Antenna Design for iRoad Markers using PEEC Modelling

Antenna Design for iRoad Markers using PEEC Modelling

Juventino de Castro Javier Martínez

Master of Science

Computer Science and Engineering

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

using PEEC modelling

Juventino de Castro Gonz´ alez Javier Mart´ınez Campos

Dept. of Computer Science and Electrical Engineering Lule˚ a University of Technology

Lule˚ a, Sweden

September 24, 2011

Supervisors:

Prof. Jerker Delsign

Ph.D. Tore Lindgren

With the enormous popularity of the road transport nowadays both of passengers and goods, and with the previsions of a continuous growing in the future the industry and the public institutions are making a considerable effort to apply the last technologies within the IT field to improve its performance and safety and reduce the ecological footprint to minimums. These ambitious aims require both to increase the technological level of the vehicles, which has evolved considerably in the last years, and to introduce the new technologies in the vial infrastructures, point which is still commercially pendant in despite of all the research projects that are being conducted worldwide.

One of these projects, named iRoad, is being conducted by a Swedish consortium of companies and universities and consists in the implementation of the distributed sensor network technology to the roads in order to collect traffic data allowing to implement later several functionalities related with the performance and safety of the transportation system. This sensor-actuator distributed network would use, regarding the inner inter- communication system, one of the many wireless radio technologies in UHF frequency band. Since in the original design of the sensor network the nodes are placed in low profile patches directly above the road shoulders surface, the object of this thesis is to determinate how the classic low profile antenna designs would perform, considering the particularities of this network configuration, and specially, the presence of an interface between two mediums so electromagnetically different such as the air and the real ground.

To approach this scenario first the problem has been modelled and simulated by using the Partial Elements Equivalent Circuit numeric technique. The post-processing of the data extracted allows to obtain some preliminary results which are valuable to orient properly the second stage, which consists in the milling of some prototypes which illustrate the issue and their measuring and evaluation in near operating conditions.

From this analysis process the results extracted according to the thesis aims are an overview of the performance of each simple antenna design both in terms of spatial per- formance and electrical performance and also a comparison between the different antenna designs based on the results of the simulations conducted using the PEEC method, which have shown the dipole as the design with best performance under the considered condi- tions.

iii

Σ ~ F = m~a

v

We want in this lines to thank all the people that have participated with their effort and dedication in this thesis. To our supervisors, Jerker Delsing and Tore Lindgren, for the time they have dedicated guiding us and their valuable advices, to Danesh Daroui for the support he gave us in the use of the multiPEEC tool, to Andreas Nilsson for providing and managing the technical mediums for this project, to Johan Bjorg for his help with the use of the EMCLab and its equipment, to Mikael Larsmark for building the prototypes used in this work and in general to all the EISLAB department for providing the resources that allowed us to carry out our work.

vii

1 Introduction 1

1.1 Background . . . . 3

1.2 Motivation . . . . 5

1.3 Thesis aims . . . . 5

2 Problem approach 7 2.1 Introduction . . . . 9

2.2 System description . . . . 9

2.3 Problem definition . . . . 11

2.4 Model characterization . . . . 16

2.4.1 EM simulation . . . . 16

2.4.2 Modelling of antennas and their iRoad environment . . . . 21

3 Antenna design and simulation 25 3.1 Introduction . . . . 27

3.2 Linear elements . . . . 28

3.2.1 Horizontal electric dipole . . . . 29

3.2.2 Horizontal electric monopole . . . . 38

3.3 Patches . . . . 45

3.3.1 Rectangular Patch . . . . 45

3.3.2 Trimmed corner patch . . . . 52

ix

3.4.1 Dipole with parasitic director elements . . . . 57

3.5 EBG planes . . . . 62

3.6 Simulation results . . . . 63

4 Antenna construction and measurement 65 4.1 Introduction . . . . 67

4.2 Manufacturing process . . . . 67

4.3 Measurement process . . . . 68

4.4 Printed dipole for 2.4GHz . . . . 71

4.5 Microstrip rectangular patch for 2.4GHz . . . . 76

4.6 EBG planes . . . . 80

4.7 Error Analysis . . . . 82

5 Conclusions 87

A Working methodology and organization 91

References 95

x

Introduction

1

1.1 Background

According to the last annual statistics report corresponding to the year 2010[1] published by the European Union Road Federation, the transport of passengers by motor vehicles has increased by 20.2% and the transport of goods by 45.7% in the 1995-2008 period within the 27-European Union. With the popularization of the road transportation, the expansion and improvement of the road networks and the continuous increment of the vehicles fleet, the modelling and monitoring of the traffic in a large scale has become a top priority for the responsible institutions.

There are many considerations which make the existence and availability of a traffic monitoring network nowadays almost indispensable, being some of them:

• Safety is a mandatory consideration in all the improvements related to the road transportation since it is the first non-natural cause of death in the industrialized countries. The implementation of an advanced monitoring system would, for in- stance, change dynamically the road signalling or even notify the actors in case of danger.

• Operational costs of the road transport systems are high and the expected be- haviour is a continuous growth due to the increasing demand and the limited offer.

(E.g. crude oil reference price at 2-5-2011: 112USD; Differential 2008-2011: approx.

+50%). A real time monitoring system could help to optimize the traffic distribution on-the-fly causing a better global performance of the whole transport system.

• The environmental protection is a worldwide spread value and serious efforts and compromises have been made by the governments of the industrialized countries in order to fight the climatic change. The same optimal traffic organization that had economical benefits would help to reduce significantly the noxious emissions that cause this problem.

For decades several ways of implementation have been used for the road traffic mon- itoring systems, some of them are indeed largely implanted these days, from cameras placed in the most interesting and busy points of the road network, to the installation of buried inductive loops or optical sensors. However all of these techniques share at least one common aspect, they are fundamentally punctual and heavily focused. In opposition to the previously introduced paradigm, other models can be and have been proposed with maybe better characteristics and performance.

Focusing in the European Union, the European Commission has renewed the com-

promise of the members with a new ambitious objective, to halve the number of deaths

in the road by the year 2020. This commitment, which is a part of the European Road

Safety Policy Orientations 2011-2020, comes together whit a large set of directives and

recommendations, being one of them the development and deployment of an Intelligent

Transport Systems (ITS), which will be regulated by a new legal framework adopted on

July 7, 2010. This directive tries to guarantee the interoperability between the systems of each one of the member countries and guide the main aims, being the traffic information acquisition and availability one of its priorities .

Most of the safety oriented research projects in the industry of transportation go in this direction and try to exploit infrastructure-vehicle (I2V) and vehicle-vehicle (V2V) wire- less communications. Some examples in Europe are the SAFESPOT Integrated Project [3] or the CVIS (Cooperative Vehicle - Infrastructure Systems) both ran by a consortium of companies operating in very different sectors, research centres, universities and govern- mental and public institutions. In this case, both of them have proposed a very similar approach to the road safety problem, describing a scenario full of both fixed and vehicle integrated sensing platforms with a very strong communication between them by using the IEEE 802.11p standard. This standard is a modification for moving vehicles of the widely adopted wireless local area network protocol IEEE 802.11.

In Sweden, with a vehicle fleet of approximate 5.2 million (2009) and a road network of more than 400 thousand kilometres (2007), the iRoad research project was born as a common effort of the Lule˚ a University of Technology, Geveko ITS A/S, Swedish Road Administration (Trafikverket) and Embedded Internet System technology Botnia AB to provide the technological basis for future intelligent roads.

The solution proposed by Wolfgang Birk, Evgeny Osipov and Jens Eliasson[2] in 2009, the iRoad CRIS, consists in a cooperative wireless sensor actuator network (WSAN) con- formed by several units placed along the road shoulder in both directions. Each road marker unit (RMU) is composed by a power supply (batteries and photovoltaic cells) which guarantee the autonomous working but define a very strict compromise between performance and power consumption, a sensing system (magnetic sensors and accelerom- eters) that collects the raw data for feed a central processing unit, which at the same time manages the data acquisition and processing and the subsequent communication by using the IEEE 802.15.4 standard.

The computing capability of the RMUs and their ability to communicate via radio with each other makes them a very useful solution, not only for sensing and monitoring, but also for becoming an active part of a future road-vehicle intelligent and dynamic interaction. This system tries to take advantage of a distributed structure to reduce the infrastructure, maintenance and operation costs to minimums. While other proposals need auxiliary elements, this iRoad solution tries to be simple and places the RMUs directly over the road surface. This highly cooperative paradigm improves the robustness of the system but presents a high dependence on the communication system performance.

The iRoad system has already been deployed for testing in real and harsh operating

conditions along 5 kilometres in the Swedish E4 motorway near Pite˚ a, Norrboten (Sweden)

during the winter. In despite of the very severe climate conditions of the Swedish winter

the results were good, the resistance of some units have provided a very valuable feedback,

motivating the development and testing of new applications and features.

1.2 Motivation

The previously introduced iRoad system, based in a cooperative swarm of sensors dis- tributed along the road shoulders surface, presents some advantages that are not present in other proposed implementations. The reduced implantation and operation costs due to the simplicity of the required infrastructure, the possibility of complex features thanks to the simultaneous and continuous sensing and communication in both directions and the robustness and reliability of the distributed paradigms are, for example, some of them but with it also arise some technical challenges that have to be evaluated and solved.

These challenges are several and of very different nature. For instance from a pure mechanical point of view, the way the RMUs have to be built and fixed to the ground has to be carefully established in order to increase the operative life of the devices and avoid damages to the equipment and the vehicles. It remains also the always present, and widely discussed and studied in the electronics and computing market these days, compromise between the performance and the power requirements of the RMUs. Beside that one of the most interesting points pending of a deeper study is related with the inner communication performance of the system.

The design of the system with the sensing devices next to the road allows the using of relatively simple traffic detection methods but represents a huge handicap for the commu- nication structure planned from the beginning. The presence of the ground this near of the transceiver units cannot be ignored nor disregarded. Most of the systems already designed try to avoid this issue by using auxiliary elements like posts which move the transceivers away from the road surface at expenses of increasing the complexity and therefore the cost. A more concrete description of the problem will be given in the Chapter 2.

The popularization of the WPANs (Wireless Personal Area Networks) and WLANs (Wireless Local Area Networks) and the appliance of the wireless technology in more complex and dynamic scenarios makes recommendable to study deeply how the presence of the conductive ground or a comparable obstacle may affect the performance of the radio link and how that issue can be avoided.

On the other hand, the hard work carried out by the EISLAB to develop an electro- magnetic simulator based in the PEEC (Partial Elements Equivalent Circuits) approach to solve Maxwell’s equations (MultiPEEC) provides a very useful tool to model the problem and extract valuable data for later analysis.

1.3 Thesis aims

This thesis presents the results of a brief research on how the presence of the soil affects the

performance of the antennas for an UHF point to multipoint radio link in a non-free space

WPAN or WLAN scenario and what would be the most convenient hardware to build

it considering that effect. European license free ISM (Industrial, Scientific and Medical) bands of 860MHz and 2.4GHz will be considered in this study.

The thesis main investigations are:

• Find an for the iRoad location conditions suitable simple antenna design for the 860MHz and 2.4GHz ISM bands.

• Specifically address the influence of varying road and soil conditions to antenna performance.

The approach to the problem is mostly experimental with the modelling of several

antenna designs that fulfil the size requirements of the system and their simulation using

the fullwave PEEC methods to extract performance data and determine the suitability

of the solution for this concrete application. The analysis will be mainly focused in the

acquisition of the spatial performance of the antenna in terms of radiation patterns and

also the study of the electrical behaviour of the radiator highlighting its implication in the

whole system power efficiency. Real models were also built in order to measure them in

operating conditions and validate the results obtained with the previous simulations.

Problem approach

7

2.1 Introduction

The initial approach to a dynamic and distributed iRoad solution demands a high com- promise level in the communication capabilities design in order to guarantee the utility of the system, highly related with the data transmission. This requirement makes indispens- able a deep and careful study in all the layers involved in the communication processes, and particularly in the physical layer, absolute objective of the present thesis, where some particular issues affect the performance and reliability of the radio infrastructure. This chapter tries to be an overview about how the system is designed, introducing also the particular problems which condition the whole system feasibility as it was firstly designed, and a description on how several possible solutions will be evaluated in the next chapter.

The first point outlines a global description of the iRoad project. This description includes specific information about the objectives, system architecture, markers design and disposition, environmental surrounding and real-life working operation, and a brief approach to the analysis procedures (without too much depth since the design of the system is already settled in [2], and it is not the objective of this thesis work).

Immediately after, the problem the proposed solution has and this thesis tries to deal with is introduced to the reader. And finally, the procedure lines for the analysis and validation of the possible solutions are discussed.

2.2 System description

The iRoad system in development, among others, by the Lule˚ a University of Technology consists in the design and implementation of an intelligent and cooperative road infras- tructure (CRIS). The objective of the project is to set the technological basis for future intelligent road traffic, combining sensing capabilities with on-the-fly computing and com- munication. Thanks to that, it will be possible to provide many services both to the road users, as warnings or traffic information, and to the road and traffic management insti- tutions, allowing them, for instance, to obtain live traffic data which could be used for behaviour modelling and prediction. This ambitious project started few years ago with the design of the hardware and infrastructure, and with some low functionality testing in order to validate the first designs.

The most of the functionality of the whole system falls, due to it distributed character, on a small piece of hardware called Road Marker Unit (RMU) (see Figure 2.1) which is placed along the road shoulders in both directions, as it is shown in Figure 2.2. Each device has a size, after enclosure, of just 100mm wide, 140mm long and 7mm high.

One RMU operates as a single node inside the wireless sensor-actuator network (WSAN)

that defines the system, where each element computes and shares its measured information

concerning to the traffic on the road. The network disposition derived from the spatial

markers positioning can be understood as a string, where two parallels elements rows (one

Figure 2.1: Road Marker Unit

per road direction) form the network topology. In the first development stages accom- plished by the consortium, the RMUs were able to, using the LEDs array integrated in their structure, improve the visibility in adverse weather and lightning conditions and also to measure and transmit several parameters related with the condition of the infrastructure such as temperature and with the traffic.

Figure 2.2: RMUs positioning on the road surface

The proposed RMU core is Mulle, a miniature embedded system with wireless commu- nication capabilities manufactured by EISTEC AB[3] and designed for serving as node for a networked wireless sensor platform. This system is composed, in the hardware aspect, by a Renesas M16C/62P microcontroller working up to 24MHz, a wireless communica- tion module based on the Atmel RF230 transceiver unit which uses the IEEE 802.15.4 standard implementing the ZigBee protocols (either on 2.4GHz or 868MHz depending on the version of the device), a 2 Megabytes flash memory for data storage, a temperature sensor, and several I/O lines. The RMU also contains two Lithium-polymer rechargeable batteries with a capacity of 750mAh each one complemented by a flexible solar cell as power supply, magnetic sensors and accelerometers for register the vehicles circulation, and LEDs arrays for lightning. The software that manages the device provides support for a wide range of the most common communication protocols by using the lwIP stack, a light implementation of the TCP/IP protocol for low performance devices. The code is open source allowing its modification in order to add new features and functionalities with complete control of the process, avoiding burdening the global performance in terms, for instance, of energy consumption or communication delay.

Going back to a higher level and focusing in the network infrastructure design the system can be considered as composed by three wireless links (see Figure 2.3).

The first one, and the main object of study in this thesis, is the communication be-

tween the RMUs. They have the ability to share data between them by using the ZigBee

Figure 2.3: iRoad network architecture

protocol and this is done by setting an ad hoc structured network, where all the markers are at the same time sources and consumers of data, and intermediate in its transmission.

The flexibility of this network is very interesting, allowing the development of complex features which combine data from different locations and directions of the road, and the improvement of the system robustness by providing alternative data routing. It is im- portant to notice that the concrete layout of the RMUs placement depends strongly on the radio coverage of the transceiver module in both directions, which at the same time depends on the terrain topology.

The second link is established between a WSN/3G gateway device, placed also near the road but with a bigger span than the markers, and some of the closest RMUs. Using this connection some of the data produced within the wireless sensor network would be routed out of the road. This link is also based in the IEEE 802.15.4 standard. The data that has to be routed out would flow through the RMU multi-hop network until it reaches the gateway RMU which would send it to the next gateway.

The last one is the link between the WSN/3G gateway and the network of a 3G operator. The data produced by several iRoad sections would be transmitted then from the WSN/3G gateway to one of the mobile phone operators BTS (Base Transceiver Station) and then routed to its destination.

2.3 Problem definition

Focusing in the first wireless link mentioned in epigraph 2.2, behind the peer to peer communication between two contiguous or non contiguous RMUs underlie some technical issues that cannot be ignored in order to keep the balance in the desired trade-off between power consumption and communication performance.

As it has been explained in the previous points, the wireless sensor network intelligent

nodes (RMUs) would be concretely placed along the road shoulders surface, just over the

asphalt, forming two strings parallel to the marking lanes (see Figure 2.2). Due to it very

reduced dimensions this design means the transceiver units will be working close to the

ground surface. Commonly the first approach to an UHF radio link analysis is to consider

a free space propagation scenario where the characteristics of the elements involved are not influenced by the environment and then add step by step different irregularities such as ground reflection enhancement or fading, geo-climatic conditions, etc. that polish the initial model. But in the operating conditions the RMU transceiver has to work more aspects must be considered.

Since the transceiver operates in the 868MHz or in 2.4GHz license-free ISM band of the EM spectrum the wavelengths in the free space would be:

λ

≈0.35m λ

= 0.125m (2.1)

At these frequencies the antenna electrical heights above the ground which due to size limitations of the marker has to be less than 7mm, are approximately of λ/50 and λ/18 respectively. With those results at sight the antenna cannot be considered any more as isolated and with ideal characteristics but as a complex system conformed by the antenna itself and the ground surface which modifies strongly the electrical and electromagnetic characteristics of the antenna located in the free space. The presence of the ground which acts as a mirror, with characteristics that will be discussed in 2.4, for the charges distribution introduces a reflected version of the radiated beam which interferes with the one that comes directly from the source modifying significantly the original radiation properties.

To analyse the reflection problem that radiating systems suffer when they are placed near a conductive plane, an equivalent problem can be proposed. Since the field in any point of the ‘far-field’ zone can be considered the summation of the direct and ground reflected radiation, the ground plane can be substituted by another radiating element placed symmetrically under it provided that the boundary conditions set by the PEC plane still being fulfilled, this is that the tangential electrical field component has to be zero on the surface and so the perpendicular magnetic field component. To satisfy those conditions the image should be inverted depending on the polarization of the source as it is shown in Figure 2.4.

Figure 2.4: Equivalent images for EM sources near a PEC.[4]

The combined field of both, real and image, sources could be written as the field of an

isolated radiating element placed in the origin weighted by a scalar value dependent of h

and θ known as array factor which modify strongly its radiation pattern.

Focusing now on the circuital model of the transceiver-antenna system, other of the basic parameters of the antenna that is also influenced by the ground reflection is the input impedance due to the mutual couplings. An isolated antenna does not receive any outer influence but when there is present more than one radiating element the whole system behaves as a linear multiport network, in which the voltages and currents of every element are the summation of a self component and an outer component produced by the excitation of the other elements that conform the scenario. In the particular case of a single antenna above a conductor plane the equivalent scenario is an array composed by two antennas. In that scenario the voltages and currents on the real antenna would be influenced by the image through the crossed coupling parameter z

which depends both on the distance between elements and their orientation.

Figure 2.5: Horizontal dipole over a PEC and its image.

V

V



= z

z

z

z

 I

I



(2.2)

I

= −I

(2.3)

Z

= V

I

= z

I

+ z

I

I

→Z

= z

− z

(2.4)

The analysis presented in the equations 2.2, 2.3 and 2.4 is simple while considering basic radiating elements like a horizontal linear element (see Figure 2.5) but it becomes less evident with more complex antenna configuration[5]. The input impedance parameter Z

and more concretely its relation with the impedances of the feeding circuit will determinate the power acceptance of the antenna and since it is highly frequency-varying, it resonance frequency and usable bandwidth. This entire means that the presence of a conductive plane in the proximities of an antenna affects not only the spatial radiation parameters but also it frequency behaviour obeying to modify it “free-space” design to fulfil the requirements of the application.

Other aspect to keep in mind is how the size limitations set by the existence of a

previous physical design affects the radiocommunications system performance and the

antenna layout. Firstly the height of the RMU, as it is described in Section 2.2, is limited

to 7mm which eliminates any possible solution based on volumetrical elements and force

the use of very low profile planar designs. Because of that, this thesis will focus on the analysis of antenna designs suitable for being printed over a dielectric substrate. The second aspect related to the size of the RMU that condition the design of the antenna is that since the planar dimensions are 100mm wide and 140mm long, the maximum length of the antenna in any direction represents, compared with the wavelength at the two frequencies of interest, an electrical length of:

l

≈ {0.14×0.1}

0.35 ≈ {0.4×0.3}λ (2.5)

l

≈ {0.14×0.1}

0.125 ≈ {1.1×0.8}λ (2.6)

At those frequencies the behaviour of the model can be considered almost the same, as it will be explained in Section 2.4, but the since the available electrical length for the antenna is different is expected to have different performance in each bands. In particular theory prove that the electrically bigger an antenna is more complex the radiation pattern can be designed in the sense that can be more directive and with more flexibility in it orientation. Considering that the better results, according to the theory, can be achieved in the 2.4GHz band is there where this thesis will go deeper proposing also some solutions for the lower frequency band.

Once the problems that the possible solutions have to face have been outlined let us introduce some design characteristics of the application which are related with the validity of the solutions. In the Section 2.2 was described how the RMUs are placed along the road but without specify all the implications this layout has. Since the markers form a string in both side of the road and they should communicate with the other units placed in the same chain in both directions, it would be desirable that the designed antenna has two maximums of radiation in the azimuthal plane separated angularly 180

and with an elevation close to 0

. If that were possible according to the issues the presence of the ground plane involve it would be an appropriate solution for the vertically and horizontally straight sections of the road but other factors are included when dealing with curve sections.

For simplify the analysis and because it is the most common case in the high speed roads let us consider all the curves sections as simple circular curves (SCC), this means they join two straight sections by a circular arc. Then two RMUs placer in a curve like this can be described as it is shown in Figure 2.6.

Assuming the antenna mounted in the marker units have their maximums of radiation in the line tangent to the curve at the placement point in both directions, then the angle (β) with which one antenna “see” the other one are determined by the following geometric equations [6].

CL = rcrd(α) = 2r sin

 α 2



(2.7)

Figure 2.6: Representation of two RMUs placed in a SCC.

E = T tan  α 4



= r

cos  α 2

 − 1 (2.8)

F = r cos

 α 2



(2.9)

L = 2πrα

360 → α = 360L

2πr (2.10)

tan β = E + F CL/2 =

r



 1 cos

 α 2

 − cos

 α 2





 r sin  α

2

 =

=

1 − cos

 α 2

 cos  α

2

 sin  α

2

 =

2sin

 α 2

 sin(α) =

=

2sin

 360L 4πr



sin

 360L 2πr

 →

→ β = arctan









2sin

 360L 4πr



sin

 360L 2πr











(2.11)

Where r is the radius of the curve and L the distance between markers following the

road path. This allows establishing a relationship between the chosen hop size and the

beamwidth of the mounted antennas by selecting a limit value for the curvature radius.

Using as example an 80kmph stretch, the minimum horizontal radius as stated by the UE- members design standards, vary between 230m and 280m[7]. The use for the calculation of the most limiting value, 230m and a distance between RMUs of 50m, for instance, would return, according to the equation 2.11, a minimum beamwidth of approximately 12

in the azimuthal plane.

120 Kmph (r=500m) 80 Kmph (r=230m) 60 Kmph (r=110m)

L (m) BW L (m) BW L (m) BW

10 2

10 3

10 6

25 3

25 7

25 14

50 6

50 13

50 27

100 12

100 25

100 53

200 23

200 50

200 105

Table 2.1: Some examples of minimum beamwidth (approx.) for different curve radius and dis- tances between RMUs

The case of a vertical curvature when it is concave it should not represent a problem greater than the propagation in flat surfaces due to it is expected ever better behaviour of the antennas for elevation angles greater than 0

than in the xy plane. However, in the case of convex curvatures, the line of sight could be lost if the hop size is large in comparison to the curvature causing an important fading effect which can even make impossible the communication.

2.4 Model characterization

As it was mentioned in the Chapter 1, the approach followed for trying to find a proper antenna design that cover all the requirements is not theoretical but it takes the theory as a basis for then model and simulate several possible solutions. The data extracted from the simulation allows dismiss the useless solutions and focus the analysis on the most promising ones to start the empirical testing in the lab. With this at sight is undeniable that the characteristics of the scenario modelling and the simulation procedure have a very important role in the validity of the first stage results.

2.4.1 EM simulation

The electromagnetic behaviour of a scenario is given by the solution of the well known

Maxwell’s equations. These are a set of four partial differential equations (2.12, 2.13,

2.14 and 2.15) that together form a system that describes how the electrical charges and

currents distribution, the media characteristics and the electrical and magnetic fields are related.

Differential formulation

∇ × ~ H = ~ J + ∂ ~ D

∂t

∇ × ~ E = − ∂ ~ B

∂t

∇ · ~ D = ρ

∇ · ~ B = 0

Integral formulation

I

L

H · ~ ~ dl = Z

S

( ~ J + ∂ ~ D

∂t ) · ~ dS (2.12)

I

L

E · ~ ~ dl = − Z

S

∂ ~ B

∂t · ~ dS (2.13)

Z

S

D · ~ ~ dS = Z

v

ρ

dv (2.14)

Z

S

B · ~ ~ dS = 0 (2.15)

To introduce the dependence of the solution with the material characteristics of the media more equations have to be considered (equations 2.16, 2.17, 2.18). These last three set of equations receive the name of EM constitutive relations.

D = ε ~ ~ E (2.16)

B = µ ~ ~ H (2.17)

J = σ ~ ~ E (2.18)

The analytical solution of the equations mentioned above would give an exact descrip- tion of how a system behaves in EM terms. However the attempt to solve a real scenario analytically requires the application of complex mathematics artefacts and usually reach- ing a solution it is not even possible for non-trivial problems. To deal with this limitation the numerical techniques for solving the system in practical scenarios is being widely used.

The numerical techniques are based on the appliance of several simplifications to concrete problems allowing the obtaining of approximate solutions within the limits of an accept- able margin of error. Other important aspect to keep in mind is that the possibility of solving complex electromagnetic problems by using a numerical approximation is closely related to the availability of computing resources since the calculations are both repetitive and heavy.

Several techniques for computational electromagnetic (CEM) have been developed that

serve better for one kind of problems than for others, each one with its own particularities,

being some of the most popular ones:

• Finite Elements Method (FEM)

• Finite Different Method (FDM)

• Method of Moments (MoM)

• Partial element equivalent circuit (PEEC)

As it can be seen in the Maxwell’s equations detailed in this section they can be written both in integral and differential form, and the formulation each method choose to solve makes an important difference in terms of suitability for a concrete scenario. In the case of the methods mentioned above, the first two uses the differential formulation and the last two the integral one. The main differences between these two groups of techniques are the structure discretization policy and the solved variables. While the differential methods require the whole structure to be discretized and computed, the integral ones only discretize and compute the material parts, which leads to a less computational cost.

On the other hand the integral method provides the solution in terms on circuital variables such as voltages and currents while the differential ones have directly the ~ E and ~ H fields as output variables.

All the antenna design performance simulations included in this thesis, will be done by using PEEC. This integral CEM method, as it was said, only requires material parts of the scenario to be considered and provides voltages and currents as solution which is indicated in this case since the most important points are to get both the free space electromagnetic behaviour and the circuital behaviour.

The theory basis of the method[8] start with an expression for the total electric field E ~

.

E ~

(~ r, t) = ~ E

(~ r, t) − ∂ ~ A(~ r, t)

∂t − ∇φ(~r, t) (2.19)

And from it derives the general electric field integral equation (EFIS).

ˆ

n × ~ E

(~ r, t) = ˆ n ×

" ~ J (~ r, t) σ

#

+ ˆ n ×

"

X

k=1

µ Z

vk

G(~ ~ r, ~ r0) ∂ ~ J (~ r0, t

)

∂t dv

#

+ ˆ n ×

"

X

k=1

∇ ε

Z

vk

G(~ ~ r, ~ r0)q(~ r0, t

)dv

#

(2.20)

From that last equation and dividing the current densities ~ J and the charge distributions q

into their subcomponents according to their nature (equations 2.21 and 2.22) the PEEC EFIE is derived

J = ~ ~ J

+ ~ J

= ~ J

+ ε

(ε

− 1) ∂ ~ E

∂t (2.21)

Figure 2.7: Equivalent PEEC circuit for a conductive wire[10].

~

q

= ~ q

+ ~ q

(2.22)

ˆ

n × ~ E

(~ r, t) = ˆ n × " ~ J

(~ r, t) σ

#

+ ˆ n ×

"

X

k=1

µ Z

vk

G(~ ~ r, ~ r0) ∂ ~ J

(~ r0, t

)

∂t dv

#

+ ˆ n ×

"

X

k=1

ε

(ε

− 1)µ Z

v_k

G(~ ~ r, ~ r0) ∂

E(~ ~ r0, t

)

∂t

dv

#

+ ˆ n ×

"

X

k=1

∇ ε

Z

v_k

G(~ ~ r, ~ r0)q

(~ r0, t

)dv

#

(2.23)

Once at this point discretization is performed. The material structures are divided into a volumetric grid which can be non-uniform and non-orthogonal if this is required in order to increase the accuracy of the computed solution. Some possible simplifications due to the material characteristics cam also be applied before the components of 2.23 are interpreted for each cell as interconnected discrete elements (inductances, capacitors, resistors, etc.) of an electric equivalent quadrupole (see Figure 2.7). This equivalent circuit is then solved using the classical SPICE techniques providing at the end the results in circuital terms allowing, trough a post processing[9], the obtaining of the ~ E and ~ H fields.

In order to easily analyse the results of the simulation applied to the antenna design,

two tools have been developed that take the raw data the PEEC solver returns and extract

from its two basic antenna parameters, which are the electric field pattern, for analysing

the spatial characteristics of the antenna radiation, and the return losses, which provides an

idea of the electrical behaviour of the antenna within the whole radio system. For obtaining

the field pattern, a test sphere fully containing the antenna is placed in the far-field zone

(equation 2.24) of simulation scenario which allows retrieving the electric field data in a

discretized spherical space. Then, by keeping the angular information and assigning to each

point as radial component the value of its corresponding field module, a 3D visualization of

the electric field radiation pattern is obtained. This three dimensional figure is also sliced

in several planes which provide more concrete data about the radiation behaviour. To facilitate direct comparisons between each antenna performance, these radiation patterns are normalized by the maximum field module, obtaining then normalized diagrams that will show which percentage the electric field is spread out in. Although this allows an easier visual comparison of the spreading, the maximum field value in each case is saved, because combined with the information of the pattern it permits an absolute power balance analysis at any specified direction, which is decisive for the global performance study.This balance is particularly useful in the horizontal plane, where it specifies which antenna reaches a possible RMU point with higher intensity.

Figure 2.8: (a) Field spherical probe. (b) 3D normalized field patter of a half-wavelength dipole placed over the x axis

R > 2D

λ (2.24)

N (θ, φ) = |E

(θ, φ)|

|E

| (2.25)

On the other hand, for the obtaining of the input impedance and the return losses the

circuital output information provided by the PEEC solver is used. The input impedance

is calculated directly from the voltages and currents in the input terminals (equation 2.26)

and then, taking as normalized impedance Z

= 50Ω, the return losses are computed by

using the equation 2.27 for the desired frequency span. Although the transceiver Atmel

RF230 RF-output is adapted to a 100Ω load, the reference value was chosen this way for

being a standard for this type of applications and components. Since it is interesting to

study this parameter along a relatively wide number of frequencies and each computation

could take a long time depending on the complexity of the model, cubic interpolation

has been used for obtain a well approximate impedance and losses curves even when the

number of sampling points it is not very high. Of course this interpolation process leads

to possible errors but since performing the PEEC simulation for many frequency points

implies the increasing of the computation load and therefore the time and guaranteeing a

short enough gap between simulation points this interpolated solution will be considered

for comparing and approximating the later measures. The results obtained by this method

are relatively accurate with the theoretical derivation taking in consideration the simplifi- cations that the modelling implies, such as the material discretization and the feeding gap.

In the Figure 2.9 the input impedance values can be observed for a dipole and also how, when it is resonant Im(Z

= 0), the resistance is a bit higher but very close to theory expected value of 73Ω. It is also visible how its evolution with the frequency (or electrical length) meets the analytical results.

Z

= V

I

(2.26)

RL(f ) = −20 log    

Z

(f ) − 50 Z

(f ) + 50    

(2.27)

Figure 2.9: Simulation of the input impedance for a λ/2 dipole around its frequency of resonance.

With those two parameters the performance of the radiating element can be evaluated both in terms of spatial characteristics and power efficiency at the frequency band of interest allowing establishing it suitability for this application.

2.4.2 Modelling of antennas and their iRoad environment

Since this thesis tries to determinate the validity of several antenna designs for a very concrete scenario in which strict design limitations are present, the way that the scenario is modelled for the simulation process is crucial for the later accuracy and applicability of the obtained results. In real operating conditions, as it was outlined in Section 2.2, the devices that will mount the antennas are going to be placed directly over the road shoulders, this means a maximum height above the road of 7mm, which is imposed by the physical design of the RMUs.

With that distribution, and assuming the most of the time the road sections will be

straight, the medium for the antenna transmission and reception and for the EM wave

propagation can be considered as a layered structure formed by the free air, the road sur- face and the soil. The first one, the air, which compounds the whole z-positive semi-space, is the layer containing the antennas and in which the wave propagation phenomena will occur. Regarding its electromagnetic behaviour, air, and in particular air present above solid terrain (due to its less concentration of humidity), presents an electrical conductivity very close to zero and a relative dielectric constant ε

= 1.00059, almost the same as the vacuum, so it will be modelled in the PEEC simulations as perfect vacuum. This will allow, since the PEEC method approximates the integral formulation of the Maxwell’s equations (see epigraph 2.4.1), to decrease significantly the computational costs without losing accuracy. Of course, it implies dealing with a simplified model which cannot be used for simulate more complex phenomena like absorptions or diffractions that may occur in a real environment specially in the presence of water vapour, hydro-meteors and other particles in suspension that are present in the atmosphere.

Regarding the second layer presented in the model, the road, it can be considered in turn as the aggregations of several layers according to the classic techniques of asphalted road design, each one with its own electrical characteristics. As it is shown in Figure 2.10 the road is composed by three different stratums identified as surface, base and subbase. Due to its composition, very similar to the soil’s one, the base and subbase will be considered in this model for simplicity as contained on it, being then the road-soil structure modelled as the juxtaposition of only two materials.

Figure 2.10: Profile of the layered model of the road-soil structure

The surface layer, the upper one, is usually made of an asphalt mixture composed

by bitumen binders, a particle aggregate, air voids and water. However, for the heavy

load roads due to the high resistance and performance required, is common to use an

asphalt mixture known as Hot-mix asphalt concrete, which has the particularity of using

high temperatures to reduce its viscosity and dry the particles in the aggregate in order

to reduce the moisture content. This is important since the water is the main actor in

the electric conduction of mineral aggregates, its low concentration in the mixture affects

the electrical behaviour of the material. Several researches have been done in the electric

characterization of the asphalt mixes, especially for the development of quality control and

damage detection systems. Their results [10] [11] shown at microwave frequencies that

both the conductivity and the complex component of the dielectric permittivity are not

very significant, and the real part ε

≈ 5 depending on the filler and aggregate considered and its density. As an average, the value of ε

= 5 has been chosen for the material in the model. Regarding its thickness, it widely varies depending on several parameters like the planned load of the road, the established normative and recommendations, the mixture used, etc. so we have chosen 30mm as an average value for the simulations.

The last layer, which covers the base, subbase and subgrade (natural soil) layers, is a composition of mineral particles, air, free water and bound water in different concen- trations depending of the nature of the terrain [13]. There have been several attempts to measure and model the electric behaviour of the soil with relative success but one general conclusion is that it mostly depends on the moisture content of the considered sample.

With that in mind, it is immediate to assume that the soil characteristics will be strongly conditioned by the seasonal changes as it has been already empirically shown [14]. The variability of the electrical properties of this layer makes the modelling very complex. To deal with this the first approach is to consider the entire multi stratum structure as the joint of a dielectric material with real dielectric constant ε

= 10 as the average for the subbase layer in [13] which also match the values in [14] and [15]. The conductivity effect of the deepest layer, the subgrade, is added in the model by placing a conductive sheet, without any thickness and with a conductivity constant σ = 0.05S/m [14] assuming a dry weight moisture content around the 20%.

Up to now, the model has been described by a multi-layered medium, composed by two dielectric layers placed over an electrical low-conductivity layer. Considering this model as an infinite planar surface, any source situated above will radiate electromagnetic power both to the free space and to the ground surface. Some of the power radiated to the ground will penetrate into the model and some of them will return reflected interfering with the free space radiation. In order to simplify even more the road model, and since most of the power will be reflected in the air-asphalt interface, it is possible to discard the second dielectric layer to the detriment of that penetration power, as the reflected power, the only one of these two components that influence in the z > 0 subspace radiation (the region of interest for the thesis aims), approximates to the one defined by the interaction with only the upper dielectric layer with a non-perfect conductive surface under it. In order to validate the particularization shown in Figure 2.11, some tests were carried out on PEEC solver by comparing the results (Figure 2.12) and the expected values from other techniques [16]. The results confirm the approximation is reasonable, and due to the excessive computation time required for solving the original model, the last proposed model will be taken as basis for performing the later simulations. It is important to notice that since all the designs will be simulated under the same environmental conditions the comparison of the result could be done but due to the possible maladjustments with the real ground condition they cannot be directly extrapolated to the real operating scenario and precise a later testing and measuring.

The model presented can be refined in order to consider several climatic phenomena

the devices may suffer in operating conditions. For instance a wet road surface due to

rainy conditions can be considered by adding a thin dielectric film in the air-road interface

with a dielectric constant ε

≈ 70 [17]. Also snowy scenario can be simulated by covering

Figure 2.11: Simplified of the air-road-soil interface for PEEC simulations

de device with a dielectric block with ε

≈ 1.5 [18].

Figure 2.12: Simulation results for a λ/2 dipole placed in the x axis and λ/4 over the ground model (Figure 2.11). (a) 3D Normalized Field Pattern for z > 0. (b) E-plane for z > 0.

Regarding the planar extension of the model ideally it should cover the whole z < 0 subspace, but since the dimensions of the antennas are limited and taking as reference a size of approximately λ/2, according equation 2.24 we will consider a finite surface with a size given by equation 2.28.

R >

2  λ 2



λ →L = 2R > 4λ

4λ = λ (2.28)

The discretization of the material blocks presented in the model has to follow some

rules in order to guarantee the well functioning and accuracy of the PEEC method. For

connected materials it is necessary to assure that the nodes of each cell exactly correspond

to the nodes in the contiguous ones [8]. To keep an acceptable accuracy in the simulations,

the dimensions of the cells cannot exceed under any circumstance the size of λ/20 [8] which

is L

= 17.28mm and L

= 6.25mm for f = 868MHz and f = 2.4GHz respectively.

Antenna design and simulation

25

3.1 Introduction

Once the characteristics of the air-road-ground interface model have been set and the problems that underlie in the working scenario have been introduced, this chapter will present the parameters and results of the simulations conducted for several concrete an- tenna designs. The results will then be evaluated for each design in term of how they fulfil the spatial requirements, this mean that the radiation pattern points in the desired directions with acceptable gain values and the beam is wide enough to allows transmission in curve sections of the road (see Section 2.3), but also in terms of electrical behaviour in order to guarantee a proper integration with the transceiver unit maximizing the radiated power. It will be also of interest to establish comparisons between all the designs under analysis in order to choose for a later construction and testing which could provide a better performance when deployed in operating conditions.

One more time it is important to remember that the RMUs impose a very strict size limitation, especially regarding to the height of the solution and that is why this thesis is focused only in very low profile antenna designs suitable for being built in a printed circuit board. The antenna designs under analysis in this chapter will be some of the most common printed layouts such as dipoles or patches which present good characteristics for the application in the communication subsystem of a wireless distributed sensor network.

These antenna designs, which present a low profile and surface and are easy to model, build and integrate, have been widely used for WLAN applications and their performance is widely documented in general conditions. Other more innovative techniques like the use of High Impedance Surfaces (HIS) are also analysed in order to evaluate how they can improve the radiation performance in this particular scenario.

The use of printed antennas for working in frequencies in the band from UHF to mi-

crowaves have become popular thanks to its low cost, reduced profile and dimensions,

ease of production and mounting but it implies to suffer some disadvantages related with

its efficiency and to keep in mind during the design stage many different aspects which

seriously affects its final performance [19]. The first aspect is of course the design of the

radiating element itself, for instance the desired kind of antenna and its feeding circuit

characteristics. Once the design bases are set it is important to consider the electromag-

netic environment of the antenna. This means most of the idealized formulas for lengths

and sizes calculation carry an important error if basics aspects like the characteristics of

the substrate the antenna will be printed in or the possible presence of coupling sources

are ignored. The printed antennas have the particularity of operate, due its nature, in an

inhomogeneous media, the interface between two material which will modify important

parameters such as the frequency of resonance as it will be shown in the this and the

next chapter. At last, due to power efficiency reasons, it is important to guarantee the

electrical compatibility between the antenna and the transceiver circuits which in most of

the cases will force the inclusion of an impedance matching circuit in order to decrease as

much as possible the power losses caused by wave reflections in the impedance interfaces

which produces the undesired standing waves.

After obtaining the results of some simulations of different basic antenna layouts and comparing them with the theoretical expected results and the results of measurements published, it has been decided to split up the analysis in two parts. The first one studies the spatial radiation characteristics, and does not include the substrate for simplicity reasons since no big changes are expected and could introduce simulation errors. The normalized radiation patterns in the azimuthal and elevation planes are obtained, studied and compared with expectations and the previous cases, and at the end of this chapter, a power balance between all the simulations in the horizontal plane is done by checking the absolute value of the electric field radiated in the optimal direction on that plane.

The second part of the analysis tries to determinate the electrical characteristics of the antennas and their frequency parameters, and in this case a model of the substrate used is considered since the results depend highly on its characteristics. The input impedance in each scenario is obtained for a wide range of frequencies and is compared to the referee impedance to get an impression of the possible return losses. The combination of these parameters would allow to anticipate the possible results of later measures to determine which design would lead to a better compromise between the distance between contiguous RMUs and the beamwidth that allows the system to be adapted to the characteristics of the road, and how the antenna solution can be introduced in the whole electronic design avoiding the presence of the road surface to decrease the power efficiency.

3.2 Linear elements

It is not surprising that the design carried out during this thesis begins with the study of the oldest and simplest antennas, thus minimizing the structure complexity and ensure thereby well known and documented results which can help in the first stages to refine the simulation methods and parameters used, while lying a solid base to start from.

Since the ground plane must be always present in the study, the first experiments will focus on finite length linear current elements under the presence of the soil model defined in Section 2.3. As it has been commented before, the ground significantly affects to the radiation characteristics, which vary from the results obtained in the discussed antennas analysis in a free space medium. The antennas behaviour in vacuum is supposed to be known, although it is briefly described here and used to understand the changes produced by the introduction of the ground reflected components.

The antenna designs considered in this epigraph as possible solutions were proposed by

adapting the characteristics of linear antennas to the concrete parameters of the system,

such as dimensions, ground plane influence and frequencies of operation. The height

limitation concretely, eliminates the possible applications of all the vertical linear antenna

designs such as the monopole which would be in this case very convenient since it uses

the reflection to enhance the radiation along the ground plane (θ = 0). Focusing then

on the low profile linear antennas, horizontal printed dipole and monopole appear as the

two most interesting choices for analysis, since they compose the basis for a wide part of

planar printed antennas used and required in wireless communications nowadays. For the

two operation frequencies, 868MHz and 2.4GHz, the classical resonant λ/2 dipole needs lengths of 17.3cm and 6.25cm respectively, but the planar size limits for the RMUs (14cm x 10cm) would dismiss the first option in its classical design. Nevertheless, the resonant dipole will continue being considered as an antenna solution for both frequencies since in its real design the dimensions could be reduced. Neither printed monopoles for these two frequencies require high spatial magnitudes, less than a few centimetres of length and height.

Summarizing, the next analysis is orientated to study the cases discussed above: the ideal horizontal electric dipole for 2.4GHz and 868MHz followed by their respective printed real dipoles, and a T-shape monopole also designed for both frequencies, all of them subjected to a highly near asphalt model presence.

3.2.1 Horizontal electric dipole

The horizontal dipole is composed by two wires (as known as arms) symmetrically posi- tioned respect a central point and with their lengths directed along one axis. This axis is orthogonal to the ground plane normal, which is situated horizontally below the dipole.

For convenience, in the models and simulations the plane is considered to extend along the x-y plane, while the dipole is placed at a height h above it, centred and placed along the y-axis, as it is shown in Figure 3.1.

Figure 3.1: Horizontal electric dipole on y-axis above ground plane

With this disposition, the E-field expression of an infinitesimal dipole in the far-field zone is simplified [16], being non-zero in an only one direct component, and it corresponds to:

E

= jη kI

le

4πr

sin φ (3.1)

where I

is the current amplitude constant, l the dipole length, η = pµ/ε is the

intrinsic impedance of the medium, k = 2π/λ the wave-number, r

the distance from the

doublet to the observation point, and the angle φ represents the elevation from the y-axis

toward the observation point, which can be derived in spherical coordinates as:

sin φ = q

1 − sin

θ sin

φ (3.2)

Using the images theory and supposing the ground plane as a perfect conductor, a virtual source can be introduced symmetrically respect the plane and below it, which produces a field component similar to the original, equation 3.3, where ρ corresponds to the reflection coefficient and it is ρ = −1 for a perfect electric conductor.

E

= jρη kI

le

4πr

sin φ (3.3)

That means that the total E-field on a point above the ground surface can be calculated as the sum of the two field components produced by the original and the virtual elements.

Inside the PEC and below it the fields cannot flow and are equal to zero. Approximating the distances r

and r

by far-field observations, both for amplitude and phase variations, the total field above the ground surface is given by:

E

= E

+ E

= jη kI

le

4πr

q

1 − sin

θ sin

φ[2j sin(kh cos θ)] (3.4) Up to now for this derivation, the ground plane the antenna is affected by has been considered as a perfect electric conductor (σ = ∞), but due to the particular case this antenna undergoes to, it is necessary to study the reflection over a ground plane similar to the asphalt, where the surface is not an ideal conductor and derives losses. However, a flat surface will continue being assumed in order to simplify the calculations. Introduc- ing a finite conductivity and a relative permittivity in the images problem the reflection coefficient becomes more complicated, but some singular cases can be estimated:

ρ =



 

 

 

 

− η

cos θ

− η

cos θ

η

cos θ

− η

cos θ

for φ = 0, π η

cos θ

− η

cos θ

η

cos θ

− η

cos θ

for φ =

,

(3.5)

where incident and reflected angles over the interface are given by Snell’s law:

γ

sin θ

= γ

sin θ

(3.6)

Therefore, the field over the ground plane can be now calculated as:

E

= jη kI

le

4πr

q

1 − sin

θ sin

φ h

e

+ ρe

i

(3.7)

Solving this expression for some values and obtaining normalized patterns, it is possible to get an approximate idea of the field radiation, and compare these cases with the perfect electric conductor (PEC) results, as shown in Figure 3.2 from [16]. The radiation direction changes completely from the dipole in the free space case: the ground surface acts as a mirror that forces the whole radiation to appear in the half-space above the ground, transforming the original toroidal pattern into an broadside pattern

. However, the effects of the variation on the ground plane electrical characteristics do not produce significantly different changes in the pattern shape. The reflection coefficient does not vary far from the ideal case (ρ = −1), and this involves in similar radiation beam directions.

Figure 3.2: Elevation plane (φ = 90

) amplitude patterns of an infinitesimal dipole above two different planes: PEC and real earth (σ = 0.01S/m, ε

= 5).[16]

Analysing the antenna behaviour using PEEC solver as simulation method requires a complete description of the model in terms of geometry and electrical properties, and therefore some considerations must be previously taken referred to global spatial dimen- sions and the PEEC requirements. The parameters concerning the horizontal dipole are given in the Table 3.1. By combining them with the proposed model for the ground plane detailed in epigraph 2.4.2, the geometry of the complete system introduced in PEEC solver as input is shown in figure 3.3.

Parameters Values

Height over ground plane 5mm

Length 6.25cm (λ/2)

Wide 2µm

Height 2µm

Feeding gap 2µm

Conductivity 5.8·10

S/m (Annealed copper)

Table 3.1: Parameters of the ideal dipole above imperfect ground plane

In order to characterize the response of this system using PEEC, a frequency domain analysis was carried out by introducing a sinusoidal current between the two arms. The

1

Adopting this term usually used for arrays for referring to a perpendicular to the antenna surface

radiation beam