STUDY OF CONFORMAL ANTENNA ARRAY BEAMFORMING
CHARACTERISTICS USING K-BAND WAVEGUIDE ELEMENTS
Nithin Reddy Gudur
B.Tech., Jawaharlal Nehru Technological University, India, 2006
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2010
STUDY OF CONFORMAL ANTENNA ARRAY BEAMFORMING
CHARACTERISTICS USING K-BAND WAVEGUIDE ELEMENTS
A Project
by
Nithin Reddy Gudur
Approved by:
__________________________________, Committee Chair
Preetham B. Kumar, Ph.D.
__________________________________, Second Reader
Fethi Belkhouche, Ph.D.
___________________________
Date
ii
Student: Nithin Reddy Gudur
This is to certify that this student has met the requirements for format contained in the
University format manual, and that this project is suitable for shelving in the Library and
credit is to be awarded for the project.
___________________, Graduate Coordinator
Preetham B. Kumar, Ph.D.
Department of Electrical and Electronic Engineering
iii
_________________
Date
Abstract
of
STUDY OF CONFORMAL ANTENNA ARRAY BEAMFORMING
CHARACTERISTICS USING K-BAND WAVEGUIDE ELEMENTS
by
Nithin Reddy Gudur
This project will focus on the application of advanced electromagnetic simulation
software 4NEC2 for the far-field characterization of a 3-element K-band array of
waveguide antenna. Previous modeling efforts have shown a significant difference
between simulated and measured data. The key effort in this project will be to minimize
the difference between simulated and measured data by use of the 4NEC2 software. The
simulation will be carried out on both a 3-element array of open-ended waveguides. The
main application of these arrays in the far-field is in satellite K-band applications, where
we would require multiple beams that can be controlled in beamwidth and position. The
conformal nature of the array described in this work has the ability to control the beam
positions and beamwidth by adjusting the conformal nature of the array.
, Committee Chair
Preetham B. Kumar, Ph.D.
______________________
Date
iv
ACKNOWLEDGEMENT
Man has made language to express his feelings. Yet, we find ourselves short of
words when it comes to thanking all those who have rendered necessary help for the
completion of this project.
First and foremost I would like to express my gratitude and thanks to my advisor,
committee chair and graduate coordinator Dr. Preetham Kumar for his expert guidance
and constant support throughout this project. His openness and enthusiasm have taught
me correct way of working with new technologies and has improved my knowledge of
the subject.
I am extremely thankful to Mr. Fethi Belkhouche, my second reader for reviewing
this work and for his valuable suggestions in improving the same. It is my duty to
recognize the efforts of Electrical Engineering Department and the management for
creating an interactive atmosphere for learning.
I would also like to take this opportunity to thank the considerate faculty and staff
of Electrical and Electronics Engineering Department who have been supporting me
throughout my curriculum.
v
TABLE OF CONTENTS
Page
Acknowledgement………………………………………………………………………..v
List of Tables…………………………………………………………………………....vii
List of Figures.…………………………………………………………………......…...viii
Chapter
1. INTRODUCTION……………………………………………………………………..1
2. 4NEC2 ELECTROMAGNETIC SIMULATION SOFTWARE ……………………….….3
2.1 Introduction to 4NEC2………………………………..……………...……………..3
2.2 Additional Features of 4NEC2...................................................................................4
2.3 4NEC2 Project Flow..................................................................................................4
2.4 Configuration ……………………………………..…………………………..........5
2.5 Steps for Drawing a Geometric Model………………….………………………….6
3. DESIGN OF 3 ELEMENT K – BAND ARRAYS……………..………………...….11
3.1 K – Band Frequency Range and Applications…………………………………….11
3.2 K – Band Array Design …………..….……………………………………………14
3.3 K – Band Array Configurations …………………………………………….….....15
4. SIMULATION RESULTS FOR K - BAND WAVEGUIDE ARRAY ……...……17
4.1 Simulation Results for 3 Element Waveguide Array.............................................17
5. CONCLUSION AND FUTURE SCOPE …………………………………………….39
References……………………………………………………………………………......41
vi
LIST OF TABLES
Page
1. Table 3.1: Element Positions of K-band Array…………………….……………….....15
vii
LIST OF FIGURES
Page
1. Figure2.1: Main Window.........................................................................................6
2. Figure 2.2: Geometry Edit Window…………………………………...……..........7
3. Figure 2.3: Geometry Edit Window Showing Voltage Source at a Point..............8
4. Figure 2.4: Geometry Edit Window Showing Frequency/Ground Selection..........8
5. Figure 2.5: Geometry Edit Window Showing Conductivity/Dielectric Constant...9
6. Figure 2.6: To Calculate NEC Output Data...............…….………....……….........9
7. Figure 2.7: Window Showing Selection of Pattern…....……………..….............10
8. Figure 2.8: Window Showing Far Field pattern and its Equivalent Values……10
9. Figure 3.1: Element Horizontal………………………………...................…...…15
10. Figure 3.2: Positive Spherical Geometry...............................................................16
11. Figure 3.3: Negative Spherical Geometry……………………………………….16
12. Figure 4.1: 4NEC2 Input .nec file Showing the Simulation Parameters...............18
13. Figure 4.2: 4NEC2 3D Schematic When all Waveguide Elements are in Line....19
14. Figure 4.3: 4NEC2 Input .nec File Showing the Geometry Parameters: Array
Elements are in Line....………………………………………………………..…20
15. Figure 4.4: Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 0O
Plane: Array Elements are in Line....………..………………………………...…21
16. Figure 4.5: Far-field pattern of K-band Waveguide Array at 18GHz & phi=90O
Plane: Array Elements are in Line....………..………………………………...…22
17. Figure 4.6: 4NEC2 3D Schematic When Center Array Element (Z axis) is 2cm
behind the Outer Elements..............………………………………………….....23
viii
18. Figure 4.7: 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 2cm behind the Outer Elements...........................................................24
19. Figure 4.8: Far-field Pattern of K-band Waveguide Array at 18GHz & phi=0O
Plane: Center Element is 2cm behind the Outer Elements ….……………….….25
21. Figure 4.9: Far-field Pattern of K-band Waveguide Array at 18GHz & phi=90O
Plane: Center Element is 2cm behind the Outer Elements.…….………………..26
22. Figure 4.10: 4NEC2 3D Schematic When Center Array Element (Z axis) is 4cm
behind the Outer Elements.....…............................................................................27
23. Figure 4.11: 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 4cm behind the Outer Elements….......................................................28
24. Figure 4.12: Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 0O
Plane: Center Element is 4cm behind the Outer Elements…................................29
25. Figure 4.13: Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 90O
Plane: Center Element is 4cm behind the Outer Elements…................................30
26. Figure 4.14: 4NEC2 3D Schematic When Center Array Element (Z axis) is 2cm
ahead of the Outer Elements.....……….……………………………………......31
27. Figure 4.15: 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 2cm ahead of the Outer Elements........................................................32
28. Figure 4.16: Far-field Pattern of K-band Waveguide Array at 18GHz & phi=0O
Plane: Center Element is 2cm ahead of the Outer Elements………………....….33
29. Figure 4.17: Far-field Pattern of K-band Waveguide Array at 18GHz & phi=90O
Plane: Center Element is 2cm ahead of the Outer Elements………………...…..34
30. Figure 4.18: 4NEC2 3D Schematic When Center Array Element (Z axis) is 4cm
ahead of the Outer Elements.....….........................................................................35
31. Figure 4.19: 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 4cm ahead of the Outer Elements…....................................................36
32. Figure 4.20: Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 0O
Plane: Center Element is 4cm ahead of the Outer Elements….............................37
ix
33. Figure 4.21: Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 90O
Plane: Center Element is 4cm ahead of the Outer Elements….............................38
x
1
Chapter 1
INTRODUCTION
The study of conformal microwave antenna arrays at higher frequencies is an area
of great interest where considerable discussion has taken place but further data needs to
be provided. It can be challenging to build an accurate model. The uses of such antennas
are many and therefore acquiring data to characterize such antennas is important.
In
the
communication
field,
aircraft-to-satellite
and
satellite-to-satellite
communication requires high gain beams that can be steered over a wide area of
coverage. It is proposed that a hemispherical conformal array could produce such desired
characteristics [6-9].
The goals of this project were to design and accurately simulate a multielement microwave antenna array operating in the K-band frequency range (18 GHz – 26
GHz), but particularly at 18 GHz with the capability of conforming to various
geometries. The effects of mutual coupling between array elements were avoided by
making element spacing greater than one wavelength. The downside of avoiding mutual
coupling is the grating lobes formed due to such wide element spacing. It has been
shown that optimizing conformal geometry can result in controlling grating lobe levels
while achieving desired field radiation coverage.
Much work has been done in the study of planar microwave antenna arrays.
Measurements at frequency 18 GHz have been made and documented. Such antennas
have fixed element spacing in all three X-Y-Z coordinates making them planar.
The
2
fixed nature of such antennas makes it easier to build arrays using many more elements
than used in this research.
The work performed in this project involves using linearly polarized K-band
waveguide elements operating at 18 GHz. The X and Y coordinates are set in fixed
positions by the mounting structure. The unique aspect of work performed in this project
is the capability of the antenna array to conform to various volumetric geometries.
The results of this project were positive. Certain compromises needed to be made
from original design in order to achieve a working antenna array. However that was to be
expected. Mathematics involved modeling an individual waveguide element, modeling
the array factor for a given set of X, Y and Z coordinates, and combining the two models
to arrive at a final model of the entire antenna array. The mathematical model was
incorporated into 4NEC2 software environment for simulation purposes.
This report is organized as follows: Chapter 1 gives a brief introduction into the
array system, which is the focus of this work. Chapter 2 gives a brief introduction about
4NEC2, which is the electromagnetic simulation software used in this project and its
features and functions. Chapter 3 gives a brief introduction about the K band frequency
and its various applications. Chapter 4 lists the simulation results for K band array
waveguides that were simulated using 4NEC2. Chapter 5 is the conclusion of this project.
It also deals with the future scope of work on this project.
3
Chapter 2
4NEC2 ELECTROMAGNETIC SIMULATION SOFTWARE
2.1 Introduction to 4NEC2
The Numerical Electromagnetic code (4NEC2) is a user oriented computer
code for the analysis of the electromagnetic response of antennas and other metal
structures. 4NEC2 is a
windows based tool for creating, viewing, optimizing and
checking 2D and 3D style antenna geometry structures and generate, display and
compare near-field or far-field electromagnetic patterns for both the starting and
experienced antenna modeler. It was designed by Arie Voors. [12]
We used 4NEC2 ver. 5.8.1 which has the following features:
 Graphical 2D and 3D visualization of Far- and Near-field data and Geometry structures.
 Drag and drop style Geometry Editor to assist the starting antenna modeler.
 Capable of running up to 11000 wires and/or segments (limited by the max of 2Gb of
windows on-board memory)
 Sophisticated real-time 3D geometry and pattern viewer showing real wire-radius.
 Interactive Smith chart visualization for freq-sweeps.

Geometry builder to create cylinder, patch, plane, box, helix and parabola shaped
structures using auto-segmentation and/or equal-area rules.
The user is expected to draw the structure, specify material characteristic for each
object and identify ports, sources and special surface characteristics. The system then
generates the necessary field solutions. The next section describes the various steps to be
4
followed in order to develop the structure, bring about the solution and analyze the same
for any given structure.
2.2 Additional Features of 4NEC2
Some of the additional capabilities of the software include:

Software based on the mininec code

3D patterns for both geometry and fields

Extensive library of antennae

Built in optimizer
As mentioned above, 4NEC2 software has some extensive features related to an
antenna modeling. The extensive library in 4NEC2 has several predefined functions that
are available to use in the project. Also 4NEC2 has a built in optimizer which helps you
in optimizing your design for the best solution. It can compare different types of patterns
that are obtained as a result and decide the best among them.
2.3 4NEC2 Project Flow
The main steps in creating a project in the 4NEC2 software are as follows:

Configuration

Drawing

Source/Load

Frequency
5

Environment

Solution

Plot
2.4 Configuration
To configure 4NEC2 5.8.1, the below steps should be followed.
Click 4NEC2 5.8.1 to start the design
Click: File Open 4NEC2 in/output file  filename (Takes you to a folder where there
are many built in designs. Open any one of them)
Click: Settingsselect NEC editor (new).
Click: A new window will open showing all the coordinates of the geometrical structure
which can be edited. If we want to model a new structure from here following steps
should be followed:
Click: File New  Save asfilename
Now, a new design interface has 3 sub-windows: Main window, geometry window and
geometry edit window.
6
2.5 Steps for Drawing a Geometric Model
On Windows machine Open 4NEC2 5.8.1:
The main window appears as follows
Figure 2.1: Main Window
7
The next step would be to draw the geometrical structure.
Click Edit  Input (.nec) file .The following window called geometry edit window will
open:
Figure 2.2: Geometry Edit Window
The next step is to specify the type of source/load whether it is voltage or current and also
specify the coordinates of the point where exactly we want to insert the source/load. For
example if your source is voltage then following window shows the selection of voltage
source:
8
Figure 2.3: Geometry Edit Window Showing Voltage Source at a Point
The next step in the design is to specify the frequency/ground. The following figure
shows the selection of the frequency/ground:
Figure 2.4: Geometry Edit Window Showing Frequency/Ground Selection
9
If you choose real ground then you need to specify the ground type, conductivity and
dielectric constant. The following figure shows that:
Figure 2.5: Geometry Edit Window Showing Conductivity/Dielectric constant
The next step in the design is to calculate the radiation pattern and other patterns. The
following procedure is to be followed:
Figure 2.6: To Calculate the NEC Output Data
10
Now if we want to get far field pattern select the far field pattern and click generate as
follows:
Figure 2.7: Window Showing Selection of Pattern
Following results show up:
Figure 2.8: Window Showing Far Field Pattern and its Equivalent Values
11
Chapter 3
DESIGN OF 3 ELEMENT K – BAND ARRAYS
3.1 K-Band Frequency Range and Applications
The IEEE K band is a portion of the electromagnetic spectrum in the microwave
range of frequencies ranging between 18 and 26.5 GHz is absorbed easily by water vapor
(H2O resonance peak at 22.24 GHz, 1.35 cm).
Subdivisions
The IEEE K band is conventionally divided into three sub-bands:

Ka band: K-above band, 26.5–40 GHz, mainly used for radar and experimental
communications.

K-band 18-26.5 GHz

Ku band: K-under band, 12–18 GHz, mainly used for satellite communications,
terrestrial microwave communications, and radar, especially police traffic-speed
detectors.
The Ku band (pronounced "kay-yoo") is a portion of the electromagnetic spectrum in
the microwave range of frequencies. This symbol refers to "K-under" (in the original
German, "Kurz-unten", with the same meaning) in other words, the band directly below
12
the K-band. In radar applications, it ranges from 12 to 18 GHz according to the formal
definition of radar frequency band nomenclature in IEEE Standard 521-2002 [11].
Ku band is primarily used for satellite communications, most notably for fixed
and broadcast services, and for specific applications such as NASA's Tracking Data
Relay Satellite used for both space shuttle and ISS communications. Ku band satellites are
also used for backhauls and particularly for satellite from remote locations back to a
television network's studio for editing and broadcasting. The band is split into multiple
segments that vary by geographical region by the International Telecommunication
Union (ITU). NBC was the first television network to uplink a majority of its affiliate
feeds via Ku band in 1983. Some frequencies in this radio band are used for vehicle speed
detection by law enforcement, especially in Europe [11].
Advantages
Compared with C-band, Ku band is not similarly restricted in power to avoid
interference with terrestrial microwave systems, and the power of its uplinks and
downlinks can be increased. This higher power also translates into smaller receiving
dishes and points out a generalization between a satellite’s transmission and a dish’s size.
As the power increases, the dish’s size can decrease. [8] This is because the purpose of
the dish element of the antenna is to collect the incident waves over an area and focus
them all onto the antenna's actual receiving element, mounted in front of the dish (and
pointed back towards its face); if the waves are more intense, less of them need to be
collected to achieve the same intensity at the receiving element.
13
The Ku band also offers a user more flexibility. A smaller dish size and a Ku band
system’s freedom from terrestrial operations simplify finding a suitable dish site. For the
end users Ku band is generally cheaper and enables smaller antennas (both because of the
higher frequency and a more focused beam). Ku band is also less vulnerable to rain fade
than the Ka band frequency spectrum.
The satellite operator's Earth Station antenna do require more accurate position
control when operating at Ku band than compared to C band. Position feedback
accuracies are higher and the antenna may require a closed loop control system to
maintain position under wind loading of the dish surface.
Disadvantages:
There are, however, some disadvantages of Ku band system. Especially at
frequencies higher than 10 GHz in heavy rain fall areas, a noticeable degradation occurs,
due to the problems caused by and proportional to the amount of rainfall (commonly
known as "rain fade"). [10] This problem can be mitigated, however, by deploying an
appropriate link budget strategy when designing the satellite network, and allocating a
higher power consumption to compensate rain fade loss. The Ku band is not only used for
television transmission, which some sources imply, but also very much for digital data
transmission via satellites, and for voice/audio transmissions.
14
The higher frequency spectrum of the Ku band is particularly susceptible to signal
degradation, considerably more so than C-band satellite frequency spectrum. A similar
phenomenon, called "snow fade" (where snow or ice accumulation significantly alters the
focal point of a dish) can also occur during winter precipitation. Also, the Ku band
satellites typically require considerably more power to transmit than the C-band satellites.
Under both "rain fade" and "snow fade" conditions, Ka and Ku band losses can be
marginally (but significantly) reduced using super-hydrophobic Lotus effect coatings.
3.2 K-Band Array Design
The antenna array structure consists of K-band open waveguide, and the array
element positions, corresponding to the center of each waveguide aperture, are listed in
Table 1.
Each waveguide element is 19.5 cm in length with an aperture size of 4 mm x
10.5 mm, and copper wall thickness of 1 mm. Using the standard equation [1], the cutoff
frequency for the dominant TE10 mode employed here was calculated to be 14.286 GHz,
which is well below the operating frequencies utilized in this study.
A number of beam forming applications were realized by switching among
different element combinations. Additionally, axial z-axis shift of the array elements
permits control of the beam width; however, such a shift also alters the shape of the array.
In this paper, three different cases of the central element shift were considered: forward
shift (convex surface with negative radius), no shift (planar surface with infinite radius),
and backward shift (concave surface with positive radius). The central element no. 1 is
15
the focusing element of the array: axial movement of this element allows the operator to
control the conformal radius of the array.
Element Number
X Position
Y Position
Z Position
(cm)
(cm)
(cm)
1
0
0
variable
2
0
-2.5
0.0
3
0
2.5
0.0
Table 3.1: Element Positions of K-band Array
3.3 K-Band Array Configurations
In this work, the horizontal configurations was studied, as illustrated in Figure
3.1.
1
2
3
Figure 3.1 - Element Horizontal
geometry
16
Positive and negative geometries were considered for each of these configurations
to study the bandwidth control properties of the array. A positive spherical geometry is
illustrated in Figure 3.2 with its conformal sphere located in front of the antenna, while
the negative spherical geometry is shown in figure 3.3, with its conformal sphere in the
rear of the antenna.
di
R
R
di
R-zi
R-zi
zi
zi
Figure 3.2 - Positive Spherical Geometry Figure 3.3 - Negative Spherical Geometry
The parameter R represents the radius of the conformal sphere and di is the
distance of the ith element from the central element, whose position is selected as the
reference (0, 0, 0). The axial position of ith element is determined from the following
geometrical considerations:
d 2  (R  z)2  R2
Or
z  R  R2  d 2
17
Chapter 4
SIMULATION RESULTS FOR K- BAND WAVEGUIDE ARRAY
This chapter details the simulations studies performed on the 3-element conformal
array that was described in the previous chapter. The simulation studies were done using
the 4NEC2 software.
4.1 Simulation Results for 3 Element Waveguide Array
The simulation parameters are as follows:
Source/Load: Voltage Source (1+j0) V
Frequency of Simulation: 18 GHz
Environment: Free space
The schematic, the far field pattern and the resultant electric field generated using 4NEC2
software is discussed here. The relevant figures of the same are also shown below. As
mentioned earlier we consider three cases of the waveguide array, one with all elements
in line and the other two configurations are obtained by positioning the center element
backward and forward, relative to the central focusing element.
18
The figure below shows the input simulation parameters.
Figure 4.1 4NEC2 Input .nec File Showing the Simulation Parameters
19
Case 1: All the waveguide elements are in line
Figure 4.2 4NEC2 3D Schematic When all Waveguide Elements are in Line
The above figure 4.2 shows the 3D view of the waveguide array when all the elements
are in line.
20
The input .nec file showing the geometry parameters for the simulation is shown below.
Figure 4.3 4NEC2 Input .nec file Showing the Geometry Parameters: Array
Elements are in Line
21
The following figure shows the far field pattern of the waveguides at phi = 0O.
Figure 4.4 Far-field Pattern of K-band Waveguide Array at 18 GHz& phi = 0O
Plane: Array Elements are in Line.
22
The following figure 4.5 shows the far field pattern of the waveguide array in the phi =
90O plane.
Figure 4.5 Far-field Pattern of K-band Waveguide Array at 18 GHz& phi = 90O
Plane: Array Elements are in Line.
23
Case 2: Center array element is 2 cm behind the other two elements
Figure 4.6 4NEC2 3D Schematic When Center Array Element (Z- axis) is 2cm
behind the Outer Elements.
The above figure shows the 3D view of the waveguide array when center array element
(Z- axis) is 2 cm behind the other two elements.
24
The input .nec file showing the parameters for the simulation is shown below.
Figure 4.7 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 2cm behind the Outer Elements
The above figure of the waveguide array geometry table shows that the center array
element (Z- axis) is 2 cm behind the other two elements.
25
The following figure shows the far field pattern of the waveguides at phi = 0O.
Figure 4.8 Far-field Pattern of K-band Waveguide array at 18 GHz & phi = 0O
Plane: Center Element is 2cm behind the Outer Elements.
26
The following figure shows the far field pattern of the waveguides at phi = 90O.
Figure 4.9 Far-field Pattern of K-band Waveguide Array at 18 GHz & phi = 90O
Plane: Center Element is 2cm behind the Outer Elements.
27
Case 3: Center array element is 4 cm behind the other two elements
In this section the center element of the waveguide array is 4 cm behind the other two
elements. The geometrical structure of the resultant configuration is shown below.
Figure 4.10 4NEC2 3D Schematic When Center Array Element (Z axis) is 4cm
behind the Outer Elements
The above figure shows the 3D view of the waveguide array when center array element
(Z- axis) is 4 cm behind the other two elements.
28
The input .nec file showing the parameters for the simulation is shown below.
Figure 4.11 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 4cm behind the Outer Elements
The above figure of the waveguide array geometry table shows that the center array
element (Z- axis) is 4 cm behind the other two elements.
29
The following figure shows the far field pattern of the waveguides at phi = 0O.
Figure 4.12 Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 0O
Plane: Center Element is 4cm behind the Outer Elements
30
The following figure shows the far field pattern of the waveguides at phi = 90O.
Figure 4.13 Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 90O
Plane: Center Element is 4cm behind the Outer Elements
31
Case 4: Center array element is 2 cm ahead of the other two elements
Figure 4.14 4NEC2 3D Schematic When Center Array Element (Z axis) is 2cm
ahead of the Outer Elements
The above figure shows the 3D view of the waveguide array when the center array
element is 2 cm ahead of the other two elements
32
The input .nec file showing the parameters for the simulation is shown below.
Figure 4.15 4NEC2 input .nec File Showing the Geometry Parameters: Center
Element is 2cm ahead of the Outer Elements
The above figure of the waveguide array geometry table shows that the center array
element (Z- axis) is 2 cm ahead of the other two elements.
33
The following figure shows the far field pattern of the waveguides at phi = 0O.
Figure 4.16 Far-field Pattern of K-band Waveguide Array at 18GHz & phi=0O
Plane: Center Element is 2cm ahead of the Outer Elements
34
The following figure shows the far field pattern of the waveguides at phi = 90O.
Figure 4.17 Far-field Pattern of K-band Waveguide Array at 18GHz & phi=90O
Plane: Center Element is 2cm ahead of the Outer Elements
35
Case 5: Center array element is 4 cm ahead of the other two elements
In this section the center element of the waveguide array is 4 cm in front of the other two
elements. The geometrical structure of the resultant configuration is shown below.
Figure 4.18 4NEC2 3D Schematic When Center Array Element (Z axis) is 4cm
ahead of the Outer Elements.
The above figure shows the 3D view of the waveguide array when center array element is
4cm ahead of the other two elements.
36
The input .nec file showing the parameters for the simulation is shown below.
Figure 4.19 4NEC2 Input .nec File Showing the Geometry Parameters: Center
Element is 4cm ahead of the Outer Elements
The above figure of the waveguide array geometry table shows that the center array
element (Z- axis) is 4 cm ahead of the other two elements.
37
The following figure shows the far field pattern of the waveguides at phi = 0O.
Figure 4.20 Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 0O
Plane: Center Element is 4cm ahead of the Outer Elements
38
The following figure shows the far field pattern of the waveguides at phi = 90O.
Figure 4.21 Far-field Pattern of K-band Waveguide Array at 18GHz & phi = 90O
Plane: Center Element is 4cm ahead of the Outer Elements
39
Chapter 5
CONCLUSION AND FUTURE SCOPE
This project has succeeded in presenting several items. First a working K-Band
antenna array operating at 18 GHz with the ability to conform to various geometries was
designed and secondly, a software simulation package was created in the 4NEC2
environment which has been proven to successfully model actual antenna performance
for any given set of parameters. Lastly data is shown for 3 – element horizontal antenna
array configurations, for a range of conformal geometries, which include both positive
and negative geometry configurations of the array. This data has been summarized and
discussed.
The general results show that for severe conformal geometries with small radii,
field radiation pattern is more focused. The field radiation pattern is stronger as the
center, =0, is approached. As conformal geometry becomes more planar, spherical or
circular radii approach infinity, the field radiation patterns broaden out and become more
uniform over the 180 scanning range. Although grating lobes were present in field
radiation patterns they did not become overpowering and would not hamper antenna
performance.
The results of this project were positive. Certain compromises needed to be made
from original design in order to achieve a working antenna array. However that was to be
expected. Mathematics involved modeling an individual waveguide element, modeling
40
the array factor for a given set of X, Y and Z coordinates, and combining the two models
to arrive at a final model of the entire antenna array. The mathematical model was
incorporated into 4NEC2 software environment for simulation purposes.
Future work would focus on the design of other linear antenna array
configurations such as a vertical array, or even a planar array configuration, and to test
the radiation properties of these array configurations. The ultimate use of the array is to
control the beam position and beam width by use of the conformal geometry, and study
the effectives of positive and negative conformal array surfaces.
41
REFERENCES
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Array Technology”, IEEE Transactions on Antennas and Propagation, January
1981, Volume AP-29, Number 1, pages 25-35.
[2] Morton, T.E.; Pasala, K.M., ‘Performance analysis of conformal conical arrays for
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on Aerospace and Electronic Systems,
Volume 42, Issue 3, July 2006 Page(s):876 – 890.
[3] G.D. Hopkins, D.L. Sherman, K.P. Pullen,
R. Zagrodnick, ‘A K-band microstrip
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[4] G. Caille; E. Vourch; M.J. Martin; J.R. Mosig; M. Polegre, Conformal array antenna
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[5] L.C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part I:
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of the IEEE, July 1997, Volume 85, Number 7, pages 1031-1056.
[6]
T.S.M. Maclean, Principles of Antennas: Wire and Aperture, Cambridge University
Press, 1986, pages 244-247.
[7]
Constantine A. Balanis, Antenna Theory: Analysis and Design, Harper and Row
Publishers Inc., 1982, pages 204-228, 235-243.
42
[8]
David M. Pozar, Microwave Engineering, Addison-Wesley Publishing Company,
1990, pages 141-153, 716.
[9]
Lal C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part I:
Performance Improvement, Feasibility, and System Considerations”, Proceedings
of the IEEE, July 1997, Volume 85, Number 7, pages 1031-1056.
[10] David M. Pozar, “Beam Transmission of Ultra Short Waves: An Introduction to the
Classic Paper by H. Yagi”, Proceedings of the IEEE, November 1997, Volume 85,
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[11]
http://en.wikipedia.org/wiki/Ku_band [Ku band]
[12] http://home.ict.nl/~arivoors/ [NEC based antenna modeler and optimizer by Arie
Voors]