Activeintegrated aperture lens antenna - DiVA portal

DEGREE PROJECT IN ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITSSTOCKHOLM, SWEDEN 2021

Activeintegratedaperture lens antenna

Jesús Ventas Muñoz de Lucas

KTH ROYAL INSTITUTE OF TECHNOLOGYELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Activeintegrated aperture lens antenna

Thesis submitted for the degree of

Master of Science in Electrical Engineering

and

Máster Universitario en Ingeniería de Telecomunicación (MUIT)

AuthorJesús Ventas Muñoz de LucasKTH Royal Institute of Technology

Place for ProjectStockholm, Sweden

ExaminerÓscar QuevedoTeruelDivision of Electromagnetic Engineering (EME)KTH Royal Institute of Technology

Supervisor

Qiao Chen

Division of Electromagnetic Engineering (EME)

KTH Royal Institute of Technology

ii

Abstract

Luneburg lens antennas are gaining popularity in new communication systems,

as increasingly higher frequencies are being used. Broadband fullymetallic

implementations of Luneburg lenses, such as RinehartLuneburg lenses, constitute

simple, cheap and efficient beamformers. However, Luneburg lenses need to have one

amplifier per port, which constrains the maximum power that can be transmitted and

increases the cost of the system.

In this thesis, an investigation to integrate amplifiers within the aperture of Luneburg

lenses is conducted. This concept allows for increasing the maximum transmitted

power with reduced costs.

Special attention has been paid to the design principles. Active integration without

altering the Luneburg lens functionality has been a key task in this work.

A design in Kaband (2640 GHz) has been also exemplified in order to show the

feasibility of the concept. The final design includes transitions to a PCB in the aperture

of the Luneburg lens, where amplifiers can be mounted. Good results were obtained

in terms of directivity and sidelobe levels, and the antenna achieves a scanning range

up to ±64 with reasonable scan losses.

iii

Sammanfattning

Luneburgs linsantenner blir alltmer populära i nya kommunikationssystem eftersom

högre frekvenser används. Det finns bredbandiga Luneburglinser som är helt

metallicof, som RinehartLuneburglinsen, vilket gör den till en enkel, billig och

effektiv strålformare. Luneburglinser måste dock ha en förstärkare per port, vilket

begränsar den maximala sändningseffekten och ökar kostnaden för systemet.

I den här avhandlingen undersöks hur man kan integrera förstärkare, monterade på

ett PCB, i Luneburglinsernas öppning. Detta tillvägagångssätt gör det möjligt att öka

den maximala överförda effekten och minska kostnaderna.

Särskild uppmärksamhet har ägnats åt konstruktionsprinciperna. Att hitta en

geometri som gör det möjligt att integrera förstärkare inuti utan att ändra Luneburg

linsens strålningsegenskaper har varit en viktig uppgift i detta arbete.

En specifik konstruktion för Kabandet (2640 GHz) har också utvecklats för att visa

att konceptet är genomförbart. Den slutliga utformningen omfattar övergångar till

ett kretskort i Luneburglinsens öppning, där förstärkare kan monteras. Resultaten

visar på rimliga värden för riktverkan och sidolobnivåer, och antennen har ett

avläsningsområde på upp till ±64.

iv

Resumen

Las lentes de Luneburg se están haciendo cada vez más populares en los nuevos

sistemas de comunicaciones, debido al uso de frecuencias cada vez más altas. Existen

implementaciones totalmente metálicas y de banda ancha de las lentes de Luneburg,

como las lentes de RinehartLuneburg, lo que las convierte en conformadores de haz

simples, baratos y eficientes. Sin embargo, las lentes de Luneburg necesitan tener un

amplificador en cada uno de sus puertos, lo que limita lamáxima potencia que se puede

transmitir e incrementa el coste del sistema.

En este trabajo de fin de Máster se lleva a cabo una investigación que busca la

integración de amplificadores, montados en una PCB, dentro de la apertura de las

lentes de Luneburg. Este enfoque permite transmitir potencias mayores y además

reduce costes.

Se ha puesto especial atención en los principios de diseño. Encontrar una geometría

que permite integrar amplificadores dentro sin alterar las características de radiación

de la lente de Luneburg ha sido uno de los puntos clave de este trabajo.

También se ha desarrollado un diseño específico en banda Ka (2640 GHz) para

mostrar la viabilidad de la idea. El diseño final incluye transiciones a un PCB en

la apertura de la lente, donde se pueden incluir los amplificadores. Los resultados

muestran valores razonables de directividad y lóbulos secundarios, y la antena permite

un rango de escaneo de hasta ±64.

v

Acknowledgements

This work ends up a beautiful life stage. I will never forget my university years and the

great people I have met here.

First, Iwould like to thankmyparents, whichhave always supportedmeandhavemade

the person I am today. AndAlba, for beingwithme in the good and badmoments.

I would like to say thank you to my supervisor Qiao, for all the guidance, help, advice

and knowledge provided to me throughout these months at KTH. Also to my examiner

Óscar Quevedo, not only for givingme this opportunity but also for the good treatment

and support duringmy stay in Sweden. And, of course, to all my colleagues and friends

from the Master student room in the lab. I have spent really good moments with all

you and it would not have been the same without you. Last, but not least, to all my

friends.

vi

Acronyms

CPW Coplanar Waveguide

GEO Geostationary Earth Orbit

IDFT Inverse Discrete Fourier Transform

ITU International Telecommunication Union

LEO Low Earth Orbit

LNA Low Noise Amplifier

MMIC Monolithic Microwave Integrated Circuits

PA Power Amplifier

PEC Perfect Electric Conductor

PCB Printed Circuit Board

PPW Parallel Plate Waveguide

SNR Signal to Noise Ratio

SLL Side Lobe Levels

SMT Surface Mount Technology

TEM Transverse Electromagnetic

vii

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Luneburg lens and State of the Art . . . . . . . . . . . . . . . . . . . . . 3

1.3 Motivation and goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Scope of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Design Principles and Theoretical Background 72.1 Multilayer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Circular Array Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Basic Array Antenna Theory . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.3 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.4 Aperture discretization analysis . . . . . . . . . . . . . . . . . . 23

2.3 Ridge Rectangular Waveguide . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Designs and Results 303.1 Transition design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Full multilayer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.1 Multilayer structure without transition . . . . . . . . . . . . . . . 38

3.2.2 Multilayer structure with transition . . . . . . . . . . . . . . . . . 43

3.2.3 Multilayer structure with transition and 9 ports . . . . . . . . . . 45

4 Conclusions and Future Work 50

References 52

viii

CONTENTS

A Analysis of Social, Economic, Environmental and EthicalImplications 56A.1 Social Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.2 Economic implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.3 Enviromental implications . . . . . . . . . . . . . . . . . . . . . . . . . . 57A.4 Ethical implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

B Cost and price of the project 59

ix

Chapter 1

Introduction

1.1 Background

Emerging wireless communication systems are demanding higher data rates, and

hence larger bandwidth, to enable new use cases. This has motivated companies and

academia to increase the frequency, moving up to the millimeter wave band, where

more bandwidth can be used. Moreover, the size of the components is reduced as the

frequency increase, allowing more compact systems and easier integration.

The fifthgeneration (5G) of mobile communication systems is one important example

of such emerging communication systems. 5G is aimed at achieving up to 20 Gbps

peak speed in the downlink and latencies not higher than 1 ms for some use cases. One

of the main usage scenarios of 5G reported by international telecommunication union

(ITU) [1] is devoted to covering high demands of data in highpopulated and high

mobility situations. The previous capacity and speed requirement can be achieved

at high frequencies, such as the millimeter wave band, as higher bandwidths can be

used. However, the use of higher frequencies implies also higher freespace losses, so

using directive antennas is a good option in these systems. They are characterized for

having a narrow beam, allowing the system to focus the power in a given direction.

Additionally, scanning capability is needed when using directive antennas in order

to achieve a wide coverage. Furthermore, having scanning capability allows to use

beamforming and nulling techniques to reduce interference between users, which is

an important challenge in scenarios with high density of users.

Mega constellations of satellites are also emerging nowadays. The geostationary earth

1

CHAPTER 1. INTRODUCTION

orbit (GEO) satellites have been widely used since they allow high coverage and have a

fixed relative position, so global coverage can be easily achieved with them. However,

GEO satellite communications have to deal with high propagation delay and high

propagation losses due to the high altitude of geostationary orbit [2]. Therefore, low

earth orbit (LEO) satellites have become a good alternative to overcome the drawbacks

of classical GEO satellites. LEO orbits have altitudes between 500 km and 2000 km, so

path losses and propagation delay are noticeably reduced. However, as LEO satellites

are close to the Earth surface, theymove with a high relative velocity. If high data rates

are desired, as in these emerging mega constellations, then steerable antennas with

directive beams have to be used.

The use of directive antennas with scanning capability is then a key point in the

communication systems of these emerging scenarios. Luneburg lens antennas have

become a good choice for achieving high directivity while having good scanning

capability, without high scan losses. This type of antenna was not widely used in the

past because they were bulky at low frequencies, but their popularity have increased

nowadays with these emerging applications at higher frequencies. Unlike phased

arrays, Luneburg lens antennas avoid using complex feeding networks and phase

shifters. Moreover, fullymetallic implementations of Luneburg lens antennas [3–5]

can achievewide band and low antenna losses due to the absence of dielectricmaterials

in the antenna. Several feeding ports are typically included in Luneburg lens antennas

to achieve the desired angular coverage.

In typical communication systems, a power amplifier (PA) is included to increase the

output power in the transmitter and a low noise amplifier (LNA) is placed in the

receiver in order to amplify the received signal without decreasing significantly the

signal to noise ratio (SNR). The output power provided by a single amplifier is limited

by the size and by the supply voltage [6]. Nevertheless, high output powers are required

in these next generation communication systems, so in order to overcome this power

limitation, spatial power combining is becoming a research topic. With the power

combining approach, the signal can be amplified in a parallel manner giving rise to

a higher overall power[7, 8]. Smaller and less powerful amplifiers are used in spatial

power combiningnetworks, so the final cost is reduced. Furthermore, the use of several

amplifiers in a spatial combining network increase the robustness and reliability of the

system. In a single amplifier architecture, the whole system is down if the amplifier

breaks, while the system could continue working if one amplifier from the combining

2


network is faulted.

1.2 Luneburg lens and State of the Art

Luneburg lens antennas were first introduced in 1944 by Rudolf K. Luneburg. A

Luneburg lens is a spherically symmetric gradientindex lens characterized by a

varying refractive index with the radius according to Eq. 1.1. If the lens is placed in the

air, there are no reflections at the boundary of the Luneburg lens, since the refractive

index is 1 in the surface.

n(r) =

…2−

( r

R

)2(1.1)

The feeder of the antenna is ideally a point source placed in the surface, and due to the

varying refractive index, a collimated beam is achieved in the diametrically opposite

side of the lens. In other words, a spherical wave from the feeder is turned into a plane

wave after going through the lens. The spherical symmetry of the Luneburg lens allows

for placing several feeders along the surface, each one producing a directive beam in a

different direction. The sketch in Figure 1.1 shows a Luneburg lens with two feeders, A

and B, giving rise to collimated beams towards different directions in the other side of

the lens.

Figure 1.1: Luneburg lens sketch

Luneburg lens antennas are made of dielectric materials and have a spherical shape

in the classical implementation. According to Equation 1.1, the refractive index have a

continuous variation, but in a real design they can be only made with a finite number

of dielectricmaterials, and hence a stepped variation in the refractive index. One of the

first designs using steppedindex implementations was performed in 1958 [9], where

hemispherical shells with the appropriate refractive index were stacked to design the

Luneburg lens. However, these designs with dielectric shells have a complicated

3


manufacturing process afterwards, and alternative implementations of Luneburg lens

antennas have been proposed in recent years.

One way of getting the gradient index variation of Equation 1.1 is employing

metasurfaces. The variation of some parameters in the metasurface modifies its

dispersion diagram and hence does the refractive index. One example of this approach

is shown in [10], where a 2D Luneburg lens is designed using a mushroomtype unit

cell in a printed circuit board (PCB). The size of the unit cell is kept, and the refractive

index is adjusted by modifying the size of the printed patch. The size of the patches

arranged in the final design varies with the radius of the lens, so that the refractive

index varies with the radius according to Equation 1.1. The design carried out in [11]

is another example of this approach using printed transmission lines onto a copper

cladded substrate with a relative permittivity close to 1. Two different transmission

lines are proposed, and the geometrical parameters of both are varied in order to

achieve the desired refractive index at each point on the final lens design. However,

the previous implementations of Luneburg lens antennas are lossy due to the use

of dielectric materials. The same idea using fullymetallic unit cells has been also

proposed, so that there are no dielectric losses. In [12], the unitcell consists of two

metallic plates including a pin inside a square hole with glidesymmetry, avoiding the

use of lossy dielectrics. The refractive index is adjusted changing the pin height.

The previous approaches achieve good performance in a wide band, being the

complexity their main drawback. Another alternative implementation of Luneburg

lens antennas are geodesic lenses, that were first introduced by R. F. Rinehart [13].

Geodesic lenses are 3D fullymetallic implementations of the Luneburg lens in a

homogeneous medium with a parallel plate waveguide (PPW). The height z of the

metallic lens changeswith the radial coordinate ρ according to the differential equation

1.2, which is proved tomimic the behaviour of the refractive index variation of Equation

1.1.

∂z

∂ρ= −

Ã(1

2+

1

2√

1− ρ2

)2

− 1 (1.2)

Several implementations of geodesic lenses exist in the literature. One example

appears in [5], where a fullymetallic geodesic Luneburg lens is designed working at

60 GHz. Geodesic lenses employs outofplane deformation in the third dimension,

4


so they sometimes bulkier than other implementations, which can be problematic

in spaceconstrained systems. For this reason, there is research focused in folding

geodesic lenses, so that the overall height can be reduced [3, 4]. Furthermore, compact

designs of geodesic lenses are a research topic. For example, the design of a compact

half geodesic Luneburg lens is proposed in [14] using a ground plane to halve the size

of the lens.

1.3 Motivation and goals

Luneburg lens antennas have become a very interesting option to include in new

wireless communication systems, specially geodesic lenses. They can achieve directive

beams in a wide band while providing scanning capability without significant scan

losses, and also avoiding the use of dielectric materials, as explained in the previous

sections. In order to achieve scanning capability, several ports are typically used in

Luneburg lens antennas.

Having several ports would imply to have one amplifier per port when including the

antenna in a real communication system. Moreover, these systems typically handle

high powers, meaning that powerful, and hence expensive, amplifiers are needed in

each port. Furthermore, the maximum output power of the amplifier is limited by the

size of the device.

Therefore, the main goal of this project is to study the possibility of integrating a set of

amplifiers within the aperture of a fullymetallic Luneburg lens. If the amplifiers are

included in the aperture instead of in the ports, there are several advantages:

• The robustness and reliability of the system increase, because all the

amplifiers are shared by all the ports, so that, if one amplifier is down, the system

is still able to work.

• The overall cost of the amplifiers is reduced, since less powerful amplifiers

are needed. Even ifmore amplifiers are needed in the aperture, the cost of a single

smaller amplifier is highly reduced and the final cost is still reduced.

• The system can handle higher output power in the transmitting link, because

the power is spatially distributed along the aperture.

• Thedynamic range is improved in the receiving link. The overall phase noise

5


is reduced as the number of amplifiers increase, because the noise fluctuations

add incoherently [15].

• A further control on the aperture illumination, so that optimal side lobe levels

(SLL) is possible by setting the gain of the different amplifiers, depending on their

position in the aperture.

1.4 Scope of the project

This project is aimed to be a proofofconcept about the integration of several

amplifiers in the aperture of a fullymetallic geodesic Luneburg lens antenna. The

first requirement of the project is to find a proper system architecture that allows the

integration of the amplifiers within the aperture.

In this project, monolithic microwave integrated circuits (MMIC) technology

amplifiers have been considered, because they are easier to integrate in a fullymetallic

structure. The amplifiers will be placed on a PCB, so transitions from the fullymetallic

structure to the PCB have to be designed.

Finally, the performance of the full structure including the PCB inside has to be

assessed.

The Luneburg lens is going to work in the Kaband (2640 GHz), and the bandwidth

has been imposed to be higher than a 20%.

1.5 Outline

In Chapter 2 all the theoretical background needed for this project, as well as some

design considerations are explained. The reasons and limitations affecting the main

features of the antenna designed in this project are stated here.

Chapter 3 covers the different designs included in this work. The transition from a

fullymetallic waveguide to a PCBwhere the amplifiers are integrated is explained here.

Finally, the full structure design, where the amplifiers could be finally integrated, is

also stated here.

In Chapter 4 the main conclusions extracted from this thesis and the future work are

presented.

6

Chapter 2

Design Principles and TheoreticalBackground

This chapter is aimed at explaining the design process, including all the considerations,

assumptions, methodologies and models used along this work. The basic theory

to properly understand this work is also presented in this chapter. However,

basic knowledge about electromagnetic theory, waveguides and the main antenna

parameters is assumed.

The antenna proposed in this work has several stacked layers, in order to enable the

integration of amplifiers inside without distorting significantly the radiation pattern.

Here, the reasons behind the use of amultilayer design are presented. A circular array

model is also described in this section, because it has been very useful to analyze the

antenna and decide its final architecture. Ridge rectangular waveguides have been

used to divide the aperture in different subapertures where amplifiers are placed, so

the reasons for using them as well as the main features of this type of waveguide are

stated here. Finally, a comparison among several amplifiers available in the market is

presented, in order to assess the different options and choose the most suitable.

As mentioned before, the design considered in this work will be working in Kaband

(2640 GHz) and the bandwidth has to be of at least 20%.

7

CHAPTER 2. DESIGN PRINCIPLES AND THEORETICAL BACKGROUND

2.1 Multilayer structure

As mentioned before, the main goal of this project is to study the feasibility of

integrating several amplifiers along the aperture of a fullymetallic geodesic Luneburg

lens.

If several amplifiers are going to be included in the aperture of the antenna, one

important consideration to keep in mind is the need of discretizing (or sampling) the

aperture. That is, the aperture has to be divided in different parts in order to place

one amplifier in each of them, in such a way that one transmission line is opened

in each of them. The geometry of these transmission lines defines the maximum

number of amplifiers that can be placed in the aperture. Isolation between the different

discretized lines must be ensured, since undesired coupling would affect the final

performance of the antenna.

A Luneburg lens antenna produces a phase distribution along the aperture that gets

a planar phase front in the diametrically opposite direction to the feeding point.

According to Huygens principle, the circular aperture of the Luneburg lens can be

thought as an infinite set of point sources with a relative phase distribution that

produces a planewave. Discretizing (or sampling) the aperture consists of taking only a

fraction of those point sources, keeping the relative phase distribution generated by the

Luneburg lens. After sampling the aperture, the fields of each sampled subaperture

are confined inside a transmission line, where they are amplified. Figure 2.1 shows

a sketch illustrating this idea of aperture discretization. The Luneburg lens antenna

is inside a metallicshielded structure, fed by a rectangular waveguide and with the

aperture discretized into several transmission lines.

LuneburgLens

Feed

PEC

TransmissionLines

Figure 2.1: Aperture discretization

When the continuous aperture is turned into a discretized aperture, consisting of a

8


finite number of transmission lines, it can be modelled like a circularring array. This

circular array model will allow to know the maximum distance that can be assumed

between discretized elements and other parameters. It will be explained with more

detail in the next section.

The idea of sampling the aperture is close to the structure proposed in [16], where

a Luneburg lens is used as a beamforming network for a circular array of Vivaldi

antennas. In [16], the aperture of the Luneburg lens is sampled using coaxial cables

to feed the array elements with the proper phase distribution got by the Luneburg

lens.

After the fields in the aperture are sampled and confined inside transmission lines,

amplifiers are included inside each line boosting the signal. The amplifiers considered

in this project are MMIC with a surface mount technology (SMT) packaging, so that

they will be mounted on a PCB in order to ease the integration process. However, the

considered transmission lines that discretizing the aperture are metallic structures, so

transitions from fullymetallic waveguides to PCB technology have to be designed. The

design of the transition will be discussed with more detail in the next chapter.

When the signal is amplified, the fieldsmust be combined again and be radiated to free

space. The phase distribution got by the Luneburg lens in the aperture has to be kept

in order to get a directive beam in the desired direction. However, according to Figure

2.1, the radial coordinate of the discretized aperture is modified after amplifying. If

the aperture is thought as a circular ring array, the effect of including this transmission

lines is similar to displacing each element in the radial direction. All the transmission

lines have the same length, so the phase distribution of all the elements is kept.

Nevertheless, the distance between elements, and hence their relative position, is

different than before sampling. Modifying the geometrical arrangement of the sampled

points gives rise to aberrations, even if the phase distribution between elements is

kept.

As the relative position between the sampled elements is modified, the fields can not

be radiated immediately after amplifying the signal. One solution for correcting these

aberrations is to include phase shifters, but this approach would make the Luneburg

lens useless, since it has been already included to get a proper phase distribution.

Furthermore, this would make the structure more complex and expensive. Another

option could be adjusting the distances of the different transmission lines, so that

9


a directive beam is achieved after amplifying. However, this adjustment could be

only done for one beam, loosing the scanning capability, which is one of the main

requirements for this antenna.

The proposed solution to overcome these displacement of the elements after

discretizing the aperture is to use a multilayer structure. Stacking the different layers

ensures all the elements are placed in the initial radial position when the radiation to

free space is produced.

There are different ways of integrating the amplifiers in the antenna while ensuring

the elements are in the right position for radiation. Three approaches to proceed

are proposed in Figure 2.2, where different side views of the Luneburg lens with one

example transmission line are sketched.

Luneburg Lens

(a)

Luneburg Lens

(b)

Luneburg Lens

(c)

Figure 2.2: Different approaches for multilayer structure. (a) Amplifiers in theperpendicular plane, (b) Amplifiers in the intermediate layer (c) Amplifiers in thebottom layer

The geometry proposed in Figure 2.2 (a) (left) places the amplifier in a perpendicular

plane with respect to the lens. This approach is the most similar to the one in [16]

and becomes a very compact solution. However, the proposed design works at higher

frequencies, so that the wavelength is reduced, and hence does the distance between

elements in order to keep the same electrical distance. This implementation would

require perpendicular transitions to a folded PCB or a set of PCBs, resulting in a

very expensive structure. In Figure 2.2 (b) (center), the aperture is discretized, then

includes a transition to a second layer where the amplifier is included and finally a

transition to a third layer where radiation to free space occurs. This approach is also

a compact design if the first bending is placed close to the Luneburg lens. However,

due to the distance limitation between sampled elements, the transmission lines are

very close each other in the transition from the second to the third layer, and there is

not enough room to arrange them together. This issue highly complicates the design

of a proper transition from the second to the third layer. Finally, the arrangement

shown in Figure 2.2 (c) (right) proposes to place the amplifiers in the bottom layer,

then use the intermediate layer only to come back to the initial radial position, and

10


finally, the radiation occurs in the third layer. As the transmission lines are arranged

radially (Figure 2.1), the distance between consecutive transmission lines is larger after

amplifying, so there is muchmore room to place the transition to the second layer. For

the same reason, there is also more room to design the transition from the second to

the third layer. The main drawback of this geometry is to be bulkier than the previous

ones. However, in the final design an extra space is in any case needed to place the

entire feeding network of the Luneburg lens, so this increase in size is affordable.

Due to the limitations mentioned previously in options (a) and (b) from Figure 2.2, the

option (c) is going to be implemented in this project.

PCBLuneburg Lens Bottom Layer

Interm. Layer

Top Layer

Figure 2.3: Multilayer structure Side view

Bottom Layer

LuneburgLens

Feed

PEC

TransmissionLines

PCB

Intermediate Layer

TransmissionLines

Top Layer

FlaredAperture

Figure 2.4: Multi layer structure Top View (Bottom layer in the left, intermediatelayer in the center and top layer in the right)

The bottom (or first) layer contains the feeding ports of the antenna, a Luneburg lens

inside a perfect electric conductor (PEC) and the transmission lines along the aperture

utilized to discretize it. The transitions to the PCB are inside each transmission line, in

the bottom layer. After going through the amplifiers, the transmission lines are then

bent to the intermediate (or second) layer. This intermediate layer is only intended to

11


return to the initial radial position. Finally, the waves travelling inside the different

transmission lines are combined into a flared aperture, and radiated to free space.

The side view of the multilayer structure, including one transmission line, is shown in

Figure 2.3 and the top views of the different layers are shown in Figure 2.4.

2.2 Circular Array Model

2.2.1 Basic Array Antenna Theory

An array antenna is formed by a set of radiating elements arranged in an arbitrary

shape. The radiation pattern of the array antenna is determined by the contribution of

all the fields radiated by the individual elements. Thus, the relative position between

the geometry of the array, as well as the individual radiation pattern of the different

elements are the key features affecting the radiation pattern of the array. In a general

case, the elementary radiators can be different and can be arranged in any shape, but

in this work all the elementary radiators will be the same, so more attention will be

paid to this case.

This type of antennas allow to synthesize radiation patterns with a desired directivity,

SLL and shape. Array synthesis is possible choosing a convenient geometry, individual

elements and also the right feeding amplitude and phase distribution for each of

them.

Due to the linearity of Maxwell equations, the contribution of the different radiators

in far field can be added to obtain the final radiation pattern, as presented in Equation

2.1. The approximations in Equation 2.1 are valid in farfield, since |−→r | ≫ |−→ri |. Thismathematical model assumes low coupling between elements, so that all the radiators

keep their original radiation patterns as if they were isolated.

−→E (r, θ, ϕ) =

N−1∑i=0

−→E i (r, θ, ϕ) =

N−1∑i=0

−→E i0 (θ, ϕ) e

−jk|−→r −−→ri |

|−→r −−→ri |≈

≈N−1∑i=0

−→E i0 (θ, ϕ) e

−jkrejk−→ri ·r

r=

e−jkr

r

N∑i=1

−→E i0 (θ, ϕ) e

jk−→ri ·r

(2.1)

The arrangement of the elements has been considered arbitrary so far, but in this work

12


only the circular or ring arraywill be used. For this reason, two typical array geometries

will be presented: linear arrays and circular arrays. Linear arrays are also considered

here because they are the most basic model and they help to understand better any

other geometry.

An array antenna is considered to be linear if all the elements are arranged in a straight

line. Moreover, the analysis presented here will consider all the radiators to be the

same, with the same radiation pattern, and evenly spaced. The typical geometry of this

type of 1D linear array is shown in Figure 2.5, where it has been considered to be in

the z axis in order to simplify the mathematical formulation.

y

z

θ

−→r

d

Figure 2.5: Linear array

Equation 2.1 can be particularized to the linear array case of Figure 2.5, so that−→ri = idz

and the elementary pattern term can be taken out of the sum, because it is the same for

all the elements. The only difference between the electric field of each element comes

from the feed, so the electric field of the ith element is−→Ei0(θ, ϕ) =

−→E0(θ, ϕ)·ejk

−→ri r ·Aiejαi ,

being−→E0 the radiated field of the element in (0, 0). This element in the origin is taken

as reference, soAi and αi are the feeding amplitude and phase, respectively, of the ith

element relative to it. For this particular case of linear arrays, the radiated field is given

by Equation 2.2.

It can be seen that the contribution of the elementary pattern and the array feeding

together with the geometrical parameters can be separated in the equation. On one

hand, the elementary pattern term contains not only the single element pattern, but

also its polarization vector. On the other hand, the term known as array factor,

AF (θ, ϕ) depends on the geometry and the feeding of the radiators. If the radiators

13


have a non directive elementary pattern, then the array pattern is mainly dependant

on the array factor.

−→E (r, θ, ϕ) =

−→E0

e−jkr

r

N−1∑i=0

Aieαiejk

−→ri ·r =−→E0

e−jkr

r

N−1∑i=0

Aiej(ikdcosθ+αi) =

−→E0

e−jkr

r· AF (θ, ϕ)

(2.2)

The array factor is particularly interesting when the array excitation has a progressive

phase, αi = iα. In this case, the array factor can be calculated with the inverse

discrete fourier transform (IDFT) of the amplitude distribution coefficients as shown

in Equation 2.3. The maximum of the array factor will occur, according to Equation

2.3, whenΨ = 2πn, n ∈ Z. Ψ can take only the set of values corresponding to θ ∈ [0, π],

which have physical meaning, as they represent a value of the angular coordinate θ. As

Ψ = kdcosθ + α, then Ψ ∈ [−kd+ α, kd+ α].

AF (θ, ϕ) =N−1∑i=0

Aieji(kdcosθ+α) =

N−1∑i=0

AiejiΨ = IDFTAi (2.3)

If there is more than one n ∈ Z fulfilling Ψ = 2πn with Ψ ∈ [−kd+ α, kd+ α], then the

array factor will have more than one maximum. This typically happens if the distance

between elements is so large, and it is usually undesired, because this means splitting

most of power among more than one direction. These undesired lobes in another

directions are known as grating lobes and they can be avoided placing the elements

close enough depending on α. Safe values of d for not having grating lobes are those

fulfilling d < λ/2. However, there is also a lower bound in the minimum d that can be

used, imposed by the physical size of the elementary antennas.

It can be seen from the previous explanations that the beam can be steered modifying

the phase distribution of the array elements. On the other hand, the amplitude can

control the SLL. In the case of uniform and progressive phase, the array factor

shape and the amplitude distribution are related with a IDFT, as obtained in Equation

2.3.

There are more techniques to synthesize arrays with a given shape or a given value of

SLL and directivity, likeWoodyardLawson synthesis, Schelkunoffmethod andDolph

Chebyshev method. This type of techniques are not relevant for this work and will not

14


be described here, but more details can be found in classical books like [17].

Another type of array antennas are circular arrays. For these specific arrays, the

elements are arranged inside a circle. In this work only circular arrays having elements

in one ring will be considered and they will be referred indistinctly as circular or ring

arrays. An example of this type of circular arrays is shown in Figure 2.6.

x

y

z

−→r

−→riRn∆ϕ′

Figure 2.6: Circular Array

Equation 2.1 can be also written for the specific case of circular arrays. The considered

array has N elements, arranged in a ring with radius R in the XY plane, and the

elements will be considered to be evenly spaced, with an angular distance of ∆ϕ′

between adjacent elements. Thus, −→ri = Rcos (i∆ϕ′) x + Rsin (i∆ϕ′) y, and −→ri · r =

Rcos (ϕ− i∆ϕ′) sinθ. The farfield of the array is particularized to the ringarray case

in Equation 2.4.

−→E (r, θ, ϕ) =

e−jkr

r

N−1∑i=0

−→Ei (θ, ϕ) e

jkRcos(ϕ−i∆ϕ′)sinθ =

=e−jkr

r

N−1∑i=0

Ai

−→E0 (θ, ϕ− i∆ϕ′) ejkRcos(ϕ−i∆ϕ′)sinθ

(2.4)

The circular array model needed in this thesis will be done in the horizontal XY plane,

so Equation 2.4 can be written only for θ = π/2 to remove the dependance on θ. This

15


particularization gives rise to Equation 2.5.

−→E (r, π/2, ϕ) =

−→E (r, ϕ) =

e−jkr

r

N−1∑i=0

Ai

−→E0 (ϕ− i∆ϕ′) ejkRcos(ϕ−i∆ϕ′) (2.5)

Circular arrays can be analyzed with the phase mode theory [18], taking advantage

of the periodicity in the excitation function and the single element far field. The

starting point of this theory is to assume an array of infinite elements, that is, a

continuous source. The excitation function in the discrete case is given by a set of

coefficients A0, A1, . . . , AN−1 for the different radiators, so in the continuous caseit becomes a function A (ϕ′), which is indeed 2π periodic. The periodicity allows

A (ϕ′) to be expanded in a Fourier series (Equation 2.6) with the coefficients obtained

from Equation 2.7. The single element pattern (Equation 2.8), E0 (α) (excluding the

polarization vector), can be also expanded in a Fourier series as it is also periodic, being

α = ϕ− i∆ϕ′ for the element located in the position ϕ′.

A (ϕ′) =∞∑

m=−∞

Cmejmϕ′

(2.6)

Cm =1

2π

∫ π

−π

A (ϕ′) e−jmϕ′dϕ′ (2.7)

E0 (α) =∞∑

p=−∞

Dpejmα (2.8)

In a continuous case (infinite elements), Equation 2.5 can be replaced by Equation

2.9.

−→E (r, ϕ) =

e−jkr

r

1

2π

∫ π

−π

A (ϕ′)−→E0 (ϕ− ϕ′) ejkRcos(ϕ−ϕ′)dϕ′ (2.9)

When Equations 2.6 and 2.8 are inserted into Equation 2.9, the total radiated far field

can be found. Moreover, the total radiated field is also a 2π periodic function and can

be expanded in a Fourier series. The total radiated field is given by Equation 2.10,

and according to this, each mode Em in the sum can be related to its corresponding

excitation mode Cm according to Equation 2.11. Here, Dp are the coefficients of the

elementary pattern expansion, j is the imaginary unit and Jm−p(kR) is the first kind

16


andm− p order Bessel function.

−→E (r, ϕ) =

e−jkr

r

∞∑m=−∞

Cmejmϕ′

∞∑p=−∞

Dp

2π

∫ π

−π

ej(m−p)(ϕ′−ϕ)ejkRcos(ϕ′−ϕ)dϕ′ =

=e−jkr

r

∞∑m=−∞

[Cm

∞∑p=−∞

Dpjm−pJm−p(kR)

]ejmϕ′

=e−jkr

r

∞∑m=−∞

Emejmϕ′

(2.10)

Em = Cm

∞∑p=−∞

Dpjm−pJm−p(kR) (2.11)

The elementary radiation pattern of typical array elements have the highest mode

amplitudes in the low order modes, so a truncation in the sum in p considering only

somemodes provides approximationswith very small errors inmost cases. That sum in

p coming from the single radiation pattern, which also depends on the Bessel functions,

can be seen as an scaling factor between the excitation coefficients and the radiated

field coefficients.

This analysis canbeused to synthesize the desired total radiationpattern, by getting the

excitation coefficients needed to get the required pattern. The total radiation pattern

can be expressed as a sum of phase modes (Equation 2.10), which in a real case can be

truncated considering onlyM modes, withM fixed to limit the error to an affordable

value. Finally, the excitation coefficients Cm are obtained with equation 2.11. When

choosing the number of modesM to synthesise the total pattern, it must be taken into

account that when m increases, the sum∞∑

p=−∞

Dpjm−pJm−p(kR) goes typically to 0, so

higher modes does not have an important effect on the pattern.

In a practical case, the circular array has a finite number of elements, N . If there is

only a finite number of elements (evenly spaced), the excitation source is multiplied

by a sum of Dirac’s delta functionN−1∑i=0

δ(ϕ′ − i2π/N). Applying Fourier transform

properties, it comes that the effect in the excitation source spectrum is a periodic shift

of it with period N/2π. A similar behaviour occurs in the total radiation pattern, but

the coefficients are scaled by a factor which depends on the sum of Bessel functions

(Equation 2.11). The Bessel functions here act as ”window” functions to reduce

the effect of those shifted versions of the spectrum, avoiding possible grating lobes.

17


Therefore, in circular arrays grating lobes may also appear if the distance between

elements is not small enough. In this case, the Bessel functions depend on R, so the

bigger R is, the more number of elements N are needed to avoid grating lobes.

The previous analysis is interesting to understand the origin of grating lobes in ring

arrays and how to avoid them. However, the phase mode theory method is not very

practical in some situations because there are toomany parameters to adjust, specially

in the case of non isotropic elementary patterns. Another method called Aperture

Projection Method [19] is faster and hence more appropriate to analyze the case

presented here. Thismethod starts fromaplanar aperture, with an already synthesised

pattern, and the amplitude distribution is projected on the circular array contour, as

sketched in Figure 2.7. The phase distribution can be calculated to have a directive

beam in the desired direction.

Linear Aperture

IluminationCurved aperture

projection

Figure 2.7: Aperture Projection Method

2.2.2 Model description

As introduced in the previous sections, when the aperture is sampled and the waves

are confined inside the transmission lines, the lens starts to behave like a circular

array. Therefore, the effect of discretizing the aperture can be analysed with circular

array theory. Based on that, the model presented here can be used to predict how the

radiation pattern is affected when the aperture is discretized. It also allows to study

themaximum allowable distance between elements and the influence of modifying the

geometry of the array. The model is a quick way for knowing the factors that would

limit the performance of the antenna, before doing any full wave simulation.

Figure 2.8 shows an sketch of this circular array model. The Luneburg lens will have

several feeding ports, and the aperture is discretized into a finite number of points,

which will be the radiating elements of the array.

Several key parameters are needed to build the model:

• The aperture illumination, in order to determine the amplitude distribution of

18


FeedingPoints

RadiatingPoints

LuneburgLens

Figure 2.8: Circular arraymodel in a Luneburg lenswith a discretized aperture Sketch

the circular array. This is determined by the feeding ports of the Luneburg

lens. The feeding ports of the proposed antenna are going to be rectangular

waveguides.

• The phase distribution in the aperture, which provides the relative phases of the

array elements. This can be obtained using a raytracing model, knowing that an

ideal Luneburg lens produces a planar phase front in the diametrically opposite

direction.

• The elementary patterns, which are given by the single radiators, in this case the

transmission lines that sample the aperture. Ridged rectangular waveguides will

be used for this purpose. The choice of this specific type of waveguide will be

motivated later.

The feeding ports in the final antenna are going to be rectangular waveguides, in

particular the one shown in Figure 2.9a. In order to simplify themodel and avoid using

full wave simulation, the radiation pattern can be approximated by a function with a

similar shape. Typical approximations for the main beam of rectangular waveguides

or horn patterns are the cosine function cospϕ in linear units, where p is fixed to fit the

beamwidth, and the parabolic model, given by ϕ(dB)/ϕ3dB.

These two models have been validated with a fullwave simulation of the waveguide

shown in Figure 2.9a, using PEC boundary conditions in the top and the bottom of

the waveguide. The exponent p of the cosine function has been adjusted to the 3dB

beamwidth of the feeding waveguide. In Figure 2.9b a comparison between both

models is shown. Although both are a good approximation, the parabolic model

is better for angles above 30. Thus, the only information required for getting the

aperture illumination is the 3dB beamwidth of the feeder, which can be calculated

or estimated. However, the cosine model is very fast to adjust when the specific

beamwidth value is not known.

The phase distribution in the aperture can be estimated with a simplified raytracing

model, starting from the planar phase front produced by a Luneburg lens, in an ideal

19


(a) Feeding waveguide. Dimensions: a =7.2 mm, b = 1.75 mm.

−90 −60 −30 0 30 60 90−20

−15

−10

−5

0

ϕ()Norm.Radiation

Pattern(dB)

cospϕ (ϕ/ϕ3dB)2 Full Wave Simulation

(b) Radiation patterns

Figure 2.9: Feeding model validation

case.

The phase distribution in the aperture is calculated following the model shown in

Figure 2.10. Starting from a planar phase front and taking the element in (R, 0) (polar

coordinates) as a reference, the phase difference needed of a element positioned at

an arbitrary angle α can be calculated with Equation 2.12. The path difference to get

the planar phase front is obtained using basic geometry in Figure 2.10, and the phase

difference is calculated multiplying the path difference by the wave number.

∆φ = R · (1− cosα) · 2πλ

= k ·R · (1− cosα) (2.12)

Finally, the elementary patterns of the array elements can be approximated using the

same method stated previously to approximate the feeding radiation patterns, since

the array elements will be double ridge rectangular waveguides. Then, a cosqϕ model

will be used, where p = q, because the feeder and the elements have in general different

patterns.

20


∆φ

α

R

x

y

Phase Fronts

Figure 2.10: Phase distribution raytracing model

2.2.3 Model validation

The model has been validated using a Luneburg lens with a continuous aperture, as

shown in Figure 2.11. The model was validated by simulating a continuous aperture

with a full wave simulator (CSTMicrowave Studio) and the obtained radiation pattern

was compared with the result provided by the model. The continuous aperture has

been modelled with an array of a large number of elements, precisely 700. The feeder

of the structure in Figure 2.11 is a rectangular waveguide, and the parameters of the

model (p,q and ϕ3dB) have been adjusted according to the feeder beamwidth. Themodel

parameters generally change with frequency.

The elementary patterns have been assumed to be a cosqϕ with q = 0.5 in order to have

radiators with poor directivty that properly imitates the continuous aperture.

(a) (b)

Figure 2.11: Structure for circular array model validation

Figure 2.12 shows the comparison between the radiation pattern obtained with the

model and with full wave simulation for different frequencies. The model shows good

21


fitting with full wave simulation for different frequencies.

−90−60−30 0 30 60 90−40

−30

−20

−10

0

ϕ()

Norm.Radiation

Pattern(dB)

cospϕ (ϕ/ϕ3dB)2 Full Wave Simulation

(a) f = 30 GHz

−90−60−30 0 30 60 90−40

−30

−20

−10

0

ϕ()

Norm.Radiation

Pattern(dB)

(b) f = 34 GHz

−90−60−30 0 30 60 90−40

−30

−20

−10

0

ϕ()

Norm.Radiation

Pattern(dB)

(c) f = 38 GHz

Figure 2.12: Array model validation with continuous aperture

This model can then be used to analyze the effect of discretizing the aperture, with a

proper adjustment of the parameters. It could be also utilized to assess the degradation

in terms of radiation pattern when one or several amplifiers break.

22


2.2.4 Aperture discretization analysis

One of the main goals of the circular array model is to analyze the impact of increasing

or decreasing the distance between sampled elements in the radiation pattern. This is

a key parameter in the design, since it will determine the type of transmission line that

should be used to discretize the aperture. Another important parameter to be analyzed

is the effect of having an offset in the radial position of the elements.

Figure 2.13 shows a sketch with the general geometry of the discretized aperture. The

distance between elements is represented by d, and the offset with respect to the ideal

radius is represented by o.

o

dx

y

Luneburg

Lens

RadiatingPoints

Offset

RadiatingPoints

Ideal

Figure 2.13: Aperture discretization with offset radiators

According to the array theory presented before, if the distance between elements

is increased too much, grating lobes appear in undesired directions. The antenna

proposed in this work has to be directive in one direction, so having grating lobes

is an important inconvenient, not only because it decreases the directivity, but also

because these grating lobeswillmean transmitting high amounts of power to undesired

directions. The effect of increasing the distance between elements have been analyzed

in Figure 2.14a, where it is clear that for a distance d = λ between elements an

important grating lobe is produced. Thus, the distance between elements must be

kept as close as possible to d = λ/2 in order to avoid grating lobes. This limitation

will affect the choice of a proper transmission line, which will be discussed in the next

section.

23


Another important distortion in the radiation pattern can arise from placing the

radiators in a different radial position compared to the sampling points, as mentioned

before. The main impact on the radiation pattern is the loss of directivity due to the

phase aberrations introduced when moving the elements. This is shown in Figure

2.14b. Offsets below λ/2 are affordable, whereas offsets above λ completely distort

the radiation pattern.

−90−60−30 0 30 60 90−40

−30

−20

−10

0

ϕ()

Norm.Radiation

Pattern(dB)

d/λ = 0.5 d/λ = 0.75 d/λ = 1

(a) Different element distance (o = 0)

−90−60−30 0 30 60 90−40

−30

−20

−10

0

ϕ()

Norm.Radiation

Pattern(dB)

o/λ = 0 o/λ = 1 o/λ = 2

o/λ = 0.5 o/λ = 1.5

(b) Different offset (d = λ/2)

Figure 2.14: Normalized radiation patterns for different offset and element distances

2.3 Ridge Rectangular Waveguide

The choice of the transmission line used to discretize is of great relevance in this

project, since this will determine the final system architecture, the transitions needed

to insert the PCB within the antenna and the transitions to the different layers of the

antenna.

The transmission line must be isolated from the neighbouring lines, avoiding

undesired couplings and phase aberrations. In an ideal case, the phase and amplitude

of the sampled fields should be kept after sampling the aperture. The amplitude

distribution will depend mainly on the transition from the continuous aperture to the

transmission lines. If the amplitude distribution were distorted, the main undesired

effect would be an increase in the SLL. Furthermore, this distortion on the amplitude

distribution could be corrected if amplifiers with gain control are used, adjusting the

24


gain of each amplifier. However, if the phase is not kept, the radiation pattern may be

completely distorted if the distortion is high enough. Thus, the transmission lines that

discretize the aperture must keep the phase distribution produced by the Luneburg

lens.

Another important limitation in the choice of transmission lines is the distance

between elements, which can not be much bigger than λ/2, in order to avoid grating

lobes, as explained in the previous section.

It is preferred that the transmission lines are closed to ensure that there is no

coupling between lines. However, closed waveguides does not allow the propagation

of transverse electromagnetic (TEM) modes, and hence there is only propagation

above a cutoff frequency, which depends on the geometry and dimensions of the

waveguide. The cutoff frequencies of the classical rectangular and circular waveguides

are summarized in Table 2.1.

WaveguideFundamentalMode

Cutofffrequency

Rectangular

a

b TE10

c

2a√εr

Circular

a TE11

p′11c

2πa√εr

Table 2.1: Cutoff frequency for classical waveguides

According to Table 2.1 the cutoff frequency of a holey rectangular waveguide is fc =

c/2a, which corresponds to a cutoff wavelength of λc = 2a, and hence the minimum

width to be above cutoff is amin = λ/2 for a given frequency. However, the distance

between transmission lines should not be much higher than λ/2 in order to avoid

grating lobes, as mentioned before. The rectangular waveguide is very dispersive

when working at frequencies close to the cutoff. Circular waveguides have a similar

problem. A holey circular waveguide has a cutoff wavelength of λc = 2πa/p′11, where

p′11 is the first zero of the derivative of the firstorder and first kind Bessel function,

J ′1(x). Therefore, the minimum radius is amin = λ · p′11/2π ≈ 0.293λ and the minimum

distance between lines is close to 0.6λ. For this reason, the traditional rectangular and

circular waveguides are definitely not a good option to discretize the aperture.

A waveguide with lower cutoff frequency for the same width must be found, in order

25


to decrease the distance between elements. The cutoff frequency of a rectangular

waveguide can be reduced by adding ridges, giving rise to a ridge rectangular

waveguide. This kind of waveguide can be a single ridge rectangular waveguide (Figure

2.15a) or double ridge rectangular waveguide (Figure 2.15b). Both types reduce the

cutoff frequency for the same width, because the fields are well confined, between

the ridges in the double ridge cases, and between the ridge and the bottom in the

single ridge case. This approach has been followed in [20, 21] to design a fullymetallic

Rotman lens minimising the distance between lines.

br

r1

a

b

(a) Single

br

r1

a

b

(b) Double

Figure 2.15: Ridge rectangular waveguides

In this project, only the doubleridge rectangular waveguide will be included, mainly

because it allows to have a shorter transition to PCB. This transition will be presented

in the next chapter.

Figure 2.16 shows a comparison between the dispersion diagrams, including only the

fundamental mode, in both a rectangular waveguide and a doubleridge rectangular

waveguide of the same width, a = 4mm. It is clear that the cutoff frequency is lower

when adding the ridges in thewaveguide. Ridge rectangularwaveguides have a broader

monomode bandwidth and they are also less dispersive than rectangular waveguides

(considering the same dimensions), which is another important advantage. The cut

off frequency is reduced as the distance between ridges, br, is decreased. The closer

the ridges are, the lower the cutoff frequency is. However, as these waveguides will be

manufactured in two pieces fastened with screws, having a very small gap between

ridges might be problematic when assembling the structure. Thus, the distance

between ridges has been chosen to have a cutoff frequency below the lowest frequency

in the band, with a margin, to avoid working extremely close to the cutoff.

The dimensions of the doubleridged rectangular waveguide of Figure 2.16 can fulfill

the requirements of this project, because there is propagation in the entire Ka

band, while keeping affordable distances between adjacent lines. Thus, the double

26


π/4 π/2 3π/4 π0

20

40

60

80

100

120

k (rad/mm)

f(GHz)

ab

br

r1

Figure 2.16: Dispersion diagram of rectangular waveguide (red) and double ridgerectangular waveguide (blue). a = 4mm, b = 1.75mm, r1 = 2mm, br = 0.35mm

ridge rectangular waveguides used to discretize the aperture will have the following

parameters:

• a = 4mm

• b = 1.75mm

• r1 = 2mm

• br = 0.35mm

2.4 Amplifier

The amplifiers will be mounted on a PCB and properly integrated in the different

transmission lines. The PCB will have several layers. The amplifier will be mounted

on the top layer, and the necessary DC circuit used to feed the amplifier will be placed

on the bottom layer.

The transmission lines are double ridge rectangular waveguides, as introduced in

27


the previous section, and the main limitation when integrating the amplifiers is the

available room, due to the small width of these waveguides. This project is intended to

be a proof of concept, so amplifiers with high gain are not needed here.

According to the aforementioned reasons, simplicity and small size are the most

important features to account for when choosing the amplifiers. Table 2.2 shows a

comparison among different amplifiers available in the market and working in Ka

band, considering different criteria to compare them. The most important parameter

is the size due to the space limitation, as mentioned before, but also the DC bias should

be as simple as possible for the same reason. There are some models that require two

different voltages for feeding the amplifier, which would make more complex the PCB

design in the future and hence should be avoided. On the other hand, the gain is not

a relevant parameter, but it has been included in the table to get an insight about the

typical gain of MMIC amplifiers in Kaband.

Model Manufacturer Frequency Band (GHz) Size (mm2) DC Bias Gain Control Amplifier Price

AMM6702SM Marki Microwave 20 50 4 x 4 mm 2 Voltages 23 dB NO 1400 SEKCMD299K4 CustomMMIC 18 40 4 x 4 mm 1 Voltage 16 dB NO 480 SEKHMC1040 ADI 24 – 43.5 3 x 3 mm 1 Voltage 23 dB NO 450 SEKHMC263 ADI 24 36 4 x 4 mm 1 Voltage 20 dB NO 450 SEKMAAL011111 MACOM 22 38 3 x 3 mm 1 Voltage 19 dB NO 400 SEKMAAAL011129 MACOM 18 – 31.5 2 x 2 mm 1 Voltage 23 dB YES 350 SEKTSS44+ Mini Circuits 22 – 43.5 3 x 3 mm 1 Voltage 17 dB YES 300 SEKXL1010QT MACOM 20 38 3 x 3 mm 1 Voltage 17 dB NO 400 SEK

Table 2.2: Comparison between different amplifier models available in the market.

The amplifiers with a size bigger than 3mm× 3mm have been discarded, because the

width of the ridgerectangular waveguide is 4mm, and also those with a complicated

DC bias circuit. Another relevant parameter is the bandwidth of the amplifier, which

has to be as wide as possible, of at least a 20% subband within Kaband. The best

tradeoff among all the options in Table 2.2 is the TSS44+ fromMini Circuits, because

it is a 3mm× 3mm amplifier, with simple bias. Furthermore, the TSS44+ covers the

whole Kaband, is cheap and includes a control voltage for switching off the amplifier,

which can help to control the SLL of the antenna. This amplifier will be taken as

reference for all the designs performed along the project. The S parameters of the

TSS44+ are shown in Figure 2.17. The S11 parameter, shown in Figure 2.17a, can be

considered as an upper bound of the overall S11 of the transitions to PCB that will be

designed. In other words, the S11 of the designed transitions has to be good enough so

that the totalS11 is limited by the amplifier andnot by the transition performance.

28


26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(a) S11

26 28 30 32 34 36 38 40−60

−50

−40

−30

−20

−10

0

f (GHz)

|S12|(dB)

(b) S12

26 28 30 32 34 36 38 400

5

10

15

20

f (GHz)

|S21|(dB)

(c) S21

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S22|(dB)

(d) S22

Figure 2.17: Amplifier TSS44+ S parameters

29

Chapter 3

Designs and Results

In this chapter, the designs accomplished in this thesis and the simulated results are

presented.

First, a transition from double ridge rectangular waveguide to PCB is designed, to

enable the integration of the amplifiers in the discretized aperture of the antenna. The

transition has been designed in different steps, in order to ensure a 50Ωmatching with

the amplifier, while keeping a good performance in terms of reflection coefficient. The

behaviour of these transitions is critical for the entire system, and they should not limit

the overall system performance.

Finally, the full antenna structure, including an ideal Luneburg lens with a discretized

aperture, is presented. As a first approach, the full structure has only one feeding

port and does not contain any transition, in order to validate the concept of aperture

discretization. Finally, the aforementioned transitions to PCB are included, to assess

their impact in the main antenna parameters, and also several ports added to assess

the scanning capability of the structure.

3.1 Transition design

The aperture of the antenna is discretized into double ridge rectangular waveguides

with the dimensions stated in Figure 2.16. As explained in previous chapters, the

amplifierswill bemounted on aPCB, so that a transition from the fullymetallic double

ridged rectangular waveguide to a printed transmission line, such as microstrip or

coplanar waveguide (CPW), has to be designed.

30

CHAPTER 3. DESIGNS AND RESULTS

There are different approaches to design transitions from fullymetallic waveguides to

printed technology. One way is to use slot coupling to go from a metallic waveguide to

a printed transmission line placed in another layer. The design of [22], for example,

proposes a transition from ridge gap waveguide to microstrip line using a stepped

transformer in the ridge waveguide and a slot in the microstrip ground plane. Designs

from rectangular waveguide to microstrip using slot coupling have been also proposed

[23]. However, this type of designs are not suitable for the proposed structure

for several reasons. If slot coupling were used, microstriptomicrostrip transitions

similar to [24–26] would be required in the intermediate layer if a slot coupling

transition is also going to be used from the intermediate to the top layer. What is more,

the second slot coupling transition might have not enough room, as the transmission

lines are closer in the transition to the top layer. Another type of transitions from

waveguide to printed lines are perpendicular transitions including probes to allow

the coupling. For example, [27, 28] propose printed patches with different shapes

to produce coupling into the microstrip line. This type of transition would require

either plenty PCB or a flexible PCB, which are expensive solutions. Coaxial probes are

another way, like the design in [29], but they are very prone to human errors during

the assembly of the full structure, apart from having similar drawbacks to those of the

aforementioned slot coupling. Another design approaches include inline transitions,

where Chebyshev transformers are a good solution for matching impedances. In

[30], a stepped transition frommicrostrip to doubleridge rectangular waveguide with

chamfered ridges is designed.

The transition proposed in this project will be an inline transition from double ridge

rectangular waveguide to microstrip. The configuration is backtoback, as it begins

and ends with the doubleridge rectangular waveguide and includes the microstrip

line between. The amplifier has an input impedance of 50Ω in both input and output

pads, so the line where the amplifier is placed should have 50Ω in order to ensure good

matching. The transition design is carried out in different steps, in order to get a wide

band transition with the required 50Ωmatching in the amplifier ports.

The first approach in the transition design is shown in Figure 3.1. The substrate

utilized for this transition is Rogers R04350Bwith a dielectric constant εr = 3.66 and a

thickness hsubs = 0.168 mm, following the suggested mounting provided in the TSS

44+ amplifier manufacturer website. The transition includes a stepped impedance

transformer, that goes from the initial distance between ridges, br = 0.35 mm, to

31


the substrate thickness hsubs = 0.168 mm. Most of the electric field in the double

ridge rectangular waveguide is well confined between the ridges. For this reason, the

line impedance can be approximated as a parallel plate waveguide of width r1 and

distance between plates br, being the line impedance approximated by Z0 ≈ η0brW

,

where η0 = 120π is the impedance of free space. The length of each step in the stepped

transition is close toλ/4, so this value has been taken as an starting point for f = 30GHz.

The structurewas then optimized by adjusting the parameters to fulfill the design goals.

As can be seen in Figure 3.1b and 3.1c, there is a tip in the metallic part ensuring the

electric contact between the metallic waveguide and the signal trace in the microstrip

line. The values of hcav and Lmicr were selected to avoid unwanted resonances inside

the cavity.

(a) 3D view

(b) Side cut (c) Top cut

Figure 3.1: Doubleridge rectangular waveguide to microstrip transition. a = 4 mm,L0 = 2mm,L1 = 2.76mm,L2 = 2.42mm,L3 = 0.52mm,Lmicr = 21.04mm, hcav = 1.51mm, hsubs = 0.168 mm, h0 = 0.35 mm, h1 = 0.29 mm, h2 = 0.21 mm, g = 1 mm,Wmicr = 0.9mm, r1 = 2mm.

The S parameters of this transition in Kaband are shown in Figure 3.3. The S11 is

below 20 dB over the entire band, and the S21 is greater than 0.6 dB. The dielectric

losses are the main contribution to the losses in this transition. Figure 3.2 shows the

magnitude in dB(V/m) of the electric field in the transition, within the dielectric and

between the ridges (Figure 3.2a) and a side cut view throughout the symmetry axis of

the geometry (Figure 3.2b). It can be seen that the electric field is well confined in the

microstrip line, without significant unwanted modes in the cavity.

The width of the previous microstrip line is 0.9mm and the substrate height is

32


(a) Top View

(b) Side View

Figure 3.2: Doubleridged rectangular waveguide to microstrip transition Electricfield magnitude

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(a) S11

26 28 30 32 34 36 38 40−3

−2.5

−2

−1.5

−1

−0.5

0

f (GHz)

|S21|(dB)

(b) S21

Figure 3.3: Double ridge rectangular waveguide tomicrostrip transition S parameters

0.168mm. According to the approximated formulas for calculating the line impedance

of a microstrip line stated in [31], the impedance of this microstrip line is 26.8Ω.

Therefore, if the amplifier were placed in this microstrip line, there would be a

significant mismatch because the transmission line has not 50Ω. Another drawback of

this implementation is its size. The microstrip line length should be reduced as much

as possible in order to minimize dielectric losses, while ensuring that unwantedmodes

in the cavity are prevented. The minimum size of the transition is limited by the room

needed to mount the amplifier and also by the size of a 50Ω matching network that

will be added in the microstrip line.

The width of the signal trace in the microstrip line has to be reduced to increase the

33


characteristic impedance up to 50Ω. One manner to achieve a 50Ω line is to design a

transition in the PCB from the initialmicrostrip line included in the previous transition

(Figure 3.1) to a 50Ω line. The proposedmatching circuit in the PCB is shown in Figure

3.4. A backtoback stepped transformer is proposed, where both the width of the

signal trace and the gap between the signal trace and the side grounds are optimized.

The line in the center part of Figure 3.4a, which has the dimensions recommended

by the amplifier manufacturer, has a characteristic impedance of 50Ω. The total

length of the PCB have been reduced from 21.04mm to 15.06mm, having enough

room to place the impedance transformer and the amplifier without using needless

space. The side grounds included in this design are necessary to place the lines that

will feed the amplifiers. In order to avoid unwanted modes between the bottom and

side grounds, some vias will surround the signal trace, as shown in Figure 3.4b. Thus,

the predominant mode is the quasiTEM mode of a microstrip line. Another mode

can be excited between the signal trace and the side grounds, typical in CPW, but this

mode is not predominant in this case, since the gap between the signal trace and the

side ground is not small enough. The S parameters of this network are shown in Figure

3.6. The S11 is below 15 dB in the whole band, and below 20 dB between 27GHz and

39GHz, which is better than the S11 of the amplifier and hence does not deteriorate

too much the overall performance.

(a) 3D view (b) Vias (continuous model)

Figure 3.4: Microstrip line impedance matching to 50Ω. L0 = 2 mm, L1 = 1.28 mm,L2 = 1.31mm, L3 = 1.17mm, L4 = 1.77mm,W0 = 0.9mm,W1 = 0.56mm,W2 = 0.34mm,W3 = 0.28mm, g0 = 1mm, g1 = 1.07mm, g2 = 0.54mm, g3 = 0.41mm, g4 = 0.2mm, dvias = 0.1mm

The vias shown in Figure 3.4b are a continuous wall of PEC, but in a real case these

vias are small cylinders connecting the side and the bottom grounds. The real vias

are discrete, but when placed in a row they act similarly to a continuous PEC. This

continuous model is a good approximation of the real case and it greatly facilitates the

optimization process. When the optimum design was obtained, then the continuous

vias were replaced by discrete ones and the result was compared with the continuous

34


vias model. The S11 of both cases are compared in Figure 3.5.

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

Figure 3.5: Discrete (blue) and Continuous (red) vias comparison

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(a) S11

26 28 30 32 34 36 38 40−3

−2.5

−2

−1.5

−1

−0.5

0

f (GHz)

|S21|(dB)

(b) S21

Figure 3.6: Microstrip line impedance matching S parameters

The PCB from Figure 3.4 can replace the microstrip line included in the initial

transition, giving rise to a doubleridge rectangular waveguide to microstrip transition

matched to 50Ω. The new transition matched to 50Ω is shown in Figure 3.7. The

overall transition length has been reduced compared to the initial case, as the PCB

35


is now shorter. The dimensions of the stepped transformer in the double ridge

rectangular waveguide have been slightly adjusted to have a good matching, since the

microstrip line has been modified and hence the input impedance.

The electric field magnitude in the transition matched to 50Ω is presented in Figure

3.8. In this case, some radiation occur in the center part of the PCB as seen in Figure

3.8b, which produces unwanted resonances. This radiation occurring in the center

part is 10 dB below the maximum, so the effect does not significantly affect the overall

transition performance.

The S parameters of this transition are shown in Figure 3.9. The S11 is below 20 dB

between 27GHz and 39GHz and below 15 dB in the whole Kaband, and hence it will

not significantly worsen the overall system performance. The magnitude of S11 of the

amplifier shown in Figure 2.17a around 26GHz is smaller than the S11 of the transition

from Figure 3.9a, meaning that the transition limits the system around that frequency

However, the lower limit of the band is not very relevant for this project, because the

Luneburg lens antenna will have a small aperture and hence low directivity in that

case.

(a) 3D view

(b) Side cut (c) Top cut

Figure 3.7: Doubleridge rectangular waveguide to microstrip transition. L0 = 2mm,L1 = 2.62 mm, L2 = 2.55 mm, L3 = 0.53 mm, Lmicr = 15.06 mm, hcav = 1.51 mm,hsubs = 0.168mm, h0 = 0.35mm, h1 = 0.29mm, h2 = 0.2mm

When the transition design is concluded, the next step is to include the amplifier

inside the transition to evaluate the overall performance of the transition with the

amplifier mounted on the PCB. A physical model of the amplifier is not available,

so the amplifier itself cannot be included in the full wave simulator. However, the

36


(a) Top View

(b) Side View

Figure 3.8: Doubleridged rectangular waveguide to microstrip transition matched to50Ω Electric field magnitude

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(a) S11

26 28 30 32 34 36 38 40−3

−2.5

−2

−1.5

−1

−0.5

0

f (GHz)

|S21|(dB)

(b) S21

Figure 3.9: Microstrip line impedance matching S parameters

S parameters are provided by the manufacturer (Figure 2.17), so a networkbased

analysis can be performed.

The transition from Figure 3.7 is a 2port network, but it can be slightly modified to

add 2 extra ports where the amplifier can be connected. The modified structure with

the two extra ports is shown in Figure 3.10a. The right and left sides of the transition

have been isolated, so that the amplifier can be mounted in the center part of the

transition.

Since the Sparameters of the amplifier are known, the CSTschematics can be used

to get the Sparameters of the 2port network obtained when connecting the amplifier

37


between Port 2 and Port 3 in the structure of Figure 3.10a. The network scheme is

shown in Figure 3.10b, where the input of the amplifier is connected to Port 2 and the

output to Port 3.

The S parameters of the transition with the amplifier connected are shown in Figure

3.11. This result can be compared with the S parameters of the amplifier itself (Figure

2.17) to assess the reflections and losses produced by the transition. The magnitude

of S11 and S22 are very similar in both cases, being the only important degradation

between 26 and 27GHz, as expected from the previous results. The S21 and S12 are

very close with and without the transition in the whole band. Therefore, according

to these simulation results, the transition barely affects the amplifier gain, reflection

coefficient and reverse isolation.

(a) Transition 4Port networkdefinition (Topview)

(b) Amplifier and transition networksconfiguration in CST Schematics

Figure 3.10: Transition and amplifier TSS44+ connection

3.2 Full multilayer structure

In this section the multilayer structure simulations and results are presented. The

geometry sketched in Chapter 2 (Figures 2.3 and 2.4) has been built inCSTMicrowave

Studio and simulated. It was first simulated without the PCB, in order to study the

effect of the aperture discretization in the radiation pattern. The transition of Figure

3.7 is included afterwards in the bottom layer, to assess the degradation it introduces

in terms of radiation pattern and reflection coefficient. Finally, several ports are added

to evaluate the scanning capability of the full antenna.

3.2.1 Multilayer structure without transition

The first simulation model includes the metallic multilayer structure with an ideal

Luneburg lens inside. The antenna model is fed with a single waveguide port. A 3D

view of the structure can be seen in Figure 3.12, where the Luneburg lens is blue in

38


26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(a) S11

26 28 30 32 34 36 38 40−60

−50

−40

−30

−20

−10

0

f (GHz)

|S12|(dB)

(b) S12

26 28 30 32 34 36 38 400

5

10

15

20

f (GHz)

|S21|(dB)

(c) S21

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S22|(dB)

(d) S22

Figure 3.11: TSS44+ integrated in the 4port transition (solid line) andTSS44withouttransition (dashed line) S parameters

color. The aperture of the Luneburg lens is discretized and the waves are confined

within double ridge rectangular waveguides with dimensions a = 4mm, b = 1.75mm,

r1 = 2mm and br = 0.35mm according to Figure 2.15b definition.

(a) 3D View (b) 3D View (interior)

Figure 3.12: Multilayer structure without transition CST model 3D view

39


In order to better understand the geometry, several cuts are presented to see the

interior and the different layers. Figure 3.13 shows a side cut made through the

symmetry axis. The feeding port is on the left part and the Luneburg lens is positioned

in the center. Then, the side cut of the central double ridge rectangular waveguide

can be seen. Linear tapers are used as smooth transitions from the lens aperture to

the ridge waveguides. A linear taper is zoomed in 3.14. In the intermediate layer, the

confined waves return to the initial position, and finally the ridge waveguides radiate

to free space in the top layer through a rotated linear taper. It can be seen that the

lines have a small offset o from the ideal position. The reason of this offset is to

avoid overlapping between lines. This offset has been set as small as possible, so that

aberrations are minimized.

Figure 3.13: Multilayer structure without transition CSTmodel Side view. Ltaper = 5mm, L1 = 35.6mm, h1 = 4.75mm, h2 = 7.25mm, o = 1.45mm

Figure 3.14: Linear taper

Figure 3.15 shows the top view of the different layers. The cut has been made with

planes crossing between the waveguides’ ridges.

• The bottom layer (Figure 3.15a) includes the feeding port, which is a rectangular

waveguide of 7.2 x 1.75mmxmm. The ideal Luneburg lens is centered inside, and

it has a radius of 25mm, that is, a diameter of 5λ at 30 GHz. The aperture of the

lens is discretized into 17 lines, separated 5mm each other (λ/2 at 30 GHz). This

40


value has been chosen as a tradeoff between cutoff frequency of the waveguide

and grating lobes.

• The intermediate layer (Figure 3.15b) includes the 17 waveguides coming back to

the initial radial position. It is not possible to go further back because the lines

would overlap.

• The top layer (Figure 3.15c) includes another set of linear tapers to smooth the

transitions towards the flare.

(a) Bottom layer

(b) Intermediate layer (c) Top layer

Figure 3.15: Multilayer structurewithout transitionCSTmodel Top view. RLuneburg =25mm,W = 5mm,Wfeed = 7.2mm.

Figure 3.16 shows the reflection coefficient in the feeding port of the antenna. The

magnitude of this S11 remains below −10 dB for all the frequencies between 30 and

40 GHz and below −7 dB from 26 to 40 GHz. This value of reflection coefficient

is affordable in this structure, since the signal is amplified afterwards. However, it

could be further optimized by replacing the linear tapers by other solutions. These

optimizations have not been carried out in this work, because the main goal of the

project is to proof the idea of amplifier integration. This idea can be extended to

41


future designs with given specifications, where the optimization process of the specific

structure becomes a key task.

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

Figure 3.16: Multilayer structure without transitions to PCB inside S11

The directivities achieved for different frequencies are shown in Figure 3.17. The

maximum directivity and the SLL depend on the frequency. This variation arises

from the dispersive nature of the different parts of the structure (tapers, bends,

transitions...). However, the obtained values are consistent with the expected values

for a 50mm diameter Luneburg lens. The SLL are −15.4 dB at 30 GHz, −13.3 dB at 34

GHZ, −12.5 dB at 38 GHz and −15.9 dB at 40 GHz. For the remaining band the SLL

has similar values, varying from −17 dB in the best case and −11.5 dB in the worst.

The directivity is 14.22 dBi at 30 GHz, 14.65 dBi at 34 GHz, 14.09 dBi at 38 GHz and

13.61 dBi at 40 GHz. These values are consistent with the aperture size. The directivity

increases typically with frequency, because the electrical size of the aperture also does.

However, when the frequency increases, the electrical distance between elements,W/λ

and the electrical offset o/λ also does. When the frequency is incremented, the pattern

is slightly distorted, and hence the directivity decreases somewhat in the upper part of

the band (3840GHz). The electrical distance has been kept within reasonable values in

the entire band, and it will be seen later that the variations with frequency in directivity

and radiation pattern arise mainly from the dispersive transitions and tapers included

in this design and the internal reflections.

42


−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(a) f = 30 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(b) f = 34 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(c) f = 38 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(d) f = 40 GHz

Figure 3.17: Multilayer structure without transitions to PCB Radiation patterns

3.2.2 Multilayer structure with transition

The previousmultilayer structure was able to keep the directive beamproduced by the

Luneburg lens. Therefore, the use of this multilayer structure allows to discretize the

aperture while maintaining the advantages of the Luneburg lens. The next step is to

include the previously presented transitions from double ridge rectangular waveguide

to PCB where the amplifiers will be mounted. These transitions will be included in the

bottom layer, but they could also be included in the intermediate layerwithout affecting

the final performance. The side view of the multilayer structure after including the

transitions is shown in Figure 3.18. The top view of the different layers are shown

in Figure 3.19, being the transitions to PCB included in the bottom layer the only

43


difference with respect to the previous case.

Figure 3.18: Multilayer structure with transitions to PCB CST model Side view.Ltaper = 5 mm, L1 = 4 mm, Ltr = 25.4, L2 = 6.2 mm, mm, h1 = 4.75 mm, h2 = 7.25mm, o = 1.45mm

(a) Bottom layer (b) Intermediate layer

(c) Top layer

Figure 3.19: Multilayer structure with transitions to PCB CST model Top view

Figure 3.20 shows the reflection coefficient S11 magnitude in the feeding port. It is

compared with the reflection coefficient obtained before introducing the transition,

44


and it can be seen that the transitions do not worsen the performance. This result was

expected, since the S11 of the transition isolated is much smaller than the S11 of the full

structure without the transition.

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

Figure 3.20: Multilayer structure with (solid line) and without (dashed line)transitions to PCB inside S11

The radiation patterns are shown in Figure 3.21 with solid line and they are compared

to the previous case, which are in dashed line. The shape of the main beam is similar,

but the side lobe levels modifies slightly with respect to the case without transitions.

The reason of this variation is the inclusion of the transitions, which slightly modify

the frequency response of the lines. The aforementioned variations in SLL reduce the

directivity. The directivity for this case is 14.25 dBi at 30 GHz, 13.49 dBi at 34 GHz,

13.61 dBi at 38 GHz and 13.03 dBi at 40 GHz.

3.2.3 Multilayer structure with transition and 9 ports

The structure designed so far works properly when the transitions to microstrip are

included. In the previous cases, only one port was added in order to assess the aperture

discretization and the performance after including the transitions. However, one of the

main advantages of Luneburg lens antennas is the scanning capability, which provides

high angular coverage sharing the same aperture by all the ports. For this reason, 9

ports in total have been included in the antenna to get scanning capability.

Figure 3.22 shows the top and side views of the multilayer structure after adding 8

extra ports. The ports do not overlap each other, and have been separated 16, so that a

coverage up to 64 canbe obtained. An additional line has been added in each side of the

45


−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(a) f = 30 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(b) f = 34 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(c) f = 38 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(d) f = 40 GHz

Figure 3.21: Multilayer structure with PCB (solid line) and without PCB (dashed line) Radiation patterns

aperture in order to minimize the scan losses, so that the aperture has 19 transmission

lines in this case.

The feeding network of this multiport architecture has been slightly modified

compared to the previous structures. In this case, the port is bent and the waveguide

ports feed the structure from the bottom part, as can be seen in Figure 3.22a. Themain

reason of thismodification are some limitations introduced by the full wave simulation

software. CSTMicrowave Studio does not allow to create waveguide ports misaligned

with respect to the axis, and hence all the ports must be in a plane orthogonal to one

of the Cartesian axis. The edges of the bend have been chamfered, as shown in Figure

3.23a. The dimensions have been optimized in order to minimize the S11, ensuring it

46


(a) Side view (b) Top view (Bottom Layer)

Figure 3.22: Multilayer structure with 9 ports CST model. α = 16

is much smaller than the S11 of the full antenna. w1 and w2 were optimized and the S11

is below −24 dB in the entire band.

(a) Side view

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

(b) S11

Figure 3.23: Chamfered bend in feeding ports. w1 = 2mm, w2 = 0.7mm

Having good isolation between ports, as well as affordable reflection coefficients,

are important considerations in the design of the structure. Figure 3.24a shows the

reflection coefficient at each port from Figure 3.22. It can be seen that the reflection

coefficient in all the ports is very similar to the previous caseswith only one port (Figure

3.20), being below−10 dB in nearly all the band, apart from a few peaks which are still

below −7 dB. The coupling from port 1 (in the center) to the other ports is stated in

Figure 3.24b. The coupling is below −10 dB for all the ports in the entire band. The

remaining ports show a similar behaviour. These results state that most of the power

is caught by the lines, and hence, amplified.

47


The radiation patterns obtained when feeding from the different ports are shown

in Figure 3.25, where each pattern has been drawn with the same colour than its

corresponding port in Figure 3.22b. It can be seen in Figure 3.25 that a scanning angle

up to 64 can be obtainedwith this structure for all the frequencies. The different beams

are separated 16, which is the angular separation between adjacent ports. The scan

losses in this antenna depend on the frequency, due to the dispersive nature of the

structure. The scan losses at 30 GHz are 0.36 dB. At 34 GHz scan losses are 1.45 dB, at

38 GHz they are 1.12 dB and finally at 40 GHz this value is 0.5 dB. It can be seen that

the worst case has 1.45 dB of scan losses and the best case has 0.36 dB.

Directivity and SLL are different from the previous cases (Figure 3.21), specially in

the upper part of the band. In Figure 3.25, the directivity at 30 GHz is 13.5 dBi, 13.75

dBi at 34 GHz, 14.22 dBi at 38 GHz and 14.85 at 40 GHz. The SLL are below −14 dB

at all frequencies. The reason of these variations is the addition of the new ports in

the structure. Before adding the ports, the power reflected back to the lens was very

likely to couple again into a different waveguide and was, thus, radiated somewhere.

When the ports are added, most of those reflections turn into coupling in the other

ports when arriving there and they are not reflected back. For this reason, the SLL

have been reduced in the central beam, and the directivities have improved.

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|S11|(dB)

S11 S22 S33 S44 S55

(a) Reflection coefficients

26 28 30 32 34 36 38 40−40

−30

−20

−10

0

f (GHz)

|Sn1|(dB)

S21 S31 S41 S51

(b) Coupling from Port 1

Figure 3.24: S parameters multilayer structure with 9 ports

48


−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(a) f = 30 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(b) f = 34 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(c) f = 38 GHz

−90−60−30 0 30 60 90−15

−10

−5

0

5

10

15

ϕ()

Directivity(dBi)

(d) f = 40 GHz

Figure 3.25: Multilayer structure with 9 ports Radiation patterns

49

Chapter 4

Conclusions and Future Work

This project has been aimed at enabling the integration of multiple amplifiers inside

the aperture of a fullymetallic Luneburg lens antenna. Placing the amplifiers inside

the aperture instead of having them at the ports not only reduces the overall cost

of the system, but also permits to handle higher transmission powers, increases the

robustness and eases the control in the antenna parameters.

Different approaches for the integration of the amplifiers in the aperture has been

presented in this work. A multilayer architecture with the amplifiers in the bottom

layer was chosen as the best tradeoff after stating advantages and drawbacks of the

different options. The integration of amplifiers is achieved by discretizing the aperture

into a finite number of subapertures. Each subaperture contains a transmission

line where a PCB with an amplifier mounted can be included. The antenna has been

modelled and analyzed as a circular array after sampling the aperture. With thismodel,

the most important design considerations and limitations for the performance of the

Luneburg lens were obtained. The conclusions derived from this model have been key

for obtaining the final architecture of the antenna andmotivates the use of doubleridge

rectangular waveguides in the subapertures. They allow affordable distance between

lines without excessive dispersion, being a good tradeoff.

The aforementioned design considerations and guidelines were, therefore, used to

design a fullmultilayer structure, which demonstrates the feasibility of this technology

to integrate amplifierswithin a fullymetallic Luneburg lens antenna. First, a transition

from double ridge rectangular waveguide to microstrip line, where the amplifiers can

be mounted, was designed with full wave simulation. This transition showed good

50

CHAPTER 4. CONCLUSIONS AND FUTUREWORK

performance in terms of reflection coefficient, with values below −20 dB between 27

and 39 GHz. Finally, a full multilayer structure was designed, having the transitions

and nine feeding ports inside. The final structure shows a S11 below−7 dB in the entire

Kaband between 26 and 40 GHz, and below −10 dB for most of the frequencies apart

froma fewpeaks. The directivity and SLLdepend on the frequency, but they are similar

to those expected from a Luneburg lens of the same size.

This work is intended to be a proof of concept and the design presented does not

have stipulated specifications to fulfill. The main goal of this project is to show

the feasibility of the proposed method to integrate amplifiers. For this reason, the

flare, the linear tapers and the transitions from the lens aperture to the double ridge

rectangular waveguides are not optimized. However, if this structure were used in

a communication system with given specifications, it could be optimized to fulfill

the requirements (increasing the lens size to improve directivity, optimize tapers

and transitions to improve S11...), while keeping the basic design principles stated

here.

This work is the beginning of a research line that will continue, and hence there ismuch

future work that can continue the contributions started here:

• Replace the ideal Luneburg lens by a geodesic Luneburg lens.

• Optimization of linear tapers, flare and the aperture discretization transitions to

waveguide.

• Analyze gap and misalignments that may arise during the assembling of

the transition designed. Improve the robustness of the transition against

misalignments.

• Find a physical MMIC model to include the amplifier in full wave simulation.

• Manufacture prototypes to verify the results obtained in full wave simulation.

• Analyze and design a similar structure working at higher frequencies (V band).

51

Bibliography

[1] ITUR. IMT Vision Framework and overall objectives of the future

development of IMT for 2020 and beyond. Tech. rep. International

Telecommunication Union, Sept. 2015.

[2] Su, Y., Liu, Y., Zhou, Y., Yuan, J., Cao, H., and Shi, J. “Broadband LEO Satellite

Communications: Architectures and Key Technologies”. In: IEEE Wireless

Communications 26.2 (2019), pp. 55–61. DOI: 10.1109/MWC.2019.1800299.

[3] Liao, Q., Fonseca, N. J. G., and QuevedoTeruel, O. “Compact Multibeam Fully

Metallic Geodesic Luneburg Lens Antenna Based on NonEuclidean

Transformation Optics”. In: IEEE Transactions on Antennas and Propagation

66.12 (2018), pp. 7383–7388. DOI: 10.1109/TAP.2018.2872766.

[4] Fonseca, Nelson J. G., Liao, Qingbi, and QuevedoTeruel, Oscar. “Equivalent

Planar Lens RayTracing Model to Design Modulated Geodesic Lenses Using

NonEuclidean Transformation Optics”. In: IEEE Transactions on Antennas

and Propagation 68.5 (2020), pp. 3410–3422. DOI:

10.1109/TAP.2020.2963948.

[5] Petek, M., Zetterstrom, O., Pucci, E., Fonseca, N. J. G., and QuevedoTeruel, O.

“FullyMetallic RinehartLuneburg Lens at 60 GHz”. In: 2020 14th European

Conference on Antennas and Propagation (EuCAP). 2020, pp. 1–5. DOI:

10.23919/EuCAP48036.2020.9135587.

[6] Lianming, Li, Jiachen, Si, and Linhui, Chen. “Design of Power Amplifier for

mmWave 5G and Beyond”. In: IEEE Transactions on Antennas and

Propagation 36.4 (2019), pp. 579–588. DOI:

10.16356/j.1005-1120.2019.04.004.

52

https://doi.org/10.1109/MWC.2019.1800299

https://doi.org/10.1109/TAP.2018.2872766

https://doi.org/10.1109/TAP.2020.2963948

https://doi.org/10.23919/EuCAP48036.2020.9135587

https://doi.org/10.16356/j.1005-1120.2019.04.004

BIBLIOGRAPHY

[7] Roev, A., Taghikhani, P., Maaskant, R., Fager, C., and Ivashina, M. V. “A

Wideband and LowLoss Spatial Power Combining Module for mmWave

HighPower Amplifiers”. In: IEEE Access 8 (2020), pp. 194858–194867. DOI:

10.1109/ACCESS.2020.3033623.

[8] Kang, Y., Jin Pin, X., and Zheng Hua, C. “A full Kaband waveguidebased

spatial powercombining amplifier using eplane antiphase probes”. In: 2014

IEEE International Wireless Symposium (IWS 2014). 2014, pp. 1–4. DOI:

10.1109/IEEE-IWS.2014.6864257.

[9] Peeler, G. and Coleman, H. “Microwave steppedindex luneberg lenses”. In:

IRE Transactions on Antennas and Propagation 6.2 (1958), pp. 202–207.

DOI: 10.1109/TAP.1958.1144575.

[10] Dockrey, J. A., Lockyear, M. J., Berry, S. J., Horsley, S. A. R., Sambles, J. R.,

and Hibbins, A. P. “Thin metamaterial Luneburg lens for surface waves”. In:

Phys. Rev. B 87 (12 Mar. 2013), p. 125137. DOI: 10.1103/PhysRevB.87.125137.

URL: https://link.aps.org/doi/10.1103/PhysRevB.87.125137.

[11] Pfeiffer, C. and Grbic, A. “A Printed, Broadband Luneburg Lens Antenna”. In:

IEEE Transactions on Antennas and Propagation 58.9 (2010),

pp. 3055–3059. DOI: 10.1109/TAP.2010.2052582.

[12] Manholm, L., Brazalez, A. A., Johansson, M., Miao, J., and QuevedoTeruel, O.

“A twodimensional all metal luneburg lens using glidesymmetric holey

metasurface”. In: 12th European Conference on Antennas and Propagation

(EuCAP 2018). 2018, pp. 1–3. DOI: 10.1049/cp.2018.0795.

[13] Rinehart, R. F. “A Family of Designs for Rapid Scanning Radar Antennas”. In:

Proceedings of the IRE 40.6 (1952), pp. 686–688. DOI:

10.1109/JRPROC.1952.274061.

[14] Fonseca, Nelson J.G., Liao, Qingbi, and QuevedoTeruel, Oscar. “Compact

parallelplate waveguide halfLuneburg geodesic lens in the Kaband”. In: IET

Microwaves, Antennas & Propagation 15.2 (2021), pp. 123–130. DOI:

https://doi.org/10.1049/mia2.12028. URL: https:

//ietresearch.onlinelibrary.wiley.com/doi/abs/10.1049/mia2.12028.

[15] York, R. A. “Some considerations for optimal efficiency and low noise in large

power combiners”. In: IEEE Transactions on Microwave Theory and

Techniques 49.8 (2001), pp. 1477–1482. DOI: 10.1109/22.939929.

53

https://doi.org/10.1109/ACCESS.2020.3033623

https://doi.org/10.1109/IEEE-IWS.2014.6864257

https://doi.org/10.1109/TAP.1958.1144575

https://doi.org/10.1103/PhysRevB.87.125137

https://link.aps.org/doi/10.1103/PhysRevB.87.125137

https://doi.org/10.1109/TAP.2010.2052582

https://doi.org/10.1049/cp.2018.0795

https://doi.org/10.1109/JRPROC.1952.274061

https://doi.org/https://doi.org/10.1049/mia2.12028

https://ietresearch.onlinelibrary.wiley.com/doi/abs/10.1049/mia2.12028

https://ietresearch.onlinelibrary.wiley.com/doi/abs/10.1049/mia2.12028

https://doi.org/10.1109/22.939929

BIBLIOGRAPHY

[16] Chou, H. T., Chang, S. C., and Huang, H. J. “Multibeam Radiations From

Circular Periodic Array of Vivaldi Antennas Excited by an Integrated 2D

Luneburg Lens Beamforming Network”. In: IEEE Antennas and Wireless

Propagation Letters 19.9 (2020), pp. 1486–1490. DOI:

10.1109/LAWP.2020.3006561.

[17] Balanis, Constantine A. Antenna theory: analysis and design. John wiley &

sons, 2016.

[18] “Circular Array Theory”. In: Conformal Array Antenna Theory and Design.

John Wiley Sons, Ltd, 2006. Chap. 2, pp. 15–47. ISBN: 9780471780120. DOI:

https://doi.org/10.1002/047178012X.ch2.

[19] “Conformal Array Pattern Synthesis”. In: Conformal Array Antenna Theory

and Design. John Wiley Sons, Ltd. Chap. 10, pp. 395–420. ISBN:

9780471780120. DOI: https://doi.org/10.1002/047178012X.ch10.

[20] Gomanne, S., Fonseca, N. J. G., Jankovic, P., Galdeano, J., Toso, G., and

Angeletti, P. “Rotman Lenses with Ridged Waveguides in QBand”. In: 2020

14th European Conference on Antennas and Propagation (EuCAP). 2020,

pp. 1–5. DOI: 10.23919/EuCAP48036.2020.9135218.

[21] Gomanne, Sophie, Fonseca, Nelson, Jankovic, Petar, Toso, Giovanni, and

Angeletti, Piero. “Comparative Study of Waveguide Rotman Lens Designs for

Q/V Band Applications”. In: Oct. 2019.

[22] Molaei, B. and Khaleghi, A. “A Novel Wideband Microstrip Line to Ridge Gap

Waveguide Transition Using Defected Ground Slot”. In: IEEE Microwave and

Wireless Components Letters 25.2 (2015), pp. 91–93. DOI:

10.1109/LMWC.2014.2382658.

[23] Huang, X. and Wu, K. “A Broadband USlot Coupled MicrostriptoWaveguide

Transition”. In: IEEE Transactions on Microwave Theory and Techniques

60.5 (2012), pp. 1210–1217. DOI: 10.1109/TMTT.2012.2187677.

[24] Yang, L., Zhu, L., Choi, W., and Tam, K. “Wideband vertical

microstriptomicrostrip transition designed with crosscoupled

microstrip/slotline resonators”. In: 2015 AsiaPacific Microwave Conference

(APMC). Vol. 2. 2015, pp. 1–3. DOI: 10.1109/APMC.2015.7413129.

54

https://doi.org/10.1109/LAWP.2020.3006561

https://doi.org/https://doi.org/10.1002/047178012X.ch2

https://doi.org/https://doi.org/10.1002/047178012X.ch10

https://doi.org/10.23919/EuCAP48036.2020.9135218

https://doi.org/10.1109/LMWC.2014.2382658

https://doi.org/10.1109/TMTT.2012.2187677

https://doi.org/10.1109/APMC.2015.7413129

BIBLIOGRAPHY

[25] Anand, G., Lahiri, R., and Sadhu, R. “Wide band microstrip to microstrip

vertical coaxial transition for radar EW applications”. In: 2016 AsiaPacific

Microwave Conference (APMC). 2016, pp. 1–4. DOI:

10.1109/APMC.2016.7931432.

[26] Huang, X. and Wu, K. “A Broadband and Vialess Vertical

MicrostriptoMicrostrip Transition”. In: IEEE Transactions on Microwave

Theory and Techniques 60.4 (2012), pp. 938–944. DOI:

10.1109/TMTT.2012.2185945.

[27] Kumar, G. A. and Poddar, D. R. “Broadband Rectangular Waveguide to

Suspended Stripline Transition Using Dendritic Structure”. In: IEEE

Microwave and Wireless Components Letters 26.11 (2016), pp. 900–902.

DOI: 10.1109/LMWC.2016.2615009.

[28] Głogowski, R., Zürcher, J., Peixeiro, C., and Mosig, J. R. “KaBand Rectangular

Waveguide to Suspended Stripline Transition”. In: IEEE Microwave and

Wireless Components Letters 23.11 (2013), pp. 575–577. DOI:

10.1109/LMWC.2013.2281408.

[29] Wei Tang and Xiao Bo Yang. “Design of Kaband probe transitions”. In: 2011

International Conference on Applied Superconductivity and Electromagnetic

Devices. 2011, pp. 25–28. DOI: 10.1109/ASEMD.2011.6145059.

[30] MontejoGarai, J. R., Marzall, L., and Popović, Z. “Octave Bandwidth

HighPerformance MicrostriptoDoubleRidgeWaveguide Transition”. In:

IEEE Microwave and Wireless Components Letters 30.7 (2020),

pp. 637–640. DOI: 10.1109/LMWC.2020.3000283.

[31] Pozar, D.M.Microwave Engineering, 4th Edition. Wiley, 2011. ISBN:

9781118213636. URL: https://books.google.es/books?id=JegbAAAAQBAJ.

55

https://doi.org/10.1109/APMC.2016.7931432

https://doi.org/10.1109/TMTT.2012.2185945



https://doi.org/10.1109/ASEMD.2011.6145059


https://books.google.es/books?id=JegbAAAAQBAJ

Appendix A

Analysis of Social, Economic,Environmental and EthicalImplications

This appendix contains a reflection about how the work developed in this thesis might

affect the society and the environment. The work carried out is within the beginning

of a research project, aimed at proofing a concept which can be useful in the industry

to be applied in future communication systems. For this reason, only potential uses

are known and the specific systems where it will be used are still not perfectly clear, so

quantifying the impacts of this project in the society is not an easy task. The analysis

will be done considering possible scenarios where this work may be included, as well

as the research process.

A.1 Social Implications

The project presented in this thesis is the beginning of a research line aimed to enhance

civil telecommunications. Each new mobile generation have had great influence in

people life, contributing more and more to a digital transformation in many aspects

of the society. The new fifth generation, also known as 5G, will play a key role in

changing the way of doing many daily and professional activities nowadays. Some

ideas like driverless cars can become reality due to 5G, and this concept, for example,

will completely change the driving paradigmwhen becoming a reality. There aremany

56

APPENDIX A. ANALYSIS OF SOCIAL, ECONOMIC, ENVIRONMENTAL AND ETHICALIMPLICATIONS

other use cases of 5G that impact straightly to the society, affecting healthcare (remote

surgering) and our hobbies (streaming of high quality video in real time) among others.

The concept of integrating amplifiers and its advantages proposed in this project can

not only be applied to mobile communications, but also to other areas like satellite

megaconstellations and radar systems. These megaconstellations also affect society,

as they are aimed to get global coverage allowing connectivity even in themore isolated

and rural areas. Therefore, even though the isolated idea of amplifier integration

does not affect directly to the society, the system where the concept is applied clearly

does.

A.2 Economic implications

One of the benefits of using distributed amplifiers is the cost reduction it implies.

Having numerous small integrated amplifiers is cheaper than having only a few

powerful amplifiers, because the price of a single amplifier is highly reduced. This

fact becomesmore important at higher frequencies, where powerful amplifiers become

harder to design and more expensive. In that case, power combining becomes a good

and cheaper alternative.

The project covered in the thesis is aimed to be a proof of concept in Kaband, but the

same concept is intended to be also applied at higher frequencies in the future, such as

Vband or Eband.

A.3 Enviromental implications

Themain environmental effects of the structure proposed in this project arise from the

manufacturing process. The final structure is fullymetallic, meaning that metal slabs

have to be drilled to obtain the designed geometry, producing waste coming from the

disposal of those drilled parts. Hopefully, mostmetals used tomanufacturemicrowave

devices and antennas, can be recycled and hence reused.

The system proposed has indirect influence in the environment through the

applications where is used. The fifth generation of mobile communications will turn

the society into a more connected one, including not only people using the technology

but also sensor networks. This enhancement in use and capability of these new

57

APPENDIX A. ANALYSIS OF SOCIAL, ECONOMIC, ENVIRONMENTAL AND ETHICALIMPLICATIONS

technologies implies an increase in the energy consumption. In addition to mobile

communications, this work can be used in satellite communication systems, where the

emerging megaconstellations could have a negative impact to the environment as a

result of the space trash produced at the end of satellites life.

A.4 Ethical implications

The main ethical impact the system may have is related to unethical nonintended

uses (e.g. military uses) or ethical issues in the applications where it might be

included.

As the work presented here contains only a part and not a whole communication

system, it could be misused and included in military, illegal or unethical systems.

Nevertheless, this particular work is intended to be used only in civil systems,

contributing the society to improve our lives quality and promoting technological

development.

58

Appendix B

Cost and price of the project

In this annex the total cost of this project is estimated, considering the human

resources, material and objects needed, licenses of simulation softwares and further

indirect costs.

The human resources involved in this project are a Master Electrical Engineer and

a Senior Electrical Engineer to supervise the project. A typical monthly salary of

an electrical engineer with less than 5 years of experience in Sweden is 32800 SEK,

which corresponds approximately to 3280 €. The salary of a person having between

5 and 10 years of experience amounts to 43300 SEK (close to 4330 €). Assuming

the typical workload of 40 hours per week and 4.5 weeks per month, the price of

one hour of work is around 18 €/hour for the Master Electrical Engineer and 24

€/hour for the supervisor. A master thesis requires 900 hours for a student, and

around 150 hours for the supervisor, considering that the supervisor is working in

another tasks simultaneously. Therefore, the human costs associated to the project

are 24 · 150 + 18 · 900 = 19800 €.

The main physical resource needed for this project was a desktop computer with the

following specifications summarized in Table B.1.

With the prices of Table B.1, and adding a 50% to account for the other components

and extras (monitor, operative system, case, etc.) and the benefit for the seller, the

cost of the desktop computer is estimated to be around 1530€. This computer has been

utilized for 6months, so assuming and amortization time of 7 years, the cost associated

to the computer in this project is 109.28 €.

59

APPENDIX B. COST AND PRICE OF THE PROJECT

Component Model Approx. Price

CPU Intel Core i77700 3.60GHz 450 €SSD ADATA SSD DM900 1 TB. 150 €RAM 64 GB DDR4 2400 MHz 320 €GPU AMD Radeon R5430 100 €

Table B.1: Main components price desktop computer

The essential software used here have been MATLAB and CST Microwave Studio. An

annual license of MATLAB costs 800 €, and the CST cost for one year can be estimated

around 2000 €. As the project lasts 6 months, and assuming both software used only

for this project, the overall cost coming from licenses is 1400 €.

Apart from the previous costs, there are indirect costs arising fromnondirect expenses

such as light, water, paper, printers usage, meeting rooms usage, internet, etc. The

indirect costs are estimated as a 15% of the direct costs presented before, since

the exact cost cannot be known. Thus, the indirect costs can be estimated to be

(19800 + 109.28 + 1400) · 0.15 = 3196.40 €.

Finally, the industrial profit after selling the solution is set to 6%, resulting in a profit

of (19800 + 109.28 + 1400 + 3196.40) · 0.06 = 1470.30 €.

The work carried out in this thesis is within a research project, so the product to be

sold can be the outcome of the research and/or amanufactured prototype. Therefore, if

selling the results, the Value Added Taxes (VAT) has to be added to the aforementioned

costs and profit. As the project has been developed in Sweden, where VAT is 25% of

the final price. The VAT is (19800 + 109.28 + 1400 + 3196.40 + 1470.30) · 0.25 = 6494

€.

The final budget of the overall project is summarized in Table B.2.

60

APPENDIX B. COST AND PRICE OF THE PROJECT

Cost Object Price (€)

Human Resources 19800 €Material Resources 109.28 €Licenses 1400 €Indirect Costs (15 %) 3196.40 €Industrial Profit (6 %) 1470.30 €

Price without VAT 25975.98 €

VAT 6494 €

Total price 32469.98 €

Table B.2: Total project budget

61

TRITA-EECS-EX-2021:391

www.kth.se

Activeintegrated aperture lens antenna - DiVA portal

Documents

Transcript of Activeintegrated aperture lens antenna - DiVA portal