Design Of Rectangular Microstrip Patch Antenna Biology Essay

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In this project,method of moments based IE3D software is used to design a Microstrip Patch Antenna with enhanced gain.

The aim of the project is to design a rectangular Microstrip Patch Antenna with enhanced gain and bandwidth and study the effect of antenna dimensions Length (L) , Width (W) and substrate parameters relative Dielectric constant (εr) , substrate thickness on antenna gain and bandwidth.

The conducting patch can take any shape but rectangular and circular configurations are the most commonly used configuration. Other configurations are complex to analyze and require heavy numerical computations.

The length of the antenna is nearly half wavelength in the dielectric; it is a very critical parameter, which governs the resonant frequency of the antenna. In view of design, selection of the patch width and length are the major parameters along with the feed line depth.

Desired Patch antenna design is simulated by using IE3D simulator. And Patch antenna is realized as per design requirements.

Contents

CHAPTER 1

Introduction To Microstrip Patch Antenna

INTRODUCTION

Communication between humans was first by sound through voice. With the desire for slightly more distance communication came, devices such as drums, then, visual methods such as signal flags and smoke signals were used. These optical communication devices, of course, utilized the light portion of the electromagnetic spectrum. It has been only very recent in human history that the electromagnetic spectrum, outside the visible region, has been employed for communication, through the use of radio. One of humankind's greatest natural resources is the electromagnetic spectrum and the antenna has been instrumental in harnessing this resource.

1.1 Aim and Objectives

Microstrip patch antenna used to send onboard parameters of article to the ground while under operating conditions. The aim of the thesis is to design rectangular Microstrip Patch Antenna with enhanced gain and bandwidth and study the effect of antenna dimensions Length (L) , Width (W) and substrate parameters relative Dielectric constant (εr), substrate thickness (t) on the Radiation parameters of Bandwidth and Beam-width.

1.2 Antenna Characteristics

An antenna is a device that is made to efficiently radiate and receive radiated electromagnetic waves. There are several important antenna characteristics that should be considered when choosing an antenna for your application as follows:

• Antenna radiation patterns

• Power Gain

• Directivity

• Polarization

1.3 Microstrip Patch Antenna

In its most fundamental form, a Microstrip Patch antenna consists of a radiating patch on one side of a dielectric substrate which has a ground plane on the other side as shown in Figure.

Figure 1.1: Microstrip patch antenna

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.

In order to simplify analysis and performance prediction, the patch is generally square, rectangular, circular, triangular, and elliptical or some other common shape.

For a rectangular patch, the length L of the patch is usually 0.3333λo< L < 0.5 λo, where λo is the free-space wavelength. The patch is selected to be very thin such that t << λo (where t is the patch thickness). The height h of the dielectric substrate is usually 0.003 λo≤h≤0.05 λo. The dielectric constant of the substrate (εr) is typically in the range 2.2 ≤ εr≤ 12.

Microstrip patch antennas radiate primarily because of the fringing fields between the patch edge and the ground plane. For good antenna performance, a thick dielectric substrate having a low dielectric constant is desirable since this provides better efficiency, larger bandwidth and better radiation. However, such a configuration leads to a larger antenna size. In order to design a compact Microstrip patch antenna, substrates with higher dielectric constants must be used which are less efficient and result in narrower bandwidth. Hence a trade-off must be realized between the

antenna dimensions and antenna performance.

1.4 Advantages and Disadvantages

Microstrip patch antennas are increasing in popularity for use in wireless applications due to their low-profile structure. Therefore they are extremely compatible for embedded antennas in handheld wireless devices such as cellular phones, pagers etc...

.

Some of their principal advantages discussed by Kumar and Ray are given below:

• Light weight and low volume.

• Low profile planar configuration which can be easily made conformal to host surface.

• Low fabrication cost, hence can be manufactured in large quantities.

• Supports both, linear as well as circular polarization.

• Can be easily integrated with microwave integrated circuits (MICs).

• Capable of dual and triple frequency operations.

• Mechanically robust when mounted on rigid surfaces.

Microstrip patch antennas suffer from more drawbacks as compared to conventional antennas.

Some of their major disadvantages discussed by and Garg et al are given below:

• Narrow bandwidth

• Low efficiency

• Low Gain

• Extraneous radiation from feeds and junctions

• Poor end fire radiator except tapered slot antennas

• Low power handling capacity.

• Surface wave excitation

Microstrip patch antennas have a very high antenna quality factor (Q). It represents the losses associated with the antenna where a large Q leads to narrow bandwidth and low efficiency.

Q can be reduced by increasing the thickness of the dielectric substrate. But as the thickness increases, an increasing fraction of the total power delivered by the source goes into a surface wave. This surface wave contribution can be counted as an unwanted power loss since it is ultimately scattered at the dielectric bends and causes degradation of the antenna characteristics. Other problems such as lower gain and lower power handling capacity can be overcome by using an array configuration for the elements.

1.5 Different Feed Techniques And Transmission Line Model

Feed Techniques

Microstrip patch antennas can be fed by a variety of methods. These methods can be classified into two categories- contacting and non-contacting.

In the contacting method, the RF power is fed directly to the radiating patch using a connecting element such as a microstrip line.

In the non-contacting scheme, electromagnetic field coupling is done to transfer power between the microstrip line and the radiating patch.

Different Types of Feeding Techniques

Figure 1.2:Comparison of different feed techniques

Table 1.1:Comparison of different feed techniques

1.6 Transmission Line Model

This model represents the microstrip antenna by two slots of width W and height h, separated by a transmission line of length L. The microstrip is essentially a non-homogeneous line of two dielectrics, typically the substrate and air.

Figure 1.3.a: Microstrip Line Figure 1.3.b: Electric Field Lines

Hence, as seen from Figure 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-electromagnetic (TEM) mode of transmission, since the phase velocities would be different in the air and the substrate. Instead, the dominant mode of propagation would be the quasi-TEM mode. Hence, an effective dielectric constant (εreff) must be obtained in order to account for the fringing and the wave propagation in the line. The value of εreff is slightly less then εr because the fringing fields around the periphery of the patch are not confined in the dielectric substrate but are also spread in the air as shown in Figure above. The expression for εreff is given by Balanis as:

Where εreff = Effective dielectric constant

Εr = Dielectric constant of substrate

H = Height of dielectric substrate

W = Width of the patch

Consider Figure below, which shows a rectangular microstrip patch antenna of length L, width W resting on a substrate of height h. The co-ordinate axis is selected such that the length is along the x direction, width is along the y direction and the height is along the z direction.

Figure 1.4: Microstrip Patch Antenna

In order to operate in the fundamental TM10 mode, the length of the patch must be slightly less than λ/2 where λ is the wavelength in the dielectric medium and is equal to λo/√εreff where λo is the free space wavelength. The TM10 mode implies that the field varies one λ/2 cycle along the length, and there is no variation along the width of the patch. In the Figure shown below, the microstrip patch antenna is represented by two slots, separated by a transmission line of length L and open circuited at both the ends. Along the width of the patch, the voltage is maximum and current is minimum due to the open ends. The fields at the edges can be resolved into normal and tangential components with respect to the ground plane.

Figure 1.5.a:Top View of Antenna Figure 1.5.b:Side View of Antenna

It is seen from Figure b) 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, 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 by

Hammerstad as:

The effective length of the patch Leff now becomes:

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

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

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

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

1.7 Organization of the Thesis

An introduction to microstrip antennas was given in Chapter I. Apart from the advantages and disadvantages, the various feeding techniques and models of analysis were listed.

Chapter II deals with the Basic parameters that are considered while designing of Microstrip patch antenna. The theory of radiation, various parameters and design aspects were discussed.

Chapter III provides the design and development of U-slotted and E-shaped Microstrip antenna with enhanced gain and bandwith.

Chapter IV provides the design and development of phi shaped microstrip antenna with more enhanced gain and bandwith compared to previous U-slotted and E-shape.

Chapter V gives the Conclusion to this project and

suggests the future scope of work.

CHAPTER 2

Properties of a Basic Microstrip Patch

A microstrip or patch antenna is a low profile antenna that has a number of advantages over other antennas it is lightweight, inexpensive, and easy to integrate with accompanying electronics. While the antenna can be 3D in structure (wrapped around an object, for example), the elements are usually flat; hence their other name, planar antennas. Note that a planar antenna is not always a patch antenna.

The following drawing shows a patch antenna in its basic form: a flat plate over a ground plane (usually a PC board). The center conductor of a coax serves as the feed probe to couple electromagnetic energy in and/or out of the patch. The electric field distribution of a rectangular patch excited in its fundamental mode is also indicated.

Figure 2.1:Basic Microstrip patch antenna with probe feeding

The electric field is zero at the center of the patch, maximum (positive) at one side, and minimum (negative) on the opposite side. It should be mentioned that the minimum and maximum continuously change side according to the instantaneous phase of the applied signal. The electric field does not stop abruptly at the patch's periphery as in a cavity; rather, the fields extend the outer periphery to some degree. These field extensions are known as fringing fields and cause the patch to radiate. Some popular analytic modeling techniques for patch antennas are based on this leaky cavity concept. Therefore, the fundamental mode of a rectangular patch is often denoted using cavity theory as the TM10 mode.

Since this notation frequently causes confusion, we will briefly explain it. TM stands for transversal magnetic field distribution. This means that only three field components are considered instead of six. The field components of interest are: the electric field in the z direction, and the magnetic field components in x and y direction using a Cartesian coordinate system, where the x and y axes are parallel with the ground plane and the z axis is perpendicular.

In general, the modes are designated as TMnmz. The z value is mostly omitted since the electric field variation is considered negligible in the z axis.

Hence TMnm remains with n and m the field variations in x and y direction. The field variation in the y direction (impedance width direction) is negligible; thus m is 0. And the field has one minimum to maximum variation in the x direction (resonance length direction); thus n is 1 in the case of the fundamental. Hence the notation TM10.

2.1 Dimensions

The resonant length determines the resonant frequency and is about l/2 for a rectangular patch excited in its fundamental mode. The patch is, in fact, electrically a bit larger than its physical dimensions due to the fringing fields. The deviation between electrical and physical size is mainly dependent on the PC board thickness and dielectric constant.

A better approximation for the resonant length is:

This formula includes a first order correction for the edge extension due to the fringing fields, with:

· L = resonant length

· λ d = wavelength in PC board

· λ 0 = wavelength in free space

· er = dielectric constant of the PC board material

Other parameters that will influence the resonant frequency:

· Ground plane size

· Metal (copper) thickness

· Patch (impedance) width

2.2 Impedance Matching

Looking at the current (magnetic field) and voltage (electrical field) variation along the patch, the current is maximal at the center and minimal near the left and right edges, while the electrical field is zero in the center and maximal near the left and minimal near the right edges. The figures below clarify these quantities.

Figure 2.2:Current distribution on the patch surface

Figure 2.3:Voltage(U),Current(I) ,Impedance(Z) distribution along the patch's resonant length

From the magnitude of the current and the voltage, we can conclude the impedance is minimum (theoretically zero W) in the middle of the patch and maximum (typically around 200 W, but depending on the Q of the leaky cavity) near the edges. Put differently, there is a point where the impedance is 50 W somewhere along the "resonant length" (x) axis of the element.

2.3 Radiation Pattern

The 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 (cfr. 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 beamwidth (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. An example of a radiation pattern can be found below.

Figure 2.4:Typical radiation pattern of a square patch

So far, the directivity has been defined with respect to an isotropic source and hence has the unit dBi. An isotropic source radiates an equal amount of power in every direction. Quite often, the antenna directivity is specified with respect to the directivity of a dipole. The directivity of a dipole is 2.15 dBi with respect to an isotropic source. The directivity expressed with respect to

the directivity of a dipole has dBd as its unit.

2.4 Antenna Gain

Antenna gain relates the intensity of an antenna in a given direction to the intensity that would be produced by a hypothetical ideal antenna that radiates equally in all directions (isotropically) and has no losses. Since the radiation intensity from a lossless isotropic antenna equals the power into the antenna divided by a solid angle of 4π steradians, we can write the following equation:

Although the gain of an antenna is directly related to its directivity, the antenna gain is a measure that takes into account the efficiency of the antenna as well as its directional capabilities. In contrast, directivity is defined as a measure that takes into account only the directional properties of the antenna and therefore it is only influenced by the antenna pattern. However, if we assumed an ideal antenna without losses then Antenna Gain will equal directivity as the antenna efficiency factor equals 1 (100% efficiency). In practice, the gain of an antenna is always less than its directivity.

The gain of a rectangular microstrip patch antenna with air dielectric can be very roughly estimated as follows. Since the length of the patch, half a wavelength, is about the same as the length of a resonant dipole, we get about 2 dB of gain from the directivity relative to the vertical axis of the patch. If the patch is square, the pattern in the horizontal plane will be directional, somewhat as if the patch were a pair of dipoles separated by a half-wave; this counts for about another 2-3 dB. Finally, the addition of the ground plane cuts off most or all radiation behind the antenna, reducing the power averaged over all directions by a factor of 2 (and thus increasing the gain by 3 dB). Adding this all up, we get about 7-9 dB for a square patch, in good agreement with more sophisticated approaches.

2.5 Methods To Enhance Gain In Microstrip Patch Antenna

Most compact microstrip antenna designs show decreased antenna gain owing to the antenna size reduction. To overcome this disadvantage and obtain an enhanced antenna gain, several designs for gain-enhanced compact microstrip antennas with the loading of a high-permittivity dielectric superstrate or the inclusion of an amplifier-type active circuitry have been demonstrated.

Use of a high-permittivity superstrate loading technique gives an increase in antenna gain of about 10 dBi with a smaller radiating patch.

An amplifier-type active microstrip antenna as a transmitting antenna with enhanced gain and bandwidth has also been implemented.

2.6 Polarization

The plane wherein the electric field varies is also known as the polarization plane. The basic patch covered until now is linearly polarized since the electric field only varies in one direction. This polarization can be either vertical or horizontal depending on the orientation of the patch. A transmit antenna needs a receiving antenna with the same polarization for optimum operation.

The patch mentioned yields horizontal polarization, as shown. When the antenna is rotated 90°, the current flows in the vertical plane, and is then vertically polarized.

A large number of applications, including satellite communication, have trouble with linear polarization because the orientation of the antennas is variable or unknown. Luckily, there is another kind of polarization circular

polarization. In a circular polarized antenna, the electric field varies in two orthogonal planes (x and y direction) with the same magnitude and a 90°

phase difference. The result is the simultaneous excitation of two modes, i.e. the TM10 mode (mode in the x direction) and the TM01 (mode in the y direction). One of the modes is excited with a 90° phase delay with respect to the other mode. A circular polarized antenna can either be

righthand circular polarized (RHCP) or lefthand circular polarized (LHCP). The antenna is RHCP when the phases are 0° and 90° for the antenna in the figure below when it radiates towards the reader, and it is LHCP when the phases are 0° and 90°.

2.7 Bandwidth

Another important parameter of any antenna is the bandwidth it covers. Only impedance bandwidth is specified most of the time. However, it is important to realize that several definitions of bandwidth exist impedance

bandwidth, directivity bandwidth, polarization bandwidth, and efficiency bandwidth. Directivity and efficiency are often combined as gain

bandwidth.

Impedance bandwidth/return loss bandwidth

This is the frequency range wherein the structure has a usable bandwidth compared to a certain impedance, usually 50 Ω. The impedance bandwidth depends on a large number of parameters related to the patch antenna

element itself (e.g., quality factor) and the type of feed used. The plot below shows the return loss of a patch antenna and indicates the return loss bandwidth at the desired S11/VSWR (S11 wanted/VSWR wanted). The bandwidth is typically limited to a few percent. This is the major disadvantage of basic patch antennas.

Figure 2.5:VSWR bandwidth Calculation

Important note: Different definitions of impedance bandwidth are used, such as:

VSWR = 2:1 and other values, S11 values other than -10 dB, the maximum real impedance divided by the square root of two [Z(Re)/√2, bandwidth], etc. This tends to turn selecting the right antenna for a specific application into quite a burden.

Directivity/gain bandwidth

This is the frequency range wherein the antenna meets a certain directivity/gain requirement (e.g., 1 dB gain flatness).

Efficiency bandwidth

This is the frequency range wherein the antenna has reasonable (application dependent) radiation/total efficiency.

Polarization bandwidth

This is the frequency range wherein the antenna maintains its polarization.

Axial ratio bandwidth

This bandwidth is related to the polarization bandwidth and this number expresses the quality of the circular polarization of an antenna.

CHAPTER 3

Study of U-slotted and E-shaped Microstrip Patch Antenna

3.1 Introduction

In this chapter, the design parameters and results for a U-sloted and E-shaped rectangular microstrip patch antenna in IE3D software is explained and the results obtained from the simulations are demonstrated. The microstrip patch design is achieved by using probe feed technique. These patches were studied because they offer high bandwidth and gain.

3.2 Design Specifications for U-slotted rectangular patch

The essential parameters for the design of a rectangular microstrip Patch Antenna are:

•Length (L): The two sides are selected to be of equal length and is 36 mm each.

•Width (W): The two sides are selected to be of equal length and is 26 mm each.

•Frequency of operation (fo): The resonant frequency of the antenna must be selected appropriately. The resonant frequency selected for our design is 4.5 GHz.

•Dielectric constant of the substrate (εr): The dielectric material selected for our design has a dielectric constant of 1.03. A substrate with a high dielectric constant has been selected since it reduces the dimensions of the antenna.

•Height of dielectric substrate (h): For the microstrip patch antenna to be used in cellular phones, it is essential that the antenna is not bulky. Hence, the height of the dielectric substrate is selected to be 5mm.

•Slot Length along the X axis (lx): The length of slot along the X axis was adjusted to be 12 mm in order to obtain better results.

•Slot Length along the Y axis (ly): The length of both slots along the Y axis was adjusted to be 20 mm in order to obtain better results.

•Slot Width (w): The width of all the four slits was selected to be 2 mm.

Hence, the essential parameters for the design are:

• L = 36mm

• W = 26mm

• lx = 12mm

• ly = 20 mm

• w = 2mm

• fo = 45 GHz

• εr = 1.03

• h = 5 mm

3.3 Simulation Results in IE3D

Designed Patch

Figure 3.1: Designed Patch

S Parameter:

Figure 3.2: S Parameter display

Parametric Study of U-Slotted rectangular patch by varying probe feed point position:

Feed Point Position (mm,mm)

FREQUEBCY(F1)

(GHz)

FREQUENCY(F2)

(GHz)

Bandwidth(%)

(2,0)

4.41

4.92

10.93%

(-2,0)

4.41

4.92

10.93%

(0,-2)

4.49

5.35

17.47%

(0,-3)

4.39

4.94

11.78%

(0,-1)

4.33

5.16

17.49% *

(0,-0.5)

4.34

5.06

15.31%

(2,-2)

4.51

5.31

16.29%

(-2,-2)

4.50

5.32

16.7%

Design of E-shaped patch with dual substrate for gain and bandwidth enhancement:

The E-shaped patch is formed by inserting a pair of wide slits at the boundary of a microstrip patch.

Figure. Equivalent circuits of (a) Rectangular Patch and (b) Eshaped Microstrip Antennas.

A common rectangular patch antenna can be represented by

means of the equivalent circuit of Fig.(a). The resonant frequency is

determined by L1C1. At the resonant frequency, the impedance of the

series LC circuit is zero, and the antenna input impedance is given by

resistance R. By varying the feed location, the value of resistance R

may be controlled such that it matches the characteristic impedance of

the coaxial feed. When a pair of slots is incorporated, the equivalent circuit can be modified into the form as shown in Fig.(b).

The second resonant frequency is determined by L2C2. Analysis of the

circuit network shows that the antenna input impedance is given by

The imaginary part of the input impedance is zero at the two series

resonant frequencies determined by L1C1 and L2C2, respectively. Of

course, this is by no mean the exact model of the E-shaped antenna

because the equation shows that there is a parallel-resonant mode between the two series-resonant frequencies. Nevertheless, it serves to

explain the operating principle of the antenna design. If the two series resonant frequencies are too far apart, the reactance of the antenna at

the midband frequency may be too high and the reflection coefficient

at the antenna input may be unsatisfactory. If the two series-resonant

frequencies are set too near to each other, the parallel-resonant mode

may affect the overall frequency response and the reflection coefficient

near each of the series-resonant frequencies may be degraded. The

question now is: how would the slot length, slot width, slot position

and the length of center arm affect the values of L2 and C2?.

This patch shape has shown to enhances gain as well as bandwidth of microstrip patch antenna.

E-shaped patch with coaxial probe feeding for gain as well as bandwidth enhancement:

a)

b)

Figure.a) E-shaped patch b) Substrate Dimensions

The geometry of the proposed antenna is shown in fig.a). A rectangular patch of dimensions L x W separated from the ground plane using two substrates 1) a foam substrate (εr1) of thickness h1 and the other 2) substrate(εr2) of thickness h2. The E-shape is located in the center of the patch. The location of the slots on the patch can be specified by parameter W2. The width and length of the slots are denoted by W1 and l. The rectangular patch is fed using 50Ω coaxial probe with inner diameter of 0.65mm.

SIMULATED RESULTS AND ANALYSIS

In order to evaluate the performance of the proposed antenna, the antenna is simulated through the simulation tool IE3DTM [13]. The analysis of the antenna for different physical parameter values has been done by varying one of them and keeping others as constant. It is carried out here to study the flexibility in designing this of single layer patch antenna.

Parametric Study of E-patch by varying w1,w2 and l

Figure.S-Parameter Results compared by varying slot width w1

From the figure we find that the S-Parameter bandwidth is maximum for w1=2mm which is represented in black.

Figure.S-Parameter Results compared by varying slot length l

From the figure we find that the S-Parameter bandwidth is maximum for l=18mm which is represented in black.

Figure.S-Parameter Results compared by varying slot width w2

From the figure we find that the S-Parameter bandwidth is maximum for l=18mm which is represented in black.

The S-Parameter is less than -10dB in the frequency range of 3.99 GHz to 5.17 GHz for the best result.

Best results were obtained for the following values of W1,W2,l and dp.

l =18mm

w1 =2mm

w2 =5mm

dp =6mm

Figure. Simulated Return Figure. Simulated VSWR Curve

Loss Curve

The simulated return loss value was found to be below -10dB within the frequency range of 3.99 GHz and 5.17 GHz. The value of VSWR was also found to be within 1 and 2 in this range. A bandwidth of 25.7% was achieved.

Figure. Simulated Z-parameter Figure. Gain Vs Frequency

A maximum gain 8.8 dBi was attained at the frequency of 4.50 GHz. The gain was found to be above 6 dBi in the entire bandwidth region.

The Z-parameter was also within the acceptable range.

E plane(x-z) H plane(x-y)

Figure. E and H plane Radiation Pattern

Chapter 4

Design of Phi shaped Microstrip patch antenna in IE3D with enhanced

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