design array of microstrip antenna.docx

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Design of Microstrip Antenna Array

Nguyen Trong Quynh- Class Telecommunications-Advanced Training Program-Course 53 Page 1

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

CENTER FOR TRAINING OF EXCELLENT STUDENT

GRADUATION THESISProject:


Students : Nguyen Trong QuynhTelecomucation - AP - K53

Advisors : Lam Hong Thach Ph.D

Hanoi, 5 - 2013


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CENTER FOR TRAINING OF EXCELLENT STUDENT

GRADUATION THESISProject:

Design Array of Microstrip Patch Antenna

Students : Nguyen Trong Quynh Telecommunication K53

Advisors : Lam Hong Thach Ph.D

Critical Staff :

Hanoi, 5 2013


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MINISTRY OF EDUCATION AND TRAINING SOCIALIST REPUBLIC OF VIET NAM

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY Independence Freedom Happiness

--------------------------------------- --------------------------

ENGINEERING THESIS MISSIONFull name: . Student Identity: Course: ....... School: Center for Training of Excellent Students Subject: ........................1. Thesis Title: 2. Initial data: 3. Content of theory and equation:

4. Graphs and drawings: 5. Advisors Full name: ..... 6. Starting Date: 7. Finishing Date: ..

Date: ././.. Dean of subject Advisor

Student had been completed and submitted this thesis in: ././

Critical staff

MINISTER OF EDUCATION AND TRAINING



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ENGINEERING THESIS COMMENT

Full name: . Student Identity:

Subject: . Course: .. Advisor: . Critical Staff: . Content of thesis: Comment of Critical Staff:

Date: ././.. Critical Staff

(Signature)


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CONTENTSLIST OF FIGURES ..................................................................................................................................7

LIST OF TABLE ....................................................................................................................................10

ACKNOWLEDGEMENT ......................................................................................................................11

ABSTRACT ............................................................................................................................................12

INTRODUCTION ..................................................................................................................................13

CHAPTER 1 ...........................................................................................................................................13

MICROSTRIP ANTENNA ....................................................................................................................13

1.1 MICROSTRIP ANTENNA ..........................................................................................................14

1.1.1 The basic shape of the micro-strip antenna ............................................................................15

1.1.3 The digital power supply for micro strip antennas (feed method) .........................................19

1.1.4 Bandwidth of MSA ................................................................................................................22

1.1.5 Principle of the radiated micro strip antennas ........................................................................24

1.1.6 Radiation field of micro strip antenna ....................................................................................27

1.1.7 The polarized waves ...............................................................................................................31

1.2 ANALYSIS MODELS MICROSTRIP ANTENNA ....................................................................32

1.2.1 Model line (Transmission Line) .............................................................................................33

1.2.2 Model cavity ..........................................................................................................................44

CHAPTER 2 ...........................................................................................................................................55

MICROSTRIP ANTENNA ARRAY .....................................................................................................55

2.1 TWO ARRAY ELEMENT ...........................................................................................................57

2.2 N ELEMENT LINEAR ARRAY - MINUTES OF UNIFORM UNIFORM AND DISTANCE 60

2.2.1. Broadside array and End-Fire array ......................................................................................64

2.2.2 Phased Scanning Array ..........................................................................................................68

2.3 N ELEMENT LINEAR ARRAY - THREE DIMENSIONAL PROPERTIES ............................70

2.3.1 N elements along the z axis ....................................................................................................70

2.3.2 N elements along the X or Y axis ..........................................................................................71

2.4 N ELEMENT LINEAR ARRAY - UNIFORM DISTANCE, BORDER HETEROGENEITY ...722.4.1 Coefficient array.....................................................................................................................73

2.4.2 Binomial Arrays .....................................................................................................................75

2.4.3 Schebyscheff Arrays ............................................................................................................77

2.5 TWO DIMENSIONAL ARRAY ..................................................................................................78

2.5.1 Coefficient array.....................................................................................................................78


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2.5.2 Beamwidth .............................................................................................................................82

2.5.3 The orientation .......................................................................................................................84

2.6 CHANGE OF RADIATION PROPERTIES OF TWO-DIMENSIONAL ARRAY ANTENNA 84

2.7 INFLUENCE MUTUAL CONSTRUCT BETWEEN TWO MICROSTRIP ANTENNA ......87

CHAPTER 3 ...........................................................................................................................................90

DESIGN AND SIMULATION MICROSTRIP ANTENNA .................................................................90

3.1 DESIGN AND SIMULATION OF A MICROSTRIP PATCH ANTENNA ...............................90

3.1.1 Design ....................................................................................................................................90

3.1.2 Simulation ..............................................................................................................................93

3.2 DESIGN AND SIMULATION OF MICROSTRIP PATCH ANTENNA ...................................97

3.2.1 Design ....................................................................................................................................97

3.2.2 SIMULATION OF MICROSTRIP PATCH ANTENNA ARRAY .......................................99

REFERENCES......................................................................................................................................104


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LIST OF FIGURES

Figure 1.1: Microstrip Antenna

Figure 1.2 - The micro strip antennas form commonly used

Figure 1.3 - Power by transmission line

Figure 1.4 - Power by cables coaxial

Figure 1.5 - Power grafting using slot - Aperture coupled

Figure 1.6 - Power close coupling method - Proximity Coupled

Figure 1.7 - Distribution of charge and current in the antenna of rectangular strips.

Figure 1.8 - Effective Dielectric Constant

Figure 1.9 - Physical length and effective length piece patch

Figure 1:10 - Patch and Rectangle in the equivalent circuit model of the transmission

line

Figure 1.11 - Change the location of the feed impedance to match

Figure 1:12 - electrical distribution and power lines

Figure 1:13 - Analysis of micro-strip antenna pattern axis coordinates

Figure 1:14 - The mode of the antenna radiation range

Figure 2.1 - Four types of antenna array geometry

Figure 2.2 - 2 geometry of the array elements along the z-axis at

Figure 2.3 - If the remote array and phase diagram of N isotropic elements


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Figure 2.4 - Graph of the three-dimensional radiation array broadside and broadside /

end-fire

Figure 2.5- two-dimensional graph of the radiation array broadside and broadside /

end- fire

Figure 2.6 - Graph of radiation of three-dimensional and two-dimensional array of 10

identical scanning elements (N=10, 0coskd , 0 =600 , d= / 4 )

Figure 2.7 - N linear array of isotropic elements placed along the x axis\

Figure 2.8 - The layout of the antenna element

Figure 2.9 - Correlation coefficient amplitude of an array of 10 elements.

Figure 2.10 - Geometry of linear array and two-dimensional array

Figure 2.11 - The degree half power beam width of the main beam and the direction0

Figure 2.12 - Block Diagram impact process signals through complex weights.

Figure 2.13- Sort band antenna in the plane of E and H

Figure 3.1 - Window simulation program

Figure 3.2 - frequency response of S parameters

Figure 3.3 orientation of the antenna

Figure 3.4 - Grap of 3D radiation

Figure 3.5- The Smith Chart

Figure 3.6- 2-dimensional array system

Figure 3.7- 2x2 2D array system designed


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Figure 3.9 - frequency response of S parameters

Figure 3.8 - Window simulation program of patch antenna array

Figure 3.10- Bandwidth of patch antenna array

Figure 3.11 Orientation of the array of antenna

Figure 3.12 - Grap of 3D radiation

Figure 3.13 The Smith Chart


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LIST OF TABLE

Table 2.1 The null point, half of the maximum power, maximum sidelobes for uniform

amplitude array broadside

Table 2.2 The beam width for uniform amplitude array broadside

Table 3.1: The antenna design parameters

Table 3.2: The calculated parameters patch antenna 2.4 GHz range

Table 3.3 - S11 parameter

Table 3.4- S 11 parameter


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ACKNOWLEDGEMENT

The completion of this thesis could not have been fulfilled without the support

of many people, to whom I am profoundly indebted.

Firstly, I would like to express my deepest gratitude to my supervisors, Mr. Lam

Hong Thach (Ph.D.), for his immeasurable assistance and valuable comments

throughout the conduct of the research.

Secondly, I am thankful to teachers of my faculty for their consultancy and

attentiveness to the completion of my thesis paper.

Last but not least, I am particularly thankful to the support I have had from my

family and friends during the five years of my tertiary study and their encouragement

when I conducted this graduation thesis.


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ABSTRACT


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INTRODUCTIONA patch antenna (also known as a rectangular microstrip antenna) is a type of

radio antenna with a low profile, which can be mounted on a flat surface. It consists of

a flat rectangular sheet or "patch" of metal, mounted over a larger sheet of metal calleda ground plane.

In this orientation, the thesis is divided into three chapters as follows:

Chapter 1: Microstrip antenna

Chapter 2: Microstrip antenna array

Chapter 3: Design and Simulation microstrip antenna

CHAPTER 1

MICROSTRIP ANTENNA
http://en.wikipedia.org/wiki/Antenna_(radio)http://en.wikipedia.org/wiki/Ground_planehttp://en.wikipedia.org/wiki/Ground_planehttp://en.wikipedia.org/wiki/Antenna_(radio)


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1.1 MICROSTRIP ANTENNA

The concept of band radiation was first initiated by Deschamps in 1953. But it

was not until 20 years later, an antenna engineering applications of the new range is

made. Micro-strip antenna experiments were first developed by Howell and Munson

and continue research and development in many different areas.

Micro-strip antenna simplest including a very thin metal patch (thickness t


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Figure 1.1 - Microstrip Antenna

There are dielectric backgrounds can be used to design micro-strip antenna and

dielectric constants are usually in the range 2.2 < r


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Coaxial-line feeds, where the inner conductor of the coax is attached to the

radiation patch while the outer 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 tomodel, especially for thick substrates (h > 0.02 0).

All micro-strip antenna is divided into four basic categories: micro-strip patch

antenna, micro strip dipole, slot antennas used in engineering, antenna band traveling-

wave behavior.

Micro str ip patch antenna

A micro-strip patch antenna includes a conductive patch as flat or planar

geometry on one side of the piece of dielectric substrate and ground plane on the other

surface of the substrate. Patch antenna with strips of different types, but their radiation

characteristics virtually identical because they act like a dipole. Among the micro-strip

patch antennas, antenna square and circle are two types of commonly used and widely

used.

Dipole microstrip

Dipole micro strip antenna shaped like a square patch of bands but different

ratio L / W. The width of the dipole typically less than 0:05 wavelengths in free space.

Dipole radiation pattern of the antenna patch and strips of the same great features but in

others, such as radiation resistance, bandwidth and cross-polarized radiation, they

hardly differ. Dipole antennas, the range of suitable for high frequency applications

because they use pieces of dielectric substrate thickness is relatively thick so that they

achieve significant bandwidth. The choice of source model is very important and must

be taken into account when analyzing micro-strip dipole antenna.

Printed Slot Antenna


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Printed Slot Antenna structure includes a slot in the ground plane of a grounded

substrate (substrate ground). This slot can have many different shapes such as

rectangles, circles, candles, .. This type of antenna radiation in both directions means

that our radiation on both sides of the slot, we can create unidirectional radiation usinga reflective surface on one side of the slot.

Traveling -Wave M icrostri p Antennas (M TA)

MTA is constituted by a series of chain conductors together or a strip of the line

is long enough and wide enough to support the TE mode transmission. In particular,the antenna is grounded and the other end is the impedance to avoid standing waves on

the antenna. MTA antenna can be designed to direct the beam in any way from

broadside to endfire.

1.1.2 Characteristics of Microstrip Antennas (MSAs)

Micro strip antennas (MSAs) have many advantages compared to traditional

antennas. Therefore, micro-strip antenna used in many applications in the range of bands from 100MHz to 100GHz. MSA has proven to be an effective emission devices

for many applications with many advantages, however, it is still a number of

weaknesses that need to be overcome.

Advantages:

There is the small size and weight, thin thickness.

Low production costs, easy mass production.

Ability to linearly polarized with the simple power engineering.


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The supply lines and the impedance components can be producedsimultaneously with the fabricated antenna.

Easy integration with other MIC on the same substrate.

Flexibility between circularly polarized and linearly polarized.

Compatible for personal mobile devices.

Disadvantages:

MSA have narrow bandwidth and tolerance issues.

Some MSA with low gain.

Ability to low-power storage.

Almost all radiation MSA in half the space above the ground plane.

There is excess radiation from transmission lines andconnections.

MSA has a very narrow bandwidth, typically only about 1-5%, this is the

biggest drawback in the application of MSA to cover a broad spectrum.

With the advantages that MSAs that become suitable for many applications.

Some applications of MSAs:

The antenna used in radio communications to a compact MSA is used.

The radar reflector used MSA emission ranges.

Aviation information systems and satellite MSA arrays used to locate

Smart Weapons used by the MSA their compact size.

GSM and GPS can also use the MSA.


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1.1.3 The digital power supply for micro strip antennas (feed method)

Due antenna with a range of radiation on a surface of the dielectric substrate so

the technique to power micro-strip antenna baseline by using a micro-strip transmission

line or a coaxial probe through the ground plane connection to the metal patch microstrip antennas. Along with the development of science and technology, a new power

supply specifications for the micro strip antennas have been studied and developed.

Currently, the common method used to supply power for micro-strip antenna is: use the

power of strip transmission lines, coaxial probe, join slot (aperture-coupling), liver

transplantation (proximiti-coupling).

The choice of power supply is dependent on many different factors. However,

the most important factor is the efficiency of energy transfer between the radiation and

the power that is to be coordinated resistance between two parts together. In addition,

the impedance transformation step, the bend .. also give rise to leakage radiation and

surface wave attenuation. The unexpected radiation raises the secondary radiation of

the antenna radiation pattern of bands. minimizing radiation leakage and the effects of

radiation on the plot it is one of the key factors evaluating the supply is good or not?

1.1.3.1 Power transmission range by transmission line

The stimulus for micro-strip antenna micro strip transmission lines on the same

substrate is a natural choice because the patch can be considered as a transmission

range of both open and can be designed on the same circuit. However, this technique

has several limitations. It is the unwanted emission from the feed line to feed the line

size is negligible compared with patch (for example in the case of L is small enough

for a few mm).


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Patch

GND

Feed

Figure 1.3 - Power by transmission line

1.1.3.2 Power by coaxial probe

Power over probe is one of the most basic methods for high-frequency

transmission capacity. With this feed, the feed section of the core is connected to the patch, ground plane connected to the outside. The advantage of doing this is simple in

design process, with the ability to feed at every position on the patch panel so easy to

coordinate resistance. However, the downside is this:

First, because the feed using the feed should be made to the outside antenna is

not perfectly flat and loses its symmetry. Second, the need for a powered coaxial range

would require increasing the number of connections and thus would be difficult to

manufacture and reduced reliability. Third, the need to increase bandwidth of the

antenna is required to increase the thickness and length of the probe. As a result,

radiation leaks and the inductance of the probe increases.

Patch

im tip xc in

Cp ng trc

r GND

Patch

Figure 1.4 - Power by cables coaxial


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1.1.3.3 Power slot transplant method - Aperture coupled

GND

r2r1

Patch

khe

ng cp ngun vi di

Figure 1.5 - Power grafting using slot - Aperture coupled

Power method often used to eliminate the unnecessary radiation of the

microstrip line. The structure consists of two dielectric layers. Patch antenna is placed

on top, in the middle ground with small slot 1 slot, transmission line feed at the bottom

dielectric layer. Typically, the dielectric pads above low dielectric constant, the

dielectric layer under high dielectric constants have aimed to optimize the antenna's

radiation. However, this method difficult to implement power to do so many layers,

and the thickness of the antenna increases. This method is supplied for Narrowband

(narrow bandwidth).

1.1.3.4 Power grafting using near - Proximity Coupled

This structure consists of two dielectric layers, piece patch antenna located on a

piece of dielectric, the feed line in between two dielectric layers. This method has the

advantage of removing the maximum height that the radiation of power lines (line

feed) and broadband (approximately 13%).


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GND

r2r1

Patch

ng cp ngun vi di

Figure 1.6 - Power close coupling method - Proximity Coupled

This method is also called electromagnetic coupling method. This method is

essentially capacitive coupling between the patch and the power supply. Parameters of

the two layers can be selected to improve bandwidth and reduce radiation leaks in the

open end of the transmission line. Also for this reason, the thickness of the second

dielectric layer is thinner. Radiation in this case will be greater. However this method

more complex manufacturing and production.

1.1.4 Bandwidth of MSA

As we know, the biggest drawback of the MSA is the width of the bandwidth.

Bandwidth (BW) can be determined through a standing wave ratio (VSWR),

impedance changes in the frequency or radiation parameters. for circularly polarized

antenna, BW are axial ratio (AR).

BW is determined by the frequency at which the impedance is the ability of the

antenna within a given limit. BW of the MSA inversely proportional to the quality

factor Q:

1VSWR BW

Q VSWR (1-1)

The VSWR is determined by the reflection coefficient :


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1 | |1 | |

VSWR

(1-2)

Reflection coefficient assessment reflected signal at the antenna feed poin

is determined by the input impedance of the antenna Zin and Zo the characteristicimpedance of the feedline:

in o

in o

Z Z Z Z

(1-3)

Generally, the BW is defined in the frequency that is less than 2 VSWR (return

loss


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From the above formula we can see if we can increase W, the increasing BW,

but W is limited by because if W> can not single-mode transmission.

1.1.5 Principle of the radiated micro strip antennas

We know that the radiation of micro strip lines, a structure similar to the micro-

strip antenna, can be significantly reduced if the dielectric substrate is used and the

thickness of thin dielectric coefficient is relatively low. In other words, it helps to

radiation micro strip antennas better with higher radiation efficiency. Thus, in a range

of antennas, we use the dielectric coefficient of low permeability. Radiation from

micro-strip antenna can be determined from the distribution between the patch and the

ground plane or in the form of electric current distribution on the surface of the patch.

At a micro-strip antenna is powered by a high frequency source (microwave

source). The power supply for the patch to form the charge distribution at the top and

bottom of the patch, as well as on the surface of the ground plane. Under the effect of

the thrust force formed by the interaction of the electrons with the same sign, on the

surface of the patch makes a number of charges in the periphery of the surface patch

moving from bottom to top surface patch. The movement of electrical charge to form

on the surface of the patch under the current density vector and vector current density

on the surface.

J t

J b r h

W

Figure 1.7 - Distribution of charge and current in the antenna of rectangular strips.


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As in most of the antenna is very small ratio because the electrical attraction

between the dominant and the most concentrated and line charge still exists beneath the

surface patch. And so, only a small amount of movement from the edge of the patch

piece on top of the patch to form a small way to the edge of the tangent patch.Therefore, to simplify the calculation, we approximate that the tangential magnetic

field is zero and the tangential magnetic field can be established from the walls around

the perimeter of the patch. The assumptions are more reasonable than in the case of

dielectric substrate thickness thin with large dielectric constants. Similar to the case of

the electromagnetic field, because the thickness of the dielectric substrate is very thin

compared to the wavelength in the dielectric layer transmission, so the high variability

along the electric field is constant and almost perpendicular to the surface the patch.From the condition of the electric and magnetic fields, the patch can be seen as the

model of a resonant cavity (cavity) with the electromagnetic field radiation above and

below (due to the electric field perpendicular to the surface of patch) and four along the

wall from the edge of the patch (due to tangential magnetic field is almost zero). From

the resonance condition of the cavity just mentioned, only the TM mode can be

transmitted in the resonant cavity.

Four side walls of the cavity corresponding to the four slot radiation. Patch of

micro strip antennas can be represented by a vector corresponding current density.

Meanwhile, the four slots in the side radiation is characterized by the vector density

and lines respectively with the electric and magnetic fields in the radiation slot.

n a J n H (1-8)

a s M n E (1-9)

Since we consider dielectric substrate t J thickness on the current density should

be very small compared with the current density b J of the patch below. Therefore, will


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be set to zero to indicate that virtually no radiation from the surface of the patch.

Similarly, the tangential magnetic field along the edges of the patch and the

corresponding current density s M is set to zero. Therefore, only one other current

density component vector density s M is not along the lines of patch perimeter. In order

to demonstrate the presence of the ground plane image we use the theory that the

current density will double compared to when not at the ground plane. The density of

the new line will be:

2 a s M n E (1-10)

The electromagnetic field in the slot radiation determined:

0.a E z E for two slots of length W and height h

0. sina x

E z E L

on slot length L and height h

Due to the conditions considered above, we realize as a result of the radiation of

the slot along the x-axis is almost zero because the current distribution and reversed by

the slots together. However, the results of radiation along the y axis exists in the formof a strip of two components with the same current density component amplitude and

phase and separated by a distance L - length of the patch. Thus, radiation from the

patch can be described as two longitudinal slots (vertical slots).

The analysis of longitudinal slots in dielectric medium heterogeneity is a very

difficult problem to the gaps along the slit is replaced by two flat (planar slots). For the

micro-strip antenna configurations can also be represented by the corresponding slots

of the same type.


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1.1.6 Radiation field of micro strip antenna

If radiation from antennas that great line from surfaces like walls along the

perimeter of the patch. In another method, but a bit more radiation field is determined

from the power line on the surface of the conductive patch antenna piece of strip. Bothmethods are considered equivalent. The micro-strip antenna radiation is sometimes

seen as the radiation range of open circuit transmission line. The graph of a radiation

transmission openings of similar range of radiation pattern of a Hertz dipole. This

method is also used to calculate the effects of radiation on the quality factor Q of the

resonance box of strips. Theoretical and experimental results shows that the high

frequency attenuation due to radiation higher than the attenuation due to dielectric and

conductance. In addition, it also shows that the range of open circuit transmission lineradiation is more powerful when made with thick dielectric layer with low dielectric

constant.

Vectors that are used to determine the radiation field due to the currents.

1.1.6.1 The vector and a formula for calculating the radiation

First, we assume that there exist lines from. Where electric and magnetic field at

any point P (r, , ) external antenna is represented as follows:

1( )m E r F

(1-11)

1( ) .( . )m H r F j F

j

(1-12)

With a dielectric constant and is the absolute permeability of the mate

the letter "m" implies that the by- line from cause and is the angular frequency. Thvector F is defined as follows:

0 | '|

( ') '4 | ' |

jk r r

s

e F M r dS

r r

(1-13)


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In particular, the constant k 0 is the free space wave and surface current density

from the point of origin at a distance r '.

Similarly, using the vector A , the currents induced by can be performed

1( ) .( . )e E r F j A

j

(1-14)

1( )e H r A

(1-15)

In particular, since the vector is given by

0 | '|

( ') '

4 | ' |

jk r r

s

e A J r dS

r r

(1-16)

Therefore, the total current due to both the source and cause of

1 1( ) .( . )e m E r E E A j A F

j

(1-17)

1 1( ) .( . )e m H r H H F j F A

j

(1-18)

For the remote, the components of net components perpendicular to thedirection of propagation, ie, and component. In particular from the line, we h

H j F v H j F (1-19)

In free space:

0 0 0( ) ( ) E r H H H j F F (1-20)

Which 0 120 is constant free space. Similarly, when looking only at

current own:

E j A v E j A (1-21)


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And in free space:

0

r E H

(1-22)

Far field is described by the following conditions: r >> r 'or r >> 2

0

2 L , where L

is the length of the slot. Hence, from (1-13) instead of | ' |r r = r- r'cos in the

numerator and | ' |r r in the denominator, we get:

0

0 'cos( ') '4

jk r jk r

s

e F M r e dS

r

(1-23)

And from:

0

0 'cos( ') '4

jk r jk r

s

e A J r e dS

r

(1-24)

In which case is the angle by and. Here, we will apply the results to constructthe far field distribution of rectangular lines.

1.1.6.2 Radiated Power

Radiated power of the antenna can be calculated by taking the integral of the

Poynting vector radiation slots:

1Re ( )

2r aperture P E H dS (1-25)

For micro-strip antenna, electromagnetic field inside the patch pieces

perpendicular to the ground plane and the conductive pads and magnetic fields are

parallel to the edge of the antenna. Also, we can calculate the radiated power from the

radiation graph the following equation:

2 2 2

0

1(| | | | ) sin

2r P E E r d d

(1-26)


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1.1.6.3 Power Dissipation

Power dissipation in micro-strip antenna attenuation inductor including Pc and

Pd dielectric loss:

2 ( . *)2

sc

s

R P J J dS (1-27)

In which, Rs is the real part of the impedance of the metal surface, S is the area

of the patch piece and the surface current density.

We calculate the dielectric loss by integrating over the entire volume of the

cavity resonance of bands:

2 2" "| | | |2 2d V S

P E dV h E dS (1-28)

With is the angular frequency, "is the imaginary part of the complex permeability and h is the slice thickness of the pieces.

1.1.6.4 Energy accumulation

Energy accumulation of micro strip antennas is the total energy of both electric

and magnetic components:

2 21 ( | | | | )4t e m V

W W W E H dV (1-29)

In particular, is the magnetic permeability. At the resonant frequency electric magnetic energy are equal. When the accumulated energy

2

| |2T s

hW h E dS

(1-30)

1.1.6.5 Resistance to

Almost all micro strip antennas must be coordinated preparation of the source

impedance and load it into the calculation of the antenna impedance is very important.


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field vector describes a point in space as a function of time is always directed along a

street, then known as the linear polarization. However, the electric candle shape that

outlines a case ellipse, the ellipse called polarization. Linear polarization and circular

polarization are special cases of elliptical polarization because they can be achievedwhen the ellipse becomes a straight line or a circle, respectively.

* Polarization vector:

Polarization vector P (, ) is given by:

( , ) ( , )( , )

( , )

F F P

F

(1-36)

With : 2 2( , ) | ( , ) | | ( , ) | F F F (1-37)

( , ) F : The amplitude field function

1.2 ANALYSIS MODELS MICROSTRIP ANTENNA

There are many different methods to analyze the micro-strip antenna. Each

method offers an approximate model to analyze antenna. The model is the most

popular model of the transmission line (microstrip line), model cavity (cavity model).

The models provide a meaningful analysis of great practical reality for the

reason:

Help us to reduce a large number of test cycles and removed by an impacthe design process.

Help us evaluate correctly the strengths and weaknesses of antennas bystudying its parameters.


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Provide operational principles of micro strip antennas from it as the basisthe research and development of future designs.

Transmission line model considered a micro strip antenna rectangular patch as a

piece of micro-strip transmission lines. This is the simplest model, it gives us a deeper

understanding of physics, but less accurate and difficult to apply to the transplant

model, and can not be applied to the antenna complex shapes.

Unlike the transmission line model, cavity model is more accurate but also more

complex. However, the advantage of this model can be applied on different types of

patch. Like a transmission line model, cavity model also gives an in-depth

understanding of physics and quite complex when applied to the antenna couplingmodel and it is also used quite successfully. Here, we consider the transmission line

model and the cavity model. However, it is also used in some of the results of the

design calculations and full-wave models. In particular, we consider only the micro

strip antennas as popular and most practical rectangular patch.

1.2.1 Model line (Transmission Line)

The model is the easiest way to transfer all kinds of little but for the mostaccurate results because it lacks flexibility. However, it gives a relatively clear

understanding of physical properties. A rectangular microstrip antenna can be

described as an array of radiation two narrow slits, each slit width is W, the height h

and separated by a distance L. The model describes the basic transmission range of two

slot antennas separated by a low impedance transmission line and length L. Z c

1.2.1.1 Fringing EffectsDue to the size of the patch is limited by the length and width, the border being

at the edge of the patch. General outline of a function of patch size and the height of

the dielectric layer. In-plane E-plane (xy plane), as a function of contour length ratio of

the patch, the dielectric layer length (L / h), and dielectric constant. When micro-strip


34/104



antenna L / h >> 1, border effect is reduced, but it must be taken into account because

it significantly affects the resonant frequency of the antenna.

As we know, most of the electric field lines in the dielectric layer and a portion

of a line exists in the air. When L / h >> 1, r >> 1, the electric field lines most

concentrated in the dielectric. Fringing effects in this case makes the transmission of

wide range of power seem more real size no.Khi a few waves into the dielectric layer,

and some others went into the air. Effective dielectric constant reff is used to correct

the effects of fringing effects of waves on the transmission line.

To make the effective dielectric constant, we assume the lead center line of the

strip on the size and height of the original land surface it is put into a homogeneous

dielectric layer as shown in Figure 1.9. For a transmission line with the air in the

background, the effective dielectric constant value in the range 1 < reff < r . In most

applications where a dielectric constant greater than 1 ( r >> 1), the value of the

effective dielectric constant will be close to the value of the dielectric constant is more

realistic. Effective dielectric constant is also a function of frequency. As the operating

frequency increases, most of the electric field lines should be concentrated in the

dielectric. So the line will be nearly identical to the range of transmission line located

in homogeneous dielectric with dielectric constant to the effective value of the

dielectric constant over.

At low frequencies, the effective dielectric constant is fundamental. At

intermediate frequencies the value of it and have started to increase towards the end of

dielectric constant values platform. The initial value (at low frequency) of the effective

dielectric constant can be represented as a static value.


35/104



t

h

reff

r w

(a) Microstrip line (b) Trng in

(c) Hng s in mi hiu dng

Figure 1.8 - Effective Dielectric Constant

Effective dielectric constant is given by the formula:

121 1

1 122 2

reff r reff

h

W

v i W/h >> 1 (1-38)

1.2.1.2 Effective Length, resonant frequency and the effective width

Because of fringing effects, micro-strip patch antenna of the phone looks bigger

than its physical size in the xy plane. This is demonstrated in Figure 1.10, where the

electrical length of the patch beyond some physical length L of each side, with a

function of the effective dielectric constant and width ratio of the dielectric thickness

(W / h). The difference between length and length make this power is approximated bythe formula:


36/104



0.3 0.2640.412

0.258 0.8

reff

reff

W h L h

W h

(1-39)

When the length of an extended patch on each side about the length of time the

patch is:

Lreff = L +2 L (1-40)

Suppose the dominant TM010 mode, the resonant frequency of the antenna's

range of modes as a function of length and are due by the formula:

0010

0 0

1( )

2 2r

r r

v f

L L (1-41)

In particular, the speed of light in free space. But due to fringing effects and

impact on the length of the effective dielectric constant in the formula should be

replaced by:

010

0 0 0 0

1 1( )2 2( 2 )

re

reff reff reff

f L L L

0

0 0

1

2 2r r

vq q

L L (1-42)

with 010010

( )( )

re

r

f q

f

''q'' coefficient is expressed as the coefficient contour (attenuation coefficient

length). When the height of the dielectric increases fringing effects also increase and

lead to a big difference between the edge of the radiation and the lower resonance

frequency


37/104



hr

L

(b) Mt phng ct ngang

t

L L

(a) Mt trn

Figure 1.9 - Physical length and effective length piece patch

1.2.1.3 Design Problem

Based on the simple formula has been described, a process design calculations

for a rectangular strip of the antenna is outlined. Suppose we had the initial parameters:

dielectric constant, the operating frequency f0, and the height h of the dielectric layer.

We have designed the following sequence:

Hypothesis: r , f 0 and h

Determination of: W, L

The design steps:

Step 1

To achieve efficient radiation, the width of the patch is calculated using the formula:

0 00 0 0

1 2 21 2 12 r

cW

f f

(1-44)


38/104



With c :speed of light , c = 310 8m/s

f 0 : Operating frequency of antenna

r

: Dielectric constant

Step 2

Determination of the effective dielectric constant of the micro strip antennas using the

formula

121 1

1 122 2

reff r reff

hW

Step 3

As the length increases due to side effects formula

0.3 0.2640.412

0.258 0.8

reff

reff

W h L h

W h

Step 4

Actual length of the patch can now be calculated by:

L = L reff +2 L

1.2.1.4 Electrical leads

Each slot radiation is described by any admittance Y (with conductance G and

susceptance B) are shown in Figure 1:10. The slots are named 1 and 2, the equivalent

admittance of slot 1 based on infinite width, uniform slot.

In that slot with a finite width W:

Y1 = G 1 jB 1 (1-45)


39/104



200

1 241

1120

hk W

G

;0

110

h

(1-45a)

10

[1 0.636ln( )120 o

W B k h

] ;

0

110

h

(1-45b)

L

W B1G 1 B2G 2

Yc

(a) Ming patch hnh ch nht (b) Ti tng ng

Figure 1.10 - Patch and Rectangle in the equivalent circuit model of the transmission

line

Slot 2 is considered as the best slot 1, its equivalent admittance

Y 2= Y 1 G2=G 1 B2=B 1

Electrical conductivity of a single slot can be calculated by analyzing the

radiation cavity model. Meanwhile, the inductor is calculated by the formula:

1 20

2| |

rad P GV

(1-46)

Use of electromagnetic fields radiated energy we have:

2

02

30

0 0

sin cos| | 2 sin2 cosrad

k W V

P d

(1-47)

So inductor in formula (1-46), can be calculated by


40/104



11 2120

I G

(1-48)

In which:

20

31

0

sin cos2 sin

cos

k W

I d

= sin2 cos( ) ( ) X X XSi X X

(1-48a)

X = k 0W

1.2.1.5 Input impedance at the resonant frequency

Leading the charge is calculated by reflecting the admittance of the 2nd slot in

the output of the input by the formula reflects the impedance of the transmission line.

In the ideal case, the two slits spaced about 1/2 with a wavelength in the dielectric.

However, due to fringing effects of the patch electrical length longer than its actual

length. Thus, the distance of two smaller slots / 2. If using reduced length is calculated

using the formula (1-39), the admittance of slot 2 is:

2 2 2 1 1Y G jB G jB

Or

2 1G G

2 1 B B

So the result is loaded into the resonance

1 2 12inY Y Y G


41/104



As a result the total number of load carried, the input impedance at resonance is

also real numbers:

1

1 1

2in in

in

Z RY G

(1-49)

Impedance at resonance is given by equation (1-49) does not take effect

between the two slots. If after this impact can adjust the formula as follows:

1 12

12( )in

RG G

(1-50)

In particular, the "+" for each distribution mode voltage resonance odd

(asymmetric) patch underneath and between the slots, the "-" solution for voltage-moderesonant distributed parity (symmetry). G12 mutual inductance is defined in terms of

the remote as follows:

12 1 220

1Re

| | sG E H dS

V (1-51)

With E 1 electromagnetic field radiation is 1 slot, H2 is the magnetic field

radiated by slot 2, V0 is the voltage across the gap, and the integral is taken over the

sphere of radius larger. Using some of the results already, G12 can be calculated:

2

0

312 0 02

0

sin cos1 2 ( sin ) sin

120 cos

k W

G J k L d

(1-52)

In that J 0 is the Bessel function of order 0 1. For the range of standard antennas,

mutual inductor G12 calculated from equation (1-52) is relatively small compared tothe G1 conductance formula (1-46) and (1-48).

As shown in formula (1-47) and (1-48), resistance does not depend on the

thickness h of the dielectric layer. In the real world, with very small values h ( k 0h


42/104



1), the resistance does not depend on h. From (1-47) and (1-48), we see resistance at

the resonance can be reduced by increasing the width W of the patch, this is acceptable

as long as the ratio W / L does not exceed 2 because the resonance effect of a single

patch will be interrupted when the ratio W / L exceeds 2.

Resistance resonance is given by formula (1.48), is described by the slot 1.

Resistance in resonance can be altered by grafting supply lines into some y0 from slot

# 1 as of 1:12. This technique can be used effectively to coordinate with the supply

impedance. The impedance of the transmission line is given by the formula

0

0

0 0

60 8ln

4120

1.393 0.667ln 1.4444 4

reff

c

reff

wh

w h Z

w wh h

0

0

1

1

wh

wh

(1-53)

In that w0 is the width of the strip line. Coupling impedance is calculated by:

2 22 21 1 1

0 0 0 021 2

1 2cos sin sin

2in c c

G B B R y y y y y

G G L Y L Y L

(1-54)

In which:

1c

c

Y Z

For most micro-strip antenna, 1 1c

GY

and 1 1c

BY

so formula (1:54) become

2 20 0 0

1 2

1cos ( 0) cos2 inin R y y y R y yG G L L

(1-55a)

Often the impedance with 50 ohm resistors should have


43/104



10

50cos

in

L y

R

(1-55b)

L

W

(a) V tr im feed cho patch antenna

1.0

0.75

0.5

0.25

0 0.5 1.00.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9y0/L

R i n

( y = y 0

) / R

i n ( y =

0 )

(a) th biu din tr khng vo

y0

Figure 1.11 - Change the location of the feed impedance to match

The value calculated by the formula (1:55) quite correctly compared with

experimental results. However, the introduction of a feed on the border between y0

also creates a physical slot formed a junction capacitance. Physical slot junction

capacitance and its small image to the resonance frequency (typically generate about1% change).


44/104



1.2.2 Model cavity

Micro-strip antenna similar to the homogeneous dielectric cavity and give us

higher-order resonances. The standardized field in the dielectric (between the patch and

the ground plane) can be found by looking at the exact space between the patch and theground plane as a resonant cavity is limited by the inductor material (in above and

below it), and from the walls (to see an open circuit) along the perimeter of the patch.

This is an approximate model which in principle leads to an input impedance response

(resonance value zero or infinity), and it does not emit any power to do. However,

assuming that the real case is similar to cases generated by this model, radiation

pattern, resulting in the load, and the resonances are relatively accurate in comparison

with experiment.

To better understand the resonant cavity model, we give a physical

interpretation of the formation in the cavity and the radiation through its walls. When

the energy patch received a distribution charge will be set at the top and bottom of the

patch, as well as on the surface of the ground plane. The charge distribution is

controlled by two mechanisms: one push mechanism and a suction mechanism.

Mechanism of electrical attraction between the different marks on the underside of the

patch and the ground plane tends to maintain focus on the underside of the charge

patch. The mechanism of the charge repulsion between the marks on the bottom

surface of the patch tends to push a couple of electric rings from the bottom of the

patch around the edges of the patch to the upper surface of the patch. The movement of

electrical charges creates the equivalent current density Jb and Jt corresponding surface

beneath and above the surface of the patch.


45/104



J t

J b r h

W

Figure 1.12 - electrical distribution and power lines

Since most of the range of actual antenna ratio on the dielectric height of the

patch width (h / W) is small, the dominant mechanism of smoking and most focus and

the flow of electricity primarily in underneath the patch, a few flow around the edges

of the patch. However, this current will decrease with the decrease of the ratio (h / W).

When you reach a certain limit, the flow on the surface of the patch will not, then in the

ideal case would seem to create tangential component of the magnetic field. This

allows as four surrounding walls created by the perfect surface that resulted from the

ideal case would not disturb the magnetic field and electric field distribution under the

patch. Due to the fact the limit of the ratio h / W, although small, tangential component

at the edges will not completely zero, but very small value. An approximate way we

see the walls surrounding the leads from this entirely will result in a good distribution

of the electric field and magnetic field under the standardized patch, making analysis

easier.

If micro-strip antenna is regarded as only a cavity, it will not be enough to

calculate the absolute magnitude of the electric and magnetic fields. In fact, regarded

by the walls of the cavity in which it is material loss at least, will not cavity radiation

and its impedance to be fully reflected. To calculate the radiation loss mechanisms are

included. That is taken into account radiation resistance resistors RA and two resistors

RL loss making in complex impedance on its function extremely complex. The saps

are taken into account by introducing the coefficient of loss tangent (loss of) effective.


46/104



Due to the thickness of the micro strip antennas very small waves generated within

dielectric (between the patch and ground) are subject to significant reflection when we

go to the edge of the patch. So only a small fraction of the energy to be radiated, so the

antenna is considered to be very inefficient. The patch below the standing wave can bedescribed by the wave function varies with the cosine. When the height of the very

small (h


47/104



x

z

y

h

L

W

Figure 1.13 - Analysis of micro-strip antenna pattern axis coordinates

With k x , k y , k z are constant wavelength along the axis x, y, z. As A1 , B1, A2 , B2,

C 2 , A3 , B3 is the integration constant that we need to determine based on the initial

conditions. The electromagnetic field in the cavity is related to the vector Ax by:

22

2

2

2

1

1

1

x x

x y

x z

E j k A

x A

E j x y

A E j

x z

01

1

x

x y

x z

H A

H z

A H

y

(1-56)

The boundary conditions for the above, the below patch and four walls around:

( ' 0, 0 ' , 0 ' ) ( ' , 0 ' , 0 ' ) 0

(0 ' , 0 ' , ' 0) (0 ' , 0 ' , ' ) 0(0 ' , ' 0, 0 ' ) (0 ' , ' , 0 ' ) 0

y y

y y

z y

E x y L z W E x h y L z W

H x h y L z H x h y L z W H x h y z W H x h y L z W

Solve the above equation using the boundary conditions we get

1 2 30, 0, 0 B B B


48/104



x

mk

h m = 0,1,2,

yn

k h n = 0,1,2

z

pk

h p = 0,1,2

From the above results, we have:

cos( ') cos( ') cos( ') x mnp x y z A A k x k y k z (1-57)

With mnp A is the amplitude coefficient of the MNP mode. As m, n, p is the

number of half wavelengths along the respective axes x, y, z.

We have:

2 2 22 2 2

x y z

m n pk k k

h L W

(1-58)

The coefficient kr is the wave propagation in the dielectric. From here we calculate the

resonant frequency:

2 2 21

( )2

r mnp

m n p f

h L W

(1-59)

To determine the dominant mode is the lowest resonance, we need to consider the

resonant frequency. Mode with the lowest frequency resonance mode called dominant.

The resonant frequency higher than the level determined by the operating mode. For

most of the micro-strip antenna h < L and h < W. If L> W> h, the dominant mode is

TM x010 , its resonant frequency is given by:

00101

2 2r

r

v f

L L (1-60)


49/104



With v0is the velocity of light in free space. If L> W> L/2> h mode higher than

the next (Monday) is TM x001 , its resonant frequency is given by:

0001

1

2 2r

r

v f

W W (1-61)

If L> L2> W> h, is TM x020 secondary mode (instead of TMx001), the resonant

frequency is given by:

00201

r

r

v f

L L (1-62)

If W> L> h is TMx001 dominant mode, the resonant frequency is given by (1-61).

Whereas if W> W / 2> L> h, the secondary mode is TM x002 . Distribution of the

tangential electric field along the walls surrounding the cavity mode in the TM x010 ,

TM x001 , TM x

020 , TM x

002 performed in the order shown in Figure 1.14


50/104



TMx

020

TM x010 TM x001

TMx

002

W

L

h

W

L

h

W

L

h

W

L

h

(a) TM x010 (b) TM x001

(c) TM x020 (d) TM x002

Figure 1.14 - The mode of the antenna radiation range

1.2.2.2 Radiation School - Mode TM x010

Micro-strip antenna radiation field radiation field is the sum of two element

array, with each element representing a slot. When two identical slots can be calculated

by the total generation capacity of the array for two slots.

The radiation slot

If remote power radiated by each slot is based on the equivalent current density

as follows:


51/104



00 0 0

0

sin( ) sin( )sin cos sin sin

2 2

r

r

jk r e

E E E E

E E

k hWE e k L X Z E j

r X Z

(1-63a)

0

0

sin cos2

cos2

k h X

k W Z

(1-63b)

When very small height (k0h


52/104



Use the equivalent current density of 1 slot no radiation along the axis + z is:

0

'2 2 cos s a y

e

y M nE a E

L

(1-70)

Similar to the z-axis. Using the same reasoning as for the radiation slot.

Standardized components crazy remote field radiated by each slot is given by:

0( )0 0

2 2

sin coscos

2 ( / 2)

jk r j X Y ek hL E e X Y E j Y e

r X Y

(1-71)

0( )0 0

2 2

sin coscos sin

2 ( / 2)

jk r j X Y ek hL E e X Y E Y e

r X Y

(1-72)

0 sin cos2

k h X

0 sin sin2

ek LY

When there are two slots radiation does not form a two-element array with

amplitude but opposite phase, separated along the z axis between the W and a

coefficient array is:

0( ) 2 sin cos2 z

k W AF j

(1-73)

When the total radiation field is determined by the distance (1-68) with coupling

coefficient array above. In the E-plane ( 0 0 0 0 090 ,0 90 , 270 360 ), (1-69) is

zero because the radiation field a quarter of each slot cycle suppressed by the radiation

field of the other slots. Similarly in the plane H ( 0 0 090 ,0 180 ) is the zero sum

suppressed by AF. This means that the radiation because this slot should be destroyed

by the radiation of the other slots. In fact, two slots away from the radiation the plane,

but the density of them in the other plane is small compared with the radiation and the


53/104



radiation of the two slots is often overlooked. Therefore they are not considered as

radiation slot.

1.2.2.3 The orientation

As the other antenna, the orientation is one of the important parameters, which

are defined as follows:

max max0

0

4

rad

U U D

U P (1-74)

For single-slot () to use the power of (1-30), the maximum intensity of radiation

and the radiated power can be written as follows:

22

0max 2

0 02

V W U

(1-75)

02

0 3

0 0

sin cos2 sin

2 cosrad

k W V

P d

So the orientation of a single slot is:2

00 1

2 1W D

I

(1-76)

In which

2

0

31

0

sin cossin2 sin 2 cos( ) ( )

cos i

k W X

I d X XS X X

(1-77)

With 0 X k W

Asymptotic value of the orientation is changed as follows


54/104



0

0

3.3 5.2dB

4 D W

00

W

W

(1-78)

For the second slot, the orientation given by:

20 2 0

2 215 rad

W w D

I G

(1-79)

In that rad G is radiation conductance and

2

0

3 2 02

0 0

sin cos2 sin cos sin sin

cos 2

e

k W k L

I d d

(1-80)

General orientation of D2 for two slots broadside radiation, the dominant mode

segregated schools TMx010 (distribution voltage asymmetry), can be written as

2 0 012

21 AF

D D D D g

(1-81)

122 21 AF D g ( 12 1 g ) (1-82)

D 0= the orientation of a single slit

D AF = coefficient of orientation of AF

0cos sin sin2

ek L AF

G12 = Relative normalized conductance = G12/G1

We have the asymptotic value of D2 following changes


55/104



2

0

6.6 8.2dB

8 D W

00

W

W

(1-83)

CHAPTER 2

MICROSTRIP ANTENNA ARRAY

In the previous chapter we have discussed and analyzed the characteristics ofthe antenna elements of a single strip. However, the radiation beam micro strip

antennas typically a relatively large and highly oriented, low-gain. In many practical

applications, we need to design the antenna orientation properties (high gain) to meet

some of the requirements of long-distance communication. To do that we need to

increase the size of the antenna. However, there is another way: instead of increasing

the size of one antenna would like to include multiple antennas to form a multiple

antenna system, called the antenna array, the shape and size appropriate, and each of

which is called a single antenna element antenna. In general, an antenna array can be a

set of arbitrary antenna elements, but in reality people often use these elements is

identical to facilitate the analysis and theory construction.


56/104



x

y

z

b/ Mng trn

a/ Mng tuyn tnh

c/ Mng 2 chiud/ Mng 3 chiu

Figure 2.1 - Four types of antenna array geometry

The total radiation field of the antenna array is determined by taking the vector

sum of the radiation from the antenna element. To get a level of radiation is high, the

orientation of the magnetic field vector element should resonate intersect in a desired

direction and cancel each other out in the remaining space. In an antenna array of the

same element, we can change the characteristics of the radiation through an array of the

following controls:

Changing the geometry of the array (linear, circular, rectangular, bridges).

Changing the relative distance between the particles.

Change the stimulus amplitude signal for each element.


57/104



Change phase excitation signal for each element.

Figure 2.1 illustrates some of the different geometry of the antenna array.

including uniform linear array, circular array, two-dimensional array, 3-dimensional

array

Within the scope of this topic, we will focus more research on two-dimensional

array antenna (planar array) is built on the basis of one-dimensional linear array. For

simplicity, we will first learn two-element antenna array as a basis for theory building

two dimensional array antennas.

2.1 TWO ARRAY ELEMENT

Suppose we consider an array of two elements of infinite horizontal dipole

antenna along the z axis as shown in Figure 2.2 (a):

d / 2

d / 2

1

2

r 1

r

r 2

x

y

d / 2

d / 2

r

y

r1

r2

(a) Hai dipole v hn (b) im kho st vng xa

Figure 2.2 - 2 geometry of the array elements along the z-axis at

The total radiation field of the array is the sum of the two radiation antenna

elements separately and in total the yz plane is given by:


58/104



1 2/2 /20

1 2 1 21 2

| cos | | cos |4

j kr j kr

t

kI l e e E E E a j

r r

(2-1)

In such is a phase difference signal between the two antenna elements, and

the signal amplitude of the radiation is the same two elements. When surveyed schools

in remote areas, as shown in Figure 2.2 (b), we have:

1 2

1

2

cos2

cos2

d r r

d r r

for phase change

1 2r r r for amplitude changes

Then (2-1) becomes

( cos )/2 ( cos )/20

0

| cos |4

1 | cos | 2cos ( cos )4 2

jkr j kd j kd

t

jkr

t

kI l e E a j e e

r kI l e

E a j kd r

(2-2)

It is clear from (2-2), we find the total field of the array is equal to the radiation

field of an antenna element with a number of human origin, called the coefficient array.

So for the two-element array with the same amplitude coefficient array given by:

12 cos cos2

AF kd

(2-3)

Standardized format:

1( ) cos cos2n

AF kd

(2-4)


59/104



The coefficient is a function of the array geometry and array signal phase

excitation. By changing the distance d and, or between two phases, the characteristic

element of the array factor and the total radiation field of the array can be controlled.

General form:

E (total) = [E (antenna in the benchmark)] [coefficient array] (2-5)

This expression is considered as the radiation rules for array elements in the

same array (array uniformity).

Each segment has its own array of coefficients and in general it is a function of

the number of elements in the array, the geometric arrangement, amplitude, phase andrelative distance of them. Expression array coefficient becomes easier when the

elements in the array have the same amplitude, and phase, and the same distance.

Because the system does not depend on an array of characteristics of the orient

themselves antenna radiation elements, so we can identify it by replacing the source

element carried by the (isotropic) and assuming a point source with phase, amplitude,

and position of the element to which it replaced. Once we have identified the

coefficient arrays using arrays of point sources, the radiation field of the array to getfrom (2-5).

In the previous chapter, we give the expression of the intensity of the antenna

elements of a single band, it was rewritten as follows:

00 0 0sin sinsin cos sin sin

2

jk r t ek hWE e k L X Z E j

r X Z

(2-6)

0 sin cos2

k h X

0 sin sin2

ek LY


60/104



Thus, the remaining problem is going to find the array AF system so that can get

a total field strength of micro strip antenna array. Here we will find an array coefficient

of linear arrays and two-dimensional array.

2.2 N ELEMENT LINEAR ARRAY - MINUTES OF UNIFORMUNIFORM AND DISTANCE

Considering the array of n identical elements are placed along the z axis as

shown in Figure 2.3 (a), assuming N elements have the same signal amplitude but the

phase difference between two consecutive elements is. When the array is called array

uniformity.

Coefficient array can be when we see the antenna element is the point source(isotropic source). When the element is not the source of the total radiation field is

obtained by the radiation field of an antenna element is taken as the reference (usually

at the origin) with a coefficient array of point sources. These are the rules of the

radiation field (2-5) and only applies to the array of the same element. Array factor is

calculated as follows:

( cos ) 2( cos ) ( 1)( cos )1 j kd j kd j N kd AF e e e

( 1)( cos )

1

N j n kd

n

AF e (2-7)


61/104



d

d

r3

y

r4

r2

r1

1

2

3

4

rN

N

d c o s ( )

#1

#2

#3

#4

2

3

N

#N

A F

(b) S pha(a) Cu trc hnh hc

Figure 2.3 - If the remote array and phase diagram of N isotropic elements

Rewrite the coefficient array:

( 1)

1

N j n

n

AF e (2-8)

With coskd Because the array is the sum of the coefficients of the exponential complexity so

it can be performed by any of the vector sum of the vectors have unit amplitude and

phase relative to the previous vector. This idea is shown in Figure 2.3 (b). From the

phase diagram we see that for the AF uniform arrays can be controlled by selecting the

appropriate phase relative. As for the heterogeneous array amplitude and phase can be

used to control AF.

AF array factor can be expressed in the reduced form as follows: je the two

sides of (2-8) and then be

2 3 ( 1)( ) ..... j j j j j N jN AF e e e e e e (2-9)


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Taking (2-9) except (2-8) have been

( 1) 1 j jN AF e e (2-10)

Or

( /2) ( /2)

( 1)/ 2(1/2) (1/2)

11

jN j N j N j N

j j j

e e e AF e

e e e

( 1)/ 2sin

21

sin2

j N

N

e

(2-11)

If benchmarking is taking care of the physical array, the array factor of (2-11) becomes

sin21

sin2

N

AF

(2-12)

To standardize the system so that the array of its maximum value by one unit,

then (2-12) is rewritten as follows:

sin1 2( )

1sin

2

n

N

AF N

(2-13)

For small values of , the above expression approximates

sin2( )

2

n

N

AF N

(2-14)

To find the null point of the array, we assign (2-14) to zero. That is:


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1 2sin 0 cos2 2 2n n

N N nn

d N

(2-15)

n = 1,2,3 .. ,2 ,3 , .....n N N N

the value of N will determine the degree of the null (level 1, level 2, ...). To survive, the

zero value of the expression arccosine argument is not greater than one. Thus the

number of null values may be a function of the distance d and phase deviation.

The maximum value of (2-13) occurs when:

11 ( cos ) cos2 2 2m m

kd m md

(2-16)

m = 0,1,2,

Array factor in (2-14) has only one maximum value and occurs when m = 0 in

(2-16), it means = 0. This is evident when one observes phase diagram in Figure 2.3

(b). When = 0, all vectors are located on a straight line. At this point AF module vector

sum of the vector module components. We have:

11 ( cos ) 0 cos2 2m m

kd d

(2-17)

So if you want the array direction of maximum radiation is the phase difference

between two consecutive antenna elements will be:

cos mkd (2-18)

3dB point of the array factor (2-14) occurs when

sin2( ) 0.707 ( cos ) 1.391

2 22

hn

N N N

AF kd N


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1 2.782cos2h d N

(2-19)

Once calculated the maximum angle () 3dB power half angle () is the half-

power beam width:

2h m h

For the array factor (2-14), there exists a maximum value (second maximum

sidelobes) and occurs when the numerator of (2-14) reached its maximum value, which

is

2 1sin sin ( cos ) 1 ( cos )2 2 2 2 s s

N N N skd kd

1 2 1cos2 s

sd N

( 2-20)

s = 1,2,3,

2.2.1. Broadside array and End-Fire array

In many applications we need to design the array so that the maximum radiation

direction perpendicular to the axis of the array of array (broadside, = 900 of Figure

2.3A). Then in order to optimize the design of the antenna array elements and factors

should be calculated as = 900 directions. For this antenna element can be done by

selecting the appropriate radiation pattern, but for us, we need an array of choices

about how and how the signal level for a reasonable element .

As we mentioned above, the peak of the array:

cos 0kd (2-21)

As to the design maximum radiation direction = 900 should be:

90cos 0okd (2-22)


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Therefore, for uniform linear array with maximum radiation direction is

broadside-axis perpendicular to the array - then all the elements in the array should be

mixed excitation signal (but it also has the same amplitude signals effect). The distance

between the elements can be any. However, to ensure there is no maximum valueappear in the other direction (called grating lobe), the distance between the elements is

not equal to a multiple of the wavelength ( , 1,2,3,...d n n ) when 0 . If

, 1,2,3,...d n n and 0 then:

0,1800

cos 2 cos 2od nkd n n

(2-23)

With this value instead of the one (2-13) will also make the system reach a

maximum value array. Thus for uniform arrays when 0 , d = n and maximum

broadside direction ( 90 o ), the array also has the maximum value in the direction

along the axis of the array ( 0,180 o ) - called end-fire radiation.

In the real world design, in addition to the main beam peak, people often avoid

the other peak beam (called grating lobe) have the same value as the main beam. This

requires the greatest distance between the particles must be smaller than a wavelength.That is maxd .

To illustrate the idea of this design, three-dimensional radiation pattern of the

array factor for uniform array of 10 elements (N = 10) with 0 and d = / 4 are

plotted in Figure 2.4 (a). We find the maximum value of the array radiation appears

only in the broadside direction ( 90 o ). For comparison, if the distance between the

particles d = increases the radiation pattern of the array coefficients are plotted inFigure 2.4 (b). I found out in the direction of maximum radiation, the array also

appeared in two different directions and maximum in 0o and 180 o .


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(a) Broadside, =90 0 (b) Broadside/End-fire, =0,90,180 0

Figure 2.4 - Graph of the three-dimensional radiation array broadside and broadside /end-fire

d = /4d =


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Figure 2.5- two-dimensional graph of the radiation array broadside and broadside /

end-fire

If the distance between the elements in 2d , the maximum range in

Figure 2.4 (b) in the direction 0o of moves to the corner 0 90o o , and the

maxima in direction 180 o will translate into the corner 90 180o o . When 2d

the maximum will occur in the direction and 0 , 60 ,90 ,120o o o o and 180 0.

To be clear, but what is

design array of microstrip antenna.docx

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