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

© Copyright By Ameya Ramadurgakar 2015

All Rights Reserved

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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

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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

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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

Antenn Publish Structure a Appl Institution, Freque Date Antenna Dimensio Element icati Agency or ncy Number Work Title Type ns s on Corporation Band Design and June 2013 Analysis of an Patch Norwegian X-band Square 40 cm x Milit University of 1 Phased Array 40 cm 64 ary Science X Array Patch Antenna[6] and Technology Design and February Fabrication of German and 2013 W-Band SIW Single 2.414 cm Mult American 2 Horn Element x 0.45 cm 1 iple University W Antenna using PCB process[7] in Cairo A Multilayer February PCB Dual- 2014 Polarized 9 cm x 4 Radiating Patch Linear cm(Estim Milit Italian Space 3 Element Array ate) 6 ary Agency X for Future SAR Applications[8 ] Massachusetts September Miniature Bowtie 22 cm x Mult Institute of 2013 4 Radar for Array 10cm 8 iple Technology X

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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

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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.

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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) � = √ − ( )

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is the propagation constant of the TE10 mode, = 2π/λ, and λ is the free-space

wavelength. The amplitude pattern of an H-plane = horn ω√ is� obtained as [11]

(5) sin ( sin sin �) + cos = ( ) , � The principal-plane pattern for E plane is shown sin below. sin � In equation 5 the second term is the pattern of a uniform line source of length b along the y-axis.

(6) sin ( sin sin �) + cos � = °: � = ( )[ ] sin sin � The H-plane ( pattern can be found using the following equation 7

� = °

+ cos (7) = ( ) =

+ cos , � = ° = ( ) , � = °

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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]

(10) = [ cos + ] 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

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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]

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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:

(12)

= cos + |�= = =

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]

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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.

22

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:

(13)

= cos + |�= = + = → = − (14)

�= An interesting = notecos 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]

23

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.

24

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:

25

(16) = − ℎ (17) � = − ( ) ℎ (18) = − ℎ (19) = − ( ) As microstrip based designs are not generallyℎ 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

26

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: �

8  c = 3 × 10 m/s

 m , n = mode numbers

 a , b = dimensions of the waveguide

27

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� <

28

Figure 2-13: Pitch ‘p’ and Diameter‘d’ of the SIW The guide ‘d’ wavelength is defined by the following equation[15].

(24) � � λ = ��� � √ − 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)

29

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

30

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]:

(27)

log �� = log �� + log � + log � + � − where

= Target gain factor

�

� == One log way free� + space log loss +

= log ∗ +

Note on K1 and K2

 K1 comes from the space loss equation which can also be expressed as[16]

(28) � = log [ ] (29) � = log [ ] The K1 and values are in dB and must be appropriately selected for the

different units of range and frequency. Table 1 shows this.

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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]

(30) �� � = log [ ] (31) � � = log [ ] (32) � = log [ ] 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]

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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) � + � − � = + √ + / 33

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 ( + ) (34) √� = � [ + . + . ln + .] {√

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] ��

(35) < − = � � − . [ − − ln − + � {ln − + . − � }] > {� � � 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.

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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

35

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

sideR(S becomes:

= �� + � + � + � − �� 36

=  = =

.+++.+ =

t Assumption: P = . 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:

Using K1 valuelog from the table + log above and + . = . can be estimated to be: = the Range R after further simplication

−. = = .

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

37

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.

38

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.

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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 equation and a sample calculation is shown below [20] = . or %. The

(36)

where is the broadside gain, = is � the number of elements and is the antenna losses due to efficiency..

40

= � (37) , .

= = �.

Therefore, four elements are needed indicating the gain per element is 2 dB.

Plot of Gain vs. Phased Array Elements at 9 GHz 20

18

16

14

12

10

Gain,dB 8

6

4

2

0 0 1 2 3 4 5 6 7 8 9 10 Number of Antenna Elements

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].

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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.

42

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

43

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.

44

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.

45

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- possible as the offwaveguide frequency is fora passive the S)W structure trace shown with inno green active whichelements shouldnt (such beas 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.

46

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

47

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

48

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

49

between Microstrip to SIW interfaces. The design equations pertaining to this structure are as follows [24].

we

The width of the taper line can be found as.

�� −.��+1 ��−1 (38) + � . √+ℎ/� = [ + . + . + .]

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.

50

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 calcul accurateations and performed working. There for having is a weak the antennas resonance center around frequency 11.25 GHz at as G(z well. were

51

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 52 array was created to see the structures

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

53

For the two element antenna, the which was the phase angle separation between the elements defined in the previousβ 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

54

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.

55

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.

56

Table 3-5: Simulated Antenna Elements vs. Gain and Scan Range

Number of Simulation Calculated Scan Calculated Calculated Scan Elements Gain Range(dB) range(m) for Scan range(m) for RCS 0.01m2 range(m) for RCS 1 m2 0.15m2 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 r ROGERS RO3010. This meant that the design calculations for the SIW and array spacingε 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.

57

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.

58

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

matchingperformance and fromconventional the original micro array strip design array feeding which didntnetwork. incorporate a calculated

59

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

60

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,

(ADS)© tool was used to automatically calculateKeysight®s the microstrip Advanced widths Design and System 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

61

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

62

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.

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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 (< 0.5 for any grating lobes. For 1.6 cm element spacing, the array design had toλ modified as to avoid 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.

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Figure 3-35 Top view of the array with 1.6cm element spacing

Figure 3-36 Array with 1.6cm element spacing side view

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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.

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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

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Figure 3-40: Radiation Patterns of the full array in Polar format

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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

69

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.

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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 /2. This translates to a spacing less than 1.65 cm for an operating design frequencyλ 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

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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.

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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

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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.

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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)

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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

5 ELEMENT Realised Gain, dBElement Spacing,cm Eleet Spacig i Electrical Legth,λ 11 20.5 62.7340.25 7 ELEMENT Realised Gain, dBElement Spacing,cm Eleet Spacig i Electrical Legth,λ 82.4030.25 83.5170.5 For 9 GHz , λ ~ .c λ/λ/ 0.825 cm1.65 cm

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

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elements was equal to 0.5 but showed a dramatic decline when the spacing was 0.25

. However, there was no observableλ difference in gain when the spacing was changed forλ 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

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increaseindicating in that gain. increase in number of elements in an array doesnt always show an

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

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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

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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

80

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.

� (39) � � � � = ( ) where Gt = Gr = G(as they� are both� identical antennae)

When the above equation is rearranged to obtain Gain in dB, it becomes,

(40) � �� = [ log ( ) + log ( )] �� 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. AUT is

recordedThe AUT isusing set to a powerbe on the meter receiving with the side unknown and its receivedgain antenna power set P 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

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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.

(41) � � � + = log ( ) + log ( � ) where: Gt = the Gain of the Transmit Antenna(unknown) �

(42) � � + � = log ( ) + log ( ) By solving Equations 3 and 4 simultaneously and re-arranging�� them, the following expression is obtained

(43) � = + log ( ) ��

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.

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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 ( ) �� (44) � �� + = log ( ) + log ( ) ��

� �� + = log ( ) + log ( ) ��

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So, there are essentially three rounds of measurement done. In the RHS of all

onlythree the expressions ratio of P rin/P tEquation is changing the for Rangeeach round. R and Therefore lambda λ the are equations kept constant can be and 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.

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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

entioned but only takes

Equation doesnt consider the physical factors previously m

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into account mathematical ones such as element spacing, phase separation angle and theta . β

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 SMA connector was soldered to the feeding port. For each of the above experiment,Ω 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, � +

-efficient, Z0 = characteristic impedance

Γ = reflection co 86

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 Model Equipment Used Number Agilent VNA PNA N5224A Gore N5260- Cable 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

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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.

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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. 89

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 Macom MAAL-010528 1 Amplifier(LNA) Bias-Tee Mini Circuits ZX85-12G- 2 S+ Signal Amp Mini Circuits ZX60- 2 14012L-S+ Signal Splitter Mini Circuits ZFSC-2- 1 10G+ Signal Generator HP 836208 1 Power Meter HP 437B 1 Power Meter Sensor Head HP 8481B 1 Scientific Atlanta SA 4131 1 Positioner

A DOS based sweeper program was used to automate the azimuth sweep

in a comma separated value (CSV) text file.

Theoperation raw data and was its thenraw data processed was collected using MATLAB or HFSS for analysis.

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DATA

TX ANT 1 RX ANT 2 POWER METER LNA RF SOURCE DISTANCE ‘ BIAS-T BIAS-T AMP 1 AMP 2 SPLITTER

AZIMUTH POSITIONER SPECTRUM COMPUTER ANALYSER INSIDE ANECHOIC CHAMBER CONTROL

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 > 2.5 are as follows []:

λ

: = .√

(48) : =

: > where:

D = Maximum Antenna Aperture Dimensions (m)

= wavelength (m)

λ 91

r = distance (m)

The far field condition for a large antenna is therefore satisfied as can be seen

2/ from Equation when the distance r is greater than D λ.in For a sphere an electrically of radius asmall equal antenna to or less i.e. an than antenna 0.16 whose physical dimensions can fit different from electrically largeλ [Stutzmanantennas shown and Thiele earlier p] and are the as field follows conditions are

: = ~ . (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.

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Table 4-3: Antennae Dimensions and Far Field Criterion

Antenna Maximum Aperture Passed Far Field Dimensions, cm Criterion HP/EMCO 3115 15.9 YES Homemade X-Band Horn 14.02 YES Proposed Design SIW 12.15 YES Horn

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.

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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.

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TP4

TX ANT 2 RX ANT 3 TP1 DATA TX ANT 1 RX ANT 3

TX ANT 1 RX ANT 2 POWER METER LNA RF SOURCE DISTANCE ‘ BIAS-T BIAS-T AMP 1 AMP 2 SPLITTER TP3

TP2 AZIMUTH POSITIONER SPECTRUM COMPUTER ANALYSER INSIDE ANECHOIC CHAMBER CONTROL

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

95

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 two antennae was kept constant along it can with be all seen other that factors the distance such as Rcable between type, the 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 Macom MAAL-010528 1 Amplifier(LNA) Bias-Tee Mini Circuits ZX85-12G- 2 S+ Signal Amp Mini Circuits ZX60- 2 14012L-S+ Signal Splitter Mini Circuits ZFSC-2- 1 10G+ 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.

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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

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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

98

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

cations in the UAV sector.

Additionally,which could prove it can useful be easily its intended be made proposed into a scanning appli array antenna with the introduction of phase shifting techniques at each element.

99

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.

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[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.

102

[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, .

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,"http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5517884: IEEE, 2014, .

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McGraw-Hill Inc, 08/08/2014.

103

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');

104

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;

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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;

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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;

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%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

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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.

109

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')

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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

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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');

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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;

113

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;

114

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

115

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);

116

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);

117

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)));

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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);

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%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);

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%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-');

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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

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