This paper explores the analytical methods of synthesizing linear antenna arrays. The synthesis employed is
based on non-uniform methods. In particular, the Dolph-Chebyshev and binomial methods are used, so as to
improve the directivity of the array and to reduce the level of the secondary lobes by adjusting the geometrical
and electric parameters of the array. The radiation patterns, the directivity, and the array factors of the uniform
and the non-uniform methods are presented. It is shown that the Chebyshev arrays have better directivity than
binomial arrays for the same number of elements and separation distance, while binomial arrays have very low
side lobes compared with Chebyshev and uniform excitation arrays. Finally, numerical results of both methods
are analyzed and compared.
An antenna array (or array antenna) is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antenna elements are connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together (interfering constructively) to enhance the power radiated in desired directions, and cancelling (interfering destructively) to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions.
An antenna array (or array antenna) is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antenna elements are connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together (interfering constructively) to enhance the power radiated in desired directions, and cancelling (interfering destructively) to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions.
Kinds of Propagation Models
Models of Different Types of Cells
Web Plot Digitizer Tool
Study of the parameters fc, d, hb, hm and Coverage Environments for each of OKUMURA, HATA and COST231
MATLAB Simulation
This thesis focuses on mobile phones antenna design with brief description about the historical development, basic parameters and the types of antennas which are used in mobile phones. Mobile phones antenna design section consists of two proposed PIFA antennas. The first design concerns a single band antenna with resonant frequency at GPS frequency (1.575GHz). The first model is designed with main consideration that is to have the lower possible PIFA single band dimensions with reasonable return loss (S11) and the efficiencies. Second design concerns in a wideband PIFA antenna which cover the range from 1800MHz to 2600MHz. This range covers certain important bands: GSM (1800MHz & 1900MHz), UMTS (2100MHz), Bluetooth & Wi-Fi (2.4GHz) and LTE system (2.3GHz, 2.5GHz, and 2.6GHz). The wideband PIFA design is achieved by using slotted ground plane technique. The simulations for both models are performed in COMSOL Multiphysics.
The last two parts of the thesis present the problems of mobile phones antenna. Starting with Specific absorption rate (SAR) problem, efficiency of Mobile phones antenna, and hand-held environment.
Possible media for communication
Introduction to Communication Media
Introduction to Microwave communication
Manufacturers of Microwave
Why Microwave?
Characteristics of microwave
Types of Microwave communication
Types of Microwave Links
Requirements for the microwave communication
What is LOS?
Wave Propagation in the atmosphere
Multi path Propagation
LOS Purpose & requirements
Limitations of Line of Sight Systems
Design of Line of Sight Microwave Links
K- factor
Variations of the ray curvature as a function of k
Fresnel zone
Obstacles & Loses
Knife Edge Obstacles
Smooth Spherical Earth Obstacles
Path Loss
Other losses
Why vertical polarization favorable at high freq
Antenna type & Gain
RECEIVER SENSITIVITY, FADE MARGIN AND SIGNAL TO NOISE RATIO
Fading Margin
Reliability
DESIGN OF RECTANGULAR PATCH ANTEENA USING METAMATERIAL SUBSTRATEPrateek Kumar
Dissertation part-1 presentation on design of rectangular patch antenna using metamaterial substrate by Prateek Kumar from RUSTAMJI INSTITUTE OF TECHNOLOGY BORDER SECURITY FORCE TEKANPUR GWALIOR (M.P).
Kinds of Propagation Models
Models of Different Types of Cells
Web Plot Digitizer Tool
Study of the parameters fc, d, hb, hm and Coverage Environments for each of OKUMURA, HATA and COST231
MATLAB Simulation
This thesis focuses on mobile phones antenna design with brief description about the historical development, basic parameters and the types of antennas which are used in mobile phones. Mobile phones antenna design section consists of two proposed PIFA antennas. The first design concerns a single band antenna with resonant frequency at GPS frequency (1.575GHz). The first model is designed with main consideration that is to have the lower possible PIFA single band dimensions with reasonable return loss (S11) and the efficiencies. Second design concerns in a wideband PIFA antenna which cover the range from 1800MHz to 2600MHz. This range covers certain important bands: GSM (1800MHz & 1900MHz), UMTS (2100MHz), Bluetooth & Wi-Fi (2.4GHz) and LTE system (2.3GHz, 2.5GHz, and 2.6GHz). The wideband PIFA design is achieved by using slotted ground plane technique. The simulations for both models are performed in COMSOL Multiphysics.
The last two parts of the thesis present the problems of mobile phones antenna. Starting with Specific absorption rate (SAR) problem, efficiency of Mobile phones antenna, and hand-held environment.
Possible media for communication
Introduction to Communication Media
Introduction to Microwave communication
Manufacturers of Microwave
Why Microwave?
Characteristics of microwave
Types of Microwave communication
Types of Microwave Links
Requirements for the microwave communication
What is LOS?
Wave Propagation in the atmosphere
Multi path Propagation
LOS Purpose & requirements
Limitations of Line of Sight Systems
Design of Line of Sight Microwave Links
K- factor
Variations of the ray curvature as a function of k
Fresnel zone
Obstacles & Loses
Knife Edge Obstacles
Smooth Spherical Earth Obstacles
Path Loss
Other losses
Why vertical polarization favorable at high freq
Antenna type & Gain
RECEIVER SENSITIVITY, FADE MARGIN AND SIGNAL TO NOISE RATIO
Fading Margin
Reliability
DESIGN OF RECTANGULAR PATCH ANTEENA USING METAMATERIAL SUBSTRATEPrateek Kumar
Dissertation part-1 presentation on design of rectangular patch antenna using metamaterial substrate by Prateek Kumar from RUSTAMJI INSTITUTE OF TECHNOLOGY BORDER SECURITY FORCE TEKANPUR GWALIOR (M.P).
A loop antenna has simple structure but its analysis is not easy to perform. Since a loop antenna is a dual pair of a dipole antenna, we can adopt the analysis of a dipole for a loop based on the duality theorem. By stacking a number of loops, we can increase the antenna gain and radiation resistance very easily.
A rhombic antenna is a broadband directional wire antenna co-invented by Edmond Bruce and Harald Friis, in 1931, mostly commonly used in the high frequency (HF) or shortwave band.
A dipole antenna is the simplest antenna but its radiation characteristics are very good. The main drawback of a dipole antenna is very narrow bandwidth. The analysis of a dipole antenna can be performed with integration of Hertzian dipoles.
Cell phone and mobile tower radiation hazardsNeha Kumar
Presentation at KEM Hospital on 20th September 2010 for medical doctors.
We have explained the radiation pattern of Cell tower antenna, main beam and minor beam of an antenna, who are at more danger, radiation norms adopted in different countries, calculations for amount of radiation the body may be exposed to with current radiation norms, epidemiological symptoms observed with proximity to towers, biological effects of these radiations. In particular its affect on children and pregnant women, health problems reported from cell tower radiation and other EMF sources- case studies, its impact on the environment - birds, animals, bees, plants etc.
Prof Girish Kumar from IIT Bomaby talked about the engineering aspect of cell tower antennae and I presented the biological effects on humans, animals and mentioned a few case studies.
There are several hundreds of publications which show a positive link between cell phone/ cell tower radiation and its association with illness observed in people. Several thousands of cases have been reported worldwide. All this calls for immediate precautionary actions to be taken before it gets too late.
A high gain antenna is the antenna with very high antenna gain. We can consider antenna gain as concentration ratio of input power. Using Yagi-Uda array, traveling wave, aperture, and parabolic reflector, we can design a high gain antenna.
Antenna & Array Fundamentals Technical Training Courses SamplerJim Jenkins
This three-day course teaches the basics of antenna and antenna array theory. Fundamental concepts such as beam patterns, radiation resistance, polarization, gain/directivity, aperture size, reciprocity, and matching techniques are presented. Different types of antennas such as dipole, loop, patch, horn, dish, and helical antennas are discussed and compared and contrasted from a performance - applications standpoint. The locations of the reactive near-field, radiating near-field (Fresnel region), and far-field (Fraunhofer region) are described and the Friis transmission formula is presented with worked examples. Propagation effects are presented. Antenna arrays are discussed, and array factors for different types of distributions (e.g., uniform, binomial, and Tschebyscheff arrays) are analyzed giving insight to sidelobe levels, null locations, and beam broadening (as the array scans from broadside.) The end-fire condition is discussed. Beam steering is described using phase shifters and true-time delay devices. Problems such as grating lobes, beam squint, quantization errors, and scan blindness are presented. Antenna systems (transmit/receive) with active amplifiers are introduced. Finally, measurement techniques commonly used in anechoic chambers are outlined. The textbook, Antenna Theory, Analysis & Design, is included as well as a comprehensive set of course notes.
An array antenna is a very interesting concept to control antenna radiation patterns. By using properly designed array elements, we can design a high gain or beam steering antenna very easily.
Broadside Array vs end-fire array
Higher directivity.
Provide increased directivity in
elevation and azimuth planes.
Generally used for reception.
Impedance match difficulty in
high power transmissions.
Variants are:
Horizontal Array of Dipoles
RCA Fishborne Antenna
Series Phase Array
Modeling Beam forming in Circular Antenna Array with Directional EmittersIJRESJOURNAL
ABSTRACT: The article discusses the functioning of the radio direction-finding and beamforming methods in the system of circular antenna arrays formed from the designed radiators, directional factor which is not equal to 1. Evaluation of forming of spatial pattern of cylindrical antenna array using phased method is fulfilled. DolphChebyshev window is used to reduce the side lobe level.
Wideband characteristics of density tapered array antennas IJECEIAES
In this paper, wideband characteristics of density tapered arrays are clarified by comparing directly the array factors and radiation patterns of 3 tapered arrays structures with array factors and radiation patterns of equally spaced arrays. Calculated results for a density tapered distribution array consisting of 30 elements claims that the array can perform within a bandwidth of 2.5:1 with grating lobe levels lower than -7.8 dB. Additionally, this paper shows a method of determining the effectiveness of unequal spacing arrays in the design of actual antennas. This method is based on the calculation and analysis of input impedance of array elements caused by mutual coupling effects among array elements.
Stellar Measurements with the New Intensity FormulaIOSR Journals
In this paper a linear relationship in stellar optical spectra has been found by using a
spectroscopical method used on optical light sources where it is possible to organize atomic and ionic data.
This method is based on a new intensity formula in optical emission spectroscopy (OES). Like the HR-diagram ,
it seems to be possible to organize the luminosity of stars from different spectral classes. From that organization
it is possible to determine the temperature , density and mass of stars by using the new intensity formula. These
temperature, density and mass values agree well with literature values. It is also possible to determine the mean
electron temperature of the optical layers (photospheres) of the stars as it is for atoms in the for laboratory
plasmas. The mean value of the ionization energies of the different elements of the stars has shown to be very
significant for each star. This paper also shows that the hydrogen Balmer absorption lines in the stars follow
the new intensity formula.
Spherical array of annular ring microstrip antennaswailGodaymi1
The paper discusses the analytical study of spherical arrays of annular ring microstrip antenna (ARMSA) elements excited by electric dipole. A new empirical relation for calculating the nonunifrom current amplitude distributions of these elements has been obtained. The relation contains the information about the current amplitude factor ()Δ of the antenna elements of the spherical array. The narrow beamwidth and low side lobe levels can be obtain by choosing appropriate the current amplitude factor. It is found that for current amplitude factor ()5.0=Δ the radiation pattern have narrow beamwidth and low side lobe levels compared with uniform current distribution array. Circular polarization is realized by this study depends on the spherical array geometry. By using appropriate phase of each antenna elements in spherical arrays, radiation pattern is steered without change of gain and beamwidth.
Beam Steering Using the Active Element Pattern of Antenna ArrayTELKOMNIKA JOURNAL
An antenna array is a set of a combination of two or more antennas in order to achieve improved
performance over a single antenna. This paper investigates the beam steering technique using the active
element pattern of dipole antenna array. The radiation pattern of the array can be obtain by using the
active element pattern method multiplies with the array factor. The active element pattern is crucial as the
mutual coupling effect is considered, and it will lead to an accurate radiation pattern, especially in
determining direction of arrival (DoA) of a signal. A conventional method such as the pattern multiplication
method ignores the coupling effect which is essential especially for closely spaced antenna arrays. The
comparison between both techniques has been performed for better performance. It is observed that the
active element pattern influenced the radiation pattern of antenna arrays, especially at the side lobe level.
Then, the beam of the 3x3 dipole antenna array has been steered to an angle of 60° using three
techniques; Uniform, Chebyshev and Binomial distribution. All of these are accomplished using CST and
Matlab software
Designing a pencil beam pattern with low sidelobesPiyush Kashyap
In this paper, a system has been designed for an operational frequency of 1.27 GHz consisting of an 8 element array of parasitic dipoles illuminated by a 4 element center fed array of active dipoles with Dolph-Chebyshev excitation coefficients. The array is designed to achieve a fairly pencil beam pattern suitable for direction of arrival estimation purposes. Array geometry and configuration is optimized for both active and parasitic elements using the PSO tool in FEKO. A directive radiation pattern is obtained with a gain of 14.5 dBi in the broadside direction along with a beamwidth of 30.29o. VSWR of 1.58 is achieved. Further, an iterative least square valued error estimation approach using phase control to achieve a desired array factor pattern for an n-element linear array, has been shown to be effective for larger number of iterations. The array excitation coefficients achieved were consistent with the Dolph-Chebyshev coefficients used in our antenna array design. With the ability to introduce nulls and steering the main beam in desired directions along with a pencil beam radiation pattern, beamsteering has been illustrated and the MUSIC algorithm for direction of arrival estimation has been implemented
Generation of Asymmetrical Difference Patterns from Continuous Line Source to...iosrjce
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The Influence Of Infinite Impedance Flanges On The Electromagnetic Field Of A...IJERA Editor
The problem of analysis of the electromagnetic field behaviour from the open end of the parallel-plate
waveguide with infinite impedance flanges is theoretically investigated. The case with the absence of impedance
flanges is also considered. Furthermore, we take into account particular features of the waveguide edges. The
effects of the impedance flanges and the edge features on the electromagnetic field and the radiation patterns of a
plane waveguide with flanges are demonstrated. The method of moments (MoM) technique which was used to
solve the integral equations is presented along with the numerical results.
Codalema is one of the experiments devoted to the detection of ultra high energy cosmic rays by the radio method. The main objective is to study the features of the radio signal induced by the development in the atmosphere of extensive air showers (EAS) generated by cosmic rays in the energy range of 10 PeV-1 EeV . After a brief presentation of the detector features, the main results obtained are reported (emission mechanism, lateral distribution of the electric field, energy calibration, etc.). The first studies of the radio wave front curvature are discussed as new preliminary results.
This is the presentation I gave when defending my Ph.D thesis at SLAC. The title of my defense was "Neutron Star Powered Nebulae: a New View on Pulsar Wind Nebulae with the Fermi Gamma-ray Space Telescope".
Some possible interpretations from data of the CODALEMA experimentAhmed Ammar Rebai PhD
The purpose of the CODALEMA experiment, installed at the Nan\c{c}ay Radio Observatory (France), is to study the radio-detection of ultra-high energy cosmic rays in the energy range of 10^{16}-10^{18} eV. Distributed over an area of 0.25 km^2, the original device uses in coincidence an array of particle detectors and an array of short antennas, with a centralized acquisition. A new analysis of the observable in energy for radio is presented from this system, taking into account the geomagnetic effect. Since 2011, a new array of radio-detectors, consisting of 60 stand-alone and self-triggered stations, is being deployed over an area of 1.5 km^2 around the initial configuration. This new development leads to specific constraints to be discussed in term of recognition of cosmic rays and in term of analysis of wave-front.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Design of Non-Uniform Linear Antenna Arrays Using Dolph- Chebyshev and Binomial Methods
1. J-François D. Essiben et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 8, (Part - 5) August 2015, pp.187-195
www.ijera.com 187 | P a g e
Design of Non-Uniform Linear Antenna Arrays Using Dolph-
Chebyshev and Binomial Methods
Jean-François D. Essiben1
, Martin P. M. Zanga1
, Eric R. Hedin2
, and Yong S.
Joe2
1
Department of Electrical Engineering, Advanced Teachers’ Training College for Technical Education,
University of Douala, B.P. 1872, Douala-Cameroon
2
Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University,
Muncie, IN, 47306, USA
ABSTRACT
This paper explores the analytical methods of synthesizing linear antenna arrays. The synthesis employed is
based on non-uniform methods. In particular, the Dolph-Chebyshev and binomial methods are used, so as to
improve the directivity of the array and to reduce the level of the secondary lobes by adjusting the geometrical
and electric parameters of the array. The radiation patterns, the directivity, and the array factors of the uniform
and the non-uniform methods are presented. It is shown that the Chebyshev arrays have better directivity than
binomial arrays for the same number of elements and separation distance, while binomial arrays have very low
side lobes compared with Chebyshev and uniform excitation arrays. Finally, numerical results of both methods
are analyzed and compared.
Keywords – array factor, directivity, radiation pattern, synthesis.
I. Introduction
Over the past few decades, since the concept of
using antenna arrays instead of a single element has
been developed, researchers have taken on the chal-
lenge of providing various array designs to tailor ra-
diation characteristics according to system require-
ments [1]. Synthesizing an array depends on several
factors, such as the requirements of the radiation pat-
tern, the directivity pattern, etc. The radiation pattern
depends on the number and the type of elements be-
ing used, and the physical and electrical structure of
the array. Numerous variations of antenna structures,
as well as the type of elements are available, but for
simplicity only one kind of element is used in the
whole array structure [2]. In other words, an antenna
array is composed of an assembly of radiating ele-
ments in an electrical or geometrical configuration
and, in most cases, the elements are identical (Fig. 1).
The total field of the antenna array is found by vector
addition of the fields radiated by each individual
element. Five controls in an antenna array can be
used to shape the pattern properly: the geometrical
configuration of the overall array, the spacing be-
tween the elements, the excitation amplitude of the
individual elements, the excitation phase of the indi-
vidual elements, and the particular pattern of the in-
dividual elements [2-5].
Many communication applications require a
highly directional antenna. Array antennas have
higher gain and directivity than an individual radiat
ing element. A linear array consists of elements
placed in a straight line with a uniform spacing be-
tween the elements [6]. The goal of antenna array
geometry synthesis is to determine the physical lay-
out of the array which produces a radiation pattern
that is closest to the desired pattern [5].
For the synthesis of the radiation pattern of an-
tenna arrays, various analytical and numerical meth-
ods of optimization (End-Fire, Broadside, Hansen-
Woodyard, binomial, Dolph-Chebyshev, Neural, Ge-
netic, etc.…) were developed and applied [5-10].
Here, our focus is related to the various analytical
methods. In particular, the non-uniform Dolph-
Chebyshev and binomial methods will be applied to
the synthesis of linear antenna arrays.
In this paper, we investigate the radiation pattern,
the beam-width at half-power, the array factor and
the directivity of the array. In addition, these parame-
ters are comparatively investigated for uniform and
non-uniform methods. Finally, we make a more de-
tailed analysis of the influence of the number of ele-
ments and the spacing or distance between the ele-
ments on the main characteristics of the antennas.
We also compare numerical results from all of the
different analytical methods.
The paper is organized as follows: In Section II,
we introduce the problem formulation. Section III
describes the Dolph-Chebyshev method. Section IV
describes the binomial method. Numerical results are
presented and analyzed in Section V, and finally,
section VI is devoted to the conclusion.
RESEARCH ARTICLE OPEN ACCESS
2. J-François D. Essiben et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 8, (Part - 5) August 2015, pp.187-195
www.ijera.com 188 | P a g e
Figure 1. Sketch of a linear antenna array.
II. Problem formulation
Let us consider a linear array of N - elements
aligned along the z axis, at equal separation d
from one another, as the diagram of Fig. 2 shows.
The expression of the array factor for this case is
given by the relation:
nN
n nZIAF
1
0
, (1)
where nI is the amplitude of the current excitation of
the th
n element,
j
eZ , )cos(kd , is
the angle between the radiation direction nr and the
axis of the array, 2k is the wave number, is
the wavelength, and is the progressive phase dif-
ference between the elements.
For a symmetrical distribution of the current
excitations, equation (1) becomes:
2
1
cos2
2/
1
nIAF
N
n n
.
(2)
For an even number of elements, this array factor can
be written as:
.cos2
2/)1(
10 nIIAF
N
n n
(3)
In equation (3), 0I represents the current excita-
tion of the central element of the array. If the spacing
between elements is not identical, the array is known
as a linear non-uniform array, and this condition
forces a modification of the array factor in equations
(2) and (3). However, the correspondence between
the array factor of linear uniform array of N - radiat-
ing elements (equations (2) and (3)) and the non-
uniform one is carried out either by using the bino-
mial method or with Chebyshev polynomials of order
1N . By matching similar coefficients we obtain
the excitation currents, nI , required. In such cases,
the array factors will be written in the following way:
,12cos
1
unIAF
M
n n
(4)
for an even number of sources, and
,12cos
1
1
unIAF
M
n n
(5)
for an odd number of sources, where
cos
d
u .
If we use a binomial expansion to determine these
coefficients, the array is known as non-uniform bi-
nomial. On the other hand, if it utilizes Chebyshev
polynomials, we refer to it as a non-uniform Dolph-
Chebyshev array. For each array, it is necessary to
determinate the array factor, the radiation pattern, the
directivity (
rP
U
D
4
,
where rP is the total
radiated power, and
2
AFmax
AF
U ), and the
beam-width at half-power.
1r
d
y
z
cosd
cosd
2r
3r
Nr
1I
3I
2I
NI
Figure 2. Geometry of the problem, showing a
linear antenna array of N sources.
III. Binomial array
The general problem of the synthesis of arrays is
similar to the problem of the synthesis of filters in the
theory of linear circuits, with the angle replacing
the frequency. It should be noticed that if the array
does not have axial symmetry, we need two angles,
and , to define each direction of radiation, and
then the problem becomes more complicated. But we
will confine ourselves here to arrays with axial sym-
metry.
In theory, we give ourselves a whole set of speci-
fications relating to the behaviour of the array factor
according to the angle (a gauge), and then the
mathematical problem consists of synthesizing a
function, )(AF , obeying this gauge. The idea of the
3. J-François D. Essiben et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 8, (Part - 5) August 2015, pp.187-195
www.ijera.com 189 | P a g e
binomial array is to ask if we can eliminate the sec-
ondary radiation lobes by using a different distribu-
tion function for the amplitudes of the excitation cur-
rents of the antenna array. Indeed, it is known that in
the case of an equidistant array, the appearance of
secondary lobes is inevitable when the number N of
elements increases. Moreover, the level of these lobes
never goes down below the limit of - 13.3 dB.
On the basis of the idea of Serguei A. Schelkun-
off, which rests on a simple mathematical relation
such that with the complex auxiliary variable,
)cos(
jkd
e , the array factor in the linear equidis-
tant case becomes ,)( )cos(
1
0
jnkd
N
n
neIAF
where
nI are the excitation currents. )(AF has an ampli-
tude and a phase, and becomes a polynomial of the
complex variable , where the complex coefficients
are the excitations of the elements. Assuming that
for an initial array with only two elements,
11)( j
eAF ,
it is seen that the complex polynomial 1 is can-
celled only if 1 . Further, it is known that if a
function is not null for a certain value of the variable,
the successive powers of this function are always
non-zero.
The idea is then to try to synthesize a radiation
pattern given by:
1
0
1 1
)1()(
N
n
nN
n
N
AF , (6)
where ))cos((
kdjj
ee . The solution is thus
to give to the array elements excitation ampli-
tudes, nI , corresponding to the coefficients of the
binomial theorem. These are known since the only
directions of null radiation are those of the initial
array with two elements. In this way, we can control
the existence of the secondary lobes.
IV. Dolph-Chebyshev array
Dolph indicated a method based on properties of
the Chebyshev polynomials, which gives the possibil-
ity of obtaining the maximum gain for a fixed level
of the secondary lobes imposed. This method uses the
fact that the optimal distribution of the sources ampli-
tudes is the one which gives, for the expression of the
radiated field by an alignment of N sources, the
Chebyshev polynomials of the degree )1( N . These
polynomials always present a significant maximum
level which corresponds to the maximum of the main
lobe of radiation. In addition, the polynomials pre-
sent a succession of maxima and minima of equal
amplitudes, which correspond here to the secondary
lobes. Thus, we will present the synthesis of the de-
sired radiation pattern by using Chebyshev polyno-
mials of degree 20, )( 019 xT , which will correspond,
in the Dolph method, to the radiation pattern of an
alignment of 20 sources [7].
With this method, all the secondary lobes of the
pattern have the same level, which can present disad-
vantages if we wish that the antenna ensures a certain
protection against jammers far away from the axis of
the maximum radiation. On the other hand, we can
show that an array built according to this method
always presents the maximum gain compatible with
the selected level of the secondary lobes.
In practice, the calculation of the distribution of
amplitudes will be made as follows: we fix the rela-
tionship, 0R , between the amplitude of the maximum
field of the main lobe and that of the secondary lobes.
Then 0R allows the definition of a parameter 0x , by
the formula:
)(cosh)1(cosh)( 0
1
010 xNxTR N
,
by taking into account that:
1
)(cosh
cosh 0
1
0
N
R
x .
V. Results and discussion
It is known that the radiation pattern of an array
is the product of the radiation pattern of an isolated
element multiplied by the array factor. The array fac-
tor translates the effect of the relative position and the
excitation of the elements. Clearly, the array factor is
the radiation pattern which would be obtained if all
the elements of the array were isotropic sources.
Figure 3 presents normalized array factors of the
Broadside (array with transverse radiation), End-Fire
(array with transverse radiation), and Hansen-
Woodyard considered as uniform arrays, i.e., with all
the elements having identical excitation amplitudes.
The array is composed of 11 sources with spacing
between elements of 25.0 . In the case of the
Broadside array, the normalized array factor is di-
rected towards
900 . In other words, there is no
main maximum in other directions. We can note that
obtaining this orientation requires a choice of the
excitation function and the appropriate number of
elements, taking into account the spacing between the
elements (which must be lower than to avoid un-
matched lobes). Research has shown that for a sepa-
ration between elements equal to 2 , the Broadside
radiation will see the appearance of the maximum
lobes. The End-Fire array presents the maximum
radiation directed along the axis )180( 0
. If the
separation between elements is equal to 2 , the
End-Fire radiation exists simultaneously in the two
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directions :
00 and
1800 . Concerning the
curve of the array factor for Hansen-Woodyard, we
see that the first desired maximum depends on the
progressive phase . If kd , the first desired
maximum tends either towards 0° ( kd , or
towards 180° kd . Several researchers have also
shown that the Hansen-Woodyard array is only an
extension of the End-Fire array.
Figure 3. Normalized array factor of Broadside,
End-Fire and Hansen-Woodyard arrays for
11N and 25.0d . The curve for the array
factor of Hansen-Woodyard shows that the first
desired maximum depends on the progressive
phase . If kd , the first desired maximum
tends either towards 0° ( kd , or towards
180° kd .
Figure 4 presents the radiation patterns of Broad-
side, End-Fire and Hansen-Woodyard arrays for
11N and 25.0d . As the results of simulations
show, the Broadside array presents a narrow beam.
As for the Hansen-Woodyard array, its conditions
lead to a greater directivity than those given by End-
Fire. However, we should specify that, these condi-
tions do not necessarily bring back the desired maxi-
mum directivity. The maximum cannot even occur at
00 or
1800 , and research shows that the
level of the secondary lobes cannot be greater than
13.46 dB. Clearly, the main maximum and the level
of the secondary lobes depend on the number of ele-
ments of the array. Research also shows that for a
rather large uniform array, the Hansen-Woodyard
array can also improve directivity for spacing be-
tween the elements approximatively equal to 4 .
Figure 4. Radiation patterns of Broadside, End-
Fire and Hansen-Woodyard arrays for 11N
and 25.0d . For a rather large uniform array,
the Hansen-Woodyard array can also improve
directivity for spacing between the elements ap-
proximatively equal to 4 .
Tables 1 (a) and (b) show and analyze the radia-
tion characteristics of the uniform arrays of Broad-
side, End-Fire and Hansen-Woodyard for linear an-
tennas of 11 sources and various spacing between the
sources. The tables show, (a) the level of the secon-
dary lobes and the directivity, and (b) the beam-width
at half power. We note that for the Broadside array,
an increase in spacing between elements leads to deg-
radation of the directivity and the level of the secon-
dary lobes, while the beamwidth at half-power im-
proves considerably. The best characteristics of radia-
tion are obtained with 25.0d . End-Fire and Han-
sen-Woodyard arrays present the best characteristics
of radiation when 25.0d and 55.0d , respec-
tively. For the End-Fire and Hansen-Woodyard ar-
rays, an increase in spacing between the elements
also considerably improves the beam-width at half-
power, but with certain variations when 5.0d for
the End-Fire array and when d for the Hansen-
Woodyard array. Thus, from the analysis of these
uniform arrays, the data shows that the variation of
spacing between elements makes it possible to im-
prove at most two of the above-mentioned radiation-
characteristics, but not more. In other words, it is
difficult to optimize more than two characteristics at
the same time. We also note that the improvement of
one characteristic occurs in general at the detriment
of another. Several researchers have shown that the
directivity of a Hansen-Woodyard array is always
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approximatively 1.805 times (or 2.56 dB) larger than
that of an ordinary End-Fire array [3], but our analy-
sis, as shown in Table 1(a), indicates that this rela-
tionship does not uniformly apply.
Table 1. Tables 1 (a) and (b) show and analyze the radiation characteristics of the uniform arrays
of Broadside, End-Fire and Hansen-Woodyard for the linear antennas of 11N sources and
various spacing between the sources. It is about (a) the level of the secondary lobes, of the directiv-
ity and (b) of the half-power of beam-width. It arises that the variation of spacing between ele-
ments makes it possible to improve one to two above mentioned characteristics of radiation but,
not more. In other words, it is difficult at the same time to optimize more than two characteristics.
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Figure 5. The normalized array factor of the bi-
nomial array of 11N sources, with spacing be-
tween elements varying from 25.0 to . The
binomial array with spacing between elements less
than or equal to 2 does not have secondary
lobes.
Figure 6. Radiation patterns of the binomial array
of 11N sources, with spacing between elements
varying from 25.0 to . The binomial array
usually has the smallest secondary lobes.
Figure 5 presents the normalized array factor of a
binomial array of 11 sources, with spacing between
elements varying from 25.0 to . The analysis of
the results shows that for a distance between ele-
ments less than or equal to a half-wavelength, the
secondary lobes are nearly non-existent. In other
words, a binomial array with spacing between ele-
ments less than or equal to 𝜆/2 does not have secon-
dary lobes. The secondary lobes appear when the
spacing between elements is greater than 5.0 . If the
spacing reaches the value 𝜆, the secondary lobes ap-
pear within
0 and
180 , in other words, as secon-
dary maxima.
Figure 6 presents the radiation patterns of a bi-
nomial array of 11 sources with spacing between
elements varying from 25.0 to . The analysis of
the curves shows that for a binomial array of anten-
nas with spacing between elements less than a half-
wavelength, the radiation pattern does not have sec-
ondary lobes. Thus, the array is less noisy (or at least
its intrinsic temperature is lower) and we can detect
weaker signals. For a spacing of greater than 75.0 ,
we note the appearance of secondary lobes, as seen in
Fig. 5. If we increase this spacing further to one
wavelength, the radiation is not solely in Broadside
but also in End-Fire. We can thus conclude that the
optimal spacing for the binomial array is obtained
when 65.01.0 d . Although the binomial dis-
tribution eliminates the zeros and small lobes (com-
pare Fig. 6 with Fig. 4), the width of the beam emit-
ted by the array decreases and, consequently the di-
rectivity improves. Let us notice that in the large-
sized arrays, the amplitudes of the currents can vary
considerably (according to the particular distribution
pattern), which is likely to cause difficulty obtaining
and preserving sufficiently stable power levels.
Tables 2 (a) and (b) present and analyze the ra-
diation characteristics of the binomial and Dolph-
Chebyshev arrays with odd and even numbers of
elements, i.e., with 11 and 20 sources, and with spac-
ing between sources varying from 25.0 to . Table
(a) shows that the best secondary lobe level for even
and odd numbers of elements is obtained with
75.0d . The directivity for either an even or odd
number is also degraded with increased spacing be-
tween the elements. However, this trend reverses
when d . Lastly, the beam-width at half-power,
as shown in Table (b), decreases with the growth of
spacing between elements, but it dramatically in-
creases at d . The difference between the bino-
mial array and the Dolph-Chebyshev is that Dolph-
Chebyshev has a fixed secondary lobe level. In our
case, its value is -20 dB.
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Table 2. Tables 2 (a) and (b) present and analyze the radiation characteristics of the b3inomial and
Dolph-Chebyshev arrays for 11 and 20 sources with spacing between sources varying from 25.0 to .
The difference between the binomial array and the Dolph-Chebyshev is that Dolph-Chebyshev has a fixed
secondary lobe level.
The analysis of the two non-uniform arrays
shows that for the same number of elements, the bi-
nomial array has the best results concerning the di-
rectivity and the level of the secondary lobes. The
Dolph-Chebyshev array, on the other hand, has the
best overall beam-width at half-power. As we men-
tioned above for the uniform arrays, it is difficult to
concurrently optimize more than two characteristics
of the radiation. Research has shown that the greatest
disadvantage of a binomial array is the variation of
the excitation amplitudes of the various elements of
the array, especially when the number of elements is
rather high.
The distribution technique which avoids the dis-
advantages discussed above is the Dolph-Chebyshev
distribution. When we implement this distribution, it
is necessary to specify the maximum level imposed
on the secondary lobes if we want the minimum re-
duction of the width of the beam between first zeros,
or inversely, it is necessary to specify the width of the
beam between first zeros to reduce the secondary
lobes to their minimum level.
Figure 7. The normalized array factor of the
Dolph-Chebyshev array for 11N with various
spacings: 25.0d , 5.0d , 75.0d and
d . The desired secondary lobe level is fixed
at -20 dB. We note that for a distance between the
elements d , we have only one maximum pre-
sent at Broadside
90 . As soon as this dis-
tance exceeds one wavelength d , two other
maxima also appear, at
0 and
180 (End-Fire
radiation).
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Figure 7 presents the normalized array factor of
the Dolph-Chebyshev array for 11N with various
spacings: 25.0d , 5.0d , 75.0d and
d . The desired level of secondary lobes is fixed
at -20 dB. We note that for a distance between the
elements d , we have only one maximum present
at Broadside
90 . As soon as this distance ex-
ceeds one wavelength d , two other maxima
also appears, at
0 and
180 (End-Fire radiation). A
progressive increase of this distance considerably
decreases the width of the main lobe, thus improving
the overall directionality of the array.
Figure 8. The radiation patterns of the Dolph-
Chebyshev array for 11N with various spac-
ings: 25.0d and d .
Figure 8 presents the radiation patterns of the
Dolph-Chebyshev array for 11N with two differ-
ent spacings: 25.0d and d . The directivity
for Chebyshev is better than that of a binomial array
for the same number of elements and separation dis-
tance. For a desired secondary lobe level, the beam-
width at half-power and the directivity of the radia-
tion patterns represented in Fig. 8 are given by using
the following formula for approximating the widen-
ing of the array factor:
,coshcosh
2
636.01
2
22
0
1
0
R
R
f (7)
where 0R is the ratio of the amplitude of the main
lobe to the 1st
secondary lobe, as defined earlier. The
factor of beam-widening matches the diagram of
figure 8 according to the level of the secondary lobes.
The results clearly show by application of this for-
mula that a larger value of 0R leads to a considerable
decreasing of the secondary lobe level. As in the case
with the array factor, the desired radiation in Broad-
side, with a fixed level of secondary lobes equal to -
20 dB for our case, is optimal only for one distance
between elements d . In contrast, however, two
other secondary lobes will appear in the radiation
pattern with the same amplitude as the main lobe in
End-Fire.
VI. Conclusion
In this paper, we present the solution for the
problem of synthesis of uniform and non-uniform
linear antennas arrays. We determine the level of
secondary lobes, the directivity, and the beam-width
at half-power of each array. We can conclude by ob-
serving that:
● the directivity for Chebyshev is better than that
of a binomial array for the same number of ele-
ments and separation distance,
● the optimal spacing for the Chebyshev array is
95.0d , which gives the best radiation prop-
erties, while for the binomial array the optimal
dimension is 75.0d ; the uniform array with
spacing between the elements 95.0d has the
best radiation properties,
● the binomial array has very low secondary lobes
compared with Chebyshev and uniform excita-
tion arrays because the coefficients of excitation
of the binomial array are very large,
● the binomial array usually has the smallest sec-
ondary lobes, followed in order by the Dolph-
Chebyshev array and the uniform arrays.
● for the three distributions, uniform, binomial,
and Dolph-Chebyshev, the uniform distribution
of amplitude achieves the smallest beam-width at
half-power. Next in order comes the Dolph-
Chebyshev array and the binomial array.
Finally, it is clear that for a better synthesis of
antennas arrays, the designer must find a compromise
between the level of the secondary lobes and the
beam-width at half-power. The greatest challenge
will consist in determining or choosing the values of
the coefficients of excitation for a desired pattern of
radiation.
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