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Department of Science and Technology Institutionen för teknik och naturvetenskap

Linköping University Linköpings universitet

g n i p ö k r r o N 4 7 1 0 6 n e d e w S , g n i p ö k r r o N 4 7 1 0 6 -E S

Phased array antenna element

evaluation

Jacob Samuelsson

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Phased array antenna element

evaluation

Examensarbete utfört i Elektroteknik

vid Tekniska högskolan vid

Linköpings universitet

Jacob Samuelsson

Handledare Adriana Serban

Examinator Qin-Zhong Ye

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Abstract

This thesis evaluates two array antenna elements for large phased array antennas. The two antenna concepts are a surface mounted notch element and a PIFA (Planar Inverted F Antenna). The antennas have been simulated at S-band in Ansys HFSS as a unit cell in an infinite array environment. Thereafter, a finite 7 x 7 element array of the two concepts was simulated. A corresponding 49 element array, using the notch element, was built and measured upon. Embedded element patterns and S-matrix parameters have been measured. From this result, full array antenna patterns as well as active reflection coefficients have been calculated. The measurements show very good performance for large scan angles and a wide frequency range.

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Acknowledgement

First I would like to express my gratitude for the help and support from SAAB AB during this thesis. Special thanks to my supervisor Bengt Svensson and Martin Nilsson from SAAB AB in Göteborg.

I would like to thank my supervisor Adriana Serban and examiner Qin-Zhong Ye at the Department of Science and Technology (ITN) at Linköping University for their help and support under the thesis.

Finally, I would like to thank Ansys for providing a license for HFSS under this thesis.

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Table of Contents

Abstract i

Acknowledgement ii

Table of Contents iii

List of Figures v

List of tables vii

1 Introduction . . . 1 1.1 Purpose . . . 1 1.2 Problem Formulations . . . 2 1.3 Specification of Requirements . . . 2 1.4 Delimitations . . . 2 1.5 Outline . . . 2 2 Theory . . . 4 2.1 Fundamentals of Radar . . . 4 2.2 Fundamentals of Antennas . . . 6 2.2.1 Radiation Pattern . . . 6

2.2.2 Directivity and Gain . . . 9

2.2.3 Band- and Beamwidth . . . 10

2.2.4 Polarization . . . 11

2.2.5 Scattering Parameters . . . 12

2.2.6 Amplitude tapering . . . 13

2.2.7 Beam Scanning . . . 14

2.2.8 Active Reflection Coefficient . . . 15

2.2.9 Embedded Element Pattern . . . 16

2.3 Planar Inverted F Antenna . . . 16

2.4 Surface mount notch element . . . 19

3 Method . . . 22 3.1 Simulation . . . 22 3.1.1 Model . . . 23 3.1.2 Boundaries . . . 27 3.1.3 Excitations . . . 28 3.1.4 Analysis . . . 29 3.1.5 Optimetrics . . . 30 3.1.6 Field Pattern . . . 30 3.2 Measurements . . . 31

3.2.1 Measurements of Scattering Parameters . . . 31

3.2.2 Measurements of Antenna Gain . . . 32

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4.1 Parameter sweep . . . 34

4.2 Infinite Array . . . 36

4.3 Finite Array . . . 37

5 Surface Mount Notch Antenna . . . 38

5.1 Parameter sweep . . . 38 5.2 Infinite Array . . . 42 5.3 Finite Array . . . 44 5.3.1 Scattering parameter . . . 44 5.3.2 Antenna Gain . . . 46 6 Discussion . . . 49 6.1 Results . . . 49 6.2 Simulations . . . 50 6.3 Measurements . . . 50 7 Conclusion . . . 52 Bibliography . . . 53

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List of Figures

1 Main and sidelobes in an antenna pattern, with illustration of the

beamwidth in the lobe [2]. . . 7

2 Reference coordinate system [2]. . . . 8

3 Half Power Beamwidth and Full Null Beamwidth of an antenna pattern [2]. . . . 10

4 Illustration of polarization of electromagnetic wave a) rotation of traveling wave b) elliptical polarization at Z=0 [2]. . . 11

5 Arbitrary N-port microwave network [5]. . . 12

6 Illustration of electrically beam scanning or beam steering of a uniform array [6]. . . 15

7 General PIFA element dimensions, the feed point indicates the connection of a SMA coaxial contact, [11]. . . . 17

8 The PIFA element corresponding to the (19) where the dimensions are shown [16]. . . 18

9 Vivaldi antenna design with the characteristic tapered slot. The black, is the feeding line [21]. . . . 20

10 Project manager in HFSS. . . . 22

11 PIFA element model in HFSS, single polarized. The model is the same for the initial and final model. . . 23

12 Finite array of 49 PIFA elements. . . . 24

13 Surface mount notch element with a resonance cavity single polarized where a) is the final model and b) is the initial model. . . . . 25

14 Finite array model of the Surface mount notch element. The array consists of 49 elements. . . . 26

15 Master and slave boundaries of a unit cell. . . . 27

16 Wave port exciatiation of the coaxial feed port. . . 28

17 Floquet port excitation of a unit cell. . . . 29

18 Convergence of the HFSS analysis. . . . 30

19 Measurement setup for S-parameters. . . 31

20 The Array positioned in the anechoic chamber a) array fixed on the moving arm b) close up picture. . . 32

21 The mounting of coaxial cables, a) on the antenna b) on the switch. . . 33

22 Magnitudes of reflection for parameter sweep of a) length parameter L and b) width of the radiation patch W. . . . 35

23 Magnitudes of reflection for parameter sweep of a) height parameter h and b) the feed position fp. . . . 36

24 Magnitudes of reflection for beam steering of the infinite array in q = 0°, 30° and 60° in a) E-plane or j =0° and b) H-plane or j =90° . . 36

25 Radiation pattern for PIFA in realized gain (dBi) at 3 GHz with -30 dB Taylor tapering. Beam steering in a) E-plane and b) H-plane for q = 0° (blue), 30° (green) and 60° (red). . . 37

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26 Magnitudes of reflection for parameter sweep of a) length parameter L and b) thickness parameter t. . . . 39 27 Magnitudes of reflection for parameter sweep of a) the channel

height to the cavity Lo and b) the slot line width parameter Ws . . . . 40 28 Magnitudes of reflection for parameter sweep of a) the cavity offset

from the slot line centre Coff and b) variation of the cavity height

Lc. . . . 41 29 Magnitudes of reflection for parameter sweep for cavity width Wc. . . 41 30 Magnitudes of reflection for parameter sweep of a) the offset height

for the holes in the structure hh and b) variation of the radius for

the holes hr. . . . 42 31 Magnitudes of reflection for beam steering of the infinite array in q

= 0°, 30° and 60° in a) E-plane or j =0° and b) H-plane or j =90° . . 43 32 Surface mount notch antenna in a 49 element array. . . . 44 33 Measured input reflection for element 1 for a) the full spectrum

together with simulation results and b) zoomed at the minimum

measured value . . . 45 34 Measured and simulated input reflection for element 25 . . . 45 35 Measured and simulated active reflection coefficient for the centre

element with beam steering in a) E-plane and b) H-plane . . . 46 36 Radiation pattern in realized gain (dBi) at 3 GHz, uniform tapering

without beam steering for a) j =0°, b) j = 45°, c) j = 90° and d)

j = 135°. . . 47 37 Peak realized gain versus frequency with -30 dB Taylor tapering. . . . 48 38 Radiation pattern in realized gain (dBi) at 3 GHz with -30 dB Taylor

tapering. Beam steering in a) E-plane and b) H-plane for q = 0°

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List of tables

1 Parameters of simulated Planar Inverted F Antenna . . . 24 2 Parameters of Surface mount notch element . . . 26 3 Final parameter values for simulated Planar Inverted F Antenna . . . . 34 4 Final parameter values for simulated Surface mount notch element . . 39

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1

Introduction

Radar is an acronym of Radio Detection and Ranging and is a technology wide spread over a numerus of applications. Those applications can be everything from satellite navigation to automotive safety. The primary objective of a radar application is to detect and determine an objects velocity, range and orientation. The progression in radar technology is moving towards multifunctional radar sensors. Sensors with the ability to be used not only to search and track but also in communication solutions, electronic counter measures and electronic warfare.

To realize a multifunctional radar sensor, antenna arrays are one solution. The antenna arrays provide a couple of features including multiple independent beams, computer controlled beam steering and graceful degradation [1]. To achieve the purpose of a multi-functional array, it is desired to use antennas with a high bandwidth. However, this report focuses on a moderate bandwidth antenna.

Two antenna concepts suggested by SAAB AB (hereby referred to as SAAB) in the S-band are investigated with regards to beam steering and bandwidth in a large phased array.

1.1 Purpose

The purpose of this master thesis is to investigate two antenna concepts to be used in a large phased array. The two antenna concepts investigated are a planar inverted F antenna (PIFA) and surface mount notch antenna. The antennas are designed for the specific criteria presented in the section Specification of Requirements. One of the concepts will be manufactured to verify the simulation results.

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1.2 Problem Formulations

The problem formulations in this thesis are specified according to a suggested thesis from SAAB. The problem formulation is to investigate two new array antenna elements regarding bandwidth, scan performance and suitability for low cost manufacturing.

1.3 Specification of Requirements

The specifications state the minimum requirement for the antenna concepts. The specification is defined by SAAB. The specifications are as follow:

• Centre frequency at 3 GHz • Minimum bandwidth of 0.4 GHz • -10 dB bandwidth

• Minimum of ±60° of beam steering in both azimuth and elevation.

1.4 Delimitations

In this master thesis there are a few delimitations of what will be investigated. As the focus is on the array antenna elements, only these will be investigated. Thus, a feeding network is not designed. There are also limitations on what will be investigated in the antenna elements. Regarding the PIFA, only the height, width, length and position of the feed in one direction will be investigated. The surface mount notch element antenna will only be investigated as a full metal antenna and no substrate solution will be considered. Since both antennas are thought to be a solution for a final application, there will be limitations of the dimensions of the antennas. This limitation will be a half wavelength in width and length at the highest frequency to accommodate large beam scan. The height is limited to 150 mm. The antennas will be fed with a coaxial feed and no other way of feeding will be investigated.

1.5 Outline

This report is divided into seven chapters. Chapter 1 gives the reader an introduction to the thesis, task and background information about the thesis. Chapter 2 describes the background theory needed for the thesis. The theory includes basic radar and antenna theory. Furthermore, this chapter contains theory regarding embedded element pattern and active reflection coefficient. Chapter 3 describes the simulation and measurement method. The simulation

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method walk through how the models are built, some features of the simulation tool and how the simulations are carried out. The measurements section describes how the antenna is measured, both regarding gain and scattering parameters. Chapter 4 and Chapter 5 present the results from the PIFA and the surface mounted notch antenna respectively. Chapter 6 present the discussion. The chapter gives some thought about the process and the results. Last, Chapter 7, the conclusions of the thesis are stated. The chapter gives an insight of what have been learned throughout of the thesis. For an experienced engineer with some antenna or similar background it is recommended to start reading at Chapter 4.

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2

Theory

This chapter starts with an introduction to the fundamental principles of radar. This is followed by a section describing the fundamentals of antenna theory. After the antenna theory, an introduction to the two concept antennas is presented. First, the PIFA is introduced followed by the surface mount notch antenna.

2.1 Fundamentals of Radar

Radar is a sensor used for detecting objects and to determine objects’ velocity, range and position in space. The radar sensor transmits an electromagnetic wave. The electromagnetic wave illuminates the object and thereafter it is backscattered by the object. When the wave scatters and travels back towards the radar its frequency and amplitude alters. The backscattered wave is then received by the radar and, through signal processing of the transmitted and received waves, information related to position and movement of the object is obtained.

In today’s radar applications, the transmitted electromagnetic wave might be modulated. Radio frequency (RF) and digital signal processing of the transmitted and received signal is applied to maximize the functionality and accuracy of the radar. The Introduction presented here assumes a radar system of one transmit- and one receiving antenna.

The two most important equations for radar ranging analysis is the Friis Transmission Equation (1) and the Radar Range Equation (2).

The Friss Transmission Equation states the relations between received power (�#) and transmitted power (�$) between two antennas. It is assumed that the

antennas are at a distance where the transmitted wave is planar at the receiver. �$ and �#are the gain from the transmitting respectively the receiving antenna.

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In (1), R is the range, and � is the wavelength at the operation frequency. The equations assume perfect matching conditions regarding polarization and feed.

# �$ = �$�# � 4�� * (1)

It is shown that the received power is inversed proportional to the square of the distance between the two antennas. Thus, the distance is measurable if the gain of the two antennas and the transmitted signal are known.

In radar applications, it is assumed that the object reradiates the captured power isotropically. The received power at the radar is the power reradiated from the object attenuated in free space. The Radar Range Equation (2) gives the range of the object if the radar cross section is known.

# �$

= �

**

4� +,� (2)

The radar cross section σ is the area of the object which captures enough power to reradiate to the receiver so that the received power density would equal the scattering of the actual object [2]. From (2) we can see that the gain of the antenna plays a significant role for a radar operation being a key factor to increase the range of a radar application.

The radar resolution is given by the range resolution and angular resolution. The radar is limited to detecting only one object in each resolution cell. The minimum resolvable distance is stated in (3), [3].

∆� = �2

2� (3)

Where B is the bandwidth of the transmitted pulse. The equation states that a higher bandwidth gives a higher range resolution.

The angular resolution is the minimum angular distance where two equal objects at a given distance can be isolated by the radar. The angular resolution of the radar(4).

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∆� = ��

(4)

Where k is a constant depending on the current distribution of the antenna, normally between 0.9 and 1.3 and D is the diameter of the smallest circle, which contains the entire aperture. According to (4), a larger aperture gives a

higher angular resolution [3].

Note that (3) and (4) give the conditions of a resolution cell. The resolution cell is enlarged by the distance from the antenna since the angular resolution is considered from the antenna and not individually for every resolution cell. To determine the velocity of an object, the Doppler effect is used. The Doppler effect gives rise to a frequency shift and appears when there is a relative motion between the antenna and the object, [3].

2.2 Fundamentals of Antennas

In this section the basic antenna theory necessary for understanding this thesis work is presented. First, the radiation pattern of an antenna is discussed, followed by the introduction of the gain and directivity properties of antennas. Thereafter, the antenna band- and beamwidth are introduced, followed by theoretical aspects of polarization, scattering (S-) parameters, amplitude tapering and beam scanning. Last, a section describing active reflection and embedded element pattern are presented.

2.2.1 Radiation Pattern

According to the IEEE Standard Definitions of Terms for antennas, the radiation pattern is defined as “The spatial distribution of a quantity that characterizes the electromagnetic field generated by an antenna” [4]. A few of the quantities that characterize an antenna are Field strength, directivity and polarization. Most often the radiation pattern is represented in the far-field region. The far-field region is the region where the field components of the antenna are virtually transverse and the angular distribution is independent of the radial distance. The field area stretches from a distance called the far-field distance �88 given by (5) to infinity, [2].

88 =2�

*

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Where D is the maximum dimension of the antenna and � is the wavelength of the signal radiated by the aperture.

The radiation pattern describes the electric and/or the magnetic field pattern of the aperture. These patterns can be plotted in many different manners. The most common ways are two or three dimensional plots, where the pattern is a function of azimuth and/or elevation angle. It is common that the plot of the field is normalized by the maximum of the field. The pattern can be plotted in a linear fashion or in a logarithmic way. Most common is the logarithmic way as it enhances the visualization of details from large to low values. When the pattern is plotted in a logarithmic scale, it is often referred to as a power pattern.

An isotropic antenna i.e., an antenna that’s radiates uniformly over all directions is a hypothetical antenna. With reference to Figure 1, we can see that the antenna radiation pattern consists of several lobes. There are essentially two types of lobs, the main lobe and then, sidelobes. The main lobe, also known as major lobe, is the lobe with the maximum field strength. Thus, sidelobes are the other ones. Sidelobes are also called minor lobes. If there is a side lob directed in the opposite direction of the main lobe this lobe is generally called back lobe. Sidelobes are generally unwanted.

Figure 1 – Main and sidelobes in an antenna pattern, with illustration of the beamwidth in the lobe [2].

In Figure 1 the illustration of two types of beamwidth is also shown. However, the antenna beamwidth parameter will be detailed in Section 2.2.3. The plus

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and minus sign in the figure refer to the relative polarization of the amplitude for respective lobe, [2].

The antenna pattern put into evidence the problem of the Front-to-Back ratio parameter, [2]. This ratio gives information about the amount of energy that it is radiated in the forward direction as compared to that radiated in the backward direction. As with the case of sidelobe, it is commonly desired to minimize the backward radiation, hence the importance of this parameter. It is worth to observe that antenna theory implies the use of three dimensional (3D) spherical coordinate system, as illustrated in Figure 2, for an omni-directional radiation pattern. As for any spherical coordinate system, r is the radiation distance, θ is the polar angle and φ is the azimuthal angle.

Figure 2 – Reference coordinate system [2].

In antenna arrays, a particular phenomenon might occur having as result the so-called grating lobes. Grating lobes are additional lobes of the magnitude equivalent to that of the main lobe. They appear in the visible space i.e., for theta values between ±90°. This phenomenon occurs when the spacing in a uniform array is larger than the distance d defined by (6), [2].

� � =

1

sin �2− sin �AB (6)

Where � is the spacing between the antenna array elements, � is the wavelength, �2 is the angle of the main beam from boresight and �AB is the

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angle of the grating lobe also from boresight. From (6), the distance to eliminate grating lobes in the visible space is �/2, which is commonly known as the distance to avoiding grating lobes. However, it is possible to have grating lobes when the scan angle goes to the extreme of the angular range, [1].

2.2.2 Directivity and Gain

The antenna directivity and gain are important antenna parameters that are closely related. The directivity describes the radiation intensity for an antenna in a given direction related to the radiation intensity from the same antenna if the radiation would be isotropic. In other words, how well the antenna focuses the main beam of the antenna. This is described by (7), [2].

� = � �2

= 4�� �EFG

(7)

Where � is the directivity, � is the radiation intensity of the antenna, �2 is the

radiation intensity of an isotropic source and �EFG is the total radiated power

from the antenna. In (7) the 4� factor is due to expressing average intensity of the isotropic antenna as a function of the radiated power, [2]. If the antenna would be isotropic, the directivity will be equal to one, since U equal U0. As

indicated by (7), the directivity is a dimensionless parameter, and it is usually expressed in dB.

The antenna gain is closely related to directivity with the difference that the gain also considers the efficiency of the antenna. Thus, the gain not only describes the directional pattern but also how efficient the antenna actually is. To measure how efficient the antenna is, it is assumed that there are antenna losses (P loss ) and hence, there is a difference between the radiated power P rad and the input power P in , with P rad = P in – P loss . The gain is given by (8).

� = 4�� �HI

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Note that the antenna radiation efficiency does not take into account mismatches regarding impedance nor polarization losses.

When expressing gain and directivity through dB, it is quite common to write dBi or dBd. dBi means decibel relative to an isotropic source and dBd means decibel relative to a dipole antenna. dBi and dBd are related by 2.15 dB i.e., dBi is 2.51dB greater than dBd.

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2.2.3 Band- and Beamwidth

The antenna bandwidth is the range of frequencies, where the antenna performs accordingly to the specified standard. In this work, the bandwidth is defined as the frequency range around the centre frequency where the active reflection coefficient is less than or equal to -10 dB.

Usually, there are three ways of expressing the bandwidth of an antenna. The first way is just by its frequency range for instance ±5 MHz around the centre frequency.

The second way is as a ratio. Ratio is the upper to lower frequency where the antenna performs accordingly to the specific standard. The ratio can for example be 5:1 bandwidth. This indicates that the upper boundary frequency is five times higher than the lower. Antennas with a bandwidth of 40:1 or higher are known as frequency independent antennas [2].

The third way is by a percentage. Percentage is often used to state the bandwidth of a narrowband antenna. The percentage is the difference of the upper frequency minus the lower divided with the centre frequency. For example, 5 percent bandwidth for an antenna with a centre frequency of 5 MHz gives an upper frequency boundary of 5.125 MHz or a bandwidth of 0.25 MHz.

If the antenna has a bandwidth greater than 500 MHz or uses a spectrum of minimum 20% it is considered an ultra-wide band (UWB) antenna.

Beamwidth is the angular separation between two identical dots mirrored around the maximum of a pattern. Most commonly there are two main widths considered. Those two are illustrated in Figure 3.

Figure 3 – Half Power Beamwidth and Full Null Beamwidth of an antenna pattern [2].

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The first width is the Half Power Beamwidth (HPBW). The width is given by, the angular separation in degrees between two dots on the main lobe. The dots indicate the half maxima on the lobe. If only beamwidth is stated it is referred to HPBW.

The second width is the First Null Beamwidth (FNBW). It is given by the angular separation in degrees between the firsts nulls of the antenna pattern. Additional width can be chosen to fulfil specific criteria e.g. -10 dB beamwidth. Beamwidth is an important parameter for an antenna since it describes the resolution abilities of the antenna in e.g., a radar application. A common resolution criteria states that two sources are distinguishable if the angular separation is larger than half of the antennas FNBW value.

2.2.4 Polarization

For an electromagnetic wave radiated from an antenna, the polarization describes the time varying direction and relative magnitude of the electric field. Polarization typically is dived into three categories. Those are linear, circular and elliptical polarization. A linear polarized wave has an electric field vector that lies along a constant line at all the times. This is in opposition to the case of circularly polarized waves or elliptically polarized waves.

In Figure 4a, a circular polarized wave is illustrated. The electric field vector tip describes a perfect circle in a xy-plane as the wave propagates along the z-axis. In this case, the magnitude of the electric field vector is constant through time.

a) b)

Figure 4 – Illustration of polarization of electromagnetic wave a) rotation of traveling wave b) elliptical polarization at Z=0 [2].

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In Figure 4b, an elliptical polarized field is illustrated. As in the case of circular polarization, the wave propagating along the z-axis. However, the electrical field magnitude describes an ellipse in the xy-plane.

In practice, the electrical field always is elliptical polarization, linear and circular polarization are two special cases. The polarization is in practice linear or circular when the elliptical form becomes close to those cases.

The polarization can also be traced in two different directions, counter clockwise and clockwise directions. Those directions can also be referred to left-hand polarization respectively right-hand polarization.

In antenna theory, cross and co polarization are terms used to describe the polarization of the antenna. Co polarization is defined as the polarization in which the antenna is intended to receive and radiate. Cross polarization is orthogonal to the co polarization, [2].

2.2.5 Scattering Parameters

Scattering parameters or S-parameters describe a network at high frequency by relating the incident and the reflected voltage and current waves at the ports. In Figure 5, an arbitrary microwave network is illustrated. At each port, an incident wave denoted as �K and one outgoing wave �L are represented. The outgoing wave is also commonly known as the reflected wave at the port.

Figure 5 – Arbitrary N-port microwave network [5].

The relationship between incident and reflected waves are given in form of a matrix equation (9), [5]. �ML �*L ⋮ �OL = �MMM* �*M ⋯ �MO ⋮ ⋮ �OM … �OOMK �*K ⋮ �OK (9)

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or

�L = � �K

Where an element in the matrix is defined by (10). �HS =

HL �SK

TUVW2 8XE YZS

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The equation states that, if port j is driven with a known wave (signal) of voltage �SK and the reflected voltage wave at port i is measured, then the Sij

parameter can be derived. The subscript condition in (11) says that all other ports except j have an incident wave of zero value. This means that all ports except port j are terminated with a perfect matched load, i.e., no reflections or other signal sources appear at port k, k ≠ j. In contrast with other network (circuit) representations based on magnitude and phase measurements, the scattering matrix for microwave networks introduces the wave-typical concepts e.g., incident and reflected voltage and current waves. However, it is possible to convert S-parameters network representation into impedance and admittance representation, if needed [5].

An antenna can also be seen as a two port microwave network, where the first port is the feeding line with a typical characteristic impedance of 50 Ω. The second port is the free space with an impedance of 120π Ω. In antenna analysis, the input reflection coefficient of an antenna is a crucial design parameter. In an antenna array, the ports can be arbitrarily many and the scattering matrix consist of all possible combinations of Sij.

2.2.6 Amplitude tapering

Amplitude tapering is a method to decrease sidelobes of the antenna pattern. When amplitude tapering is applied, the beamwidth is increased and the aperture efficiency is decreased, [6]. Hereby, two types of amplitude tapering are presented here. The first type uses a cosine distribution and is described by (11), [6].

� � = ℎ + (1 − ℎ)���c ��

� (11)

Equation (12) assumes that, the amplitude a(x) at the distance x from the centre of the antenna is given by a cosine function with an m exponent with m equal to one or two. The cosine function argument depends on π, the distance

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x and the total length of the aperture, L. In (12), h is the normalized pedestal

height. When uniform tapering is referenced, h = 0 and m = 1.

A second type of amplitude tapering makes use of Taylor distribution. Taylor distribution has the advantage of providing narrower beamwidth compared to the cosine distribution. The distribution gives a number of sidelobes with the desired level around the main beam. Thereafter, the remaining sidelobes are monotonically decreased. The Taylor distribution is given by (12).

� �, �, � = 1 2� � 0, �, � + 2 � �, �, � cos ��� � ILM IWM � �, �, � = � − 1 ! * 1 − � * �* *+ � − 1/2 * ILM cWM � − 1 + � ! � − 1 − � ! � = � �*+ � − 1/2 * (12)

Where A = 1/π arc cosh (Desired sidelobe voltage ratio) and � is the number of

equiamplitude sidelobes adjacent to main beam on one side, [6].

2.2.7 Beam Scanning

Beam scanning or beam steering can be achieved by several methods. These methods can use mechanical steering of the antenna or a lens to control the beam. In this work, the beam steering is controlled by a phase taper at the antenna array feed i.e., a phased array. By controlling the phase at every element in the array, the main beam is controlled as illustrated in Figure 6. The figure shows a linear array with an arbitrary number of antennas. Each element has distance of d to the adjacent element.

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Figure 6 – Illustration of electrically beam scanning or beam steering of a uniform array [6].

At every antenna, a phase shifter controls the phase of the signal to the antenna. The phase difference to achieve a desired angle of the beam is given by (13), [6].

∆� = �� ��� � (13)

Where k is the wave number, d is the distance between each element and the

desired angle. To steer the beam in both azimuth and altitude, the same principle is used.

2.2.8 Active Reflection Coefficient

In an antenna array, the reflection coefficient evaluation for a single antenna element does not results in a good, reliable representation of the frequency response of the array. This is because the mutual coupling between the antenna elements in an antenna array is missed, [7]. Instead of the reflection coefficient the active reflection coefficient is used. The active reflection coefficient represents the reflection coefficient evaluated when all the antenna elements are fed simultaneously. The active reflection coefficient for the mth element in an array of N elements is given by (14).

�c � = �cI�LS(ILc)r O

IWM

(14)

Where �cI is the scattering component describing the coupling coefficient

between the antennas m and n with the condition that the antenna m is terminated with a matched load and the nth antenna is the only one excited in

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the array. The equation measures the coupled signal for every scan �. The u indicates the phase shift between the neighbouring antennas, [8]. Thus, it represents the actual input reflection of an antenna array.

2.2.9 Embedded Element Pattern

Conventional array theory expresses the radiated array pattern in form of a multiplication of an element factor and an array factor, [9]. The element factor describes the pattern of a single well-known antenna element isolated from the array and it is equal for all these elements in the array. However, the conventional array theory does not include the mutual coupling effect in an array. To include the mutual coupling between the elements the embedded element pattern is created. This pattern is obtained by exciting an element in the array while keeping all the other elements terminated with matched loads. The embedded element pattern will be different for all elements since it takes into account the adjacent elements. Consequently, there will be noteworthy differences between the elements in the corners or those along the edges as compared to the elements in the middle of the array. If the array is considered large, the embedded element pattern will be approximated to be the same since the most elements will have a uniform surrounding. The full array antenna pattern can be obtained by superposing the embedded element patterns weighted by each individual excitation. This corresponds to using an ideal feed network.

Since the embedded element factor includes mutual coupling effects such as scan blindness and the realized gain at a given angle is proportional to the embedded element pattern gain at the same angle, it facilitates the design of antenna arrays. When measuring an antenna array, a complete feed network is not needed since it is enough to excite one element and terminate the others with matched loads. Hence, power dividers or phase shifters are not needed to evaluate and detect design errors of the antenna array, [9].

2.3 Planar Inverted F Antenna

Planar Inverted F Antenna (PIFA) Element is an antenna element commonly used in broad range mobile communication applications. Such applications are Wireless sensors, RFID and MIMO applications. The key features are the small size with a low profile, omni-directional radiation pattern, easy to manufacture at low cost, low Specific Absorption Rate (SAR) and the ability to provide high transmission data rates, [10, 11, 12]. The antenna has also been proposed as a suitable antenna for communication applications and Nano satellites due to the low profile structure, [13]. In general, the antenna is shaped like an “F” if

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observed from the side with a planar patch radiating above a ground plane. The radiating plate and the ground plate are connected by a shorting plate as shown in Figure 7.

Figure 7 – General PIFA element dimensions, the feed point indicates the connection of a SMA coaxial contact, [11].

However, there are several different variants of the antenna including everything from different patch sizes, slots in the radiating patch and the ground plane, different sizes of the shorting patch, different ways to feed the patch etc.

Antennas of PIFA type are often design by experimenting with aid of simulation tools to find appropriate dimensions for specified input impedance and bandwidth, [12]. In general, the main antenna dimensions i.e., the length and width of the radiating patch are determined by (15), [14].

2 = �

4(� + �) (15)

Where �2 is the specified center frequency, C is the speed of light, W is the width and L is the length of the radiating patch. Where L and W can be calculated according to (16) and (17), [15].

� ≈�G 4 = 1 4∙ 1 �2 �E (16) � = � 4�2 2 �E+ 1 (17)

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In (17), �Gis the wavelength at operation frequency, and �E is the dielectric constant of the substrate to be used for manufacturing the antenna.

An empirical expression reported by Hassan Tariq Chattha [16] states a relationship for the most significant parameters of the PIFA element and the radiation frequency according to (18). This expression is developed for a PIFA element does not use a coaxial feed point to the radiation patch. Instead, the PIFA element has a feeding plate next to the shorting plate with a distance of �y between these two plates, as shown in Figure 8.

�2 =

3� + 5.6� + 3.7ℎ − 3�8− 3.7�•− 4.3�y− 2.5�•

(18)

In (18) and relative to Figure 8, �8 is the width of the feed,�is the width of the shorting plate, �ythe length between the shorting plate and the feed plate

and �the distance from the shorting plate to the edge of the radiating patch. The ground plane dimensions are not included in (19) as the resonant frequency is not very sensitive to the ground plane size nor to the position, [16]. However, the ground plane size and shape will cause a significant impact on the resonant frequency when it is small compared to the wavelength. This limit is set to the minimum size of 0.21 x wavelengths if the ground plane is a square, [17]. The resonance frequency is dependent on the width of the feeding and shortening plate. If �• or �8 is increased, the resonant frequency also increases, [16].

Figure 8 – The PIFA element corresponding to the (18) where the dimensions are shown [16].

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To achieve a good impedance matching of the antenna element, there are two main parameters to alter. Those are the height of the radiating patch and the feed position. The feed position alters the impedance in the same way as in the case of a patch antenna. When the height of the antenna is low, it causes destructive effects on the field. Thus, more mismatch impedance occurs, [15].

It has been found that, the PIFA element has optimal performance regarding to gain and bandwidth if placed in a corner of the ground plane with the shortening plate at the shorter side of the ground plane, [17]. The bandwidth of the antenna is highly dependent on the height of the substrate and also the dielectric constant of the substrate. Improvement of the bandwidth can be achieved by increasing the height of the patch or by selecting a substrate with a smaller dielectric constant, [11]. A higher patch will affect the resonant frequency to a lower level. Other ways to improve the bandwidth of an PIFA element includes addition of another design element such as adding a slit or a capacitive load. The slits can be chosen in a broad variety and the effect of the slit may alter the other antenna parameters for instance the antenna gain. Capacitive loads on the patch will also alter the antenna parameters, [18]. To minimize the mutual coupling between PIFA elements in array applications a couple of solutions are proposed according to current research. One proposed solution includes an addition of a line that is suspended between the Elements feeding or shortening plates, [19].

2.4 Surface mount notch element

The Vivaldi antenna element was first proposed by Gibson in 1979, [20]. The antenna usually consists of a tapered slot on a dielectric substrate. The antenna has a couple of typical appearances and the three most common are the Exponentially Tapered Slot Vivaldi Antenna, the Antipodal Vivaldi Antenna and the Balanced Antipodal Vivaldi Antenna, [21]. Most of the theory around the Vivaldi Element is from the Vivaldi element on a substrate.

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Figure 9 – Vivaldi antenna design with the characteristic tapered slot. The black, is the feeding line [21].

The Vivaldi antenna has in theory unlimited instantaneous frequency bandwidth, with linearized polarization and constant beamwidth over the entire bandwidth. This is due to the fact that, at a given frequency only a short section of the slot radiates efficiently. The frequency alters the section where it radiates changes and thus, the relations between the radiated wavelength and the width of the slot alters proportionally, keeping the same relative shape, [22]. The Vivaldi has the capacity to achieve a constant gain over a broad frequency range, [20]. Thus, the antenna can receive and transmit over a wide frequency band especially in the millimetre-wave band. The antenna compared to a metallic horn antenna, have not as good back to front ratio and radiation efficiency, [23]. The curve of the slot in a Vivaldi antenna is given by (19), [20] [21] [22].

� � = ��•‚+ � (19)

Where y(x) is the half length of the opening slot at x and p determines the bandwidth by a magnification factor also known as the sharping factor of the antenna profile. The A and B factor determines the slot line opening at x equals to zero. The frequency limitations are dependent on the openings of the slot. The narrow end limits the upper cut off frequency, and the wider end limit the lowest possible frequency to be radiated, [21]. However, in an array, the opening of the element limits the higher frequency boundary. This is due to the antenna array condition of a half wavelength distance to the adjacent element to eliminate the effect of grating lobes. The lower radiation frequencies are then generated by exciting adjacent elements to obtain an equivalent radiator.

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It is found that the radius of the circular slot, the exponential factor p and the form of the fan-shaped structure, is of weight on the bandwidth. The exponential curve form of the structure has the function to match the impedance between the two mediums. Thus, achieve a signal radiation from the feed [23]. The antenna gain is directly dependent of the length of the taper and shape of the slot structure, [21]. The antenna element substrate is selected according to (20)(21).

0.005�2 < �…88 < 0.03�2 (20)

�…88 = �E− 1 � (21)

Where � is the thickness of the substrate and �Eis the dielectric constant of the substrate. The substrate trade-off is between losses at higher frequencies versus dimensions of the antenna element, [21].

In practice, there need to be a form of transition from the transmission line to the slot line, usually coaxial line, micro strip line or a co-planar wave guide. The antenna is usually 2-3 wavelengths, at the highest frequency, long. Around two wavelengths, at the lowest frequency, wide.

In an array of Vivaldi antennas, a short gap between the elements is often implemented. This is due to facilitate assembly and repair of the array. With a small gap between the elements it is possible to replace individual elements in the array in a manageable way. The drawback with having small gaps between the antenna elements is that they cause undesired resonances. Those resonances degrade the wideband performance of the array, [24]. Therefore, Vivaldi antennas electrically connected to their neighbours are desired to archive high performance of the array especially for a phased array due to the effect of mutual coupling.

In an application of a phased array with short pulses, it is important that the antenna performs well over a range of frequencies. The impedance matching must be good for a wide band. The array must also show the ability of retain the pulse shape. It has been found that substrate improves VSWR bandwidth and increases the delay dispersion of the array marginally.

A proposed solution for an Ultrawideband All-Metal Flared-Notch Array made by Rick W. Kindt and William R. Pickles, [25], show an array with a bandwidth of 8:1 at 45° scan.

The particular element investigated in this thesis is based on a SAAB patent, WO2016099367, [26]. The purpose of this element outline is to reduce the overall length and to move the feed point down to the ground plane level. This makes it suitable for surface mount applications.

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3

Method

This chapter describes the method used to fulfil the project tasks and is divided into two subparts. The first part describes the design process including the two antenna models, the simulations that were performed. Thereafter, the measurement setup is presented.

3.1 Simulation

A walkthrough of how the antennas have been simulated is summarized in this chapter. The text should give clear instruction in how the simulation is performed to ease reproducibility. The simulations were performed using HFSS from ANSYS, [27], which is a commercial tool using finite element method solver for electromagnetic structures. The section is divided into subparts where each part corresponds to a step in HFSS.

In Figure 10, the project manager in HFSS is shown. The project manager shows the subparts of the simulation method. The important subparts are described further under each section.

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3.1.1 Model

The two antennas are modelled in HFSS. All dimensions of the antennas are parametrized to facilitate simulation sweep of antenna parameters of interest. An easy way to test the limitation of the parameters in HFSS is by animating the desired parameters and see if the parameters physically break the boundaries.

3.1.1.1Planar Inverted F Antenna

The PIFA element is modelled as shown in Figure 11. The antenna is modelled as a perfect conductor in free space. The dielectric of the coaxial feed is modelled as lossless Teflon with a dielectric constant of 2.1. The model consists of six parts. The dielectric of the coaxial feed, the inner conductor of the coaxial feed, the ground plate, the shortening patch, the radiating patch and the box of vacuum. The thickness of the metal sheet parts are held constant throughout the simulations.

Figure 11 – PIFA element model in HFSS, single polarized. The model is the same for the initial and final model.

The ground plate has the dimensions of 42*42 mm2 with a thickness of 1 mm. The radiating patch is located in the centre of the ground plate with a distance of h above it. The radiating patch has the parameters L and W i.e., the length and width, respectively. At the end of the radiating patch, a shortening patch is located. This shortening patch is electrically connected with the ground plate and the radiating patch. The patch is modelled to always have equal width as the radiating patch. The feed is modelled as a coaxial feed where the inner radius of the dielectric is ri and the outer is r0. The dimensions of the coaxial feed match those on the 50 Ω SMA contact (RND 205-00498). The position of the feed is centred in x-axis and is parameterized along the y-axis. The used parameters are summarized in Table 1.

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Table 1 – Parameters of simulated Planar Inverted F Antenna

Parameter

Width of patch W

Length of patch in L

Height if the patch in h

Feed position from the shortening patch fp

Scan angle in Theta Thetascan

Scan angle in Phi Phiscan

The parameters Thetascan and Phiscan are used in the boundaries to control the phase shift between each element.

The finite array of the PIFA is shown in Figure 12. The array consists of 49 elements, building a 7 by 7 array. Since the array is not manufactured, there are no extra edges added.

Figure 12 – Finite array of 49 PIFA elements.

3.1.1.2Surface mount notch element

The Surface mount notch element is modelled as shown in Figure 13. The element consists of three main parts, the radiating patch, the ground plate and the coax feed. Note that the model illustrates a single unit cell, not an actual element, an actual element consists of two half neighbouring unit cells i.e., the radiating patch is two halves of an element joint together.

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a) b)

Figure 13 – Surface mount notch element with a resonance cavity single polarized where a) is the final model and b) is the initial model.

The width of an element is constrained by the higher frequency and is denoted

W in the model. Since the unit cell is a quadratic cell, the sides of the ground

plate are equally long as the width of the antenna. The thickness of the ground plate is 1 mm and held constant throughout the simulations until the manufacturing process. Note that Figure 13a has the ground plate thickness according to the manufactured ground plate. The parameter t describes the thickness of the radiating patch. The radiating patch has the length of L and the width of W – Ws, where Ws is the width of the open slot line. The physical space where the coaxial feed is mounted between the cavity and the open slot line is dimensioned with the height of Lo and is open up until the cavity starts. Thus, the open slot line connects the cavity with the free space.

The cavity is modelled as a rectangular box within the radiating patch. The limitation of the cavity is only due to the taped curvature and the ground plate. The cavity is modelled as Wc times Lc. The cavity is modelled with two considerations. To have the ability to be centred in x-axis or to be adjusted after a certain distance of (Coff) from the slot line centre. The feed centre offset (Fs) is as small as possible.

The coaxial feed is modelled as two cylinders attached to each other. The inner coax conductor is modelled as a perfect conductor with the inner radius of ri. The dielectric of the coaxial is modelled as a cylindrical form with the inner radius of ri and the outer radius r0. In the model, the dielectric of the coaxial is Teflon with a dielectric constant of 2.1. The outer coaxial conductor is not modelled instead it is assumed that the outer conductor is included in the

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ground plate. However, the important part of the coaxial feed model is the relations between the inner radius and the outer radius since it determines the input impedance of the coaxial feed. The Coaxial feed is modelled to be electrically short to minimize the effect of the coaxial feed. In Table 2, all parameters are listed.

Table 2 – Parameters of Surface mount notch element

Parameter

Width of element W

Width of slot line Ws

Height of the element L

Thickness of the element t

Width of the cavity Wc

Height of the cavity Lc

Cavity offset from slot line centre Coff Height of air channel to cavity Lo Feed centre offset from slot line centre Fs

Radius hole hr

Height of first hole hh

The four holes in the structure are modelled by hh and hr. The holes are arranged in a square pattern rotated by 45°. A finite model of the surface mounted notch antenna element is shown in Figure 14.

Figure 14 – Finite array model of the Surface mount notch element. The array consists of 49 elements.

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The finite array consists of 49 elements. As seen in Figure 14, the structure has seven rows and eight columns. The eighth column is due to the fact that the unit cell is two halves of a full element. Thus, two rows of half dummy elements are placed on the edges. This is done to simplify the manufacturing process. The bottom plate is wider than the actual antenna aperture. This is due to the measurements on the measure fixture. The four holes in the plate must align with the fixture. The rods holding the array to the fixture contributing to the extra length on the bottom plate. Furthermore, the bottom plate is design to have equal length from the corner feed point to both edges. the thickness of the bottom plate is chosen to facilitate the manufacturing process.

3.1.2 Boundaries

To simulate an array in HFSS, it is possible to simplify the model by only simulate one element as a unit cell in the entire array. This is done by utilizing the master and slave boundary functions in HFSS. To use master and slave condition a box of vacuum need to surround the object, enclosing the element in the unit cell. The entire unit cell must be filled and the model is not allowed to have intersecting objects. To assign master and slave boundaries to the model, start to select a face of the unit cell that has a normal directed towards the neighbouring cell. When an appropriate face is selected, go to HFSS>boundaries>Assign>master. A window appears where the name and the U vector of the boundary are determined. Define the U vector as in Figure 15. When the U vector is set, another vector appears. This vector is the V vector seen in Figure 15.

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After the Master boundary, the slave boundary must be set. When configure the slave boundary it must be on the opposite side of the element. To set the slave boundary, select the desired face, then select HFSS>boundaries>Assign>Slave. In the slave configuration select the associated master boundary. Then, set the U and V vector to match the master boundary. Under the Phase Delay tab, set the scan angles to the parameterized Thetascan and Phiscan. This enables the possibility to perform electrical scanning of the array.

When master and slave boundaries are set, we have to decide if there are more boundaries to be set. In this case, there is not, due to the fact that the top face will be an assigned as a floquet port and the bottom will be set as a wave port. In HFSS, a perfect conductor will be set as a perfect electric boundary.

The finite array is simulated with perfect matched layer (PML) boundary. The boundary is set with ease with the aid of the PML Wizard.

3.1.3 Excitations

In HFSS, the Excitations are the ports of the simulated structure. In this case, the first port is the wave signal port. This port simulates an incident plane wave and is commonly used where there is a coaxial feed or micro strip feed. The wave port is configured by selecting the surface where the port is connected, in this case the dielectric of the coaxial feed. When the face is selected, go to HFSS > Excitations > Wave ports. The area should be marked as shown in Figure 16 with the exception of the red arrow on the selected face.

Figure 16 – Wave port exciatiation of the coaxial feed port.

The red arrow indicates in which direction the polarity of the modes is set. This arrow is an integration line and is set by selecting define in integration line for the selected mode.

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The second port of the antenna is the top port. In this case, a floquet port is used. This port is used due to the ability to simulate oncoming waves from different angles. To take mutual coupling into account, the floquet port is used. The floquet port is configured by selecting HFSS > Excitations > Floquet port.

Figure 17 – Floquet port excitation of a unit cell.

In Figure 17, a configured floquet port is shown. The A and B vectors is the lattice coordinate system of the port and is manually configured in the floquet port configurations. An important configuration in the floquet port is the Modes Setup tab. Here, the number of modes is configured. The number of modes used by the port is calculated with the build-in calculator. The only modes with an attenuation of 0 dB/length should be chosen.

3.1.4 Analysis

In Analysis, simulation setups are presented. The Analysis determines how the simulation chooses mashing and frequencies to solve for. The first option is the solution frequency. In HFSS, there are three different options: Single, Multi-Frequencies and Broadband. Single is when the user chooses a single frequency where the meshing adapts to. Multi-frequencies are an option where the user can choose multiple frequencies for the mashing process, this option is useful if the user know critical frequencies of the system or the user have different criteria on how accurate the simulation must be for different frequencies. The last option is Broadband. This option performs similar to multi frequencies with the exception of adapting the meshing for every frequency with the same criteria. In this thesis, the single option is selected

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with the higher frequency as the solution frequency. Figure 18 shows the convergence graph of the solution.

Figure 18 – Convergence of the HFSS analysis.

After an iterative sweep, it is good to check the convergence plot. Figure 18 illustrates how well the simulation was performed. If the red curve is not under the delta S line, it is indicated to increase the number of possible iterations.

3.1.5 Optimetrics

Under Optimetrics there are options for parameter sweep, it is possible to use different conditions for optimization. However, it was not used in the frames of this thesis. Instead parameter sweeps were performed and analysed. It is possible to combine multiple parameters in one sweep or the parameters can be swept separately.

3.1.6 Field Pattern

The last step is to plot the field pattern. To plot the field, first the sources must be set. Thereafter, an infinite sphere is created by choosing Radiation, Inset far field setup and lastly infinite sphere. Then, press Compute Antenna Parameters. The field can be plotted in HFSS or exported to a file for MATLAB.

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3.2 Measurements

The measurements Section is divided into two parts. Firstly, the S-parameter measurement of the array is presented. Secondly, the gain and radiation pattern measurements are detailed. The measurements of the antenna array were conducted at SAAB’s compact antenna test range A15 facilities, [28].

3.2.1 Measurements of Scattering Parameters

The scattering matrix of the array is a 49 x 49 matrix. Since the antenna elements are reciprocal i.e., �Ic = �cI it is possible to decrease the number of measurement combinations. This is of practical importance since the total measuring time heavily dependents on the number of combinations to be measured.

The measurement setup is shown in Figure 19. The measurements are performed with a vector network analyser (VNA). The VNA has two channels with the possibility to sample a two-port network i.e., resulting in the S-parameters �MM, �M*, �*M and �**.

Figure 19 – Measurement setup for S-parameters.

The antenna array is attached to a fixture with metal rods. The fixture is keeping the antenna still above electromagnetic absorbers. In this experiment The fixture must be stabile to withstand the counterweight of the antenna. In this experiment, the antenna is secured with M10 screws by the rods. Since the

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antenna is radiating when excited by the VNA, it is important to minimize reflections from the surrounding. Hence, in front of the array, there is a wall of absorbers.

The VNA is firstly calibrated with the coaxial cables. Once the VNA is calibrated, the two coaxial cables are connected to the selected ports of the antenna. The cables are tightened with a torque wrench. After both channels are connected, all other ports on the antenna are terminated with 50 Ω. All terminations are also tightened with a torque wrench.

The procedure is repeated until all ports to be measured combinations are measured.

3.2.2 Measurements of Antenna Gain

Antenna gain measurements were conducted in the A15 compact range anechoic chamber. Measurements for the array were made in four roll cuts with 45° intervals in j. Each cut was measured with one-degree interval in �.

Before the measurements the chamber was calibrated in the frequency range. In Figure 20a, the antenna in the chamber is shown. The antenna is placed on rods positioning the antenna in the centre of the quiet zone. The rods are fastened on a fixture attached at the robot arm. In Figure 20, the antenna is directed towards the back wall. The arm has the possibility to move the antenna in a complete sphere

a) b)

Figure 20 – The Array positioned in the anechoic chamber a) array fixed on the moving arm b) close up picture.

In Figure 20b, a close up picture of the antenna in the chamber is shown. On the rods absorbers are held to protect the measurements from disturbance and reflections from the rods and instrumentation inside. Since the antenna is rotated when changing from E to H field measurements, it is important to

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control the setup to avoid anything from damaging at movements. In the background, the test range main reflector is visible.

Behind the absorbers in Figure 20b, cables between the antenna and the measurement instrumentation are connected. This is shown in Figure 21. In Figure 21a, the backside or feeding side of the antenna is shown. The array consists of 49 antenna elements where each row consists of 7 elements. In the figure, element 29-42 are connected by coaxial cables. All other elements are terminated by 50 Ω. The metal rods holding the antenna are visible.

a) b)

Figure 21 – The mounting of coaxial cables, a) on the antenna b) on the switch.

In Figure 21b, a 16 port switch is shown. The switch is used to enable element measurement one by one. The switch is connected by a coaxial cable to the measurement instrumentation, see the single black cable on the backside of the switch. The switch is then controlled by a computer through a cable, the white cable in Figure 21. To prevent any movement under measurements, the switch is secured with rubber band.

To facilitate the measurements, the antenna is only connected to 14 ports. Four measurements rounds are necessary, even if all 16 ports of the switch can be used. By only using 14 ports, it is easier to keep track on the measurements and avoid mistakes.

Finally, the data processing is performed. First, an amplitude tapering is performed. Then, the antenna diagram is centered in boresight. When the pattern is centered the phase shift for beam steering is added. These steps are performed individually for each element. Lastly, the elements are summarized to give the pattern of the entire array.

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4

Planar Inverted F Antenna

This Chapter presents simulation results for the Planar Inverted-F Antenna. Firstly, the effect of the design parameters on the antenna performance is analysed. Then, simulation results of the infinite array are shown. Finally, simulation results of the finite array are illustrated and discussed.

4.1 Parameter sweep

To design and evaluate the proposed antenna, S-parameter simulations were performed with parametrized antenna parameter. A list of these parameters is presented in Table 3. The magnitude of the S11 was of interest as a function of

frequency and as the different parameter values were swept.

In Table 3, the final values of all parameters of the Planar Inverted F Antenna are shown. The parameters hsub, ri and r0 are fixed throughout the simulations.

Table 3 – Final parameter values for simulated Planar Inverted F Antenna

Parameter Value [mm]

Width of patch W 15

Length of patch in L 27

Height if the patch in h 9

Feed position from the shortening patch fp 12

Thickness of metal sheet hsub 1

Radius coaxial feed inner conductor ri 0.635

Radius coaxial dielectric r0 2.05

In Figure 22a, simulation results when the patch length L was swept are shown. L has values between 15 and 30 mm, and a step of 1 mm. The 30 mm

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