Effective Apperture

Effective apperture is that physical part (area) of the antenna which actually remains in contact with the electromagnetic energy being transmitted or received.

Aeff = (λ2 G)/4π ….(1.3)Where

G = Gain of the antennaλ = wavelength

1.3.F. Efficiency

Efficiency of an antenna is defined as the ratio of power radiated in air by antenna to the power absorbed by the antenna terminals. This absorbed power is then lost in form of heat.The efficiency is given by

η=ηradηap (1.4)

Radiation efficiency (ηrad) is a measure of the total power radiated by the antenna (transmitted or received) as compared to the power fed into the antenna. For many antennas this value is close to 1.Aperture efficiency (ηap ) is a ratio of the effective aperture area (Ae) and the physical aperture area (Ap). It is a function of the electric field distribution over the aperture. For many antennas this value is close to 0.5

ηap = Ae/ Ap ….(1.5)1.3.G.Polarization

6 | P a g e

The polarization of an antenna is the orientation of the electric field (E-plane) of the radio wave with respect to the Earth's surface and is determined by the physical structure of the antenna and by its orientation. Thus a single wire antenna may have no polarization when mounted vertically and have different polarization when mounted horizontally. Polarization is the sum of the E-plane orientations over time projected onto an imaginary plane perpendicular to the direction of motion of the radio wave. In the most general case, polarization is elliptical, meaning that the polarization of the radio waves varies over time. There are two special type of polarization

i) Linear polarization

In linear polarization, the antenna compels the electric field of the emitted radio wave to a particular orientation. Depending on the orientation of the antenna mounting, the usual linear cases are horizontal and vertical polarization.

ii) Circular polarization

the antenna compels the electric field of the emitted radio wave to a particular orientation. Depending on the orientation of the antenna mounting, the usual linear cases are horizontal and vertical polarization.

1.4. TYPES OF ANTENNAS

Several classes of antennas have been developed over the years to be used at the different frequency ranges, and in different areas of applications. The different types of antennas are:

1.4.A.Wire Antennas

These are typical examples of wire antennas, which can be found in many applications such as on cars, buildings, ships,..etc.

(a) Dipole (b) Circular loop

7 | P a g e

(c) HelixFig 1.6 Wire antenna configurations

1.4.B. Aperture Antennas

Aperture antennas became very popular due to the increase in frequency range of operation in the microwave range. Typical aperture antennas are the horn, the slot , and the open-ended waveguide.

(a) Rectangular horn antenna (b) Cylindrical horn antenna

(a) Rectangular Waveguide

Fig 1.7 Aperture antenna configurations

1.4.C. Microstrip Antennas

Microstrip antennas became very popular in the last few decades. This is due to the advance of space explorations. They have the advantages of being conformal, low profile, easy and cheap to manufacture.

8 | P a g e

(a) Rectangular

(b) Circular

Fig 1.8 Rectangular & Circular Patch Antenna

1.4.D. Array Antennas

Many applications require radiation characteristics that may not be available by a single element. In this case, it is possible to use a collection of antenna elements in the form of an antenna array, to achieve the required radiation characteristics. The antenna elements may be similar or dissimilar.

9 | P a g e

(a) Yagi Uda Array (b)Aperture Array

(c) Microstrip Antenna (d) Slotted Waveguide Array

Fig 1.9 Typical Wire, Aperture & Microstrip Array Configuration

1.4.E. Reflector Antennas

The need to communicate over great distances, such as the case of space exploration and satellite communication, resulted in the development of reflector antennas. The most common reflector antenna is the parabolic reflector shown.

(a) Parabolic Reflector with front feed

10 | P a g e

(b) Parabolic Reflector with Cassegrain Feed

(c) Corner Reflector

Fig 1.10 Typical Reflector Configurations

1.4.F. Lens Antennas

Lens antennas are used to collimate incident divergent energy to prevent it from spreading in undesired directions. Lens antennas help transforming of divergent energy to plane waves. They can be used in the same applications as reflector antennas at high frequencies. Their sizes become very large at lower frequencies.

(a) Lens Antennas with index of refraction n > 1

11 | P a g e

(b) Lens Antenna with index of refraction n < 1

Fig 1.11 Typical Lens Antenna configuration

12 | P a g e

CHAPTER 2

MICROSTRIP PATCH ANTENNA

2.1 Introduction

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board. Microstrip antennas are becoming very widespread within the mobile phone market. Patch antennas are low cost, have a low profile and are easily fabricated.

Consider the microstrip antenna shown in Figure 2.1, fed by a microstrip transmission line. The patch antenna, microstrip transmission line and ground plane are made of high conductivity metal (typically copper). The patch is of length L, width W, and sitting on top of a substrate (some dielectric circuit board) of thickness h with permittivityε r. The thickness of the ground plane or of the microstrip is not critically important. Typically the height h is much smaller than the wavelength of operation, but not much smaller than 0.05 of a wavelength.

The frequency of operation of the patch antenna of Figure 1 is determined by the length L. The center frequency will be approximately given by:

f c ≈ c

2 L √ εr= 1

2L √ ε0 εr μ0 …….. (2.1)

13 | P a g e

Figure 2.1: Top view of patch anteena

2.2 BASIC CHARACTERSTICS

Microstrip antennas as shown in fig 2.1, consist of a very thin (t<<λo ) metallic strip (patch) placed a small fraction of a wavelength (h<< λo usually 0.003 λo ≤ h ≤ 0.05 λo) above a ground plane. The microstrip antenna is designed so its pattern is normal to the patch. This is accomplished by properly choosing the mode (field configuration) of excitation beneath the patch. End fire radiation can also be accomplished by judicious mode selection. For a rectangular patch, the length of the element is usually λ o/3 < L < λo/2. The strip (patch) and the ground plane are separated by a dielectric sheet (referred to as a substrate) as shown in fig2.1. There are numerous substrate that can be used for the design of microstrip antennas, and their dielectric constants are usually in the range of 2.2≤ εr ≤ 12. The once that are most desirable for antenna performance are thick substrates whose dielectric constant is in the lower range because they provide better efficiency, larger bandwidth, loosely bound fields for radiation in space but at the expense of larger element size. Thin substrates with larger dielectric constants are desirable for microwave circuitry because they require tightly bound fields to minimize undesired radiations and coupling, and lead to smaller elemental sizes, however, because of their greater losses; they are less efficient and have relatively smaller bandwidths. Since microstrip antennas are often integrated with other microwave circuitry, a compromise has to be reached between good antenna performance and circuit design.

Fig 2.2. Microstrip Antenna.

2.3 ADVANTAGES OF MICROSTRIP ANTENNA

1. Low profile (can even be conformal to planar and nonplanar surfaces)2. Simple and inexpensive to manufacture using modern printed circuit technology.

(use etching and photolithography)3. Mechanically robust when mounted on rigid surfaces.4. Compatible with MMIC designs.5. When the particular patch shape and moderate are selected they are very versatile

in terms of resonant frequency, polarization, pattern and impedance.6. Easy to feed (coaxial cable, microstrip line etc.)7. Easy to use in array or incorporate with other microstrip circuit elements. 8. Patterns are somewhat hemispherical, with a moderate directivity (about 6-8 dB)

14 | P a g e

2.4 DISADVANTAGES OF MICROSTRIP ANTENNA

1. Efficiency may be lower than with other antennas. Efficiency is limited by conductor and dielectric losses, and by surface wave losses.

2. Low bandwidth (but can be improved by variety of techniques). Bandwidth of few percentages is typical.

3. Poor polarization purity, Poor scan performance.4. Spurious feed radiations, low power, and higher quality factor.

2.5 DIFFERENT TYPES OF PATCHES

Often microstrip antennas are also referred to as patch antennas. The radiating element and feed lines usually photo etched on the dielectric substrate. The radiating patch may be square, rectangular, thin strip, circular, elliptical, triangular or any other configuration. These and others are illustrated in fig 2.2.

Fig 2.3 Types of Patches

Square, rectangular, dipole, and circular are the most common because of ease of analysis and fabrication, and their attractive radiation characteristics, especially low cross polarization radiation. Microstrip dipoles are attractive because they inherently process a large bandwidth and occupy less space, which makes them attractive for arrays. Linear and circular polarization is achieved with either single elements or array of microstrip antennas. Arrays of microstrip elements, with single or multiple feeds, may also be used to introduce scanning capabilities and achieve greater directivities.

2.6 FEEDING METHODS

There are many configurations that can be used to feed microstrip antennas. The four most popular feedings are the microstrip line, coaxial probe, aperture coupling and proximity coupling. These are shown in fig.2.3. The microstrip line is also a conducting strip, usually of much smaller width compared to the patch. The microstrip line is easy to fabricate, simple to match by controlling the inset position and rather simple to model. However as

15 | P a g e

the substrate thickness increases surface waves and spurious feed radiations increases, which for practical design limit the bandwidth (typically 2-5%)Coaxial line feeds, where the inner conductor is connected to the ground plane, are also widely used. The coaxial probe feed is also easy to fabricate and match, and it has low spurious radiation. However, it also has narrow bandwidth and it is more difficult to model, especially for thick substrate (h > 0.02λ) Both the microstrip feed line and the probe posses inherent asymmetries which generates higher order modes which produce cross polarized radiations. To overcome some of these problems, non contacting aperture coupling feeds as shown in the fig.2.3, have been introduced. The aperture coupling is the most difficult of all four to fabricate and it also has narrow bandwidth. However it is somewhat easier to model and has moderate spurious radiation. The proximity coupling has the largest bandwidth (as high as 13%), is somewhat easy to model and has low spurious radiation. However its fabrication is somewhat more typical. The length of the feeding stub and the width-to-line ratio of the patch can be used to control the match.

16 | P a g e

(d) Proximity-coupled Feed

Fig.2.4 Typically Feeds for Microstrip Antenna

2.7 METHODS OF ANALYSIS

There are many methods of analysis for microstrip antennas. The most common models are the transmission line, cavity and full wave (which include primarly integral equations / Moment method). The transmission line model is the easiest of all, it gives good physical insight, but is less accurate and it is more difficult to model coupling.Compared to transmission line model, the cavity model is more accurate but at the same time more complex. However it also gives good physical insight and is rather difficult to model coupling, although it has been used successfully. In general when applied properly, the full wave models are accurate, very versatile, and can treat single elements, finite and infinite arrays, stacked elements, arbitrary shaped elements and coupling. However they are most complex models and usually give less physical insight.

2.8 PATCH ANTENNA PARAMETERS

i) Quality factor

The quality factor is a figure-of-merit that representative of the antenna losses. Typically there are radiation, conduction, dielectric and surface wave losses.

1

Qt= 1

Q rad+ 1

Q C+ 1

Q D+ 1

Q sw ….(2.1)

WhereQt = Total quality factorQrad. = Quality factor due to radiation (space wave) lossesQC = Quality factor due to conduction lossesQD = Quality factor due to dielectric lossesQsw= Quality factor due to surface waves

For very thin substrates h << of arbitrary shapes including rectangular, there approximate formulas to represent the quality factors of the various losses. These can be expressed as

Qc=h√ πfμσ ….(2.2)

17 | P a g e

Qd=1

tanδ ….(2.3)

Qrad=2ωεhGt /l

….(2.4)

Where tan δ is the loss tangent of the substrate material, ζ is the conductivity of the conductors associated with the patch and ground plane, G t

lis the total conductance per unit

length of the radiating aperture and k for rectangular microstrip antenna is L/4.The Qrad as represented by 2.4 is inversely proportional to the height of the substrates. A typical variation of the bandwidth for a Microstrip antenna as a function of the normalized height of the substrate, for two different substrates, is shown in Figure 2.4. It is evident that the 35 bandwidth increases as the substrate height increases. However, the radiation efficiency of the patch antenna described by the ratio of power radiated over the input power (3.6) decreases as normalized height of the substrate increased.

η= QtQrad

….(2.5)

Fig.2.5 Efficiency and bandwidth versus substrate height at constant resonant frequency for Rectangular Microstrip patch for two different substrates.

ii) Bandwidth

The bandwidth is inversely proportional to the square root of the dielectric constant of the substrate. A typical variation of the bandwidth for a microstrip antenna as a function of the normalized height of the substrate, for two different substrates is shown in fig.2.4. It is evident that the bandwidth increases as the substrate height increases.

BW = 1/√εr ….(2.6)

18 | P a g e

The bandwidth of an antenna is defined as the range of frequency within the performance of the antenna. In other words, characteristics of antenna (gain, radiation pattern, terminal impedance) have acceptable values within the bandwidth limits. For most antennas, gain and radiation pattern do not change as rapidly with frequency as the terminal impedance does. Since the transmission line characteristic impedance hardly changes with frequency, VSWR is a useful, practical way to describe the effects of terminal impedance and to specify an antenna‟s bandwidth. For broadband antennas, the bandwidth is usually expressed as the ratio of the upper to lower frequencies of acceptable operation. However, for narrowband antennas, the bandwidth is expressed as a percentage of the bandwidth.

iii) Input impedance

There are three different kinds of impedance relevant to antennas. One is the terminal impedance of the antenna, another is the characteristic impedance of a transmission line, and the third is wave impedance. Terminal impedance is defined as the ratio of voltage to current at the connections of the antenna (the point where the transmission line is connected). The complex form of Ohm‟s law defines impedance as the ratio of voltage across a device to the current flowing through it. The most efficient coupling of energy between an antenna and its transmission line occurs when the characteristic impedance of the transmission line and the terminal impedance of the antenna are the same and have no reactive component. When this is the case, the antenna is considered to be matched to the line. The input impedance of patch antenna is in general complex and it includes resonant and non-resonant part. Both real and imaginary parts of the impedance vary as a function of frequency. Ideally, both the resistance and reactance exhibit symmetry about the resonant frequency as shown in Figure 2.5. Typically, the feed reactance is very small, compared to the resonant resistance for thin substrates.

Fig 2.6 Typical variation of resistance and reactance of a rectangular microstrip antenna.

19 | P a g e

iv) Antenna Polarization

The term polarization has several meanings. In a strict sense, it is the orientation of the electric field vector E at some point in space. If the E-field vector retains its orientation at each point in space, then the polarization is linear; if it rotates as the wave travels in space, then the polarization is circular or elliptical. In most cases, the radiated-wave polarization is linear and either vertical or horizontal. At sufficiently large distances from an antenna, beyond 10 wavelengths, the radiated, far-field wave is a plane wave.

v) Gain and Directivity

The gain of an antenna is the radiation intensity in a given direction divided by the radiation intensity that would be obtained if the antenna radiated all of the power delivered equally to all directions. The definition of gain requires the concept of an isotropic radiator; that is, one that radiates the same power in all directions. Nevertheless, the isotropic antenna is very important as a reference. It has a gain of unity (g = 1 or G = 0 dB) in all directions, since all of the power delivered to it is radiated equally well in all directions.

The gain of an antenna is usually expressed in decibels (dB). When the gain is referenced to the isotropic radiator, the units are expressed as dBi; but when referenced to the half-wave dipole, the units are expressed as dBd.

Directivity is the same as gain, but with one difference. It does not include the effects of power lost (inefficiency) in the antenna. If an antenna were lossless (100 % efficient), then the gain and directivity (in a given direction) would be the same.

2.9. Transmission line model

Basically the transmission line model represents the microstrip antenna by two slots, separated by a low impedance Zc transmission line of length L.

2.9.1. Fringing effects

Because the dimensions of the patch are finite along the length and width, the fields at the edges of the patch undergo fringing. The amount of fringing is the function of the dimensions of the patch and the height of the substrate. For the principle E plane (xy plane) fringing is a function of the ratio of the length of the patch L to the height h of the substrate (L/h) and the dielectric constant εr of the substrate. Since for microstrip antennas L/h » 1, fringing is reduced, however it must be taken into account because it influences the resonant frequency of the antenna. For a microstrip line shown in fig 3.1, typical electric field lines are also shown. This is a non homogeneous of two dielectrics, typically the substrate and the air. As can be seen, most of the electric field lines reside in the substrate and the parts of some lines exists in air. As L/h » 1 and εr » 1,the electric field lines concentrate mostly in the substrate.

20 | P a g e

Fringing in this case makes the microstrip look wider electrically compared to its physical dimensions. Since some of the waves travel in the substrate and some in the air, an effective dielectric constant εreff is introduced to account for fringing and the wave propagation in the line.To introduce effective dielectric constant, let us assume that the center conductor of the microstrip line with its original dimensions and height above the ground plane is embedded into one dielectric as shown in fig.3.1. The effective dielectric constant is defined as the dielectric constant of the uniform dielectric material so that the line of fig3.1c has identical electrical characteristics, particularly propagation constant, as the actual line of fig.3.1.a. For a line with air above the substrate, the effective dielectric constant has values in the range of 1< εreff < εr . For most applications where the dielectric constant of the substrate is much greater than unity (εr > 1), the values of εreff will be closer to the actual dielectric constant εr of the substrate. The effective dielectric constant is also a function of frequency. As the frequency of operation increases, most of the electric field lines concentrate in the substrate. Therefore the microstrip line behaves more like a homogeneous line of one dielectric (only the substrate), and the effective dielectric constant approaches the value of dielectric constant of the substrate.

Fig.2.7. Microstrip Line and its effective field lines and effective dielectric constant

For low frequencies the effective dielectric constant is essentially constant at indeterminate frequencies its values begin to monotonically increase and eventually approaches the values of the dielectric constant of the substrate. The initial values (at low frequencies) of the effective dielectric constant are referred to as the static values, and the are given by

21 | P a g e

Wh > 1 ….(2.7)

∈reff=∈r+1

2+∈r−1

2⌊1+12 h

W⌋

−12 ….(2.8)

Fig.2.8. Effective length, Resonant frequency, and Effective width

Because of the fringing effect electrically the patch of the microstrip antenna looks greater then its physical dimensions. For the principal E plane (xy plane), this is demonstrated in fig3.2a where the dimension of the patch along its lengths have been extended on each end by a distance ∆L, which is a function of the effective dielectric constant ε reff and the width to height ratio (W/h). A very popular and practical approximate relation for the normalized extention of the length is

∆ Lh

=0.412(∈reff +0.33 )(W

h+0.264)

(∈reff−0.258 )(Wh

+0.8) ….(2.9)

Since the length of the patch has been extended by ∆L on each side, the effective

length of the patch is now

Leff = L + 2∆L …. (2.10)

Therefore, for єr = 4.4, h= 1.6mm, fr =3GHz the calculated patch was 20.3 x 22.2mm.

2.9.2. Effective length(∆L), effective width(W) and resonant frequency

22 | P a g e

Because of fringing effect, the electrical dimension of the patch increases as compared to its physical dimension as shown in fig 2.8

Fig2.9. Actual and effective length of the patch antenna

Where the length of the patch increases on each side by a distance of ∆L, which is the function of effective dielectric constant and width to height ratio. The relationship between them is given by the equation

∆ Lh =0.412[ ( εreff +0.3 )( W

h +0.264)( εreff−0.258 )(W

h +0.8) ]Since the length of the patch is increased by ∆ L, hence effective length is given by

Leff =L+2∆ L

For the dominant TM 010 mode, the resonant frequency of the microstrip antenna is a function of its length. Usually it is given by

( f r )010 = c

2 L√εr ….(2.11)

23 | P a g e

2.9.3. Design

The procedure assumes that the specified information includes the dielectric constant of the substrate (ε r), the resonant frequency (f r) , and the height of the substrate h. The procedure is as follows:Specify:

ε r, f r (in Hz) and h

Determine:W, L

Design procedure:

Step1: For an efficient radiator, a practical width that leads to good radiation efficiencies is

W = c2 f r √ 2

εr+1

Step 2: Determine the effective dielectric constant of the microstrip antenna using

ε reff = εr+1

2+( εr−1

2 )(√(1+12 hW ))

Step 3: Once W is found, determine the extension of the length ∆ L

∆ Lh =0.412[ ( εreff +0.3 )(W

h +0.264)( εreff−0.258 )( W

h +0.8) ]Step 4: The actual length of the patch can now be determined by solving equation given

below for L

L = ( c2 f r √ε eff

) - 2∆ L

.

24 | P a g e

CHAPTER 3

SIMULATION SOFTWARE FEKO

3.1. INTRODUCTION

FEKO is a software product developed by EM Software & Systems - S.A. (Pty) Ltd. for the simulation of electromagnetic fields. The name is derived from a German acronym which can be translated as "Field Calculations for Bodies with Arbitrary Surface". FEKO is a comprehensive electromagnetic simulation software tool, based on state of the art computational electromagnetics (CEM) techniques. It enables users to solve a wide range of electromagnetic problems.

The software is based on the Method of Moments (MoM) integral formulation of Maxwell's equations. It uses two methods for field calculation, these methods are MoM (method of moment) and FEM (finite element method). Typical applications include:

Antennas: analysis of horns, microstrip patches, wire antennas, reflector antennas, conformal antennas, broadband antennas, arrays

Antenna placement: analysis of antenna radiation patterns, radiation hazard zones, etc. with an antenna placed on a large structure, e.g. ship, aircraft, armoured car

EMC: analysis of diverse EMC problems including shielding effectiveness of an enclosure, cable coupling analysis in complex environments, e.g. wiring in a car, radiation hazard analysis

Bio-electromagnetics: analysis of homogeneous or non-homogeneous bodies, SAR extraction

RF components: analysis of waveguide structures, e.g. filter, slotted antennas, directional couplers

3D EM circuits: analysis of microstrip filters, couplers, inductors, etc. Radomes: analysis of multiple dielectric layers in a large structure Scattering problems: RCS analysis of large and small structures

25 | P a g e

3.2. NUMERICAL METHODS

FEKO is based on the Method of Moments (MoM) and was the first commercial EM simulation software to utilise the multi-level fast multipole method (MLFMM) for the solution of electrically large problems when it was released with Suite 4.2 in June 2004. In FEKO, the MoM is hybridised with the following solution techniques:

Finite Element Method (FEM) Method of Moments (MoM) Multi-level Fast Multipole Method (MLFMM) Physical Optics (PO)

This hybridization implies that these solution techniques can be applied to different parts of the same model to optimize the solution time and results.

3.3. FINITE ELEMENT METHOD (FEM)

FINITE ELEMENT METHOD (FEM) / MoM where a FEM region is bounded with an integral equation based boundary condition to ensure full coupling between the FEM and MoM solution areas of the problem.

The FEM (its practical application often known as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler’s method, Runge-Kutta, etc.

The FEM is applicable to the odeling of electrically large or inhomogeneous dielectric bodies, which are not efficiently solvable with FEKO’s extensions to the MoM. The FEM is a volume meshing technique that employs odelingti to accurately mesh arbitrarily shaped volumes where the dielectric properties may vary between neighbouring odelingti.

The FEM/MoM odelingtion features full coupling between metallic wires and surfaces in the MoM region and heterogeneous dielectric bodies in the FEM region. The MoM part of the solution is calculated first, which results in equivalent magnetic and electric currents that form the radiation boundary of the FEM region. This hybrid technique makes use of the strengths of both the MoM and the FEM in the following ways:

The MoM is used for the efficient odeling of open boundary radiating structures where no 3D space discretisation is required.

The FEM is used for the efficient odeling of inhomogeneous dielectric bodies in term of field distributions inside the volume.

26 | P a g e

The FEM region may include complex surfaces, including:

Metallic surfaces where a skin effect is significant. Thin dielectric sheets. Metallic surfaces with a finite surface impedance. Metallic surfaces with an electrically thin surface coating.

TYPICAL APPLICATION OF THE FEM

Typical applications of the FEM/MoM and FEM/MLFMM hybrid methods include antenna simulations, radiation hazard investigations where humans interact with RF equipment, the modelling of waveguide filters with dielectric blocks in the filter and the modelling of microstrip patches on finite substrates.

3.4. METHOD OF MOMENT (MoM)

The MoM is applicable to problems involving currents on metallic and dielectric structures and radiation in free space. The MoM is a full wave solution of Maxwell's integral equations in the frequency domain. An advantage of the MoM is that it is a "source method" meaning that only the structure considered is discretised, not free space as with "field methods". Boundary conditions do not have to be set and memory requirements scale proportional to the size of the geometry in question and the required solution frequency.

Structure is decomposed into segments (i.e. Meshing). The MoM calculate the currents on each segment, or the strength of each moment,

by using a coupling Green’s function.

Moment= electrical size of segment i.e. current times the segment vector

Green’s function incorporates electrostatic coupling between the consecutive moments.

If the current distribution over space is known the charge build up at each point of structure can be calculated.

In order to enable the modeling of dielectric and magnetic bodies some of the extensions are added to the MoM

3.4.1. Surface Equivalence Principle (SEP)

27 | P a g e

The SEP introduces equivalent electric and magnetic currents on the surface of a closed dielectric body. The surface of such bodies can be arbitrarily shaped and is discretised using triangles.

Fig.3.1. Surface Equivalence Principle (Surface Mesh)

3.4.2. Volume Equivalence Principle (VEP)

The VEP allows the creation of arbitrarily shaped dielectric bodies using tetrahedral volume elements. More basis functions are typically required than for the SEP, but neighboring tetrahedra may have differing electric and magnetic properties.

Fig.3.2. Volume equivalence principle

3.5. MULTI-LEVEL FAST MULTIPOLE METHOD (MLFMM)

The MLFMM is an alternative formulation of the technology behind the MoM and is applicable to much larger structures than the MoM, making full-wave current-based solutions of electrically large structures a possibility. This fact implies that it can be applied to most large models that were previously treated with the MoM without having to change the mesh.

The MLFMM differs from the MoM in that it groups basis functions and computes the interaction between groups of basis functions, rather than between individual basis functions. The MoM treats each of the N basis functions in isolation, thus resulting in an N2 scaling of memory requirements (to store the impedance matrix) and N3 in CPU-time (to solve the linear set of equations). It is thus clear that processing requirements for MoM

28 | P a g e

solutions scale rapidly with increasing problem size. The MLFMM formulation's more efficient treatment of the same problem results in N.log(N) scaling in memory and N.log(N).log(N) in CPU time. In real applications this reduction in solution requirements can range to orders of magnitude.

TYPICAL APPLICATION OF THE MLFMM

Possible applications of the MLFMM span a wide range of problems. It is best suited to problems that include electrically large structures, e.g. antenna coupling on ships, antenna placement on aircraft and radiation hazard analysis behind a reflector antenna. The MLFMM is a very efficient solution for full-wave RCS computation and employs smart initialization methods to speed up convergence for monostatic RCS simulations.

3.6. PHYSICAL OPTICS (PO)

PO is formulated for use in instances where electrically very large metallic or dielectric structures are modelled. PO is an asymptotic high frequency numerical method of the same nature as the UTD, but is based on currents and not rays. When the MLFMM fails to resolve the problem then user moves to the PO.

FEKO hybridises the current based accurate MoM with PO in the truest sense of the word with the bidirectional coupling between the MoM and PO being maintained in the solution, i.e. modification of the interaction matrix, ensuring accuracy. A practical example would be the calculate the effect on the input impedance of a horn antenna, treated with the MoM, when in close proximity to a large structure treated with the PO. FEKO triangulates a PO region, exactly the same as it would for a MoM solution, making it a simple task to switch between solution options.

FEKO implements a number of extensions to the PO:

Fock currents to account for the effect of creeping waves over the shadow boundary region into "unlit" areas.

Correction terms to achieve more accurate current representation close to edges and wedges.

Large element PO (LE-PO): this is an alternative set of basis functions for the PO, based on plane wave functions. LE-PO does not support multiple reflections, but allows mesh sizes of multiple wavelengths. This leads to dramatic computational cost savings relative to standard PO, in cases where LE-PO is applicable.

29 | P a g e

TYPICAL APPLICATION OF THE POA typical example of how the MoM/PO hybridisation can be employed with good effect is in the analysis of reflector antennas. A large reflector antenna may be too large to analyse with the MLFMM, in which case a combination of MoM and PO is the ideal solution. The feed structure will typically be modelled with the MoM to achieve high accuracy in the currents on this part of the structure, with the reflector itself being modelled with the PO. In such a case, both the standard and large element PO will be suitable. Note that modal waveguide ports may be used in the MoM region of a hybrid MoM/PO analysis, enabling FEKO to deal very efficiently with horn feeds.

Fig. 3.3. PO modelling of a reflector antenna with MoM modellingof the feed

30 | P a g e

CHAPTER 4MICROSTRIP PATCH ANTENNA DESIGN AND

RESULT

Our objective is to design a co-axial feed patch antenna that resonates at 3.5 GHz and then vary the parameters of the antenna such that the working of the patch is optimized. We divided the simulations into three basic groups-

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

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

3) We also varied the permittivity of the dielectric and observed its effects on the performance of the patch.

4.1. Design Specifications

The three essential parameters for the design of a rectangular Microstrip Patch Antenna:

Frequency of operation (fo): The resonant frequency of the antenna must be selectedappropriately. The resonant frequency selected for my design is 3.5 GHz.

Dielectric constant of the substrate (εr): A substrate with a high dielectric constant hasbeen selected since it reduces the dimensions of the antenna. The dielectric constant for our project is 2.4.

Height of dielectric substrate (h): For the microstrip patch antenna to be used in cellularphones, it is essential that the antenna is not bulky. Hence, the height of the dielectric substrate is selected as 1.58 mm.

Hence the essential parameters for the rectangular patch antenna are

Hence, the essential parameters for the design are:

31 | P a g e

fo = 3.5 GHz ε r = 2.4 h = 1.58 mm

4.2. Design procedure

Step 1: Calculation of the width (W):

W =V o

2 f r √ 2εr+1

= 3× 108

2× 3.5× 109 √ 22.4+1

= 0.032869928

=32.8699mm or 32.87mm ….(4.1)

Step 2: Calculation of effective dielectric constant (ε reff)

ε reff = εr+1

2+(

εr−12

)(√(1+12 hW ))

= 2.4+12

+( 2.4−12

)(√(1+12 × 1.5832.87 ))

= 2.257 or 2.26 ….(4.2)

Step 3: Calculation of effective length (∆ L)

∆ Lh =0.412[ ( εreff +0.3 )(W

h +0.264)( εreff−0.258 )( W

h +0.8) ] ∆ L

h =0.412[ (2.26+0.3 )( 32.871.58 +0.264)

(2.26−0.258 )( 32.871.58 +0.8) ]

∆ Lh = 0.5137

∆ L = 0.5137 ×1.5832 | P a g e

∆ L = 0.812 ×10−3 mm ….(4.3)

Step 4: Calculation of length (L)

L = ( c2 f r √ε eff

) - 2∆ L

L = ( 3× 108

2× 3.5 ×109 √2.26 ) - 2×(0.812 ×10−3)

L = 26.88 mm ….(4.4) Step 5: Calculation of wavelength (λ)

λ = co

f √εr

λ = 3 × 108

3.5× 109 √2.26

λ = 57.016 mm ….(4.5)

Step 6: Calculation of substrate length

Ls = 6h + L

Ls = 6×1.588 + 26.88

Ls = 36.36mm ….(4.6)

Step 7: Calculation of substrate of width

W s = 6h + W

W s = 6×1.588+32.87

W s = 42.35mm ….(4.7)

33 | P a g e

4.3 Steps for patch antenna designing

Step 1: Entering desired frequency

Fig.4.1. window to enter the desired frequency

Step 2: Entering dielectric medium properties

34 | P a g e

Fig.4.2. window to enter the dielectric medium properties

Step 3: Entering desired height of the patch

(a)

35 | P a g e

(b)Fig.4.3. windows to enter the desired height

Step 4: Entering the calculated width of patch

Fig.4.4. window to enter the calculated width

Step 5: Entering the calculated length of patch

36 | P a g e

Fig.4.5. window to enter the calculated length of patch

Step 6: Entering the calculated length of substrate(ls)

Fig.4.6. window to enter the calculates length of substrate

37 | P a g e

Step 7: Entering the calculated width of substrate (Ws)

Fig.4.7. window to enter the calculated width of substrate

Step8: Providing coordinates and dimension for the substrate

Fig.4.8. window to enter the coordinates and dimension for the substrate

38 | P a g e

Step9: providing coordinates and dimension for the patch

Fig.4.9. window to enter the coordinates and dimension for the patch

Step10: Providing coordinates and dimension for transmission line feed

Fig.4.10. window to place the transmission line feed

Step11: Creating wire port

39 | P a g e

Fig.4.11.window to create the wire port

Step12: Providing the selective range of frequency

(a)

40 | P a g e

(b)Fig.4.12. window to enter the selective range of frequency

Step13: Entering the selective range of voltage

Fig.4.13. window to enter the selective range of voltage

41 | P a g e

Step14: Meshing of the patch antenna

Fig.4.14.Meshing of the patch antenna

Step14: Far field selection (Either horizontal or Vertical)

Fig.4.15. (a) Horizontal Far field selection window

42 | P a g e

Fig.4.15. (b) Vertical far field selection window

CHAPTER 5

SIMULATION RESULTS

5.1 Return lossThe return loss is simply the amount of power that is "lost" to the load and does not return

as a reflection. Clearly, high return loss is usually desired even though "loss" has negative

connotations. Return loss is commonly expressed in decibels. If one-half of the power

does not reflect from the load, the return loss is 3 dB.

Return loss is a convenient way to characterize the input and output of signal sources.fig

6.2 shows the obtained return loss value which is -16 dB at 3.368 GHz. patch antenna with

-10dB return loss is considered as good patch antenna .

43 | P a g e

Fig 5.1 Reflection Coefficient Vs Frequency

5.2. VSWR(voltage standing wave ratio)

Standing wave ratio (SWR) is the ratio of the amplitude of a partial standing wave at an antinode (maximum) to the amplitude at an adjacent node (minimum), in an electrical transmission line.

The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing wave ratio. For example, the VSWR value 1.2:1 denotes a maximum standing wave amplitude that is 1.2 times greater than the minimum standing wave value

The most common case for measuring and examining SWR is when installing and tuning transmitting antennas. When a transmitter is connected to an antenna by a feed line, the impedance of the antenna and feed line must match exactly for maximum energy transfer from the feed line to the antenna to be possible. The impedance of the antenna varies based on many factors including: the antenna's natural resonance at the frequency being transmitted, the antenna's height above the ground, and the size of the conductors used to construct the antenna.

When an antenna and feedline do not have matching impedances, some of the electrical energy cannot be transferred from the feedline to the antenna. Energy not transferred to the antenna is reflected back towards the transmitter. It is the interaction of these reflected waves with forward waves which causes standing wave patterns. Reflected power has three main implications in radio transmitters. Radio Frequency (RF) energy losses increase, distortion on transmitter due to reflected power from load and damage to the transmitter can occur.fig 5.2 shows the variation of VSWR in dB w.r.t frequency whereas fig 5.3 shows the variation of VSWR in ohm’s w.r.t.frequency

44 | P a g e

0

5

10

15

20

25

30

35

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

VS

WR

[dB

]

Frequency [GHz]

Excitation

VSWR [dB] - rinku

VoltageSource1

Fig 5.2 VSWR(dB) Vs Frequency

0

10

20

30

40

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

VS

WR

Frequency [GHz]

Excitation

VSWR - rinku

VoltageSource1

Fig 5.3 VSWR Vs Frequency

5.3. Impedance

45 | P a g e

Fig 5.4 shows the obtained impedance of a microstrip patch antenna as function of frequency

Fig 5.4 Impedance Vs Frequency

5.4. Radiation PatternThe patch's radiation at the fringing fields results in a certain farfield radiation pattern. This radiation pattern shows that the antenna radiates more power in a certain direction than another direction. The antenna is said to have certain directivity. This is commonly expressed in dB. An estimation of the expected directivity of a patch can be derived with ease. The fringing fields at the radiating edges can be viewed as two radiating slots placed above a ground plane. Assuming all radiation occurs in one half of the hemisphere, this results in a 3 dB directivity. This case is often described as a perfect front to back ratio; all radiation towards the front and no radiation towards the back. This front to back ratio is highly dependent on ground plane size and shape in practical cases. Another 3 dB can be added since there are 2 slots. The slots are typically taken to have a length equal to the impedance width (length according to the y axis) of the patch and a width equal to the substrate height. Such a slot typically has a gain of about 2 to 3 dB (c fr. simple dipole). This results in a total gain of 8 to 9 dB.The rectangular patch excited in its fundamental mode has a maximum directivity in the direction perpendicular to the patch (broadside). The directivity decreases when moving away from broadside towards lower elevations. The 3 dB beam width (or angular width) is twice the angle with respect to the angle of the maximum directivity, where this directivity has rolled off 3 dB with respect to the maximum directivity. A 3 D radiation pattern obtained is given below

46 | P a g e

Fig 5.5. 3D Radiation Pattern of Rectangular Patch Antenna in dBi

Fig 5.6.3D Radiation Pattern of Rectangular Patch Antenna in dBi

47 | P a g e

-6

-5

-4

-3

-2

-1

0

30

60

90120

150

180

210

240270

300

330

0

Far Field

Total Gain [dBi] (Frequency = 2.8 GHz; Theta = 90 deg) - rinku

HORIZONTAL

Fig 5.7. Polar Plot of Far Field in Horizontal direction

-4

-2

0

2

4

0

30

60

90

120

150180

210

240

270

300

3300

Far Field

Total Gain [dBi] (Frequency = 2.8 GHz; Phi = 0 deg) - rinku

VERTICAL

Fig 5.8. Polar Plot of Far Field in Vertical Direction

5.5. Power

Fig 5.5 shows the power(in dB) radiated by patch antenna with respect to frequency and from the figure it is clear that it offers maximum transmitted power at 3.38GHz

48 | P a g e

-12

-10

-8

-6

-4

-2

0

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Pow

er [d

B]

Frequency [GHz]

Excitation

Power [dB] - rinku

VoltageSource1

Fig 5.9. Power Vs Frequency

5.6. Current flow

Figure 5.10 shows the intensity of surface current flow

Fig 5.10 Surface current flow

49 | P a g e

CHAPTER 6

CONCLUSION AND FUTURE PROSPECT’S

Enhancement of Bandwidth and gain by varying Ws, Ls, R and Feed position. In this project the optimum feed point by using hit and trial method by using FEKO software has been found.From the simulation of patch antenna and the analysis of result shows that the following parameter-:1. Return loss is -16dB2. Bandwidth 410 MHz (-3dB Bandwidth)

The future scope of work revolves around optimization of the Microstrip Patch is partially realized.The investigation has been limited mostly to theoretical study due to lack of distributive computing platform. Detailed experimental studies can be taken up at a later stage to find out a design procedure for balanced amplifying antennas. The future scope of work also focuses on increasing the efficiency and decreasing the run time of the PSO code by using a distributive computing platform. Realization of results by the modified PSO would be concluded with the fabrication of the patch of the Microstrip Patch Antenna. Coverage of thesealternatives is beyond the scope of this article, but they should be considered during the

50 | P a g e

specification and development phases of the antenna.

REFERENCES

[1] Greig D.D, & Enlemann, H.F.,”Microstrip-A New Transmission Technique for the Kilomegacycle Range,”Proceedings of The IRE, 1952, Vol .40,No.10,pp.1644-1650.

[2] Deschamps G.A., “Microstrip Microwave Antennas”, The Third Symposium on The USAF Antenna Research & Development Program, University of Illinois, Monticello , Illinois, October 18-22,1953.

[3] Wu T.T, “Theory of the Microstrip”, Journal of Applied Physics, March, 1957, Vol. 28, No. 3, pp. 299-302.

[4] Wheeler H.A., “Transmission Line Properties of Parallel Strips Separated by a Dielectric Sheet”, IEEE Transactions on Microwave Theory of Techniques, Vol. MTT-13, pp 172-185, March 1965.

[5] Balanis, C.A., “Antenna Theory - Analysis and Design”, John Wiley & Sons, Inc 1997. 2nd edition pageno.24-78,722-752

[6] C. A. Balanis, “Advanced Engineering Electromagnetics”, New York, John Wiley and Sons, 1989.

[7] Garg, R., Bhartia, P., Bahl, I., Ittipiboon, “A., Microstrip Antenna Design Handbook”, Artech House, Inc, 2001.

51 | P a g e

[8] W.L. Stutzman, G.A. Thiele, Antenna Theory and design, John Wiley & Sons, 2nd Ed., New York, 1998.

[9] M. Amman, \Design of Rectangular Microstrip Patch Antennas for the 2.4 GHz Band", Applied Microwave & Wireless, pp. 24 - 34, November/December 1997.

[10] K.L. Wong, Design of Nonplanar Microstrip Antennas and Transmission Lines, John Wiley & Sons, New York,1999.

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

[12] Electromagnetic Waves and Radiating Systems – Edward C. Jordan and Keith G.

Balmain (2nd edn – PHI Publishers)

[13] https://www.feko.info/applications/antenna-analysis/microstrip-antennas

[14] https://www.mentor.com/electromagnetic-simulation/products/ie3d-si

[15] https://www.antenna-theory.com/antennas/patches/antenna.php

[16] https://www.feko.info/applications/white-papers/a-thin-low-profile-antenna-using-a- novel-high-impedance-ground-plane/a-thin-low-profile-antenna-using-a-novel-high-impedance-ground-plane

[17] Brian C. Wadell, Transmission Line Design Handbook, Artech House, Norwood, MA, 1991, ISBN: 0-89006-436-9.

[18] http://www.brothersoft.com/puff-download-34008.html

[19] W. F. Richards, Y. T. Lo, and D. D. Harrison, “An improved theory of microstrip antenna with applications,” IEEE Trans. Antennas and Propagation, vol. AP-29, pp, 38-46, Jan. 1981.

52 | P a g e