Investigation of a Small-Sized Omnidirectional Antenna

Degree project

Investigation of a small-sized omnidirectional antenna

Supervisor: Prof. Dolzhikov V.V.

Department of Foundations for Radio Engineering (Kharkov, KNURE) Department of Computer Science, Physics and Mathematics (Växjö, Linnaeus University)

Author: Iuliia Goncharova Date: 2012-03-23 Subject: Master thesis Level: Advanced Course code: 5ED05E

ABSTRACT

The purpose of this research is to find ways to create an omnidirectional antenna with high directivity in the vertical plane. The investigation is based on computer simulation using the program CST 2011. The objective is a narrow-band antenna that is omnidirectional in the horizontal plane and has maximum achievable directivity for a fixed size. Three of the most promising antenna designs are selected based on the current state of antenna technology. Their maximum directivities are estimated by means of well known relations in antenna theory. It is shown that the most suitable design is an omnidirectional antenna in the form of a cylindrical dipole antenna array with an active central dipole. For this antenna, excitation by means of a radial traveling wave, with a phase velocity smaller than speed of the light, is possible. It is found that for a certain value of a moderating factor it is possible to obtain a directivity that is 2.5 – 3 dB larger than that of a dipole or a linear antenna with uniform excitation. The antenna structures are modeled to determine the number of dipoles, their dimensions and the spacing between them that maximizes the directivity. Key words: Dipole, Directivity, Cylindrical antenna array, Omnidirectional antenna, Radiation pattern, Yagi-Uda dipole array.

TABLE OF CONTENTS

1 INTRODUCTION ...... 6

1.1 Thesis Approach ...... 6

1.2 Objective ...... 6

1.3 Thesis organization ...... 6

2 FUNDAMENTALS OF THE ANTENNA THEORY ...... 8

2.1 Simple antennas with low directivity ...... 8 2.1.1 Dipole and monopole ...... 8 2.1.2 Discone antennas ...... 10 2.1.3 Fractal monopoles ...... 10

2.2 Linear antenna arrays ...... 11

2.3 Ring antenna arrays ...... 16 2.3.1 Cylindrical ring antennas ...... 18

3 THE CHOICE OF ANTENNA DESIGN ...... 20

3.1 The estimation of the maximum achievable directivity of an omnidirectional antenna ...... 20 3.1.1 Linear broadside antenna ...... 22 3.1.2 Linear end-fire antenna ...... 23

3.2 Choice of the antenna type ...... 26

3.3 Results of the simulation ...... 27 3.3.1 Analysis of the dipole ...... 27 3.3.2 Simulation of the 6-element Yagi-Uda dipole array ...... 29 3.3.3 Simulation of the cylindrical discrete ring antenna made up of 8 two- element Yagi-Uda dipole arrays ...... 31 3.3.4 Simulation of the cylindrical discrete ring antenna which consists of 8 three-element Yagi-Uda dipole arrays ...... 34 3.3.5 Simulation of the cylindrical discrete ring antenna which consists of 8 four- element Yagi-Uda dipole arrays ...... 37 3.3.6 Simulation of the cylindrical discrete ring antenna constructed with 5- element Yagi-Uda dipole arrays ...... 40 2

3.3.7 Simulation of the cylindrical discrete ring antenna consisted of 8 six- element Yagi-Uda dipole arrays ...... 42 3.3.8 Investigation of the effect of a larger number of directive antennas on the radiation pattern of the cylindrical discrete ring antenna...... 45

CONCLUSIONS ...... 47

LITERATURE ...... 48

TABLE OF FIGURES

Figure 2. 1: Dipole...... 8 Figure 2. 2: Monopole...... 8 Figure 2. 3: Monopoles with balancers: а) a standard radial balancer; b) a slope balancer; с) a balancer with a closed ring; d) a coaxial dipole...... 9 Figure 2.4: Radiation pattern of a dipole with length 1.5...... 9 Figure 2.5: Discone antennas. A cone and a disk are made by:...... 10 Figure 2.6: Schematic representation of a linear antenna array...... 11 Figure 2.7: Array factor of the uniform equidistant linear antenna array...... 13 Figure 2.8: Schematic representation of an antenna array with a series excitation. 14 Figure 2.9: Linear antenna arrays for base stations...... 15 Figure 2.10: Schematic representation of a discrete ring antenna in a) local coordinates; b) coordinates for a far-field zone...... 18 Figure 2.11: Coordinate system of a cylindrical antenna array...... 19 Figure 3.1: Ideal radiation pattern of an omnidirectional antenna in horizontal plane………………………………………………………………………………20

Figure 3.2: Schematic representation of a linear broadside antenna...... 22 Figure 3.3: Schematic representation of a linear end-fire antenna...... 23 Figure 3.4: Radiation pattern of the half-wavelength dipole...... 28 Figure 3.5: Radiation pattern of the half-wavelength dipole in a) the vertical plane, b) the horizontal plane...... 28 Figure 3.6: Model of the 6-element Yagi-Uda dipole array...... 29 Figure 3.7: Radiation pattern of the 6-element Yagi-Uda dipole array...... 30 Figure 3.8: Radiation pattern of the 6-element Yagi-Uda dipole array a) in the E-plane, b) in the H-plane...... 31 Figure 3.9: Model of the cylindrical discrete ring antenna made up of two-element Yagi-Uda dipole arrays...... 32 Figure 3. 10: Radiation pattern of the cylindrical discrete ring antenna consisting of 8 two-element Yagi-Uda dipole arrays; the length of the active dipole is 0.6  , the separation between dipoles by radius is 0.4 ...... 33 Figure 3. 11: Radiation pattern of the cylindrical discrete ring antenna consisting of 2-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane...... 34 Figure 3.12: Model of the cylindrical antenna consisting of 3-element Yagi-Uda dipole arrays...... 34 Figure 3.13: Radiation pattern of the cylindrical antenna which consists of 3-element Yagi-Uda dipole arrays...... 36 4

Figure 3.14: Radiation pattern of the cylindrical antenna consisting of 3-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane...... 36 Figure 3.15: Model of the cylindrical antenna which consists of 8 four-element Yagi-Uda dipole arrays...... 37 Figure 3.16: Radiation pattern of the cylindrical antenna constructed of 4-element Yagi-Uda dipole arrays ...... 39 Figure 3.17: Radiation pattern of the cylindrical antenna consisting of 4-element Yagi-Uda dipole array: a) in the vertical plane, b) in the horizontal plane...... 39 Figure 3.18: Radiation pattern of the cylindrical antenna consisting of five-element Yagi-Uda dipole arrays...... 41 Figure 3.19 – Radiation pattern of the cylindrical antenna formed by 8 five-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane...... 41 Figure 3.20: Model of the cylindrical discrete ring antenna with six- element Yagi-Uda dipole arrays...... 42 Figure 3.21: Radiation pattern of the cylindrical antenna formed by 6- element Yagi-Uda dipole arrays...... 44 Figure 3.22: Radiation pattern of the cylindrical antenna formed by 6-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane...... 44 Figure 3.23: Radiation patterns in the horizontal plane of cylindrical discrete ring antennas which consist of 12 (a) and 16 (b) numbers of six-element Yagi-Uda dipole arrays...... 46

1 INTRODUCTION

1.1 Thesis Approach

Omnidirectional antennas have many applications especially in commercial communication. Omnidirectional antennas have no directivity in the horizontal plane, while the radiated power in the vertical plane has nulls on the axis of the antenna. They are used in communication systems in cities, at large industrial facilities and wherever there is a need to cover large areas where the direction of the receiver is unspecified. They are also used in wireless communication between personal com- puters in networks (PLAN), by means of Bluetooth and Wi-Fi, for example. Generality and low cost are the main advantages of omnidirectional antennas. The disadvantage is that the low directivity limits the range. An estimation of the directivity of an omnidirectional antenna, with fixed overall dimensions, and the design of a microwave diapason antenna, operating at 6 GHz, are the goals of this Master’s work.

1.2 Objective

 Design and simulation of an omnidirectional antenna with operating frequency 6 GHz.  The maximum height of the antenna is 60 mm, the maximum diameter of the antenna is 200 mm.  The impedance of the coaxial feed line is 50 Ohm.

1.3 Thesis organization

Chapter 1 contains introduction and objective. A review of existing constructions of omnidirectional antennas and their basic parameters is made in chapter 2. Calcu- lations of available directivities for several types of omnidirectional antennas with defined sizes are described in chapter 3. This section also describes the selection

of antenna type and provides the results of the simulation for the chosen antenna construction.

2 FUNDAMENTALS OF THE ANTENNA THEORY

Omnidirectional antennas can be divided into two groups:  simple antennas with a low directivity. Their size is smaller than the wavelength.  Antenna arrays – linear and ring arrays, their directivity can achieve large values.

2.1 Simple antennas with low directivity

2.1.1 Dipole and monopole

The simplest omnidirectional antenna is a dipole (Fig. 2.1). The radiation pattern in the H – plane is a does not depend on the azimuth. In practice use a monopole (Fig. 2.2) since for the low frequencies the overall dimensions of dipoles are big.

Figure 2. 1: Dipole. Figure 2. 2: Monopole.

A monopole is one arm of a dipole, which is placed perpendicularly to a conductive plane. The foundation is the image principle, which states that a monopole placed perpendicularly to a conductive plane, is equivalent to two monopoles with a total length equal to twice the length of the upper monopole. In this case a second monopole is a mirror image of a first monopole. To improve efficiency of monopoles and to reduce ground influence on antenna parameters uses a ground plane or a balancer under the antenna. An earth plane is a 8

system of buried conductors. A ground plane could be a system of conductors which are located on some height above the ground. The dimensions of a ground plane or a balancer must be large and the distance between conductors must be smaller than a quarter of a wavelength [4]. Standard configurations of balancers are presented in Fig. 2.3.

Figure 2. 3: Monopoles with balancers: а) a standard radial balancer; b) a slope balancer; с) a balancer with a closed ring; d) a coaxial dipole. Fig. 2.4 presents a radiation pattern of a dipole with the length 1.5.

Figure 2.4: Radiation pattern of a dipole with length 1.5. In practice one usually uses half-wavelength dipoles. It allows reduction of the side lobe levels. 9

Dipoles and monopoles have low cost and a simple configuration; they can be used for large powers, but they have a small directivity (1.7 dB). Their bandwidth is nearly 1 GHz. Dipoles are used from UHF to EHF diapasons, monopole are used for VHF up to EHF diapasons.

2.1.2 Discone antennas

Discone antennas (Fig. 2.5) are the most widespread antennas. They have a large bandwidth (above 2800 MHz) and the input resistance is 50 Ohm, but a small directivity – approximate 1 dB. There are some restrictions for the operating bandwidth for this type of antennas. For low frequencies it occurs when the length of a cone is much less than a quarter wavelength, and at high frequencies it is associated with the accuracy of fabrica- tion [4]. A bicone antenna, as a variant of a discone antenna, is used. In this case a disc is exchanged on a short cone with a big opening angle. Both antenna types are used in the diapason from LF up to EHF.

Figure 2.5: Discone antennas. A cone and a disk are made by: a) a sheet metal, b) a set of monopoles.

2.1.3 Fractal monopoles

Fractal monopoles are obtained from a classical monopole by consecutive division of their tops into two parts at a given angle (from 30° tо 60°). The full electrical

length of this antenna can be determined as a distance between a kernel of a fractal and an end of any of its branch. Each new iteration increases a number of conductive ways at ends of this antenna and decreases a resonant frequency for its fixed height. This method allows for a wide bandwidth and efficiency. The radiation pattern of a fractal monopole is very close to that of a half- wavelength dipole. A fractal technique allows placing antenna elements denser than the simple antenna elements with the same value of their mutual interference.

2.2 Linear antenna arrays

Linear antenna arrays are antennas which are formed by identical and similarly oriented radiators lying on a straight line. This antenna type can have an omnidirectional radiation pattern, which is perpen- dicular to the axis of the antenna, only when the following conditions are met:  the phase of the excitation must be identical for each element of the antenna array,  the elements must have an omnidirectional pattern. The schematic representation of a linear antenna array is pictured in Fig. 2.6.

Figure 2.6: Schematic representation of a linear antenna array.

The far-field of a linear antenna array is calculated by following formula:

E(,)  F(,) f (,), (2.1)

with F(,) – the far-field of an even radiator,

N f (,)  eij – an array factor, i0

  kdi cos  , 2 k – a wave number, k  ,   – a wavelength,

di – a distance between neighbor elements,  – an elevation angle, counted from the antenna axis,  – a phase shift between neighbor elements. For an omnidirectional equidistant antenna array, with N elements, the array factor is:

 N  sin   2 f (,)    . N  (2.2) 2

The formula (2.2) is true iff the separation between antenna elements is much smaller than the wavelength. The array factor of a uniform equidistant linear antenna array with 5 elements N=5, and separation 0.3, is presented in Fig. 2.7 [1].

Figure 2.7: Array factor of the uniform equidistant linear antenna array.

The directivity of this type of antennas is determined by the following formula as- suming that the linear dimensions of the array is much larger than the wavelength

L Dmax  2 . (2.3) 

There are two types of excitation of linear arrays:  series,  parallel.

2.2.1 Linear antenna arrays with a series excitation

An array consisting of half-wavelength dipoles with series excitation is shown in Fig. 2.8. As can be seen from the Fig. 2.8 a phasing of currents in the elements is achieved by the cross-connection of coaxial cables. External and internal conductors of half- wavelength parts are cross-connected.

Figure 2.8: Schematic representation of an antenna array with a series excitation.

Both the inner and the outer connector then act as a feed. Radiators are connected to these. The operating bandwidth is narrow for this type of antenna. This can be explained by phase errors between two neighbor elements, when the resonant frequency is shifted. The directivity of these antennas is approximately 10 dB. It is limited by the following factors: mechanical instability of a long antenna, decreasing amplitude away from the feed point (this fact is explained by the loss of a power for radiation). The narrowing of the bandwidth with increasing length is a major problem for arrays with series excitation. It is due to increased input impedance and the transfor- mation coefficient of an input circuit [4].

2.2.2 Antenna arrays with a parallel excitation

Arrays with parallel excitation have much better properties. They have an approximate constant directivity, a smooth radiation pattern and approximately constant 14

voltage standing-wave ratio for the entire operating bandwidth. For example, an antenna array consisting of 8 dipoles gives the directivity 10 dB, a relatively smooth radiation pattern and a voltage standing-wave ratio 1.48dB for frequencies 250…400 MHz. This antenna is used for air-to surface communication. Antennas can be designed by using a combination of series and parallel excitation types. For example the antenna construction can consist of two antenna arrays with series excitation, which are connected to each other by means of parallel excitation. In this case the form of the radiation pattern is more stable. Fig. 2.9 shows examples of a practical realization of linear antenna arrays for base stations. This method of mounting of radiators (Fig. 2.9a) allows a directivity of about 10 dB in the forward direction but only 4 dB in the reverse direction. The value of the directivity depends on the diameters of radiators and the distance between radiators and mast axis. The reverse directivity can be increased by finding the optimal distance between mast and radiators for fixed operating frequency and dimensions.

a b c Figure 2.9: Linear antenna arrays for base stations.

A one-side antenna (Fig. 2.9a) is used when a base station is located at a boundary of a cover region. The antenna pictured in Fig. 2.9b has a distorted radiation pattern in the vertical plane. This is explained by a phase shift which depends on the placement of di-

poles. Also, the directivity of this antenna decreases to 6 dB but it is constant for all directions in the case of a four-element antenna array. The next way to increase directivity and get a smooth radiation pattern is shown in Fig. 2.9c. In this case dipoles are placed in pairs and cophasally. This antenna array gives some improvement since the phase centers of each set lie at the mast axis. However this construction is expensive and 8 dipoles give a directivity of only 6 dB [1].

2.3 Ring antennas

There are several types of ring antennas:  continuous;  discrete. Ring antennas can have various forms (cylindrical, spherical, conical and so on). A continuous ring antenna is an antenna in the form of a hollow body of rotation made of a solid conductive material [3]. Let us divide the antenna surface into M radiating areas of equal size in order to analyze the far-field. An angular coordinate of each area in the radiation plane is  ; the radiation pattern of a separate area is G(  ,) . The antenna is excited by a continuous current I  [2]. So this antenna has a far-field given by the following expression:

M 2 E(,)   I()G(  ,)d . (2.4) 2 0

Let the excitation current symmetrical and given by the expansion:

 I()  I n cos n . (2.5) n0

The expression for the radiation pattern of an apart radiant area can be expanded into the series:

 G(  ,)  f ()Fm cos[m(  )], (2.6) n0

where f () – is an array factor. It defines a form of the radiation pattern in the vertical plane,

Fm – is an expansion coefficients of the expression of the radiation pattern in the horizontal plane. Let us insert (2.5) and (2.6) into (2.4) and integrate the obtained equation. After all operation the following formula of the far-field of a continuous ring antenna [2] is obtained:

 1 E(,)  Mf () I n Fn ()cos n , (2.7) n0  n

1 if n  0,  n   2 if n  0.

A discrete ring antenna is a set of identical antenna elements which are placed on a surface of a body of rotation. The schematic representation of a discrete ring antenna in the radiation plane is depicted in Fig. 2.10. The expression for the far-field in the horizontal plane of an equidistant discrete ring antenna looks as follows:

M jkRcos(n) E()  I nG(  n)e . (2.8) n1

а) b) Figure 2.10: Schematic representation of a discrete ring antenna in a) local coordinates; b) coordinates of the far-field zone.

2.3.1 Cylindrical ring antennas

A cylindrical ring antenna possesses an omnidirectional radiation pattern, which is narrower in the vertical plane than that of a linear antenna array. It is practical to represent a cylindrical ring antenna as a set of Q identical ring antenna arrays (rings); each ring has P elements [2]. A cylindrical discrete ring antenna is a linear antenna array which has rings of radiators as elements according. Let us assume that all radiators are identical, symmetrical and placed equidistantly on the surface of a cylinder. Let the excitation current of a p-th element of the q-th ring be:

I pq  I( p , zq ) , (2.9)

where  p – is the angle of a р-th element,

zq – is the position of a q-th ring along the z axis. The geometry and the coordinate system of a cylindrical antenna array are presented in Fig. 2.11.

Figure 2.11: Coordinate system of a cylindrical antenna array.

In the general case the expression for the radiation pattern of a cylindrical discrete antenna looks as follows:

P Q jqu E(,)  I pqG(   p ,)e , (2.10) p1 q1 whereu  kdsin , d – is the distance between rings. Basic types of omnidirectional antennas were reviewed in this section. It was found that simple omnidirectional antennas have a low directivity but also a low cost. To obtain higher directivity it is necessary to use a more complicated design that is harder to implement and more expensive. It is clear that further investigation into this field of antenna technology is needed.

3 THE CHOICE OF ANTENNA DESIGN

This section describes the design of an omnidirectional antenna with vertical polariza- tion. The directivity of the chosen antenna is also estimated. The antenna should fit into a cylindrical volume of height H  60mm and radius R 100mm. The wavelength (the operating frequency is f  6GHz) is   50mm and the impedance of the coax feed line is Z0  50Ohm. Basic requirements:  as large a directivity as possible;  simplicity of the design;  a low cost. The maximum directivity of an antenna with a specified size is estimated and used as a design criterion.

3.1 The estimation of the maximum achievable directivity of an omnidirectional antenna

The directivity of an antenna depends on its radiation pattern. The ideal radiation pattern of an omnidirectional antenna is shown in Fig. 3.1.

Figure 3.1: Ideal radiation pattern of an omnidirectional antenna in horizontal plane.

In order to calculate the maximum directivity of an omnidirectional antenna one may use [5].

4F 2 (,) Dmax   , (3.1) 2 2   F 2 (,)sindd  0  2

where F(,) – is a normalized radiation pattern,

f (,) F(,)  , (3.2) fmax (,)

 – is the elevation angle, in this case counted from the axis of the antenna,  – is the azimuth angle. With a uniform radiation (Fig. 3.1) one has:

   0,  [ 0 , 0 ]; F()  2 2 (3.3)    1,  [  ,  ].  2 0 2 0

Inserting (3.3) into (3.1) gives us: 4 4 D   . max   0  2 2 2 0  sindd 2 cos 0   0  2 2 0 After substituting of limits of the integration one obtains the following equation:

1 Dmax  . (3.4) sin0

This formula is not accurate, since an ideal radiation pattern cannot be realized, but it shows that the beamwidth must be reduced to increase directivity. Let us consider some examples.

3.1.1 Linear broadside antenna

The normalized radiation pattern of a cophased linear antenna excited uniformly (Fig. 3.2) is given by the following relation

 kH  sin cos  2 F     , (3.5)  cos  2 where k – is the wave number, k  ,   – is the elevation angle counted from the antenna axis (Fig. 3.2).

Figure 3.2: Schematic representation of a linear broadside antenna.

The First-null beamwidth of an antenna is determined using the following condition: F()  0, (3.6) so

kH cos   2 0    arccos . (3.7) 0 H The First-null beamwidth is then  2  2arccos . (3.8) 0 H

3.1.2 Linear end-fire antenna

Assume constant amplitude for the current on the antenna shown in Fig. 2.3.

Figure 3.3: Schematic representation of a linear end-fire antenna.

The radiation pattern is determined by the following expression: sin F()  R , (3.9) 

kR where   (  cos) , 2 c   – is the moderating factor of the wave in an antenna, v c – is the speed of light, v – is the phase velocity. The most interesting cases are following:   1, the phase velocity is the same as the speed of light. Antennas with this property are called ordinary antennas.

  1, the phase velocity is smaller than the speed of light. These antennas are called travelling wave antennas [5]. The First-null beamwidths of these two types of antennas are calculated. For both antenna types a half of a First-null beamwidth is determined according to the following condition: F()  0, that is    so  cos    . 0 R  2 When  1 one has cos  1 0 0 0 2

   20  2 21   (3.10)  R 

For an ordinary antenna with 1the First-null beamwidth is

 2 0  114 2 , (3.11) 0 R and for the travelling wave antenna and one has,

 2 114 . (3.12) 0 R Equations (3.11) and (3.12) that end-fire antennas can have smaller beamwidths than broadside antennas. These widths are given by:  for an ordinary end-fire antenna:

  114 2  114 , (3.13) R1 H  for a travelling wave antenna:

  114 114 . (3.14) R2 H

So for an ordinary antenna:

H 2 R  2 , (3.15) 1  and for a travelling wave antenna:

H 2 R  . (3.16) 2 

The values R1 and R2 are calculated:

R1 144mm,

R2  72mm.

It is obvious that for R2  72mm the beamwidth of an end-fire antenna will be in 1.2 times smaller than of a broadside antenna and consequently have a larger directivity. The results show that end-fire antennas are better as antenna elements in an omnidirectional antenna to obtain the maximum directivity which can be achieved by antennas of this type. Two antennas are examined regarding directivity. The first one is a broadside dipole with height H= 60 mm and the second one is the end-fire antenna consisting of dipoles. The length of the end-fire antenna is R 100mm. To simplify calculations, both antennas are assumed to have toroidal radiation patterns with unit outer radius and ze- ro inner radius. The directivity of the dipole is given by [1]:

2 2F max   Ddipole   , 2  F 2  sind   2 (3.17)

 kH   kH  cos cos   cos  2 2 F       . (3.18) sin

Equation (3.18) is a normalized radiation pattern of a dipole with height H. The directivity is Ddipole  2.15dB . The directivity of the end-fire antenna array is determined as follows.

2 2F max   DCAA   , 2 2  F  sind   2

F   Fdipole Fsyst  ,

coskHsin  coskH F    , dipole (1 cos(kH))cos

 kR  sin   cos  2 F      , syst kR   cos  2    1 . 2R The directivity of the cylindrical antenna array made up of end-fire antennas (R=100mm, H=60 mm, =1.45) is 7.3 dB. The corresponding dipole has a directivity about 5 dB.

3.2 Choice of the antenna type

In this investigation one looks for an antenna that is cheap and has simple design and high directivity. In addition, it also should be as small as possible.

Hence, the investigated antenna will be a ring cylindrical antenna with Yagi-Uda dipole arrays as elements. Let the separation between elements in the Yagi-Uda be 0.35. The number of passive directors is 5 (the antenna radius equals to 87.5 mm); the number of Yagi-Uda antennas is 8. The excitation of the ring antenna array will be realized by means of one active dipole in the center. This antenna construction will be realized as follows. Hollow cylinders with width 0.35 and with inner radii 0.35, 0.7, 1.05, 1.40 and 1.75 are made of a radiolu- cent material. Printed dipoles are placed on each cylinder. Then the cylinders are placed concentrically according to radius. The dipoles are placed radially so as to form Yagi-Uda antennas. Separate parts as well as the antenna as a whole are simulated in order to maximize directivity. The simulation is performed to get maximum directivities. The program CST Studio is used for the simulation. The basic input data for the simulation:  the operating frequency is 6 GHz (the wavelength   50mm),  the coaxial feed line has a resistance of 50 Оhm,  radii of dipoles are 0.004,  the length of the active dipole is 25 mm (0.5),  the lengths of the passive dipoles are 17.5 mm (0.35, the shortening is 15% [5])  the material of the dipoles is assumed to be a perfect electrical conductor without losses. 3.3 Results of the simulation

3.3.1 Analysis of the dipole

As a first step the half-wavelength dipole with radius 0.2 mm is simulated. The radiation pattern of the dipole and its vertical and horizontal planes are presented in Fig. 3.4 and 3.5.

Figure 3.4: Radiation pattern of the half-wavelength dipole.

a) b) Figure 3.5: Radiation pattern of the half-wavelength dipole in a) the vertical plane, b) the horizontal plane.

The maximum directivity of the half-wavelength dipole with radius 0.2 mm is 2.02 dB. The input impedance then equals to 99+j73.3 Ohm. The radiation pattern of this antenna is smooth.

3.3.2 Simulation of the 6-element Yagi-Uda dipole array

As stated earlier, the separation between dipoles in the Yagi-Uda antenna is 0.35. The height of the active dipole is 0.5, while the heights of passive dipoles are 0.35. Fig. 3.6 shows the model of the antenna.

Figure 3.6: Model of the 6-element Yagi-Uda dipole array.

This antenna is simulated for several sizes of dipoles and separations between them. Results of the simulation are presented in Table 3.1.

Table 3.1 Results of the simulation of the 6-element Yagi-Uda dipole array. Length of Separation Input im- Reflection Directivity, Back lobe the active between pedance, coefficient, dB level, dB dipole,  dipoles,  Ohm dB 0.4 0.3 22-j131 -0.9 6.6 2.2 0.35 22-j129 -1 6.5 2.7 0.4 23-j131 -1 6.1 2.8 0.5 0.3 132+j91 -4 6.7 2.5 0.35 136+j98 -4 6.6 3.0 0.4 138+j98 -4 6.5 2.8 0.6 0.3 709+j23 -1 7.1 3.0 0.35 753-j11 -1 6.9 3.6 0.4 744-j10 -1 6.9 3.5

It is clear from Table 3.1 that the largest value of the directivity of the 6-element Ya- gi-Uda dipole array is 7.1 dB for the following case: — the height of the active dipole is 0.6 ; — the separation between elements is 0.3 . The radiation pattern of this antenna is depicted in Figs. 3.7 and 3.8.

Figure 3.7: Radiation pattern of the 6-element Yagi-Uda dipole array.

a) b) Figure 3.8: Radiation pattern of the 6-element Yagi-Uda dipole array a) in the E-plane, b) in the H-plane.

This antenna is directional, and its directivity is 7.1 dB. In order to obtain an omnidirectional antenna, several radially placed described antennas are needed. Consider 8 such arms with one common active dipole in the center. Let start with the cylindrical discrete ring antenna, consisting of 2-element Yagi-Uda antennas, and then add one passive dipole at each step.

3.3.3 Simulation of the cylindrical discrete ring antenna made up of 8 two- element Yagi-Uda dipole arrays

The design is shown in Fig.3.9.

Figure 3.9: Model of the cylindrical discrete ring antenna made up of two-element Yagi-Uda dipole arrays.

The results from the simulation are presented in Table 3.2. Table 3.2 Results for a cylindrical array consisting of 8 two-element Yagi-Uda dipole arrays. Length of Separation Input im- Reflection Ribbing, Directivi- the active between pedance, coefficient, dB ty, dB dipole,  dipoles,  Ohm dB 0.4 0.3 13-j133 -0.5 0 2.9 0.35 17-j130 -0.8 0 3.0 0.4 23-j132 -1 0 3.1 0.5 0.3 77+j142 -2 0 3.1 0.35 107+j160 -2 0 3.2 0.4 140+j167 -2.5 0 3.3 0.6 0.3 814+j598 -0.7 0 3.6 0.35 1051+j395 -0.7 0 3.7 0.4 1061+j121 -0.8 0 3.7

The largest value of the directivity is 3.7 dB for an antenna with active dipole length 0.6  , passive dipole length 0.35 , and the radial separation between dipoles 0.4 . This antenna is omnidirectional in the horizontal plane and has no ribbing of the radiation pattern. The radiation pattern is smooth due to a small amount of the elements and negligible interference between them. This cylindrical array is not matched to the feed line (50 Ohm) and requires an addi- tional matching circuit. The spatial radiation pattern and the patterns in the E- and H-planes of this antenna are shown in Figs. 3.10 and 3.11.

Figure 3.10: Radiation pattern of the cylindrical discrete ring antenna consisting of 8 two-element Yagi-Uda dipole arrays; the length of the active dipole is 0.6 , the separation between dipoles by radius is 0.4 .

This antenna structure is a rather more complicated than half-wavelength dipole. Be- cause of this it has the directivity 1.7 dB large than that of dipole.

a) b) Figure 3. 11: Radiation pattern of the cylindrical discrete ring antenna consisting of 2-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane.

3.3.4 Simulation of the cylindrical discrete ring antenna which consists of 8 three-element Yagi-Uda dipole arrays

The next step is the modeling of the cylindrical discrete ring antenna constructed of 3- element Yagi-Uda dipole array. The antenna is shown in Fig. 3.12.

Figure 3.12: Model of the cylindrical antenna consisting of 3-element Yagi-Uda dipole arrays.

Results of the simulation are presented in Table 3.3.

Table 3.3 Results of the simulation of the cylindrical antenna constructed of 8 three- element Yagi-Uda dipole arrays. Length of Separation Input im- Reflection Ribbing, dB Directivity, the active between pedance, coeffi- dB dipole,  dipoles,  Ohm cient, dB 0.4 0.3 11-j122 -0.6 0 2.9 0.35 12-j123 -0.6 0.1 3.2 0.4 17-j114 -0.9 0.4 3.7 0.5 0.3 75+j116 -3 0 3.2 0.35 81+j142 -2.5 0.1 3.3 0.4 101+j164 -2.3 0.2 3.7 0.6 0.3 810+j424 -0.8 0 3.6 0.35 1232+j435 -0.6 0 4.0 0.4 1293-j379 -0.6 0.4 4.5

The best value of the directivity with acceptable ribbing (0.4 dB) in the radiation pattern is 4.5 dB. This is obtained for a cylindrical array with active dipole length 0.6 , passive dipole length 0.35 , and with radial separation between elements 0.4 . This antenna has a large reflection coefficient (-0.6 dB) and requires matching devices. The radiation pattern and the sectional radiation patterns in E- and H-planes of the antenna are presented in Figs. 3.13 and 3.14.

Figure 3.13: Radiation pattern of the cylindrical antenna which consists of 3-element Yagi-Uda dipole arrays.

a) b) Figure 3. 14: Radiation pattern of the cylindrical antenna consisting of 3-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane.

It is obvious that the form of the radiation pattern is not smooth. This fact can be explained as follows. This antenna can be seen as 2 concentric discrete ring antennas with radius 0.4 and 0.8, respectively. The distance between dipoles on the outer circle is as much as 0.77 and this causes ribbing in the radiation pattern.

3.3.5 Simulation of the cylindrical discrete ring antenna which consists of 8 four- element Yagi-Uda dipole arrays

The antenna of this construction is shown in Fig. 3.15.

Figure 3.15: Model of the cylindrical antenna which consists of 8 four-element Yagi-Uda dipole arrays.

The cylindrical ring discrete antenna is simulated for several parameter combinations as shown in Table 3.4.

Table 3.4: Results of the simulation of the cylindrical antenna which consists of 8 four-element Yagi-Uda dipole arrays. Length of Separation Input im- Reflection Ribbing, dB Directivi- the active between pedance, coeffi- ty, dB dipole,  dipoles,  Ohm cient, dB 0.4 0.3 14-j119 -0.7 1.0 4.1 0.35 15-j126 -0.7 1.9 4.3 0.4 14-j115 -0.8 1.0 4.0 0.5 0.3 97+j124 -3.2 1.0 4.4 0.35 92+132 -2.9 1.9 4.7 0.4 108+j180 -2 1 4.4 0.6 0.3 890+j176 -0.9 0.9 4.7 0.35 946+j355 -0.8 2 4.9 0.4 1455-j88 -0.6 1 5.0

The maximum directivity of 5.0 dB is achieved by the antenna with the length of the active dipole of 0.6 and the separation between dipoles of 0.4. The ribbing of the radiation pattern of the antenna described above is occurred be- cause of interference between antenna elements and it equals to 1dB.This value is admissible. The spatial radiation pattern and its sections for the best antenna of this construction are depicted in Figs. 3.16 and 3.17.

Figure 3.16: Radiation pattern of the cylindrical antenna constructed of 4-element Yagi-Uda dipole arrays

a) b) Figure 3. 17: Radiation pattern of the cylindrical antenna consisting of 4-element Yagi-Uda dipole array: a) in the vertical plane, b) in the horizontal plane.

3.3.6 Simulation of the cylindrical discrete ring antenna constructed with 5- element Yagi-Uda dipole arrays

The following antenna consists of 8 five-element Yagi-Uda antennas. The design is similar but now involves 4 passive and one active dipole. Table 3.5 Results of the simulation of the cylindrical array formed by 5-element Yagi-Uda dipole arrays. Length of Separation Input im- Reflection Ribbing, dB Directivity, the active between pedance, coefficient, dB dipole,  dipoles,  Ohm dB 0.4 0.3 11-j122 -0.54 0.4 4.0 0.35 15-j122 -0.7 3.3 5.6 0.4 17-j121 -0.9 1.5 4.3 0.5 0.3 77+j129 -2.7 0.3 4.2 0.35 89+j135 -2.8 1.5 4.9 0.4 107+j152 -2.6 2.8 5.2 0.6 0.3 944+j424 -0.8 0.2 4.4 0.35 999+j167 -0.8 4.4 6.5 0.4 1248+j131 -0.7 1.5 5.1

The largest value of the directivity is 6.5 dB but in this case there is strong ribbing (4.4 dB). It is therefore better to use the parameters: — the height of the active dipole is 0.6 ; — the heights of passive dipoles are 0.35 ; — the separation between elements is 0.4 . In this case the directivity is 5.1 dB, and the ribbing only 1.5 dB. The matching to the feed line is poor (reflection coefficient -0.7) so matching devises are needed. Ribbings in the radiations patterns are caused by interference between adjacent Yagi-Uda antennas.

The radiation pattern and its horizontal and vertical sections are depicted in Figs. 3.18 and 3.19.

Figure 3.18: Radiation pattern of the cylindrical antenna consisting of five-element Yagi-Uda dipole arrays.

a) b) Figure 3. 19 – Radiation pattern of the cylindrical antenna formed by 8 five-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane.

3.3.7 Simulation of the cylindrical discrete ring antenna consisted of 8 six- element Yagi-Uda dipole arrays

This antenna is presented in Fig. 3.20.

Figure 3.20: Model of the cylindrical discrete ring antenna with six-element Yagi-Uda dipole arrays.

Results of the simulation appear in Table 3.6.

Table 3.6: Results of the simulation of the cylindrical antenna which consists of 6-element Yagi-Uda dipole arrays. Length of Separation Input im- Reflection Ribbing, Directivi- the active between pedance, coefficient, dB ty, dB dipole,  dipoles,  Ohm dB 0.4 0.3 13-j130 -0.6 4.3 5.7 0.35 14-j128 -0.6 2.8 5.2 0.4 18-j127 -0.8 3.5 5.6 0.5 0.3 87+j113 -3.3 4.2 5.9 0.35 95+j153 -2.4 2 5.4 0.4 119+j155 -2.6 3.6 6.0 0.6 0.3 814+j349 -0.9 3.6 6.4 0.35 1197+j317 -0.7 3.2 5.1 0.4 1135+j63 -0.8 2.7 5.2

In this case the best value of the directivity (6.4 dB) with acceptable ribbing (3.6 dB) was achieved for antenna with following dimensions: — the height of the active dipole is 0.6; — the heights of passive dipoles are 0.35; — the separation between dipoles is 0.3. Since the matching is poor (reflection coefficient -0.9) a matching device is needed. The radiation pattern and its horizontal and vertical sections are presented in Figs. 3.21 and 3.22.

Figure 3.21: Radiation pattern of the cylindrical antenna formed by 6-element Yagi-Uda dipole arrays.

a) b) Figure 3. 22: Radiation pattern of the cylindrical antenna formed by 6-element Yagi-Uda dipole arrays: a) in the vertical plane, b) in the horizontal plane.

The directivity of the previously described antenna is approximately 1 dB smaller than the directivity of the separate 6-element Yagi-Uda antenna array. This fact and

the ribbing of the radiation pattern can be explained by interference between adjacent directional antennas in the cylindrical array. We try to prevent ribbing by increasing the number of directive antennas to 12 or even 16.

3.3.8 Investigation of the effect of a larger number of directive antennas on the radiation pattern of the cylindrical discrete ring antenna.

The radiation pattern of the cylindrical discrete ring antenna formed by 8 six-element Yagi-Uda dipole arrays (the height of the active dipole is 0.6, heights of passive are 0.35, the spacing is 0.3) has ribbing. We try to prevent it increasing the number of directive antennas. H-section radiation patterns of the cylindrical antenna arrays with different numbers of directive elements are presented in Fig. 3.23.

b) Figure 3. 23: Radiation patterns in the horizontal plane of cylindrical discrete ring antennas which consist of 12 (a) and 16 (b) numbers of six-element Yagi-Uda dipole arrays.

As shown, radiation patterns are appreciable distorted due to the interference between Yagi-Uda dipole arrays. So the quantity-increase gives no possibility to take off the ribbing. The cylindrical discrete ring antenna with 8 six-element Yagi-Uda antennas has a large directivity considering that it is omnidirectional in the horizontal plane. The ribbing is admissible and this antenna is therefore suitable for practical use.

CONCLUSIONS

This Master’s work investigates ways of creating an omnidirectional antenna with high directivity in the vertical plane. The directivity was computed for two omnidirectional antenna types: the broadside antenna and the array formed by end-fire antennas. It was found that the directivity is 4.8 dB for the first antenna, and 7.2 dB for the second, for fixed values of the height and length. For further work, the cylindrical antenna array was chosen, in the form of 8 radially oriented Yagi-Uda dipole arrays (6- elements, 1 active and 5 passive dipoles). An explorative simulation showed that the maximum directivity of this antenna is 6.4 dB. It was also found that adjacent directional antennas interfere so as to produce ribbings in the radiation pattern. A reduction in the directivity occurs since the effective height of the simulated antenna is smaller than that of the antenna in the theoretical calculation. An increase in the number of directional antennas does not improve the radiation pattern.

LITERATURE

[1] C.А. Balanis Antenna theory: Analysis and design 3d edition, John Wiley & Sons Inc., 2005. [2] R.C. Hansen Phased array antennas, John Wiley & Sons Inc., 2009. [3] Lars Josefsson, Patrik Persson Conformal array: Antenna theory and design, John Wiley & Sons Inc, 2006 – 471 р. [4] J.L. Volakis Antenna engineering handbook 4 edition, McGrow-Hill, 2007, 1755 p. [5] Я.С. Шифрин Антенны, Издательство академии имени Говорова, 1976 – 407с. (Y.S. Shifrin Antennas, Publishing house of Govorov academy, 1976 – 407 p.) [6] Е. Янке, Ф. Эмде, Ф. Лёш Специальные функции, М.: Наука, 1964 – 344 (E. Yanke, F. Emde, F. Lesh Special functions, Moscow: Science, 1964 – 344 p.)