x band substrate integrated horn array antenna for …
TRANSCRIPT
X BAND SUBSTRATE INTEGRATED HORN ARRAY ANTENNA
FOR FUTURE ADVANCED COLLISION AVOIDANCE SYSTEM
by
AMEYA RAMADURGAKAR
B.S., Drexel University, 2011
A thesis submitted to the Graduate Faculty of the
University of Colorado Colorado Springs
in partial fulfillment of the
requirements for the degree of
Master of Science
Department of Electrical and Computer Engineering
2015
ii
© Copyright By Ameya Ramadurgakar 2015
All Rights Reserved
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iv
To my parents, Surésh and Alka, for their infinite love,
support, and to my sister Aditi for her everlasting love and encouragement
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ACKNOWLEDGMENTS:
My paramount appreciation goes to my academic advisor Dr. Heather Song
(University of Colorado Colorado Springs) for her non-stop advice over the progress of my
thesis research and providing all conditions to keep my work running. I equally appreciate
the valuable feedback, guidance and help from Dr. James Lovejoy (Lockheed Martin) for
his stellar comments, critic and ideas throughout the thesis. I would also appreciate my
deepest gratitude to Dr. T.S. Kalkur (University of Colorado Colorado Springs) for his
overarching support throughout the completion of my degree. Last but in no ways the least,
I most appreciate the help of Kevin Quillen (ANSYS) for showing me the ropes and tricks
of using the HFSS software over many sessions.
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TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION __________________________________________________ 1 1.1. Overview of Collision Avoidance System _________________________________________________________ 2 1.1.1 Automated Dependent Surveillance - broadcast(ADS-B) _____________________________________ 2 1.1.2 Traffic Collision Avoidance System (TCAS) __________________________________________________ 4 1.2 State of the Art UAV Collision Avoidance System _________________________________________________ 6 1.3 Literature Search and Review _______________________________________________________________________ 7 1.4 Novelty of the Proposed Thesis Work ______________________________________________________________ 8 1.5 Scopes and Motivations of Thesis ___________________________________________________________________ 9
II. BACKGROUND AND THEORY ___________________________________ 13 2.1. Horn Antenna ______________________________________________________________________________________ 14 2.1.1 H-Plane sectoral horn __________________________________________________________________________ 14 2.2 Array Antenna ______________________________________________________________________________________ 19 2.2.1 Broadside Array Antenna ______________________________________________________________________ 21 2.2.1 End fire Array Antenna ________________________________________________________________________ 23 2.3 Dielectrically Filled Waveguide____________________________________________________________________ 24
2.4 Radar Range Equation ______________________________________________________________________________ 29
2.5 Microstrip ___________________________________________________________________________________________ 33
2.6 Summary of Theory ________________________________________________________________________________ 34
III. DESIGN _______________________________________________________ 35 3.1 Radar Range Equation (RRE) Calculations ________________________________________________________ 36
3.1.1 Design Calculations and Plots ________________________________________________ 36 3.2 Computer Design and Simulation __________________________________________________________________ 44
3.2.1 Waveguide Design and Simulation ___________________________________________ 44 3.2.2 Antenna Design and Simulation ______________________________________________ 46 3.2.3 Microstrip to SIW Feed Transition and Network Design __________________________ 49 3.2.4 Single Antenna Element Design and Simulation ________________________________ 50
3.3 Array Antenna Design and Simulation _____________________________________________________________ 52
3.4. Feeding Network Technique Analysis and Application ___________________________________________ 59
3.5. Methods to Enhancing Performance in Array Antennas __________________________________________ 76
IV. MEASUREMENT AND RESULT DISCUSSION _____________________ 80 4.1 Antenna Gain Measurement Techniques ___________________________________________________________ 80
4.1.1 Three Antenna Gain Measurement Technique __________________________________ 83 4.2 Calculated, Simulated and Measured Array Facto _________________________________________________ 84 4.3 Experiment Setup ___________________________________________________________________________________ 86
4.3.1 S11 Measurement Test _________________________________________________________________________ 86 4.3.2 Radiation Pattern Setup _______________________________________________________________________ 90 4.3.3 Gain Measurement Setup ______________________________________________________________________ 94
V. CONCLUSION AND FUTURE WORK ______________________________ 98
REFERENCES ____________________________________________________ 101
APPENDICES _____________________________________________________ 104 RADAR RANGE EQUATION ____________________________________________________________________ 104
Subsrate Integrated Waveguide Dimension Calculator Code ___________________________ 116 Array Factor calculator and radiation pattern plotter ______________________________________________ 120
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TABLES
Table 1-1: Basic system requirement (compatible with 1090 ES) ..................................... 2 Table 1-2: Link Budget calculation for ADS-B system..................................................... 2 Table 1-3: TCAS Levels of Protection ............................................................................... 4 Table 1-4: Previous and currently related research and work. ............................................ 9 Table 1-5: Final specification of the proposed design thesis array antenna ..................... 12 Table 2-1: Constant K1 in a Two Way Radar Range Equation ........................................ 22 Table 2-2: Constant K2 in a Two Way Radar Range Equation. ....................................... 22 Table 3-1: Gain Range vs Scan Range. ............................................................................ 33 Table 3-2: Simulated Antenna Elements vs. Gain and Scan Range. ................................ 47 Table 3-3: Number of Elements vs Element Spacing Study Results. ............................... 66 Table 4-1: Return Loss Test Measurement Equipment Used ........................................... 87 Table 4-2: Details of Components Used in Radiation Pattern Measurement ................... 90 Table 4-3: Antennae Dimensions and Far Field Criterion ................................................ 93 Table 4-4: Component Listing for Gain Measurement Experiment ................................. 97 Table 4-5: Main Lobe Measured Absolute Gain .............................................................. 98
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FIGURES
Figure 1-1: TCAS II Block Diagram .................................................................................. 6 Figure 2-1: H-Plane horn .................................................................................................. 14 Figure 2-2: H-Plane (x-z) cut of an H-plane sectorial horn .............................................. 15 Figure 2-3: E and H normalized plane patterns for H plane sectoral horn ....................... 17 Figure 2-4: E and H normalized plane patterns for H plane sectoral horn ....................... 18 Figure 2-5: Array Factor/Pattern Multiplication ............................................................... 20 Figure 2-6: Broadside Array Radiation pattern ................................................................ 21 Figure 2-7: Array factor patterns of a 10-element uniform amplitude broadside array .... 22 Figure 2-8: Three-dimensional amplitude patterns for end-fire arrays toward 0 and 180 degrees .............................................................................................................................. 23 Figure 2-9: Array Factor patterns for ordinary end fire array at different phase excitation........................................................................................................................................... 24 Figure 2-10: Geometry of the dielectric slab waveguide (a) Perspective view (b) Side View .................................................................................................................................. 25 Figure 2-11: Substrate Integrated Waveguide .................................................................. 26 Figure 2-12 Dimension definition of rectangular waveguide ........................................... 27 Figure 2-13: Pitch ‘p’ and Diameter‘d’ of the SIW .......................................................... 29 Figure 2-14: Monostatic Array Antenna System .............................................................. 30 Figure 2-15: Equivalent Circuit Model of the RRE .......................................................... 30 Figure 2-16: A typical cross section view of a microstrip line ......................................... 33 Figure 3-1: Thesis Design Cornerstones ........................................................................... 35 Figure 3-2: MATLAB generated value for Range ............................................................ 37
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Figure 3-3: MATLAB plot of Range vs. Receiver Sensitivity with TX and RX Gain = 10dB .................................................................................................................................. 38 Figure 3-4: MATLAB plot of Range vs. Receiver Sensitivity with TX and RX Gain = 20dB .................................................................................................................................. 39 Figure 3-5: MATLAB plot of Range vs. Receiver Sensitivity ......................................... 40 Figure 3-6: Gain vs Number of Phased Array Elements at 9 GHz ................................... 41 Figure 3-7: Gain Range vs Scan Range Plot ..................................................................... 42 Figure 3-8: Regular Waveguide with Metal Side Walls ................................................... 45 Figure 3-9: SIW X-Band Waveguide ............................................................................... 45 Figure 3-10: S-Parameter response overlay of SIW and Regular Waveguide .................. 46 Figure 3-11: Horn Antenna Structure Design using SIW at reduced height .................... 47 Figure 3-12: S11 (Return Loss) simulation results for the Horn Antenna structure shown in Figure 3-10 .................................................................................................................... 47 Figure 3-13: Horn Antenna Structure Design using SIW at normal X-Band waveguide . 47 Figure 3-14: Realized gain of the Horn Antenna structure from Figure 11...................... 48 Figure 3-15: Field Propagation Animation through the Horn Structure ........................... 49 Figure 3-16: Back to Back Transitions Simulation Model ............................................... 49 Figure 3-17: Single Element Antenna Structure ............................................................... 50 Figure 3-18: S11 Response from the Single Element Antenna Structure .......................... 51 Figure 3-19: Gain Response Pattern from the Single Element Structure at 9 GHz .......... 52 Figure 3-20: Two Element SIW Horn Antenna Array...................................................... 53 Figure 3-21: Element Spacing Consideration ................................................................... 54 Figure 3-22: S11 response for two element array ............................................................. 54 Figure 3-23: Realized Gain response from two element array ......................................... 55
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Figure 3-24: Five Element Array Design .......................................................................... 56 Figure 3-25: Five Element Array Gain Response ............................................................. 56 Figure 3-26: Simulated S11 response as per fabrication specifications ............................. 58 Figure 3-27: Simulated Gain response as per fabrication specifications .......................... 58 Figure 3-28: Version 1 of feeding network modification ................................................. 60 Figure 3-29: Version 1 Array Antenna S11 response ....................................................... 60 Figure 3-30: Version 2 of proposed Array Design with Quarter Wave Matching Feeding........................................................................................................................................... 61 Figure 3-31: S11 response of version 2 .............................................................................. 62 Figure 3-32 Radiation Pattern of version 2 of proposed design ....................................... 62 Figure 3-33 Realized Gain of version 2 of the proposed array design with quarter wave matching feed network ...................................................................................................... 63 Figure 3-34: Rectangular Plot of Directivity (dB) vs. Phi Angle ..................................... 64 Figure 3-35 Top view of the array with 1.6cm element spacing ...................................... 65 Figure 3-36 Array with 1.6cm element spacing side view ............................................... 65 Figure 3-37 Array with 1.6cm element spacing perspective view .................................... 66 Figure 3-38: S11 response of the array with 1.6 cm element spacing ............................... 67 Figure 3-39: Directivity 3D radiation pattern of the array structure ................................. 67 Figure 3-40: Radiation Patterns of the full array in Polar format ..................................... 68 Figure 3-41: Overlay rectangular radiation pattern plots between full array model and single element AF estimation............................................................................................ 69 Figure 3-42: Overlay Plot of Flare Angle ......................................................................... 71 Figure 3-43: Alternating Stackup Arrangement of Array Elements having a separation’d’ of 1.6cm ............................................................................................................................ 72 Figure 3-44: Single element transition structure stripline location ................................... 73
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Figure 3-45: Overlay Radiation Pattern ............................................................................ 73 Figure 3-46: 3D polar radiation pattern plot for single element with 40 degree flare angle............................................................................................................................................ 74 Figure 3-47: Polar overlay plot of single element, full array, AF estimation ................... 75 Figure 3-48: Directivity vs. Relative Spacing plot for a short dipole collinear array. ...... 77 Figure 3-49: Two Element Opposing Orientation SIW Horn Array Design .................... 78 Figure 3-50: Return Loss Response for Two Element Opposed Orientation SIW Horn Array Design ..................................................................................................................... 78 Figure 3-51: Two Element Realized Gain Pattern for an Opposing Element Horn Array............................................................................................................................................ 79 Figure 4-1: Fabricated Array Antenna. ............................................................................. 80 Figure 4-2: Overlay Plot of Array Factor Patterns ............................................................ 85 Figure 4-3: Antenna S11 response from Calibrated VNA ................................................. 87 Figure 4-4: Overlay S11 response ...................................................................................... 89 Figure 4-5: Anechoic Chamber Antenna and Experiment Setup...................................... 91 Figure 4-6: Proposed Antenna Array Mounted for Testing in Anechoic Chamber facility at UCCS ............................................................................................................................ 93 Figure 4-7: Overlay Plot of Simulated and Measured Radiation Pattern of AUT ............ 94 Figure 4-8: Three Antenna Gain Measurement Setup ...................................................... 95 Figure 4-9: Measured Absolute Gain of AUT .................................................................. 97
1
CHAPTER 1
INTRODUCTION
Collision Avoidance Systems (CAS) have long been used in aviation industry primarily
to sense and avoid mid airborne collision between two flying bodies. However, their recent
application has extended down to vehicles such as civilian cars and unmanned aerial
vehicles (UAVs). With civilian UAV sector on the verge of a rapidly booming market for
commerce and trade, the need for a compact, high performance CAS is self-evident.
One of the primary components of a CAS is a high performance and configurable RF
front end. The CAS needs to be able to scan for a target from virtually all directions and
therefore an antenna system which can be configured to move the scanning lobe angle is
highly desirable. As an antenna is one of the major front end component in such a system,
efforts have been made by the industry to make a lightweight, compact and high
performance antenna in the past.
The UAV has long had its traditional application in the military sector. However, in the
recent past this has radically changed and it is common to find a UAV for a myriad of
civilian applications including but not limited to recreational hobby, oil and gas
exploration, environment conservation and the likes. However, most of these systems are
not automated and require an operator while the system is in action and in flight.
In the case of unattended and automated UAV or automotive sector, CAS are recently
being implemented. However, the systems are usually bulky, expensive and have very high
power requirements. One such example is the TCAS and ADS-B system commonly
employed on many commercial passenger aircrafts.
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1.1 Overview of Collision Avoidance System From the initial literature search, it was found that there were essentially two
types of collision avoidance system which are prominent in the aviation industry. They
are
1. Automated Dependent Surveillance – broadcast(ADS-B)
2. Traffic Collision Avoidance System (TCAS)
1.1. 1. Automated Dependent Surveillance – broadcast (ADS-B)
ADS-B is a newer standard adopted by the Federal Aviation Authority (FAA). It
is possible to modify the standard ADS-B transceiver to function as an airborne radar for
obstacle detection and tracking. The application is mostly for smaller piloted aircraft or
UASs that do not have the legacy Traffic Collision and Avoidance System (TCAS)
system. The basic ADS-B system requirement is as shown in Table 1-1:
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Table 1-1: Basic system requirement (compatible with 1090 ES) [1]
Additionally, the following radar equation analysis and link budget calculations below
show that for the system to effectively work, there is a constant need of high power
source, which given the current power and battery technologies is not being satisfactory
for the proposed small, light civilian automated UAV sector.
Table 1-2: Link Budget calculation for ADS-B system [1]
As shown in Table 1-2, a 500 watt power source is not a viable option when it
comes to UAVs as to generate such power would need strong power generator system
which in traditional sense is only possible in a small passenger aircraft. Therefore, it is
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imperative that the RF front end system such as antenna systems and receivers are
enhanced to attempt to achieve scan ranges with the existing ADS-B system.
One of the disadvantages of the ADS-B system is that in order for the system to
detect and avoid collisions all other aircrafts need to be equipped with ADS-B system
1.1. 2. Traffic Collision Avoidance System (TCAS)
The TCAS system has long been in use for collision avoidance in aircrafts. The
TCAS system can be broken down to TCAS I and TCAS II. The difference between TCAS
I and TCAS II system is in their coverage range.
The TCAS system operates by issuing beacons at 1030 MHz that nearby
transponders on other aircrafts respond to at 1090 MHz. The replies received are then
processed by the onboard signal processing hardware and software and relayed to the
cockpit.
As TCAS operates on the same frequency as a ground air traffic controller RADAR
system, to minimize interference the rate at which the interrogation beacon signal is sent
out is dependent on the range and the closure rate between two aircrafts. At far ranges, the
interval is every five seconds and reduces to every second.
TCAS I system are typically used in smaller planes and consists of a TCAS antenna,
signal processor and an output display. This system shows traffic within approximately to
a 5 to 10 kilometer (km) range and issues traffic advisories but is not capable of resolution
advisories [2]
A TCAS II system on the other hand utilizes two antennas and is a requirement for
all aircrafts operating in the United States with more than 30 passenger seats. One antenna
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is placed on top and the other on the bottom of the aircraft. TCAS II systems can show
traffic approximately 22.5 km in the front and 11 km behind of the aircraft. The primary
advantage of the TCAS II system is it’s ability to calculate and issue resolution advisories.
Resolution advisories are aural voice and display messages which the TCAS II system
issues to the flight crew, advising that a particular maneuver should or should not be
performed to attain or maintain minimum safe vertical separation from an intruder [3]
Table 1-3: TCAS Levels of Protection [3]
Table 1-3 shows how the TCAS system performs and interacts with other aircraft
transponder (XPDR). The Mode A and C is simply the type of surveillance used by the
target aircraft. It can be seen that when both target and own aircraft equipment are on
TCAS II system, there is traffic advisory(TA) which is an auditory and visual information
from the system to the flight crew, identifying the location of nearby traffic that meets
certain minimum separation criterion[3] and “Co-ordinated” vertical resolution advisory.
Here is a simplified block diagram of TCAS II system shown in Figure 1-1.
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Figure 1-1: TCAS II Block Diagram [3]
1.2 State of the Art UAV Collision Avoidance System
The primary goal of developing an autonomous collision avoidance system for
UAV is to make them as efficient and satisfactory compete or be on par with a manned
aircraft in terms of safety and accuracy.
Previously, one of the American Society for Testing and Materials (ASTM)
committee titled F-38 had issued a standard which was published. In it, ASTM stipulated
that a UAV was required to avoid a midair collision by detecting another airborne object
within a range of +/- 15 degrees in elevation and +/- 110 degrees in azimuth and be able to
respond and take necessary maneuvers so that a collision is avoided by at least 500 ft. [4].
This stipulation has been withdrawn since May 2014, and FAA is still in the works for
creating a standard for civilian UAV flying in National Airspace System (NAS).
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With the civilian UAV sector projected to be really taking off from the angle of
commercial, personal, and civilian security use there is an absolute need for autonomous
UAV which will be airborne in NAS to detect and avoid collisions [4]. For such systems
to work and be a commercial success there is an absolute need for antenna systems which
can scan for airborne objects but at the same time small, readily available, compact and
low cost to fabricate. The final goal of this thesis is to develop such an antenna system that
addresses the needs of the upcoming civilian UAV sector.
1.3 Literature Search and Review The Substrate Integrated Waveguide (SIW) is a relatively obscure type of
transmission line which only recently has been explored into for various applications. The
working concepts of a SIW will be discussed in the next chapter. A SIW from a top level
overview is a dielectrically filed waveguide (DFW) with VIAs serving as a guiding side
walls instead of a traditional metal sidewall. However, what sets the SIW apart from a
traditional DFW is that they can be integrated within common planar substrates and printed
circuit boards (PCB) and therefore prove to be very beneficial in designing efficient
transmission lines and circuits which are extremely light weight when compared to their
traditional waveguide counterparts. Traditional waveguides which are metal walled need
metal cladding and transitions which are usually housed in a metallic structure, all of which
adds weight.
Extensive literature search on previous published work on SIWs have focused on
designs of using it as means of transmission line in a two port network and, it was found
8
that very little past research was published to explore the possibility of using SIW based
antenna designs.
Given their design which lets SIWs be designed and integrated in commonly
available PCB substrates, across a wide range of frequency bands in the MHz and GHz
spectrum. SIWs therefore are a boon to any collision avoidance system which traditionally
demand for high performance and high power microwave front end components at high
frequencies. This requirement is all the more stressed in a small integrated form factor such
as a typical autonomous UAV application.
1.4 Novelty of the Proposed Thesis Work
As mentioned in the earlier section, the SIW is a relatively uncommon type of
transmission line technique. It’s a very potent platform to develop any RF and
Microwave system which requires high demands such as that of a vehicular CAS.
Horn Antennas have indeed been explored and researched thoroughly in their
basic traditional structural design. From the literature search that was done, there was
only work which demonstrated the use of horn antennas in SIW but that was at very high
W-Band (75 GHz – 110 GHz) frequencies [7]. At such high frequencies the free space
losses are extremely high and it proves to be impractical to design antenna systems
planned for collision avoidance especially in extremely booming and exploding civilian
UAV sector. Some literature studies have used the W-Band for collision avoidance in
automotive sector, however this is at the luxury of having a full electrical system such as
high capacity lead acid batteries, alternators etc. which can be used to generate and store
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electricity. Given a modern automobile has all these aforementioned electrical
components, it is thus possible to use the W-Band in its CAS. High losses translate to
very high power requirements which are at a premium when it comes to light, small
autonomous UAVs which are intended to deliver parcels and services to the general
public.
Therefore this civilian UAV sector certainly outcries for small, compact, low
power but high performing antennas which can attempt to meet the demands of
governmental mandated regulations from international agencies such as FAA and United
Nations International Civil Aviation Organisation (ICAO). One of the ways to enhance a
performance of an antenna is to develop an array system for it.
As of September 2015, there hasn’t been any published work found which
investigates the use of SIW based horn antennas in an array system within the X-Band
frequency regime. The study provides the scientific and engineering basis to bettering
this technology and its usage in the collision avoidance systems in upcoming wave of
civil unmanned aviation vehicles sector. [5]
1.5 Scopes and Motivations of Thesis The motivation for this thesis and research primarily stems for the need of high
performance, compact RF/Microwave systems in the civilian unmanned aerial vehicle
(UAV) sector. As the civilian airspace in many nations across the globe is being given
access to small compact UAV for commercial use, it is vital that the aviation systems
incorporated in them are state-of-the art to prevent and avoid collisions be it airborne or
while preparing for flight or decent.
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In the United States, the FAA which is the governing agency is still in the process
of defining CAS for such a commercial civilian application.
CAS antennas which have been used in the past for military and defense air systems
are heavy and physically large. Given the limited range and power availability for
lightweight civilian UAV sector, the need for a high performing, light weight, small and
low cost antenna system is most crucial.
Additionally, the antenna system which has been researched and designed for this
thesis has never been attempted before. Especially in terms of having a substrate integrated
waveguide horn antenna in an array fashion within the X-Band regime.
The previous work which was found close to the objective of this research is shown
in Table 1-4 below.
Table 1-4: Previous and currently related research and work
Number Work Title
Antenna
Type
Structure
Dimensio
ns
Antenn
a
Element
s
Appl
icati
on
Institution,
Agency or
Corporation
Freque
ncy
Band
Publish
Date
1
Design and
Analysis of an
X-band
Phased
Patch
Square
Array
40 cm x
40 cm 64
Milit
ary
Norwegian
University of
Science X
June 2013
Array Patch
Antenna[6] and Technology
2
Design and
Fabrication of
W-Band SIW
Horn
Single
Element
2.414 cm
x 0.45 cm 1
Mult
iple
German and
American
University W
February
2013
Antenna using
PCB
process[7] in Cairo
3
A Multilayer
PCB Dual-
Polarized
Radiating
Element
Patch Linear
Array
9 cm x 4
cm(Estim
ate) 6
Milit
ary
Italian Space
Agency X
February
2014
for Future
SAR
Applications[8
]
4
Miniature
Radar for
Bowtie
Array
22 cm x
10cm 8
Mult
iple
Massachusetts
Institute of
Technology X
September
2013
11
Mobile
Devices[9]
Table 1-4 is indicative of the fact that there is indeed a recent push for developing
array antenna systems in X-Band. However, most of the time this has been traditionally
restricted to military and the physical size, cost of production were relaxed factors. As
mentioned earlier, with most civilian air traffic regulators across the globe starting to look
into possible integration of UAVs for civilian and commercial usage in their national
airspace, the need to research develop antenna systems which are compact as well as
capable on such aerial vehicles is going to set off a new wave of antenna designs in terms
of requirements.
X-Band seems to be a very good candidate to develop such antenna systems as it
has traditionally been used by air traffic controllers to track and monitor airborne vehicles.
Also free space losses at X-Band are not extensive when compared to higher frequency
bands such as W band therefore relatively good detection ranges can be achieved at
moderate power. Finally, X band is comfortably away from ISM band and therefore is not
susceptible to accidental or malicious interference from devices and operators in that
allotted spectrum.
Traditional collision avoidance antennas such as the ones used in TCAS II and
ADS-B systems are big and bulky. Given the relatively ease of accessibility of space,
computing resources and power on even a small passenger aircraft, much of the
performance gamut as goal was not focused on the antenna systems but rather the onboard
and on deck DSP and electronics that fed into the RF and Microwave front end.
With the case of unmanned and autonomous aerial vehicles however, the balance
is going to shift equally between DSP/Electronics and RF and Microwave front end, given
12
the absolute stringent and limited physical space, computing and power resources on board
a typical UAV.
In its report titled Human Factors in the Maintenance of Unmanned Aircraft
published by various departments of NASA, it is mentioned from their findings that the
accident rate for UAVs is higher than for conventional aircraft [10].Therefore, one of the
impacts that the research which entails in this thesis could be that the industry as well as
academic focusses and spawns on small but high performing antenna systems specifically
targeted to UAVs operating in civilian airspace.
To address the above mentioned needs, in the proposed thesis work, a novel
compact lightweight substrate integrated waveguide based antenna array is designed,
fabricated and characterized. The designed final antenna array shows a gain of 11 dB,
dimensions of 11.475cm x 4cm operating in X-Band. The proposed antenna successfully
met its objectives and can be employed for future advanced CAS systems. Below is the
specification in Table 1-5 of the proposed antenna array design.
Table 1-5: Final specification of the proposed design thesis array antenna
Specification Value Frequency of Operation X Band(8.2 GHz to 12.4 GHz)
Array Gain Greater than 8 dB Number of Elements 4
Radiation Pattern Type Narrow to Medium Broadside Main Lobe Size Compact(Less than 12 cm by 5 cm)
Weight Extremely Light Weight(Less than 250g) Application Collision Avoidance Systems
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CHAPTER 2
BACKGROUND AND THEORY
The underlying principles of horn and array antennas, waveguides and microstrip are
crucial in the characterization of the proposed final design. The goal of this chapter is to
review the fundamentals of the pertaining topics from an electromagnetic theory
perspective.
The relevant theories of horn antennas, dielectrically filled waveguide, array antenna
and microstrip will be discussed in the following sections as they form the foundation of
the research work which was performed and presented in the subsequent sections of this
thesis. A summary of the theory applicable to this thesis, based on the developed methods
carried out in the laboratory and its practical interest concludes each subchapter.
It is of value to discuss the aforementioned relevant theories as the final proposed
design uses the concepts from each respective theory. For example, the dielectrically filled
waveguide is useful in understanding of SIW, which will be discussed in detail in this
section. The substrate integrated waveguide is transformed from a waveguide to a horn
antenna and the microstrip is useful in helping transfer and feed energy to each individual
element. Finally, each individual antenna element is arranged in an array fashion and
therefore array antenna concepts come into importance.
14
2.1 Horn Antenna Horn antennas have been very effective and enjoyed a wide array of application
through the microwave and RF spectrum since their inception. This is so because their
inherent structure provide for high gain, wide bandwidth and relatively ease of fabrication.
There are essentially three forms of horn antennas and they are listed as below:
1. H-Plane sectoral horn
2. E-Plane sectoral horn
3. Pyramidal horn
2.1.1 H-Plane sectoral horn For the purposes of this thesis, the H-Plane sectoral horn was chosen as a suitable
candidate for the design. This was because, it could be implemented in a linear fashion on
a planar substrate. This type of horn is flared in the H-plane and its geometry and
parameters are shown as follows in Figure 2-1:
Figure 2-1: H-Plane horn [11]
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Figure 2-2: H-Plane (x-z) cut of an H-plane sectorial horn [11]
As can be seen in Figure 2-2, the aperture is flared in the x plane, the phase is
uniform in the y plane. The central two variables for the construction of this type of horn
are A and RH from the above Figure 2-2 and the transceiver E and H fields arriving at the
input of the horn are in TE10 mode, when decomposed are as follows[11]
= � −��� (1)
= − / � (2)
where:
� = √ − (3)
is the wave impedence of the TE10 mode and,
� = √ − ( ) (4)
16
is the propagation constant of the TE10 mode, = ω√ � = 2π/λ, and λ is the free-space
wavelength. The amplitude pattern of an H-plane horn is obtained as [11]
= ( + cos ) sin ( sin sin�)sin sin� , � (5)
The principal-plane pattern for E plane is shown below. In equation 5 the second term is
the pattern of a uniform line source of length b along the y-axis.
� = ° : � = ( + cos ) [sin ( sin sin�)sin sin� ] (6)
The H-plane (� = ° pattern can be found using the following equation 7
= ( + cos ) =
= ( + cos ) , � = °, � = °
(7)
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Figure 2-3 E and H normalized plane patterns for H plane sectoral horn [12]
It can be seen in Figure 2-3 that the general pattern for E and H-plane differ. The
E-plane is generally having a larger beam width than the H-plane. The directivity of a H-
plane sectoral horn can be approximated through a family of universal directivity curves.
For a given axial length R0, at a given wavelength, there is an optimal aperture width A
corresponding to the maximum directivity.
Optimal directivity can be obtained if the relation between A and R0 is
= √ = √ (8)
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Figure 2-4: Universal directivity curves for an H-plane sectoral horn [13]
In Figure 2-4, taking axial length (R0 = 6λ) as an example, and A/λ = 4.5 on the x-axis,
and ( λ/b) DH = 32 on the y-axis, it is possible to find what is the optimal aperture width
‘A’ which corresponds to the max directivity of 32. In this case, it works out as below
= . → = . .
= .
=
(9)
Assuming the substrate height ‘b’ to be 1λ, the = 32(dimensionless) which translates
to 30.1 dB.
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2.2 Array Antenna
An antenna array is a group of antennas arranged in a particular way to achieve
performance enhancements such as gain, directivity, scanning area etc. It is important to
look into the two basic types of arrays i.e broadside and end fire arrays.
In a typical array design, there are always parameters that can be utilized to
manipulate the overall pattern of the antenna. They are as follows
Geometrical configuration of the entire array(linear, circular, spherical)
Excitation Phase of the individual elements
Excitation amplitude of the individual elements
Relative displacement or spacing between the elements
Relative pattern of each element
For the research purposes of this work, the geometrical configuration and spacing
between the elements were more closely introspected to achieve a desirable performance.
It is also vital to understand the concept of Array Factor while designing an array
antenna. The total field from an array antenna equals to the field of a single element
multiplied by a ‘factor’ which is commonly referenced as the ‘Array Factor (AF)’. The
Array factor for a ‘n’ element array antenna in normalized form can be calculated as [12]
= [ cos + ] (10)
where k is the wave number, d is the spacing between the elements and β is the phase
separation between the elements.
Thus, the AF is a function of separation ‘ ’, and phase ‘ ’ which can be varied
and adjusted to control the characteristics of the entire array and therefore total directivity
20
and gain. Hence the resulting E field of an array can be described with the following
Equation 9[12]
� � � = × [ ] (11)
The above equation is also referred to as pattern multiplication and can be applied
to antenna arrays with identical elements. For example, taking a look at the two element
array field pattern below with identical elements and phase, it can be realized that using
pattern multiplication, the total field of the array is different and can be manipulated
using the variables element spacing and phase separation.
Figure 2-5: Array Factor/Pattern Multiplication [13]
21
2.2.1 Broadside Array Antenna For applications where there is a need to have the maximum radiation to be in the
direction normal to the axis of the array, the broadside array antenna is useful. This
means the θ0 = 90 degrees. This indicates:
= cos + |�= = = (12)
So to have the maximum radiation directed broadside to the axis of the array, it is
important to have the phase excitation of all elements to be the same i.e. β = 0. To avoid
grating lobes in other directions, the separation between the elements should not equal to
the multiples of wavelength i.e. d ≠ nλ (n = 1, 2, 3…).
Figure 2-6: Broadside Array Radiation pattern [12]
22
Figure 2-6 shows a typical pattern for a 10 element broadside array with element
spacing to be λ/4. It can be observed that there is still some energy radiated in the end fire
region but not as prominent in the broadside.
Figure 2-7: Array factor patterns of a 10-element uniform amplitude broadside array [14]
It is noticeable in the Figure 2-7 how the spacing affects the overall radiation pattern
of an array. As mentioned earlier, if the spacing ‘d’ is integer multiples of wavelength λ,
then there will be grating lobes which appear alongside the main lobe. However, if the
spacing is fraction such as ¼ of the wavelength then there are no grating lobes.
23
2.2.1 End fire Array Antenna An end fire pattern is the converse of a broadside pattern i.e. θ0 = 0 or θ0 = 180.
To have the maxima directed towards either of these theta values, the phase between
elements should be:
= cos + |�= = + = → = − (13)
= cos + |�= = − + = → = (14)
An interesting note to observe is if the element separation ‘d’ = λ/2 then end-fire
radiation can simultaneously exist at both θ0 = 0 and θ0 = 180 which can be seen in Figure
2-8. A comparison of ordinary and end fire array pattern is shown in Figure 2-9
Figure 2-8: Three-dimensional amplitude patterns for end-fire arrays toward 0 and 180 degrees [12]
24
Figure 2-9: Array Factor patterns for ordinary end fire array at different phase excitation [14]
2.3 Dielectrically Filled Waveguide The Dielectrically Filled Waveguide (DFW) is a structure which is composed of
two dielectric slab sandwiched between two metal plates. The electromagnetic energy is
guided through total internal reflections from dielectric boundaries.
The importance of bringing the theory into light is because it leads to a specialized
structure called substrate integrated waveguide (SIW) which will be used as a guiding
structure to propagate electromagnetic waves to the antenna section of the design. A SIW
as will be explained further in this section is a reduced height DFW. Additionally a DFW
becomes a SIW by the replacement of side metallic walls with vias. Although this decrease
in height compared to a ‘regular’ waveguide increases capacitance per length and in turn
reducing the impedance the electromagnetic wave sees.
25
Figure 2-10 shows a sample geometry of the structure. Dielectric waveguides
have non-zero fields outside the guide unlike a metal waveguide and therefore both the
inside and outside fields need to be taken under consideration for analysis. For a
dielectrically filled waveguide to guide electromagnetic energy, the fields must be
confined within the slab and must also decay exponentially outside the slab.
Figure 2-10: Geometry of the dielectric slab waveguide (a) Perspective view (b) Side View
There are two common theories to handling dielectrically filled waveguides. For
the analytic purposes of this thesis research, the Wave theory is considered.
Wave Theory
Ray Theory
For the DFW to be propagating the wave energy, the electromagnetic field must
be confined to the vicinity of the slab and must decay exponentially away from the slab.
The field propagation equation therefore can be divided into two halves
= { − � − , � + , (15)
where Ca : above slab, Cb : below slab[14]
The E and H-field components can be found using the following equation:
26
= − ℎ (16)
= −( �ℎ ) (17)
= − ℎ (18)
= −( ℎ ) (19)
As microstrip based designs are not generally efficient in high frequency and high
power applications given to nature of short wavelengths, waveguide based designs are
usually employed. But given the fact that microstrip designs can be easily manufactured
when compared to waveguide, a balanced tradeoff transmission line structure called SIW
has been developed. A simple SIW structure is shown below.
Figure 2-11: Substrate Integrated Waveguide
In Figure 2-11, the red portion of the structure is the cavity filled substrate which
is guided all the way with metallic VIAs (shown in grey). The height of the via along the z
axis is equal to the height of the substrate (shown in green). Both the top and the bottom
layers are metal.
One of the advantages of using SIWs is the ability to integrate within common
dielectric filled metal cladded laminates which are commercially available. This also
27
makes them very lightweight, ease of fabrication with common prototyping machines such
as LPKF and economically viable option for creating high performance designs in high
frequency applications. By creating metallic plated via ‘walls’ in the guide structure and a
metal structure on the top coupled with a ground plane at the bottom, the structure behaves
as a dielectrically filled waveguide to an electromagnetic wave launched at one end or one
port.
The decreased height does have an effect when compared to a regular waveguide
in terms of impedance the wave sees as the capacitance/length increases. The following are
the design equations and variables are crucial in designing a SIW:
Figure 2-12 Dimension definition of rectangular waveguide [15]
The design equations pertaining to SIW are as shown below. Beginning with the standard
equation for finding the cut-off of an arbitrary waveguide which is:
= �√ � + � (20)
where:
c = 3 × 108 m/s
m , n = mode numbers
a , b = dimensions of the waveguide
28
Therefore, the cut-off frequency for the TE10 fundamental mode is:
= (21)
The fundamental mode of a SIW is therefore only affected by ‘ ’ width dimension and
not the ‘b’ height. This is important observation as it shows that waveguides can be
fabricated on a typical substrate which are mostly restricted in the thickness or ‘b’ height.
The width dimension ( for a DFW can be found out for the same waveguide if the
dielectric constant (�� of the material which makes up the substrate is known by the
following equation:
= √�� (22)
Having known the cutoff frequency and the width dimensions, the values can then be
passed on for design of the SIW. The two essential design rules as per the published work
the substrate integrated circuits - a new concept for high-frequency electronics and
optoelectronics is that:
the pitch(center to center distance) between two vias must be less than twice the
diameter
< (23)
the diameter of each via is smaller than the fifth of the guide wavelength(λg)
< λ�
29
Figure 2-13: Pitch ‘p’ and Diameter‘d’ of the SIW
The guide ‘d’ wavelength is defined by the following equation[15].
λ� = �√�� � − � (24)
The theory of DFW and SIW and the equations associated with it that were
discussed in this section is most crucial in creating the fundamental design of the proposed
antenna system. Most of the equations and requirements for building a SIW were put in
computation software MATLAB, which enabled the calculation of initial design values.
2.4 Radar Range Equation
It is important to discuss the Radar Range Equation (RRE) which is derived from
the Friis transmission equation. The Friis transmission equation can be used to estimate
many factors of a microwave communication systems operating in a certain environment.
One of the basic forms of the Friis transmission equations is shown below.
�� = ( � ) � ��� (25)
where: �� is the Received Power in dBm, �� is the Transmit Power in dBm, � is the
Transmit antenna gain in dB, � is the Receive antenna gain in dB, R is the distance
between the transmit and receive antenna in meters(m)
30
Using Equation (25), it is possible to estimate and calculate the link budget required
for a particular microwave wireless transmission system if some of the values of the
elements are known beforehand. This will be explored in much detail in the following
section as it provides the basis to getting the performance of the phased array antenna
system developed given certain conditions and/or criterion are met or provided.
The general design specification of the array antenna developed for this thesis is
based on the specifics and parameters from this equation. It is assumed that the antenna
system which will be used in a radar system for collision avoidance is monostatic i.e. both
the transmit and receive array antennas are co-located.
Figure 2-14: Monostatic Array Antenna System [16]
The equivalent circuit of the Figure 2-14 is as below in Figure 2-15. Notice that the free
space loss doubles as the energy is transmitted or reflected back from the target to the
receiver
Figure 2-15: Equivalent Circuit Model of the RRE [16]
As there are many forms of the RRE and many were used to identify which is the
best suited to the application case, a report is created showing the different types of RRE
and/or gain. MATLAB was used to perform a parametric analysis to mostly find the gain
31
vs. range by setting other parameters in the respective equations constant. The parameters
that were kept constant or fixed are noted on the top of every plot.
���� = � � �� [ � ] (26)
When the above equation is simplified in terms logarithms it becomes [16]:
log �� = log �� + log � + log � + � − (27)
where
� = Target gain factor
� = log � + log +
= One way free space loss = log ∗ +
Note on K1 and K2
K1 comes from the space loss equation which can also be expressed as[16]
= log [ � ] (28)
= log [ �] (29)
The K1 and values are in dB and must be appropriately selected for the
different units of range and frequency. Table 1 shows this.
32
Table 2-1: Constant K1 in a Two Way Radar Range Equation [16]
K2 comes from the Target Gain Factor ( � equation which can also be
expressed as[16]
� = log [ � �] (30)
� = log [ � ] (31)
= log [ �] (32)
The K2 and � Values are in dB and are dependent on RCS, frequency and
dimensions. Therefore the K2 differs and varies according to type of the RCS unit
and frequency. It is summarized in the table below
Table 2-2: Constant K2 in a Two Way Radar Range Equation [16]
33
2.5 Microstrip The microstrip line is a planar type transmission line which has been proven to be
very popular given its ease of fabrication and integration. A typical geometry for a
microstrip structure is shown below.
Figure 2-16: A typical cross section view of a microstrip line
It is important to understand that the type of electromagnetic propagation in a
microstrip is ‘Quasi TEM’. This is primarily because the presence of a dielectric material
i.e. εr ≠ 1 between two the conductor and a ground plane. The microstrip line usually has
most of its field lines between the dielectric region between the strip and the conductor and
also in the air above the substrate. This makes phase matching at interfaces not possible
since the phase velocity of TEM fields in the dielectric region governed by /√�� whereas
in the air region above the conductor it is c, showing in turn that the pure TEM wave is not
supported by microstrip lines.
Some of the important design equations and parameters for microstrip are effective
dielectric constant, characteristic impedance and W/d ratio. They are discussed and shown
below [17]
� = � + + � − √ + / (33)
34
The effective dielectric constant for a microstrip line encompasses both the air
and the dielectric regions. If the dimensions of a microstrip line are provided, it is
possible to find the characteristic impedance Zo which can be found as[17].
= { √� ln ( + ) �√ [ + . + . ln + . ] (34)
On the other hand if the characteristic impedance Z0 and the dielectric constant �� is
known, the W/d ratio can be found out using the equation below [17]
= { − < � [ − − ln − + �� −�� {ln − + . − .�� }] > (35)
2.6 Summary of Theory The theories that were discussed were directly employed in the design of the
proposed design. The RRE and Friis transmission equation were useful in calculating the
link budget and estimating the scan range for gain ranges. Horn antenna theory was useful
is finding the flare angle of the horn element in the array and the array factor equation was
useful in estimating the radiation pattern. The SIW design equations were useful in
calculating the dimensions required for modelling the waveguide part of the antenna and
finally the microstrip equations were useful in calculating the width of the microstrip feed
to the waveguides of the proposed design.
35
CHAPTER 3
DESIGN
Each of the individual theory which was explained in the previous chapter is
instrumental in creating the final design for the proposed antenna. As mentioned
previously a MATLAB® [18] script code was created which prompted the user on the
design parameters and requirements. That aided in updating the simulation model
created with ANSYS© HFSS ® [19] software quickly. The simulation model was also
created in parts which will be demonstrated in this chapter.
Additional design parameter optimizations were also done on the final simulation
model to achieve a desired performance specification. Once the final design was locked
down, it was exported into a 3D modeler to create fabrication GERBER files which were
sent out to a third party PCB manufacturer. Due to very tight tolerances involved in the
design, it was not possible to fabricate this design in house at the University of Colorado
Colorado Springs facilities.
Figure 3-1: Thesis Design Cornerstones
Figure 3-1 above shows the four essential cornerstones which were
developed for the final antenna design. Each of the following sections in this chapter
is focused on the design of each of these cornerstones. But before all the design
36
could be started a lot of analysis was performed in terms of performance and
specifications using the radar range equation (RRE) mentioned in the previous
chapter. The RRE was put into a MATLAB script and fed various initial conditions so
that a performance ballpark could be estimated. This is explained in detail in the
following section.
3.1 Radar Range Equation (RRE) Calculations
The RRE was presented in the previous chapter in detail. The equation was
input in MATLAB and there were multiple plots generated by changing various
parameters. The plots are all range versus receiver sensitivity but with parameters
changed such as transmit and receive antenna gain and transmit power.
All the calculation and plots were conducted for 9 GHz frequency which falls
under the X-band spectra.
3.1.1 Design Calculations and Plots
A sample calculation resulting the scan range of given some initial condition is shown
as below.
Receiver Sensitivity = �� + � + � + � − where: = log + log +
� = log + log + or if Receiver Sensitivity is assumed to be �� the right hand side R(S becomes: = �� + � + � + � − ��
37
=
= = = . + + + . +
Assumption: Pt = . dBm � = dB �= dB and �� = - dBm = . The R(S = . and when the left hand side L(S is equated with the right hand side R(S it becomes: log + log + . = . Using K1 value from the table above and = the Range R after further simplication can be estimated to be:
= − . = .
= .
This value also agrees from the MATLAB script developed for this calculation
and its result is shown in Figure 3-2 below.
Figure 3-2: MATLAB generated value for Range
38
Figure 3-3: MATLAB plot of Range vs. Receiver Sensitivity with TX and RX Gain = 10dB
The plot in Figure 3-3 shows how varying the radar cross section (RCS) of a
target object affects the scan range at a set gain and transmit power. The plot indicates
that the higher the front end system receive sensitivity, the further the detection
range for an object of a specific size can be. The receive sensitivity of a wireless system
depends on the components such as low noise amplifier (LNA) and the electronics
and signal processing which is embedded in it. A higher sensitive system tuned to a
particular frequency is generally one of the performance goal of a microwave system
design.
39
Figure 3-4: MATLAB plot of Range vs. Receiver Sensitivity with TX and RX Gain = 20dB
Increasing the gain of both the transmit and receive antenna by a factor of
100(20 dB) in Figure 3-4, when compared to the Figure 3-3 which used 10 dB for
antenna gain, shows that the scan range for all three target cross sections is
increased by roughly 3.16 times.
40
Figure 3-5: MATLAB plot of Range vs. Receiver Sensitivity
When the transmit power is doubled from 2 W (33.1 dBm) to 4 W (36.02
dBm) or 3 dB, as was shown in Figure 3-5 while the gain of both transmit and
receive antennas was set to 20 dB, the detection range of all three RCS objects
shows very marginal improvement when compared to Figure 3-4.
To approximate the number of elements required to achieve a certain gain
range, the following plot in Figure 3-6 was generated using the equation from the
source [20]. This is assuming antenna element efficiency = . or %. The equation and a sample calculation is shown below [20]
= � (36)
where is the broadside gain, is the number of elements and is the
antenna losses due to efficiency..
41
= � , . = � . =
(37)
Therefore, four elements are needed indicating the gain per element is 2 dB.
Figure 3-6: Gain vs Number of Phased Array Elements at 9 GHz
All of the above plots in Figures 3-3 to 3-6 ignore atmospheric conditions such
as rain, hail and snow. Water is a tough barrier to pass through for electromagnetic
waves. The transmission loss for electromagnetic waves when they propagate
through fresh water is roughly 4.3 dB [21].
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
14
16
18
20
Number of Antenna Elements
Gai
n,dB
Plot of Gain vs. Phased Array Elements at 9 GHz
42
Figure 3-7: Gain Range vs Scan Range Plot
A range estimation was performed given certain initial parameters for gain
ranges required for a scan range. This can be seen in the plot in Figure 3-7. It was
assumed that the transmit power was set to 33.1 dBm and the receiver is sensitive
enough to detect the received signal at -100 dBm. This plot can essentially be divided
into three gain ranges, 1-5 dB, 5-10 dB and 10-15 dB. The chart below summarizes all
the information from the previous plots which is helpful in understanding how
physical factors and conditions affect the needs and capabilities of the proposed
antenna design.
43
Table 3-4: Gain Range vs Scan Range
RCS,m2
Gain Range, dB 0.05 0.15 1
1 30.87 40.63 65.29
2 34.64 45.59 73.26
3 38.87 51.15 82.2
4 43.61 57.39 92.23
5 48.93 64.4 103.48
6 54.9 72.26 116.11
7 61.6 81.07 130.28
8 69.12 90.97 146.17
9 77.55 102.07 164.01
10 87.02 114.52 184.02
11 97.63 128.49 206.48
12 109.55 144.17 231.67
13 122.91 161.77 259.94
14 137.91 181.51 291.66
15 154.74 203.65 327.24
Table 3-4 shows the scan range for an object of particular RCS and the needed
gain range to detect that object given certain pre-conditions. The pre-conditions were
frequency = 9 GHz, Pt = 33.1 dBm, Pr = -100 dBm. From the three gain ranges, the
proposed antenna performance was targeted towards going in the last gain range i.e.
10-15 dB. From Figure 6 plot this is also indicative therefore the target performance
goal is met with greater than 5 elements which translates to greater than 2
dB/element in an array assuming each element efficiency to be 0.65 or greater.
Therefore, in conjunction with Table 3-4 and all the range estimates conducted in
regards to preconditions, the target antenna specification is to have an antenna
design that can achieve scan ranges of greater than or equal to 70 m for a smallest
object of 0.05 m2 RCS or greater than or equal to 160 m for a large object of 1 m2 RCS.
Given that the UAV is travelling at 20 m/s, which is relatively fast for any
autonomous airborne object, this translates to having 3 seconds to impact the
44
smallest airborne target (0.05 m2). With modern high speed electronics and signal
processing onboard, three seconds is enough time for the autonomous UAV to alter
its flight course in order to avoid the collision [22].
3.2. Computer Design and Simulation
The antenna design process was modular. This meant each component from
each of the design cornerstone (shown in Figure 3-1) was built individually, and then
integration took place with the rest after satisfactory results of the individual
component. Upon integration, there were several optimizations done on the entire
array structure, which will be discussed in the later section of this chapter.
3.2.1 Waveguide Design and Simulation
To first step in the thesis design was to build a waveguide in HFSS and then
simulate it for S-parameter results. After this the SIW was designed based on the
results of the MATLAB script which had the design equations mentioned in the
previous chapter. An overlay plot of the S-Parameter was generated to verify that the
regular X-Band waveguide results matched with the results of the SIW. The dielectric
that was used was air in both cases.
45
Figure 3-8: Regular Waveguide with Metal Side Walls
The height and width that were used in waveguide shown in Figure 3-8 was
2.28 cm and 1.016 cm respectively. These are the standard dimensions for a typical
rectangular waveguide designed to operate in the X-Band spectrum.
Figure 3-9: SIW X-Band Waveguide
The structure shown in Figure 3-9 is a SIW design. The metal via diameter
and pitch was adjusted to 0.21 cm and 0.42 cm using the design rule equation 21.
The overlay plots of the S-parameter results from the simulation are shown below.
The dielectric used was air.
46
Figure 3-10: S-Parameter response overlay of SIW and Regular Waveguide
It is important to note and observe that the S12 response from both the
structures is different. Especially there was an anomaly noted in the insertion loss for
the SIW trace. It can be seen that in Figure 3-10 plot shows a positive gain (> +0 dB)
around the cut-off frequency for the S)W trace shown in green which shouldn t be possible as the waveguide is a passive structure with no active elements (such as
amplifiers or power sources) in it. This anomaly was noted down and submitted to
the ANSYS engineering team so that they could look into it further and it was
concluded that it was just the software simulation artifact after discussion with the
team.
3.2.2 Antenna Design and Simulation
To start off the antenna design within the substrate using via as walls, only the
flare section of the horn antenna was designed. The excitation port was setup and the
return loss simulation was performed on it to check if it was operating in the X-Band.
47
Figure 3-11: Horn Antenna Structure Design using SIW at reduced height
Figure 3-12: S11 (Return Loss) simulation results for the Horn Antenna structure shown in Figure 3-10
Figure 3-13: Horn Antenna Structure Design using SIW at normal X-Band waveguide
48
Comparing Figures 3-11 to 3-13, it is noticeable that the height of the structure
in Figure 3-11 is reduced compared to the normal X-band waveguide height. The
reduced height generally implies that efficiency of the structure is decreased as
electromagnetic waves see an increase in capacitance per length.
The reduced height was a necessary step because of fabrication concerns, the
board manufacturer only made substrate thickness to a certain limit and therefore
was a design constraint. Overcoming this challenge to achieve a working antenna
reaching an agreeable gain/element value was as a significant achievement.
The realized gain and gain pattern of the horn antenna from Figure 3-11
resulted as below in Figure 3-14. Note that realized gain is the gain which is realized
from the structure after consideration of the losses involving the material dielectric,
surface roughness etc.
Figure 3-14: Realized gain of the Horn Antenna structure from Figure 11
A very directed towards bore sight radiation pattern in the YZ plane is the goal.
However, given that the proposed design can be made into a scanning array, this is
not a hard goal. The E-field propagation visualization can also be obtained through
49
the software and it can be seen in Figure 3-15 below on how an electromagnetic wave
propagates at a certain phase angle through the structure.
Figure 3-15: Field Propagation Animation through the Horn Structure
3.2.3 Microstrip to SIW Feed Transition and Network Design
This design element is unique in the sense that it essentially was helpful in
transforming from one type of transmission line technique namely microstrip to
feeding another type which is waveguide.
Figure 3-16: Back to Back Transitions Simulation Model [23]
Figure 3-16 shows the general design of a microstrip to SIW transition. The
microstrip part consists of the narrow signal layer tapering into a larger conical feed
which terminates right at the junction of the waveguide port. This type of transition
tapered design was chosen because of its relatively ease of design and integration
50
between Microstrip to SIW interfaces. The design equations pertaining to this
structure are as follows [24].
The width we of the taper line can be found as. �[ + . + . + . ] = . − . ����+1 + ��−1 √ + ℎ/� (38)
The above equation 3 is complex and therefore it was part of the design
equation script.
3.2.4 Single Antenna Element Design and Simulation
With the designs of the horn SIW antenna ready along with the design for the
microstrip to waveguide transitions, it was time to integrate both individual
structures together to design the single element of the antenna array structure.
Figure 3-17: Single Element Antenna Structure
It is observable from Figure 3-17 that, the structure is made of two section at
this stage of the design. The first section is horn antenna embedded within the
dielectric substrate with VIAs. These VIAs act as replacement for walls of the antenna.
51
The second half is the feed transition structure which is helping in moving
electromagnetic energy from a planar tapered microstrip via line to the antenna
section. The waveguide section is now flared on the other end thus effectively making
the waveguide which was originally a two port microwave structure into an antenna
which is a one port structure. The top and bottom plane of the antenna section is
copper clad while only the bottom section of the transition structure is copper
cladded.
Figure 3-18: S11 Response from the Single Element Antenna Structure
The S11 response shown in plot of Figure 3-18 is indicative that the
calculations performed for having the antenna s center frequency at G(z were accurate and working. There is a weak resonance around 11.25 GHz as well.
52
Figure 3-19: Gain Response Pattern from the Single Element Structure at 9 GHz
With the simulated single element gain coming to roughly 3.6 dB as seen in
Figure 3-19, it was indicative that the structure of a horn antenna embedded within a
substrate and having vias as walls as guiding structures proved to be of advantageous
at relatively high frequencies such as X-Band. Both the S11 and the gain response was
of significant value as they showed that it was firstly possible to design the antenna
structure within the intended frequency and secondly the gain per element value
coming to 3.6 dB promised that higher values could be achieved in an array formation.
3.3 Array Antenna Design and Simulation
With the single element responses proving to be promising to be pursued in
an array design, the next step was to see how adding another element would affect the parameters. (ence a two element array was created to see the structure s
53
behavior in an array pattern. A simple microstrip corporate feed network was used
to feed into the tapered feed transition which then transformed energy into the SIW
antenna.
Figure 3-20: Two Element SIW Horn Antenna Array
A lumped port type of excitation was used at the edge of the microstrip. It can
be seen in red in Figure 3-20. The element spacing between the two elements was
defined as the distance between the centers of the aperture of one element to the
center of the second element.
Figure 3-11: Element Spacing Consideration
54
For the two element antenna, the β which was the phase angle separation
between the elements defined in the previous chapter was considered to be zero. In
a real world application this phase angle separation would be traditionally achieved
by a specialized phased shifter hardware or in modern means through smart digital
signal processing to make this array from a broadside or end-fire array to a scanning
array. Optimal element spacing between array elements is dependent on array gain
and radiation pattern requirements.
Figure 3-22: S11 response for two element array
55
Figure 3-33: Realized Gain response from two element array parametrized over array element spacing
The S11 response for the two element array in Figure 3-22 showed a
considerable difference when compared to the single element response shown in
Figure 3-18. The resonances between 9.0 and 9.5 GHz and 11.0 and 11.5 GHz are
stronger in the sense that they are deeper and more negative, indicating that the array
antenna has minimal reflection losses around those frequency bands when compared
to its single element counterpart. The gain has also increased from 3.59 dB for the
single element to 7.61 dB as can be seen in Figure 3-23. This is a very dramatic
increase of 4.02 dB.
The next logical step in the array antenna design process was to increase the
number of elements to achieve a scan range of greater than 77 meters for a target RCS
of 0.01 m2.
56
Figure 3-44: Five Element Array Design
Figure 3-25: Five Element Array Gain Response
With the increase in elements to five in a linear array fashion, the gain
pattern response can be seen in Figure 3-25 resulting in around 11 dB. That shows
an increase of 3.4 dB from the two element array.
57
Table 3-5: Simulated Antenna Elements vs. Gain and Scan Range
Number of
Elements
Simulation
Gain Range(dB)
Calculated Scan
range(m) for
RCS 0.01m2
Calculated
Scan
range(m) for
0.15m2
Calculated Scan
range(m) for
RCS 1 m2
1 3.6 39-43 51-57 82-92
2 7.6 62-70 81-91 130-146
5 10.8 87-98 115-129 184-206
Assumption: Pt is equal to 33.1dBm, Pr is equal to -100dBm
Due to fabrication cost concerns and limited funding available, the final
antenna design was modified to be created out of a lossy FR4 subsrate instead of the
lower loss εr ROGERS RO3010. This meant that the design calculations for the SIW
and array spacing along with metal thickness needed to be readjusted and simulated
to check for S11 and Gain response.
The design was changed according to the specifications of the FR4 board
material and copper thickness as stated by the board manufacturer so that a lower
cost could be obtained. The results using the final manufacturing specifications are
as below.
58
Figure 3-26: Simulated S11 response as per fabrication specifications
Figure 3-27: Simulated Gain response as per fabrication specifications
As expected the Gain performance of the array antenna dropped by 2.24 dB
when the Rogers RO3010 material was dropped and a lossy FR4 material was used.
Figure 3-27 shows a realized gain of 8.56 dB at 9.2 GHz, whereas Figure 3-25 shows
the gain response of 10.8 dB at 11.5 GHz.
59
3.4. Feeding Network Technique Analysis and Application.
Upon the suggestion of thesis committee, it was suggested that a more
conventional type of feeding technique be investigated and designed into the final
proposed design. The previous design employed an unknown and unconventional
feeding network which proves ineffective in transferring energy from the source
excitation port to the individual elements.
As proposed in the final specifications table in Chapter 1, a strong main lobe is
required at the broadside which can be used to scan for midair targets. One of the
ways this can be achieved is to have a zero phase difference of energy at the entry of
each array element. Therefore, a matching feeding network has to be designed so that
this goal can be realized.
After some research into corporate microstrip feeding and matching methods,
it was found that quarter wave impedence matching, proved effective in the proposed
design interms of ease of manufacturability.
The proposed design was then taken through many iterations interms of its
feeding network. Each version of the iteration showed a marked improvement in the performance from the original array design which didn t incorporate a calculated matching and conventional micro strip array feeding network.
60
Figure 3-28: Version 1 of feeding network modification
It can be seen that the array design shown in Figure 3-28, has four elements
instead of the one in Figure 3-24 which has five. It was found that for a corporate
feed to be employed, the number of elements that need to be branched out to can
only be in the order of 2,4,8,16 etc. This change from 5 to 4 elements also improved
the S11 response of the structure.
Figure 3-29: Version 1 Array Antenna S11 response
61
The S11 response shows a strong resonance at 9.7 GHz and no other
resonances at other frequencies in the X-Band spectrum. This is ideal in terms of
antenna performance as a single strong resonance denotes the operating frequency
at which the antenna is efficiently transforming electromagnetic energy. This
operating frequency can then be adjusted as per the needs of the application by the
antenna engineer. Also this eliminates the need of using filters in the RF front end
which can prove as an additional design element.
The next major version change of the design was the incorporation of the
quarter wave matching microstrip in the feeding network. A sample calculation of
how the widths and lengths for each segment has been demonstrated in Chapter 2.
However, to speed up the design process, Keysight® s Advanced Design System (ADS)© tool was used to automatically calculate the microstrip widths and lengths
based on other parameters.
Figure 3-30: Version 2 of proposed Array Design with Quarter Wave Matching Feeding
The S11 response from the version 2 which included the quarter wave
matching feeding network is shown below. The structure now exhibits resonances
62
at multiple frequencies.
Figure 3-31: S11 response of version 2
At the strongest resonance frequency of 9.4 GHz of the version 2 of the
proposed design, the array structure showed the following radiation pattern and
performance characteristics.
Figure 3-32 Radiation Pattern of version 2 of proposed design
From figure 3-32, it is evident that there is no strong main lobe at boresight
(+90 degrees), but there are two strong lobes found at roughly 45 degrees apart from
the boresight at roughly 50 degrees and 130 degrees. The expected pattern from a
63
broadside array with element spacing which is not integer multiple of wavelengths as
discussed in Chapter 2 should not have grating lobes in other directions. However,
the efficiency of the structure seems to have increased after incorporating the
microstrip quarter wave feeding network and a positive gain has been realized. This
can be evidenced in the 3D realized gain polar plot below
Figure 3-33 Realized Gain of version 2 of the proposed array design with quarter wave matching feed network
A better understanding of realized pattern can be seen in the following
rectangular plot. This 2D plot was generated by setting the Theta to be equal to 90
degrees and Phi set to be the primary sweep of 360 degrees, therefore it is rotation
of the structure about the Z axis. The Y-axis is the axis where the array elements are
linear or alongside each other.
64
Figure 3-34: Rectangular Plot of Directivity (dB) vs. Phi Angle
Referring to Figures 3-34 and 3-32, it is now evident that, the principal lobes
are at roughly 50 degrees from boresight. In efforts to bring the main lobe to the
boresight, the element spacing variable and length of horn section were manipulated
to observe for any effects using the Array Factor concept discussed in Chapter 2 in
HFSS. This was manipulated by using the single element design shown in Figure 3-17
and then having HFSS do the AF multiplication rule to check and compared to the full
array design.
For the AF estimation through HFSS, the following configuration was setup for
the single element. The element spacing was ensured to be 1.6 cm (< 0.5λ as to avoid for any grating lobes. For 1.6 cm element spacing, the array design had to modified in
terms of cell placement so as to avoid the horn flaring angles did not cross into the
other cell boundary. Therefore, the elements were placed one below the other as can
be seen in the views on the following page.
65
Figure 3-35 Top view of the array with 1.6cm element spacing
Figure 3-36 Array with 1.6cm element spacing side view
66
Figure 3-37 Array with 1.6 element spacing perspective view
Figures 3-35 through 3-37 show how the array structure had to be
redesigned in efforts to bring the main lobe to the bore sight. Elements are stacked
are each element is provided with a port excitation. Note that the conventional
matching feeding network would need to be modified slightly if this method
resolves the bore sight position. The array was then analyzed and the following
results were achieved.
67
Figure 3-38: S11 response of the array with 1.6 cm element spacing
Figure 3-39: Directivity 3D radiation pattern of the array structure
68
Figure 3-40: Radiation Patterns of the full array in Polar format
69
Figure 3-41: Overlay rectangular radiation pattern plots between full array model and single element AF
estimation
Figure 3-40 shows the radiation pattern for the array antenna in two separate
the axis. When the pattern is swept for Theta angle through 360 degrees and Phi angle
70
set to 0 degrees, the pattern shows a strong main lobe at bore sight (0 Degrees).
However, given the nature of linear array, the total pattern is shifted onto the +Y axis
(as seen in Figure 3-44) and therefore, when the 2D polar plot is generated by
sweeping for Phi angle through 360 degrees and Theta angle set at 45 degrees, we see
the strong main lobe at bore sight angle(+90 Degrees).
To gain a clearer understanding of the radiation pattern, Figure 3-41 can be
used. The overlay rectangular radiation pattern chart which are set at the same Theta
and Phi angle values. However, these two charts depict a comparison between the
single element AF estimation vs. the full array model created with the same element
spacing. When the primary sweep is set to Theta and swept through 360 degrees and
Phi set to 0 degrees, the single element pattern (green trace) shows a sharper fall to
the side lobes when compared to the full array pattern(red trace) which shows a more
gradual fall to the side lobes suggesting a wider beam width. However, there is a
strong agreement that the main lobe falls at bore sight (0 degrees) with a back lobe
at around 180 degrees from both patterns.
There is a much better agreement in terms of the radiation patterns when both
the single element AF estimation and the actual full array model when the primary
sweep is set to Phi 360 degrees and the Theta at 45 degrees. Again, as evidenced
through the previous plot, there is a wider beam width shown by the full array model
versus the single element array factor estimation. However, the maxima on both of
them seem to agree i.e. at ~90 Degrees and 270 Degrees) as can be seen through the
plot.
71
In a further effort to bring the main lobe to broadside, reduce back lobe and
also decrease size of the array more design exploration was done. One of the two
parameters that was further explored was the flaring angle. The single element horn
flare angle was stepped in increments of 10 degrees from 10 to 40 degrees to observe
for any benefits in terms of reduced back lobes.
Figure 3-42: Overlay Plot of Flare Angle
The overlay plot in Fig 3-42 indicates that the flare angle of 40 degrees (red
trace) proves most effective in terms of reducing back lobe and this can be seen
between the Phi of 150 to 200 degrees.
The next step was to ensure that there were no grating lobes and hence the
spacing between the elements had to be less than λ/2. This translates to a spacing less
than 1.65 cm for an operating design frequency of 9 GHz. It was challenging to
maintain less than 1.65 cm element spacing in array given the flare angle of 40
degrees which was determined to be suitable in reducing back lobes. This was so
72
because the via elements intersected with each other when the spacing was set to 1.6
cm on the same substrate plane and this meant a change in the single element pattern
and therefore in effect the overall radiation pattern.
In efforts to mitigate this, one of the solution came out to be to have alternating
stack up of the arrangement in elements. This can be further seen in the new
arrangement of elements shown in Figure 3-43.
Figure 3-43: Alternating Stackup Arrangement of Array Elements having a separation’d’ of 1.6cm
This alternating arrangement was not only helpful in offering flexibility of
changing the element spacing, but also in helping in increasing the compactness of
the array structure. Also the transition structure which was previously a microstrip
was changd to a stripline so as to reduce energy losses and via structures were added
alongside for additional measure. A clearer view of this change can be seen in Figure
3-44, where the transition substrate is made invisible so as to show the location of
the transition structure which has been made into a stripline.
73
Figure 3-44: Single element transition structure stripline location
With that important observation noted for a single element, the next step was
to estimate the pattern using array factor estimation tool in HFSS. As described and
shown in chapter 2, the array factor is useful in estimation the radiation pattern of an
array antenna setup. Using the pattern multiplication equation 9 from Chapter 2, the
total estimated radiation pattern should be a multiplication of the single element with
the array factor.
Figure 3-45: Overlay Radiation Pattern
74
Figure 3-46: 3D polar radiation pattern plot for single element with 40 degree flare angle
The 3D radiation pattern plot of the single element is shown in figure 3-46 for
reference. From figure 3-45, it can be seen that the Array Factor pattern estimation is
scaled higher than the individual pattern which is expected. The overlay plot also
shows that the actual four element array design created does not deviate much except
slightly in between Theta values of 160 and 210 degrees. A polar representation of
Figure 3-45 is shown in Figure 3-47.
75
Figure 3-47: Polar overlay plot of single element, full array, AF estimation
Using both Figure 3-45 and 3-47 as reference it is now possible to see that
most of the much of the main beam is focused on the +Y axis, with some side lobes in
the –Y axis. It is interesting to note that the trace for full array (red) is very closely
overlapping the single element (green) when it was generally expected to align with
the array factor estimation (blue)
76
3.5. Methods to Enhancing Performance in Array Antennas
In efforts to increasing the scan range of the proposed antenna, there was
some study conducted on what can be performed to enhance the performance such
as realized gain, efficiency, radiation pattern etc. Some of the parameters which are
common but not limited to array antennas that are commonly looked into while
tuning for the earlier mentioned performance criterion are
1. Number of Elements
2. Element Spacing
3. Array element orientation and arrangement
4. Ground Plane
All of the above criterion were explored in regards to the proposed design in
this thesis to check if manipulating them resulted in performance benefits.
Specifically, the first two were explored and the following Table was created showing
the results from simulation.
Table 3-6: Number of Elements vs Element Spacing Study Results
Inferring the data from Table 3-6, it is indicative that the maximum realized
gain in the five element linear array design happened when the spacing between the
5 ELEMENT
Realised Gain, dB Element Spacing,cm Ele e t Spaci g i Electrical Le gth,λ11 2 0.5
6 2.734 0.25
7 ELEMENT
Realised Gain, dB Element Spacing,cm Ele e t Spaci g i Electrical Le gth,λ8 2.403 0.25
8 3.517 0.5
For 9 GHz , λ ~ . cλ/ λ/
0.825 cm 1.65 cm
77
elements was equal to 0.5 λ but showed a dramatic decline when the spacing was 0.25 λ. However, there was no observable difference in gain when the spacing was changed
for the seven element. It can also be inferred that the increase in number of elements
from five to seven did not incur a positive effect in terms of gain. To increase the gain
of an array by a factor of two (3 dB) it is usually required to double the number of
elements, as can be seen in the below graph which is for a collinear array made of
short dipoles.
Figure 3-48: Directivity vs. Relative Spacing plot for a short dipole collinear array [25]
Therefore, a ten element array for the proposed design in this thesis would
have occupied a large physical area and since one of the constraints on this design
was small physical footprint, this design avenue was not explored. However, an
increase in number of elements to a total of seven which is 1.4 times the five elements,
should have at the very least shown a slight increase in gain from 11 dB, thus
78
indicating that increase in number of elements in an array doesn t always show an increase in gain.
In efforts to observe if there was a performance effect of individual element
orientation with respect to each other in the proposed design array, the following
orientation modifications were done shown in Figure 3-49 where each element is
opposing the one besides it.
Figure 3-49: Two Element Opposing Orientation SIW Horn Array Design
Figure 3-50: Return Loss Response for Two Element Opposed Orientation SIW Horn Array Design
79
Plot in Figure 3-50 shows a very similar response to that shown by a single
element in Figure 3-18. However, there is only a slight increase in gain from 3.59 dB
resulting from a single element shown in Figure 3-19 to 3.82 dB for a two element
shown in Figure 3-30. This is a difference of 0.23 dB which is only a 1.054 times
increase in gain from a single element, thus showing that arranging the elements in
an opposing orientation to each other has no effect on gain or radiation pattern as
was in the case of two elements without opposing orientation. As already shown
through Figure 3-24, doubling the number of elements from single to double indeed
increase the gain by 3 dB as per general theory.
Figure 3-51: Two Element Realized Gain Pattern for an Opposing Element Horn Array
The results from literature search showed that altering the ground plane of a
monopole antenna, usually resulted in improved return loss and bandwidth of the
design [25]. As the scope of the study was pertaining to improving gain and radiation
patterns for array antennas this avenue was not given consideration
80
CHAPTER 4
MEASUREMENT AND RESULTS DISCUSSION
The final proposed Antenna design was submitted to an external PCB
manufacturer. However, due to rising fabrication costs when a ROGERS material is
used, it was decided to fabricate the design on a FR4 substrate board. To ensure that the
antenna array was demonstrable when a FR4 material is replaced, additional simulations
were performed and after verification of functionality the final design files were handed
over to the PCB manufacturer.
Figure 4-1: Fabricated Array Antenna
4.1 Antenna Gain Measurement Techniques
For antenna gain measurement, there are three commonly used methods
used to calculate gain. They are:
1. Two Antenna Method
2. Three Antenna Method
3. Gain Comparison or Gain Transfer Method
The two antenna method also known as two known antenna method is a method
which is commonly used when the antennas used are identical. The gain calculation
81
is based off the Friis transmission equation which has been introduced in the previous
chapter. The gain of the Antenna Under Test (AUT) is calculated as follows.
���� = ( � ) � �
where Gt = Gr = G(as they are both identical antennae)
(39)
When the above equation is rearranged to obtain Gain in dB, it becomes,
= [ log ( � ) + log (����)] (40)
However, in the two antenna measurement technique the AUT that need to be
measured for their gain response, need to be identical. As the existing X-Band antennae
in the University of Colorado Colorado Springs Electromagnetics Lab were of unknown
manufacturer which bore no details of records of their performance, this option was
initially considered but then replaced with the three antenna technique for maximum
accuracy. However, the two antenna method was still performed in order to compare and
as a cross validation method against the three antenna method.
For the gain comparison method, the requirement is that there needs to be a
known antenna known as the gain standard in the test setup and a third antenna
whose gain is not needed to be known. The following are the steps followed.
1. The AUT is set to be on the receiving side and it s received power PAUT is
recorded using a power meter with the unknown gain antenna set on the
transmit side.
2. The gain standard is next set to be on the receiving side and its received
power (PGS) is measured while ensuring that the transmit power and the
82
distance between the transmit and receive side is kept the same as the earlier
measurement for AUT.
With the recorded power values known at various azimuth angles, the following
two equations are evaluated based of the received power recordings of the two
steps.
+ � = log ( � ) + log (��� ) (41)
where: Gt = the Gain of the Transmit Antenna(unknown)
+ � = log ( � ) + log (��� ) (42)
By solving Equations 3 and 4 simultaneously and re-arranging them, the
following expression is obtained
= + log (��� ) (43)
The three unknown antenna method is the most accurate of the three above
mentioned method. However, it is also the most time consuming method and
computationally more intensive than the other two method. The three antenna
method is a well-established way to finding the gain of an AUT when there are no two
identical antennas available or a reference antenna available in the measurement
frequency of interest. As the available X-Band horn antennas in the lab were of
unknown manufacturer and unknown performance the three antenna method was
used to measure the gain of the proposed thesis antenna and then compared with the
two antenna method for accuracy.
83
Additionally, a MATLAB script was developed to alleviate and simplify the
process of calculating the Gain of the AUTs using the Three Antenna Method. The
script took the raw data gathered from the anechoic chamber measurements,
processed them using the three antenna method and then outputted the gain pattern
plots of each antenna based of those calculations. Finally, another script was
developed in MATLAB which calculated the array factor for pattern estimation which
based its results off user input, simulation and measurement results.
4.1.1 Three Antenna Gain Measurement Technique
The key factor in using the three antenna gain measurement method is that
none of the specs of the antennae that are involved need to be known as long as they
are designed to operate in the frequency of interest of the AUT. In essence all of the
antennae which are involved in this technique become AUTs themselves as is
evidenced by looking at the calculations below.
The method to testing is to measure all three antennas against each other. The
first antenna is first tested with the second antenna and then the third antenna. Then
the second antenna is tested with the third antenna.
+ = log ( � ) + log (����)
+ = log ( � ) + log (����)
+ = log ( � ) + log (����)
(44)
84
So, there are essentially three rounds of measurement done. In the RHS of all three expressions in Equation the Range R and lambda λ are kept constant and only the ratio of Pr/Pt is changing for each round. Therefore the equations can be re-
written as:
+ =
+ =
+ =
(45)
Solving the system of equations in Equation 7 simultaneously, it is possible to
obtain the individual gain of each antenna
= + −
= − +
= − + +
(46)
4.2 Calculated, Simulated and Measured Array Factor
Array Factor calculations have been traditionally used in Array Antenna
radiation pattern estimation using the Pattern Multiplication concept, which has
been discussed in Chapter 2 of this thesis work. Array Factor calculation and pattern
estimation are useful to quickly estimate the radiation pattern of an array antenna
system without the need of a complex antenna modelling and simulation software
which requires high computing resources and time.
85
For these purposes, a script was developed in MATLAB which calculated the
Array Factor using the Equation 8 from Chapter 2 at various azimuth angles theta in
1 degree increments. The script was also fed with simulated and measured data
obtained from HFSS simulations and anechoic chamber experiment respectively and
an overlay plot is generated.
Figure 4-2: Overlay Plot of Array Factor Patterns
The overlay patterns shown in Figure 4-2 for the array factor are similar
around their main lobe but the simulated pattern shows side lobes. One of the
possible causes for this is because the simulation design considers the microstrip
feed, the transition and horn antenna among other physical factors in the design as it
evaluates the radiation pattern. However, Equation 8, is generic to all array and is not
a design equation specifically for Substrate Integrated Horn Array. Additionally Equation doesn t consider the physical factors previously mentioned but only takes
86
into account mathematical ones such as element spacing, phase separation angle β
and theta .
4.3 Experiment Setup
For the testing and measurement of the proposed antenna, three main
experiments needed to done and they were:
1. S11 Measurement Test
2. Radiation Pattern Measurement
3. Gain Pattern Calculation
All the above three experiments were done in the Electrical Engineering
graduate research laboratories at University of Colorado Colorado Springs. The
fabricated antenna, received from the fabrication facility and then a 50 Ω SMA
connector was soldered to the feeding port. For each of the above experiment, cables
and instruments involved were calibrated to the best of capabilities and the raw data
was processed using MATLAB.
4.3.1 S11 Measurement Test After the SMA connector was soldered onto the board, one of the first test that
was done which served as a sanity test was the S11 of the antenna is helpful in
calculation of the impedance of the antenna, which in this case is the load in the
network. The following equation is used
� = = � −� + (47)
Where, Γ = reflection co-efficient, Z0 = characteristic impedance
87
Zl = load impedance
The following table summarises the devices and equipment used for each of the
experiment.
Table 4-1: Return Loss Test Measurement Equipment Used
Return Loss
Measurement Test
Equipment Used
Model
Number
Agilent VNA PNA N5224A
Cable
Gore N5260-
60023
AUT Prototype
Figure 4-3: Antenna S11 response from Calibrated VNA
After the SMA connector was soldered, the antenna was measured using the
calibrated VNA in the lab. Figure 4-3, shows that the S11 response from the antenna
88
is showing a strong resonance at 8.969 GHz, 8.334 GHz and 9.902 GHz shown by
Marker 1, 2 and 3 respectively. An overlay S11 plot between the measured and
simulated response of the array antenna is shown in the following page.
89
Figure 4-4: Overlay S11 response
From the overlay plot, it can be seen that the simulated response is shifted by
roughly 0.21 GHz from the center frequency of 9 GHz when comparing the shift between marker m and m .
90
4.3.2 Radiation Pattern Setup
The radiation pattern of the fabricated antenna was measured in the
Microwave Anechoic Chamber facility within the Electromagnetics Lab of the CU
Colorado Springs campus location. The overall setup for radiation pattern
measurement is shown In Figure 4-5 and details of the components used is listed
Table 4-2.
Table 4-2: Details of Components Used in Radiation Pattern Measurement
Component Make and Model Quantity Used
Low Noise
Amplifier(LNA)
Macom MAAL-010528 1
Bias-Tee Mini Circuits ZX85-12G-
S+
2
Signal Amp Mini Circuits ZX60-
14012L-S+
2
Signal Splitter Mini Circuits ZFSC-2-
10G+
1
Signal Generator HP 836208 1
Power Meter HP 437B 1
Power Meter Sensor Head HP 8481B 1
Scientific Atlanta
Positioner
SA 4131 1
A DOS based sweeper program was used to automate the azimuth sweep operation and it s raw data was collected in a comma separated value (CSV) text file.
The raw data was then processed using MATLAB or HFSS for analysis.
91
LNA
TX ANT 1
RF SOURCE
RX ANT 2
BIAS-TSPLITTER
SPECTRUM
ANALYSER
POWER METER
DISTANCE ‘
INSIDE ANECHOIC CHAMBERCOMPUTER
CONTROL
AZIMUTH POSITIONER
DATA
AMP 2AMP 1BIAS-T
Figure 4-5: Anechoic Chamber Antenna and Experiment Setup
The connection between the RF source and the TX antenna was setup using a
low loss cable and same applies between the RX antenna and the splitter. In all cases
the . In both the experiments, the setup was kept constant after calibration. However,
before the measurements were started, it was essential to calculate that both
antennas are operating in the Far Field region. As per literature in Stutzman and
Thiele in their book Antenna Theory and Design, the distances to the edges of far and
near fields of operation for big antennas, D > 2.5λ are as follows []:
: = . √
: =
: >
(48)
where:
D = Maximum Antenna Aperture Dimensions (m) λ = wavelength (m)
92
r = distance (m)
The far field condition for a large antenna is therefore satisfied as can be seen from Equation when the distance r is greater than D2/λ. For an electrically small antenna i.e. an antenna whose physical dimensions can fit in a sphere of radius
a equal to or less than 0.16λ [Stutzman and Thiele p ] the field conditions are different from electrically large antennas shown earlier and are as follows
: = � ~ .
: = : >
(49)
To obtain accurate radiation pattern measurements and plot therefore, both
the transmit and receive antennae must be operating in the far field region and
therefore the three far field conditions are given below [Stutzman and Thiele].
> > .
(50)
A table was created to indicate the dimensions of all antennas used for
radiation pattern measurement and showing if they each passed the three far field
criterion in Equation 12. The distance between the transmit and receive antenna was
measured to be 1.8023m using a tape measure.
93
Table 4-3: Antennae Dimensions and Far Field Criterion
Antenna Maximum Aperture
Dimensions, cm
Passed Far Field
Criterion
HP/EMCO 3115 15.9 YES
Homemade X-Band Horn 14.02 YES
Proposed Design SIW
Horn
12.15 YES
Figure 4-6: Proposed Antenna Array Mounted for Testing in Anechoic Chamber facility at UCCS
For radiation pattern test, the proposed thesis design antenna array was
made the AUT and it was set to be the receiver and placed on a positioner turn table
as shown in Figure 4-6. The LNA was connected directly after the antenna feed (not
shown) but wrapped with radio absorbing foam so as to avoid unwanted reflection
to antenna measurement. The resulting radiation pattern is shown below Figure 4-
7. The measurement was taken at 9.023 GHz.
94
Figure 4-7: Overlay Plot of Simulated and Measured Radiation Pattern of AUT
4.3.3 Gain Measurement Setup
For calculating the gain, as explained previously the three antenna method
was used. The MATLAB script developed to calculate the Gain using the three antenna
method based on the raw data provided through the chamber measurement was
used. The setup was similar to Figure 4-5, except that it essentially needed to be done
three times by switching the antennae as per the three antenna gain measurement
setup.
95
LNA
TX ANT 1
RF SOURCE
RX ANT 2
BIAS-TSPLITTER
SPECTRUM
ANALYSER
POWER METER
DISTANCE ‘
INSIDE ANECHOIC CHAMBERCOMPUTER
CONTROL
AZIMUTH POSITIONER
DATA
AMP 2
TX ANT 1 RX ANT 3
TX ANT 2 RX ANT 3
AMP 1BIAS-T
TP1
TP2
TP3
TP4
Figure 4-86: Three Antenna Gain Measurement Setup
There were multiple test points inserted in the setup where the power was
measured to calculate for the losses through the cables, connectors and components
using a zeroed and calibrated power meter. At the baseline setup, the following
equations were used to estimate the losses at different part of the setup, which were
then inputted into the MATLAB script which calculated and plotted the gain for all the
three unknown antennae that were used in the gain measurement. The frequency was
set to 9.023 GHz and the transmit continuous wave power was set to 20 dBm at the
RF signal generator source.
= � − � (51)
= � − � (52)
Note that to measure the TP4, a cable was connected from TP2 to TP3 in the
baseline setup. The cable (not shown) in Figure 4-9 showed a loss of 2.18 dB was
calculated as follows
= � − � (53)
Once the TP4 was found, the Cable between TP2 and TP3 was removed and
replaced with the appropriate antennae at both ends. Using the tape measurement
96
mentioned previously, it was then possible to calculate the Free Space Loss (FSL)
between the transmit and receive antennae using the following equation.
= ( × � × ) (54)
The R in equation 16 represents the distance between the two antennae, and
that was 1.8034m. From Figure 4-8 it can be seen that the distance R between the two antennae was kept constant along with all other factors such as cable type,
equipment and components. The arrow marks indicate the steps involved in
switching out each of the antenna during the measurement. The first measurement
was between Antenna 1 and 2, next Antenna 1 and 3 and finally Antenna 2 and 3.
The following components shown in Table 4 were used in the gain
measurement experiment.
Table 4-4: Component Listing for Gain Measurement Experiment
Component Make and Model Quantity Used
Low Noise
Amplifier(LNA)
Macom MAAL-010528 1
Bias-Tee Mini Circuits ZX85-12G-
S+
2
Signal Amp Mini Circuits ZX60-
14012L-S+
2
Signal Splitter Mini Circuits ZFSC-2-
10G+
1
Signal Generator HP 836208 1
Power Meter HP 437B 1
Power Meter Sensor Head HP 8481B 1
The three antennas that were used are mentioned in Table 4-5. Antenna 1
was the HP/EMCO 3115 bi-ridged horn, Antenna 2 was the proposed thesis SIW
horn array antenna (AUT) and antenna 3 was the homemade X-Band metallic horn.
97
Upon completion, the gain at maximum lobe for each type was recorded and is
shown in Table below.
Table 4-5: Main Lobe Measured Absolute Gain
Antenna Main Lobe Absolute Gain,
dB
HP/EMCO 3115 10.47
AUT 11.07
Home Made X-Band Horn 14.16
Once the raw data obtained from the measurement setup was fed into the
MATLAB script developed to calculate and plot gain, the AUT showed a peak
absolute gain of 11.07 dB at the main lobe and a gain of 8.735 dB at broadside (0
Degrees).
Figure 4-9: Measured Absolute Gain of AUT
98
The AUT antenna gain pattern is shown in Figure 4-9. It can be seen that the
gain pattern is showing three main lobes. The main lobe is showing a gain at
Broadside (180 Degrees) of roughly 8 dB.
CHAPTER 5
CONCLUSION AND FUTURE WORK
The SIW based horn array antenna design has met the specifications. Both the
simulated and fabricated models of the design show a gain greater than 8 dB around
center design frequency of 9 GHz. With the ROGERS RO3010 material, the design can
be made to show a gain of 11 dB.
The design also showed a good overlap between the measured and simulated
radiation pattern. However, the S11 response showed a shift between the measured
and simulated when the antenna was measured using the calibrated VNA. One of the
possible reasons for this could be due to difference in parameters between fabricated
and simulated design. A digital Vernier caliper was used to measure for some
parameters such as via radius, board thickness, copper thickness etc. There range of
difference went from 1.18mils to 4mils. Although this might seem a negligible, such
differences do need to be factored in for high frequency antenna designs such as this
one.
There were some of the difficulties in producing the results for the antennae.
The initial design was done for ROGER RO3010 material which had a high dielectric
constant value of 10.2. However, due to cost constraints the fabricated antenna had
to be done on FR4 which meant compensating for a different dielectric. FR4 is a lossy
material at high frequencies. Also it was not possible to find out what the surface
99
roughness of the material was from the manufacturer. There was a design frequency
shift noted when the FR4 material was used. But this design frequency could again be
tuned for the FR4 by manipulating the waveguide end aperture of the integrated horn
design.
The test chamber, instruments and components were also posing difficulties
in getting a more accurate reading when it came to radiation patterns. The signal
generator and the spectrum analyzer had an unknown calibration date. This showed
a difference in the measured and transmit frequency value. The cables used were very
lossy at the design frequency and hence posed the problem of inadequate SNR for
getting clean and accurate power reading. The power meter used in the testing did
not have a high dynamic range. A workaround to this would be to use the spectrum
analyzer, given its inherent high dynamic range. However the spectrum analyzer did
not yield understandable values when it was made to remotely acquire with the
sweeper program.
However these issues were certainly were mitigated when using the three
antenna technique to calculate for the realized gain. The overall design therefore
succeeded in meeting its requirements in terms of gain, size and weight and therefore
successfully achieving its goal. The design is also very modular and future iterations
of it could be made on a flexible substrate material to achieve bendable characteristics which could prove useful it s intended proposed applications in the UAV sector.
Additionally, it can be easily be made into a scanning array antenna with the
introduction of phase shifting techniques at each element.
100
There were several design updates and analyses done after the initial
fabrication and testing of the five element array. All of this was done on a lossy FR4
substrate. However, it would be interesting to see the design being done and tested
on a higher dielectric or less lossy substrate such as ROGERS RO3010. Another
element that can be research and investigated as future work is the feeding technique
for the design version which has alternating interlaced elements.
101
REFERENCES
[1]L. Haynes, C. Lin and A. Feinberg, Collision Avoidance Using ADS-B Radar, 1st ed.
Intelligent Automation, Inc, 2007, p. 6.
[2]"Collision Avoidance: ADS-B or TCAS." 123HelpMe.com. 14 Sep 2015
<http://www.123HelpMe.com/view.asp?id=43897>.
[3]Advisory Circular, Air Carrier Operational Approval and Use of TCAS II Date:
3/18/13 , AC No: 120-55C ßin important papers folder
[4] http://www.frc.ri.cmu.edu/projects/senseavoid/Images/CMU-RI-TR-08-03.pdf.
Section 4.1 User Requirements, Table 2
[5] http://infoscience.epfl.ch/record/203261/files/EPFL_TH6421.pdf, Section 1.2, page 3
[6] Fredrik Gulbrandsen, Design and Analysis of an X-band Phased Array Patch
Antenna, Norwegeian University of Science and Technology, 01/01/2014.
[7] Mohamed El-Nawawy, A.M.M.A. Allam and Maged Ghoneima, Design and
Fabrication of W-Band SIW Horn Antenna using PCB process,
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6487259: IEEE, 09/09/2014.
[8] Pasquale Capece, Nardo Lucci,Giuseppe Pelosi,, A Multilayer PCB Dual-Polarized
Radiating Element for Future SAR Applications,
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6733274: IEEE, 04/02/2014.
[9] Praveen, S., Miniature radar for mobile devices,
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6670337: IEEE, 04/02/2014.
[10] Alan Hobbs,Stanley R. Herwitz, Human Factors in the Maintenance of Unmanned
102
Aircraft,
http://www.faa.gov/about/initiatives/maintenance_hf/library/documents/media/human_fa
ctors_maintenance/maint_uav_nasa.pdf: FAA, 02/10/2014.
[11]Niklova, " LECTURE 18: Horn Antennas,"
http://www.ece.mcmaster.ca/faculty/nikolova/antenna_dload/current_lectures/L18_Horns
.pdf.
[12] Constantine Balanis, Antenna Theory, 3rd ed. , United States: John Wiley, 2014. pp
674
[13] Warren L.Stutzman and Gary A. Thiele, Antenna Theory and Design, 3rd. ed. ,
United States of America: John Wiley & Sons, 2013. pp. 374
[14] Umran S. Inan ,Aziz Inan,Ryan Said, Engineering Electromagnetics and Waves, 2nd
ed. , Prentice Hall, 2014.
[15] Bilkent University, Dimension definition of rectangular waveguide, Unknown ed. ,
http://www.microwaves101.com/encyclopedias/substrate-integrated-waveguide:
Microwaves 101.com, 2014.
[16]TWO-WAY RADAR EQUATION (MONOSTATIC) Navy Electronic Warfare
Handbook, Ed. United States Navy, http://jacquesricher.com/EWhdbk/2waymon.pdf:
United States Navy, 14/9/2014, .
[17] David M Pozar, Microwave Engineering, 4th ed. , John Wiley, 2014.
[18] Mathworks, MATLAB, R2014 ed. , Mathworks, 2014.
[19] ANSYS, HFSS, 2015 ed. , ANSYS, 2015.
103
[20] Merrill Skolnik, Radar Handbook, 3rd ed. , United States of America: McGraw Hill,
pp13.2
[21] Shan Jiang and Stavros Georgakopoulos, " Electromagnetic Wave Propagation into
Fresh Water,"www.scirp.org/journal/PaperDownload.aspx?paperID=5906: Journal of
Electromagnetic Analysis and Applications, 2011, .
[22] James K. Kuchar and Ann C. Drumm, " The Traffic Alert and Collision Avoidance
System,"https://www.ll.mit.edu/publications/journal/pdf/vol16_no2/16_2_04Kuchar.pdf:
2015, .
[23] Muhammad Imran Nawaz and Zhao Huiling, " Substrate Integrated Waveguide
(SIW) to Microstrip Transition at X-
Band,"http://europment.org/library/2014/interlaken/bypaper/CSC/CSC-09.pdf:
International Conference on Circuits, Systems and Control, 2014, .
[24] Dominic Deslandes, “Design Equations for Tapered Microstrip-to-
,"http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5517884: IEEE, 2014, .
[25] Richard C. Johnson, Henry Jasik, Antenna Engineering Handbook, 2nd ed. ,
McGraw-Hill Inc, 08/08/2014.
104
APPENDICES
1. Radar Range Equation
2. clear all;
clc;
%Radar Cross Section
RCS = 0.05; %Bird
%Lambda/Wavelength
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Range
%Assume R1 = R2, in meters and R_target = square of range
R_target = (150);
%Power Transmitted, Watts
P_t = 2;
P_t_dbm = 10*log10(P_t*1000);
%Power Received, Watts
P_r = 0.01;
P_r_dbm = 10*log10(P_r*1000);
%%Gain
Gain_squared = sqrt(((R_target.^2)*(16*pi^2)*P_r))./((P_t)*RCS*Lambda);
Gain_db = abs(10*log10(Gain_squared));
figure(1)
semilogx(R_target,Gain_db,'r','LineWidth',1.6);
grid on;
xlabel('Range,Meters');
ylabel('Gain,dB')
title('Plot of Gain vs. Range with G_t=G_r,RCS = 0.05m^2,P_t=2W,P_r=0.01W');
105
3. %From Dr Song's source
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Diameter of the antenna in meters
D = 0.001:0.001:0.5;
G = (pi^2*(D.^2))/(Lambda^2);
Gain_db = abs(20*log10(G));
figure(2)
plot(D,Gain_db,'r','LineWidth',1.6);
grid on;
xlabel('Diameter,m');
ylabel('Gain,dB')
title('Plot of Gain vs. Antenna Diameter');
4. %From Skolnik's Source
clc
clear all
%Using Skolnik's RRE with NF and SN
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Power Transmitted, Watts
P_t = 2;
%Power Transmitted, 2Watts in dBm
P_t_dBm = 10*log10(P_t*1000);
%\\Start Variable Gain\\
%Assume Gain Transmit and Receive is = 40 dB/ variable
Gain = 1:1:200;
%Radar Cross Section of a bird
RCS = 0.05;
%Denominator
%kTB = 31.62*10^-9 Watts(-65 dBm), NF = 3 dB , SNR = 14dB
%///Convert from dBm to Watts for Received Power///
%Noise Power when BW is in MHz/kHz(Equation from RF Cafe)
%Assuming 25 MHz BW
BW =25;
106
kTB = -114 + 10*log10(BW);
RHS = kTB/10;
RHS_w = (10^RHS/1000);
kTB_W = RHS_w;
%///End Conversion Process///
%Noise figure in dB
NF = 3;
%SNR in dB
SNR = 18;
%Numerator and Denominator
Den_1 = (16*pi^2)*kTB_W*NF*SNR;
Num_1 = P_t*(Gain.^2)*(Lambda^2)*RCS;
%Take the Fourth Root of the RHS
Range1 = nthroot((Num_1./Den_1),4);
figure(3)
plot(Range1,Gain,'r','LineWidth',1.6);
grid on;
xlabel('Range,Meters');
ylabel('Gain,dB')
title(char('Plot of Gain vs.Range with G_t=G_r,RCS = 0.05m^2','P_t=2W,kTB ~= -100
dBm,NF = 3dB,SNR = 14dB'));
%Noise figure in dB
NF = 0.5:0.5:3;
%SNR in dB
SNR = 18;
Gain_NF = 20;
%Numerator and Denominator
Den_1_NFvar = (16*pi^2)*kTB_W*NF*SNR;
Num_1 = P_t*(Gain_NF.^2)*(Lambda^2)*RCS;
%Take the Fourth Root of the RHS
Range1_NFvar = nthroot((Num_1./Den_1_NFvar),4);
figure(4)
plot(Range1_NFvar,NF,'r','LineWidth',1.6);
grid on;
xlabel('Range,Meters');
ylabel('Noise Figure,dB')
title(char('Plot of Range vs. NF with G_t,G_r=20,RCS = 0.05m^2','P_t=2W,kTB ~= -
100 dBm,SNR = 18dB'));
BW_var =1:10:500;
kTB_var = -114 + 10*log10(BW_var);
RHS_var = kTB_var/10;
RHS_w_var = (10.^RHS_var/1000);
kTB_W_var = RHS_w_var;
%Noise figure in dB
NF = 3;
%SNR in dB
SNR_kTBvar = 18;
%Gain in dB
Gain_kTB = 20;
%Numerator and Denominator
Den_1_kTBvar = (16*pi^2)*kTB_W_var*NF*SNR_kTBvar;
107
Num_1_kTBvar = P_t*(Gain_kTB^2)*(Lambda^2)*RCS;
%Take the Fourth Root of the RHS
Range1_kTBvar = nthroot((Num_1./Den_1),4);
figure(5)
plot(Range1_kTBvar,BW_var,'r','LineWidth',1.6);
grid on;
xlabel('Range,Meters');
ylabel('kTB,pico Watts')
title(char('Plot of kTB vs.Range with with G_t,G_r=20,RCS =
0.05m^2','P_t=2W,NF=3dB,SNR = 18dB'));
5. clc
clear all
close all
frequency = 9*10^9;
P_t = 30;
P_r = -94;
G_t= 45;
G_r= 45;
RCS = 0.01;
%Range is in kM
Range = 31;
K1 = 92.44;
K2 = 21.46;
6. Range = P_t-P_r+G_t+G_r+...
10*log10(RCS)-20*log10(9)-30*log10(4*pi)+20*log10(3);
Range_meters = abs(10^(Range/40))
7. %Calculate Senstivity Required, Given Range
clc
clear all
close all
%Frequency is in GHz i.e 5 = 5 GHz
frequency = 5;
%Transmit and Receive power in dBm
P_t = 70;
P_r = -94;
%Transmit and Receive Gain in dB
G_t= 40;
G_r= 40;
%RCS in m^2
RCS = 0.05;
108
%Range is in kM
Range = 0.17;
K1 = 92.44;
K2 = 21.46;
alpha_atten = 20*log10(frequency*Range)+ K1;
%Frequency is simply taken as 5 instead of 5 x 10^9
G_alpha = 10*log10(RCS)+20*log10(5)+K2;
Rx_sense = P_t+G_t+G_r+G_alpha-(2*alpha_atten)
8. %Let us Backwork this Out
clc
clear all
close all
%Frequency is in GHz i.e 5 = 5 GHz
frequency = 9;
%Transmit(2W) and Receive(31.62nW) power in dBm
P_t = 33.1;
P_r = -65;
%Transmit and Receive Gain in dB
G_t= 40;
G_r= 40;
%RCS in m^2
RCS = 0.05;
%Range is in kM
%Range = 31;
K1 = 92.44;
K2 = 21.46;
%Frequency is simply taken as 9 instead of 9 x 10^9
G_alpha = 10*log10(RCS)+20*log10(frequency)+K2;
%alpha_atten = 20*log10(frequency)+20*log10(Range)+ K1;
RHS = P_t+G_t+G_r+G_alpha-P_r;
RHS = RHS/2;
twenty_log_R = RHS - 20*log10(frequency) -K1;
log_R = twenty_log_R/20;
R = 10^(log_R);
R_meters = R*1000
9. clc;
clear all;
%Plot for various RCS
RCS = 0.01:0.1:10;
%Lambda/Wavelength
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Range
%Assume R1 = R2, in meters and R_target = square of range
R_target = (152.4)^2;
%Power Transmitted, Watts
P_t = 1;
%Power Received, Watts
109
P_r = 0.1;
%%Gain
Gain_squared = sqrt((P_t.*RCS/(4*pi)*(Lambda/(4*pi*R_target)))./P_r);
Gain_db = abs(20*log10(Gain_squared));
figure(2)
plot(RCS,Gain_db,'r','LineWidth',1.6);
grid on;
xlabel('RCS,m^2');
ylabel('Gain,dB')
title('Plot of Gain vs. Varying Radar Cross Section(RCS)');
10. clc;
clear all;
%Plot for various RCS(m^2)
RCS = 0.1:0.1:10;
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Range
%Assume R1 = R2, in meters and R_target = square of range
R_target = (152.4)^2;
%Power Transmitted, Watts
P_t = 400;
%Power Received, Watts
P_r_05W = 40;
P_r_1W = 4;
P_r_2W = 1;
%%Gain
Gain_squared_05W = sqrt((P_t.*RCS/(4*pi)*(Lambda/(4*pi*R_target)))./P_r_05W);
Gain_squared_1W = sqrt((P_t.*RCS/(4*pi)*(Lambda/(4*pi*R_target)))./P_r_1W);
Gain_squared_2W = sqrt((P_t.*RCS/(4*pi)*(Lambda/(4*pi*R_target)))./P_r_2W);
Gain_db_05W = abs(20*log10(Gain_squared_05W));
Gain_db_1W = abs(20*log10(Gain_squared_1W));
Gain_db_2W = abs(20*log10(Gain_squared_2W));
figure(3)
plot(RCS,Gain_db_05W,'r','LineWidth',1.6);
grid on;
hold on;
plot(RCS,Gain_db_1W,'g','LineWidth',1.6);
plot(RCS,Gain_db_2W,'b','LineWidth',1.6);
legend('P_r = 0.5W','P_r = 1W','P_r = 2W')
xlabel('RCS,m^2');
ylabel('Gain,dB')
title('Plot of Gain vs. Varying Radar Cross Section(RCS) with Pt =20W');
11.
110
12. clc;
clear all;
%PCS for Bird
%RCS = 0.01;
RCS = 10;
%Lambda/Wavelength
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Range
%Assume R1 = R2, in meters and R_target = square of range
%Plot for Various Range from 1 to 200 meters
R_target = 1:1:50;
R_target_sq = (R_target).^2;
%Power Transmitted, Watts
P_t = 20;
%Power Received, Watts
P_r = 0.1;
%%Gain
Gain_squared = sqrt((P_r/P_t)*(4*pi)*(16*pi^2)/(RCS*Lambda^2)).*R_target;
Gain_db = abs(20*log10(Gain_squared));
figure(4)
plot(R_target,Gain_db,'r','LineWidth',1.6);
grid on;
xlabel('Range,m');
ylabel('Gain,dB')
title('Plot of Gain vs. Range');
13. %From the plot in figure 4, the maximum gain for a 10 cm diameter antenna
%is about 40 dB @ 9GHz. Using this value, we calculate the number of elements
%required assuming eta(efficieny to be around 0.65)
Gain_var = 1:1:20;
N = Gain_var/(pi*0.65);
figure(6)
plot(N,Gain_var,'r','LineWidth',1.6);
grid on;
xlabel('Number of Elements');
ylabel('Gain,dB')
title('Plot of Gain vs. Phased Array Elements @ 9GHz');
Gain_var_1G = 0.1:0.1:2.5;
N1G = Gain_var_1G/(pi*0.65);
figure(7)
plot(N1G,Gain_var_1G,'b','LineWidth',1.6);
grid on;
xlabel('Number of Elements');
ylabel('Gain,dB')
111
title('Plot of Gain vs. Phased Array Elements @ 1GHz');
%Calculate Gain per element. Assuming N = 9 and Gain = 14 dB. From Skolnik
%13.15 @ 9 GHz
G_per_element = 14/(9*0.65);
%Gain per element for 1 GHz.
G_per_element_1 = 2.5/(9*0.65);
%The gain per element is rougly 3.0769 dB
%Find element spacing,
S = sqrt(G_per_element*(Lambda^2)/(4*pi))
S1GHz = sqrt(G_per_element_1*(Lambda1^2)/(4*pi))
%Find Antenna Array Size(as per Skolnik pg 13.14)
Array_size = 9*S
Array_size1 = 9*S1GHz
%Array size comes out to 13.09 cm^2 or 0.1309 m^2
%Plot for various RCS
RCS = 0.01:0.1:10;
%Range
%Assume R1 = R2, in meters and R_target = square of range
%Power Transmitted, Watts
P_t = 2;
%Power Received, Watts
P_r = 10^-3;
%Range(assuming target is a man i.e RCS = 1 and G = 40dB)
Range = sqrt((1*(40^2)*P_t*(Lambda^2))/(4*pi*P_r*(16*pi^2)));
Range1 = sqrt((1*(40^2)*P_t*(Lambda1^2))/(4*pi*P_r*(16*pi^2)));
figure(7)
plot(RCS,Gain_db,'r','LineWidth',1.6);
grid on;
xlabel('RCS,m^2');
ylabel('Gain,dB')
title('Plot of Gain vs. Varying Radar Cross Section(RCS) with Pt =2W');
14. %Compare with Original Range Equation
clc;clear all;close all
f_design = 9*10^9;
f_design_1 = 1*10^9;
c = 3*10^8;
Lambda = c/f_design;
Lambda1 = c/f_design_1;
%Power Transmitted, Watts
P_t = 2;
%Power Received, Watts
P_r = 10^-3;
Gain = 40;
RCS = 1;
konstant = sqrt((P_r*4*pi)./(P_t*RCS*(Gain^2)));
Range = sqrt((Lambda/4*pi*konstant))
Range1 = sqrt((Lambda1/4*pi*konstant))
15. %From Skolnik. This is from 1.10 assuming the The Receiver sensitivity part
%is Pr OR S_min i.e Minimum Detectable Signal equation 1.4
112
f_design = 9*10^9;
f_design_1 = 1*10^9;
c = 3*10^8;
Lambda = c/f_design;
Lambda1 = c/f_design_1;
%Power Transmitted, Watts
P_t = 2;
%Power Received, Watts
P_r = 0.1;
Gain = 40;
RCS = 1;
R_max_power4_9GHz = ((P_t*(Gain^2)*Lambda*RCS)./(((4*pi)^2)*P_r));
R_max_power4_1GHz = ((P_t*(Gain^2)*Lambda1*RCS)./(((4*pi)^2)*P_r));
R_max_9GHz = nthroot(R_max_power4_9GHz,4)
R_max_1GHz = nthroot(R_max_power4_1GHz,4)
16. clc
clear all
close all
%Using Skolnik's RRE with NF and SN
f_design = 9*10^9;
f_design_1 = 1*10^9;
c = 3*10^8;
Lambda = c/f_design;
Lambda1 = c/f_design_1;
%Power Transmitted, Watts
P_t = 2;
%Power Transmitted, #-Watts in dBm
P_t_dBm = 10*log10(P_t*1000);
%Gain in dB
Gain = 20;
%Radar Cross Section
RCS = 0.01;
%SNR of Receiver
%SNR = 60;
SNR = 10:10:60;
%Bandwidth. Check on what BW is required and how to model Bandwidth
BW = 100 * 10^3;
%Noise Power when BW is in MHz/kHz(Equation from RF Cafe)
kTB = -114 + 10*log10(BW);
%Noise Figure, in dB(From RF Cafe)
NF = 3;
%Numerator in dB
Num_1 = P_t_dBm*(Gain.^2)*(Lambda^2)*RCS;
%Denominator in dB
Den_1 = (4*pi)^3*(SNR)*(kTB*NF);
% Use LOG property to subtract denominator from numerator and then find the
% 4th ROOT
R_max_1 = nthroot((Num_1./Den_1),4)
figure(1)
plot(SNR,R_max_1,'r','LineWidth',1.6);
grid on;
xlabel('SNR, dB');
113
ylabel('Range,m')
title('Plot of SNR vs. Range @ 9 GHz kTB = 64 dB/Hz and NF =3 dB');
17. Gain = 20:10:60
%Radar Cross Section
RCS = 0.01;
%SNR of Receiver
SNR = 18;
%Bandwidth. Check on what BW is required and how to model Bandwidth
BW = 100 * 10^3;
%Noise Power when BW is in MHz/kHz(Equation from RF Cafe)
kTB = -114 + 10*log10(BW);
kTB_abs = abs(kTB);
%Noise Figure, in dB(From RF Cafe)
NF = 3;
%Numerator in dB
Num_1 = P_t_dBm*(Gain.^2)*(Lambda^2)*RCS;
%Denominator in dB
Den_1 = (4*pi)^2*(SNR)*(kTB_abs*NF);
% Use LOG property to subtract denominator from numerator and then find the
% 4th ROOT
R_max_1 = nthroot((Num_1./Den_1),4)
figure(2)
plot(Gain,R_max_1,'r','LineWidth',1.6);
grid on;
xlabel('Gain, dB');
ylabel('Range,m')
title('Plot of Gain vs. Range @ 9 GHz with SNR =18 kTB = 64 dB/Hz');
18. %Gain = 20:10:60
Gain = 18
%Radar Cross Section
RCS = 0.01;
%RCS = 0.01:0.5:10;
%SNR of Receiver
SNR = 60;
%SNR = 10:10:60;
%Bandwidth. Check on what BW is required and how to model Bandwidth
BW = 100 * 10^3;
%Noise Power when BW is in MHz/kHz(Equation from RF Cafe)
kTB = -114 + 10*log10(BW);
kTB_abs = abs(kTB);
%Noise Figure, in dB(From RF Cafe)
NF = 3;
%Numerator in dB
Num_1 = P_t_dBm*(Gain.^2)*(Lambda^2)*RCS;
%Denominator in dB
Den_1 = (4*pi)^2*(SNR)*(kTB_abs*NF);
% Use LOG property to subtract denominator from numerator and then find the
% 4th ROOT
R_max_1 = nthroot((Num_1./Den_1),4)
figure(2)
plot(Gain,R_max_1,'r','LineWidth',1.6);
grid on;
114
xlabel('Gain, dB');
ylabel('Range,m')
title('Plot of Gain vs. Range @ 9 GHz with SNR =60,Gain = 18 , NF = 3dB');
19. %Gain relative to isotropic radiator
%Gain = 10:10:60; <-- Original
Gain = 1:1:15;
f_design = 9*10^9;
c = 3*10^8;
Lambda = c/f_design;
%Distance between TX and RX Cans, in meters
r = 1;
Pr_o_Pt = (Gain.^2*Lambda.^2)./((4*pi*r).^2);
Gain_dBi = 0.5*(10*log10(Pr_o_Pt) + 20*log10(4*pi*r/Lambda));
figure(4)
plot(Gain,Gain_dBi,'r','LineWidth',1.6);
grid on;
xlabel('Gain of Circular Aperture WG, dB');
ylabel('Gain of RADAR,dBi')
title('Plot of Gain of Radar vs. Gain of Circular Aperture WG');
20. clc
clear all
close all
frequency = 9*10^9;
P_t = 30;
P_r = -94;
G_t= 45;
G_r= 45;
RCS = 0.01;
%Range is in kM
Range = 31;
K1 = 92.44;
K2 = 21.46;
Range = P_t-P_r+G_t+G_r+...
10*log10(RCS)-20*log10(9)-30*log10(4*pi)+20*log10(3);
Range_meters = abs(10^(Range/40))
21. clc
clear all
close all
%Frequency is in GHz i.e 5 = 5 GHz
frequency = 5;
%Transmit and Receive power in dBm
P_t = 70;
P_r = -94;
%Transmit and Receive Gain in dB
G_t= 40;
G_r= 40;
%RCS in m^2
RCS = 9;
%Range is in kM
Range = 31;
K1 = 92.44;
K2 = 21.46;
115
alpha_atten = 20*log10(frequency*Range)+ K1;
%Frequency is simply taken as 5 instead of 5 x 10^9
G_alpha = 10*log10(RCS)+20*log10(5)+K2;
Rx_sense = P_t+G_t+G_r+G_alpha-(2*alpha_atten)
22. %Let us Backwork this Out
clc
clear all
close all
%Frequency is in GHz i.e 5 = 5 GHz
frequency = 9;
%Transmit and Receive power in dBm
P_t = 30;
P_r = -94;
%Transmit and Receive Gain in dB
G_t= 20;
G_r= 20;
%RCS in m^2
RCS = 0.01;
%Range is in kM
Range = 31;
K1 = 92.44;
K2 = 21.46;
%Frequency is simply taken as 5 instead of 5 x 10^9
G_alpha = 10*log10(RCS)+20*log10(frequency)+K2;
alpha_atten = 20*log10(frequency)+20*log10(Range)+ K1;
RHS = P_t+G_t+G_r+G_alpha-P_r;
RHS = RHS/2;
twenty_log_R = RHS - 20*log10(frequency) -K1;
log_R = twenty_log_R/20;
R = 10^(log_R);
R_meters = R*100
Published with MATLAB® R2015b
116
2. Subsrate Integrated Waveguide Dimension Calculator Code
%Dimeension Calculator for SIW
%Predefined Contants
c = 3e8;
%The first condition is that d < lambda_guide/5.
% Find Guide Wavelength
%Need to find dimension a for SIW. According to ...
%http://www.microwaves101.com/encyclopedias/substrate-integrated-waveguide
%the relation between the waveguide cutoff frequency and a width is defined by
% The cutoff for a WR90 waveguide operating in X Band as per wiki
% http://en.wikipedia.org/wiki/Waveguide_%28electromagnetism%29 is 6.566
prompt = 'What is the SIW Design Frequency? ';
f_design = input(prompt);
f_cutoff = 6.557*10^9;
a = c/(2*f_cutoff);
%for a Dielectrically Filled Waveguide the the permittivity comes into play
%as per microwaves 101
prompt1 = 'What is the Dielectric Permittivity, E_r? ';
E_r = input(prompt1);
a_d = a/sqrt(E_r);
a_d_cm = a_d*100;
waveguide_end_w = ['The W/G end Width is ',num2str(a_d_cm),' cm'];
disp(waveguide_end_w);
%Denominator. Not sure if it's operating frequency or cutoff frequency.
%Using cut-off frequency
den = ((E_r*(2*pi*f_design)^2/c^2) - (pi/a)^2);
lambda_guide = 2*pi/(sqrt(den));
lambda_guide_1 = ['The Guide Wavelength is ',num2str(lambda_guide),' meters'];
disp(lambda_guide_1);
%So first rule is diameter should be guide wavelength/5
d_max = lambda_guide/5;
d_max_cm = d_max*100;
d_max_mils0 = ['The Max Via Diameter is ',num2str(d_max_cm),' cm'];
disp(d_max_mils0);
%In Mils that is
d_max_mils = 39370.0787*d_max;
d_max_mils1 = ['The Max Via Diameter is ',num2str(d_max_mils),' mils'];
disp(d_max_mils1);
117
r_max = d_max/2;
r_max_cm = r_max*100;
r_max_mils0 = ['The Max Via Radius is ',num2str(r_max_cm),' cm'];
disp(r_max_mils0);
%Second Condition is PITCH, p
p_max = 2*d_max_mils;
p_max_1 = p_max * 2.54*10^-5;
p_max_mils1 = ['The Max Pitch is ',num2str(p_max),' mils'];
disp(p_max_mils1);
p_max_mils2_cm = p_max*100;
p_max_cm = 2*d_max*100;
p_max_mils2 = ['The Max Pitch is ',num2str(p_max_cm),' cm'];
disp(p_max_mils2);
%Seems like with the values that result, the diameter of each via cab be
%80mils and pitch be 160 mils.
%%Width of Waveguide. from the paper 'a review on SIW & it's uStrip
%%Interconnect, Kumar'
if (p_max_cm >= d_max_cm)
disp('Pitch Is Greater than Diameter so Dimensions PASS');
end
if (p_max_cm <= d_max_cm)
disp('Diameter Is Greater than Pitch so FAIL');
end
BAND_stop = p_max_cm*((c*0.01)/f_cutoff);
if (BAND_stop < 0.25)
disp('Band_Stop Is Smaller than 0.25 so PASS');
end
% Microstrip to Rectangular Waveguide Step
%Calculate Effective Permittivity
prompt_height = 'What is the SIW/Antenna substrate Height in cm? ';
height_substrate = input(prompt_height);
118
E_eff = ((E_r+1)/2)+...
((E_r-1)/2)*(1/sqrt(1+12*(height_substrate/a_d_cm)));
E_effective_disp = ['The Effective Permittivity is ',num2str(E_eff),' Ohms'];
disp(E_effective_disp);
%Calculate Effective Impedence
Z_effective = (120*pi)/(sqrt(E_eff)*((a_d_cm/height_substrate)+...
1.393+0.667*log((a_d_cm/height_substrate)+1.444)));
Z_effective_disp = ['The Effective Impedence is ',num2str(Z_effective),' Ohms'];
disp(Z_effective_disp);
Er_over_Ef = E_eff/E_r;
Er_over_Ef_disp = ['The Er/Ef is ',num2str(Er_over_Ef)];
disp(Er_over_Ef_disp);
%From HFSS simulation we can see that a_e(effective width of the W/G) is
%2.29517 cm
a_e = 2.29517;
exponent = -0.627*(E_r/E_eff);
one_over_w_e = (4.38/a_e)*exp(exponent);
w_e = 1/one_over_w_e;
%So according Paper 'A review on SIW and it's Microstrip Interconnect'
prompt_A_e = 'What is the SIW Waveguide Port Width(in cm)?';
effective_wg_internal_width = input(prompt_A_e);
W_taper = 0.4*effective_wg_internal_width;
disp_W_taper = ['The Taper Width is ',num2str(W_taper),'cm'];
disp(disp_W_taper);
%Taper Length...according to Equation 12 in the same published source as
%above for W_Taper, the taper length should be greater than 0.5 Guide
%Wavelength but smaller than Guide Wavelength
% taper_length = 0.75*lambda_guide;
% taper_length_cm = lambda_guide*100;
% disp_W_length = ['The Taper Length is ',num2str(taper_length_cm), 'cm'];
% disp(disp_W_length);
%Calculate the microstrip width.
%Using Equation 8(in section III Design Technique)
B_width = (377*pi/(2*50*sqrt(E_r)));
119
RHS_width = (2/pi)*(B_width -1-log(2*B_width-1)+((E_r-1)/(2*E_r))...
*(log(B_width-1)+0.39-(0.61/E_r)));
W_microstrip = RHS_width*height_substrate;
disp_micrsostrip_width= ['The Microstrip Width is ',num2str(W_microstrip), 'cm'];
disp(disp_micrsostrip_width);
%Test out what multiplier they are using to calculate taper_length
taper_length_paper_cm = 1.2;
taper_length_m = taper_length_paper_cm/100;
multiplier = taper_length_m/lambda_guide;
prompt_cutoff = 'What is the Waveguide Design Cutoff Frequency(GHz)? ';
f_cutoff_paper = input(prompt_cutoff);
lambda_cutoff_paper = c/f_cutoff_paper;
lambda_guide_paper = lambda_cutoff_paper/sqrt(E_r);
multiplier_paper = taper_length_m/lambda_guide_paper;
taper_length = 0.5543*lambda_guide_paper;
taper_length_cm = taper_length*100;
disp_W_length = ['The Taper Length is ',num2str(taper_length_cm), 'cm'];
disp(disp_W_length);
f_design = 9*10^9;
lambda = 3e8/f_design;
wave_number_k = (2*pi)/lambda;
prompt_excitation_phase_thetha = 'What is the Phase between elements(in Degrees)?';
phase_between_element_thetha_degrees = input(prompt_excitation_phase_thetha);
prompt_element_spacing = 'What is the spacing between elements(in meters)?';
element_spacing = input(prompt_element_spacing);
RHS_AF_deg =
0.5*(wave_number_k*element_spacing*cos(phase_between_element_thetha_degrees));
RHS_AF_deg_rads = cos(RHS_AF_deg);
120
%Array Factor Second Equation Equation 6.7 from Class Notes on Page 14
phi = wave_number_k*element_spacing*cos(phase_between_element_thetha_degrees);
Published with MATLAB® R2015b
3. Array Factor calculator and radiation pattern plotter
4. %Array Factor Calculator and Phased Array Radiation Pattern Plotter
clear all;
close all;
clc;
%Number of Elements in the Array Prompt
prompt_element_number = 'How many elements are in the array?';
N = input(prompt_element_number);
% element numbers
%N = 2;
prompt_element_spacing = 'What is the element spacing(in meters)?';
% element spacing
d = input(prompt_element_spacing);
% theta zero direction
% 90 degree for braodside, 0 degree for endfire.
theta_zero = 0;
An = 1;
j = sqrt(-1);
AF = zeros(1,360);
for theta=1:360
% change degree to radian
deg2rad(theta) = (theta*pi)/180;
%array factor calculation
for n=0:N-1
AF(theta) = AF(theta) + An*exp(j*n*2*pi*d*(cos(deg2rad(theta)))-1);
end
AF(theta) = abs(AF(theta));
end
AF_HFSS_array= csvread('ph360_array_five.csv');
AF_HFSS_element = csvread('ph360v2.csv');
RAD_Pat_single = AF_HFSS_element(:,end);
RAD_Pat_array = AF_HFSS_array(:,end);
121
%We delete the last value of the imported raw value vector to enable
%multiplication with AF in MATLAB
RAD_Pat_single(end) = [];
RAD_Pat_array(end) = [];
Array_Pattern = transpose(AF).*RAD_Pat_single;
figure(1)
% plot the Array Factor
polar(deg2rad,AF);
title('Array Factor Radiation Pattern based on Element Spacing "d" ');
figure(2)
%Plot the Single Element pattern imported from HFSS in MATLAB
polar(deg2rad,transpose(RAD_Pat_single));
title('Single Element Radiation Pattern plot imported from HFSS');
figure(3)
%Plot the Array Radiation Pattern
polar(deg2rad,transpose(Array_Pattern));
title({'Plot of Calculated MATLAB Array Pattern';'i.e. Single Element * AF'});
figure(5)
%Plot the Array Radiation Pattern
polar(deg2rad,transpose(RAD_Pat_array));
title({'Plot of Actual HFSS Array Pattern';'i.e. Single Element * AF'});
figure(6)
polar(deg2rad,transpose(Array_Pattern));
hold on
polar(deg2rad,transpose(RAD_Pat_array));
legend('Calculated','Simulated');
title('Overlay Plot of Calculated vs Simulated Array Radiation Pattern');
norm_Calc_Array_Pattern = Array_Pattern - max(Array_Pattern);
norm_Sim_Array_Pattern = RAD_Pat_array - max(RAD_Pat_array);
figure(7)
polar(deg2rad,transpose(norm_Calc_Array_Pattern));
hold on
polar(deg2rad,transpose(norm_Sim_Array_Pattern));
legend('Calculated','Simulated');
title('Overlay Plot of Normalised Calculated vs Simulated Array Radiation
Pattern');
5. %Update 26th July 2015
% We have to normalise the AF from MATLAB
AF_norm = AF - max(AF);
figure(8)
% plot the Array Factor
polar(deg2rad,AF_norm,'r-');
122
title('Normalised Array Factor Radiation Pattern based on Element Spacing "d" ');
Array_Pattern_norm = transpose(AF_norm).*RAD_Pat_single;
figure(9)
%Plot the Array Radiation Pattern
polar(deg2rad,transpose(Array_Pattern_norm));
title({'Plot of Calculated MATLAB Array Pattern';'i.e. Single Element * AF'});
figure(10)
polar(deg2rad,transpose(Array_Pattern_norm));
hold on
polar(deg2rad,transpose(norm_Sim_Array_Pattern));
legend('Calculated','Simulated');
title('Overlay Plot of Normalised Calculated vs Simulated Array Radiation
Pattern');
norm_RAD_Pat_array = (min(Array_Pattern_norm)/max(RAD_Pat_array)).*RAD_Pat_array;
circ_shift_norm_RAD_Pat_array = circshift(norm_RAD_Pat_array,90);
figure(11)
polar(deg2rad,transpose(Array_Pattern_norm));
hold on
polar(deg2rad,transpose(circ_shift_norm_RAD_Pat_array));
view([90 -90])
legend('Calculated','Simulated');
title('Overlay Plot of Normalised Calculated vs Simulated Array Radiation
Pattern');
Published with MATLAB® R2015b