Passive and active reconfigurable microstrip reflectarray antennas

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PASSIVE AND ACTIVE RECONFIGURABLE MICROSTRIP REFLECTARRAY ANTENNAS

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PASSIVE AND ACTIVE RECONFIGURABLE MICROSTRIP REFLECTARRAY ANTENNAS

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op dinsdag 30 september 2008 om 15.00 uur

door

Mostafa HAJIAN

elektrotechnisch ingenieur geboren te Arak, Iran

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Dit proefschrift is goedgekeurd door de promotor: Prof.dr.ir. L.P. Ligthart

Samenstelling promotiecommissie:

Rector Magniﬁcus, voorzitter

Prof.dr.ir. L.P. Ligthart, Technische Universiteit Delft, promotor

Prof.ir. K. Robers, Technische Universiteit Delft

Dr.Sci. A.G. Yarovoy, Technische Universiteit Delft

Prof.dr.ir. G. Vandenbosch, Katholieke Universiteit Leuven, Belgi¨e

Prof.dr.ir. E.R. Fledderus, Technische Universiteit Eindhoven,

Prof.dr.ir. I.G.M.M. Niemegeers, Technische Universiteit Delft

Prof.dr.ir. W.C. van Etten, Technische Universiteit Twente

Thesis Delft University of Technology.

With references and with summary in Dutch. ISBN 978-90-9023134-1

Subject headings: hollow patch antenna, reﬂectarray antenna, passive- and active antennas, shared aperture antenna.

Printed in The Netherlands

Copyright c 2008 by M. Hajian

All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, includ-ing photocopyinclud-ing, recordinclud-ing or by any information storage and retrieval system, without permission from the copyright owner.

The work presented in this thesis was ﬁnancially supported by IRCTR in The Netherlands.

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Introduction

The history of antennas dates back to James Clerk Maxwell who unified the theories of electricity and magnetism, and eloquently represented their relations through a set of profound equations best known as Maxwell’s Equa-tions. The field of antenna technology is dynamic and over the last 50 years has become an indispensable partner in telecommunications technology, sys-tems and applications. The advantages of radio communications and radar in our daily life has put a significant amount of research and work on design-ing high performance antennas. While in the past antenna design may have been considered a secondary issue in overall system design, today it plays a critical role. In fact, many radio and radar system successes rely on the design and performance of the antenna.

The array antennas are most versatile in antenna systems. They ﬁnd wide applications not only in space-borne systems, but in many other

earth-bound missions. The state-of-the-art of antenna array ﬁeld is primarily

related to beam scanning array antennas. With arrays, it is to-day’s prac-tice not only to synthesize almost any desired amplitude radiation pattern, but also to scan the main lobe by controlling the relative phase excitation between the elements. However, from theoretical and practical point of view most advanced arrays are complex, and expensive and from technological point of view they are diﬃcult to be realized.

The principle as used in reflector antennas was already long time be-fore 1888 in use for optical telescopes. The demands of reflectors for use in radio astronomy, microwave communications, deep space communications, and many other applications have forced a major progress in the develop-ment and optimising of sophisticated reflector antennas. In general reflector antennas are not flexible, bulky and the proto-typing requires much time and so manpower.

In the past decade the research on analytical and experimental tech-niques for reﬂectarray antennas has received considerable attention for

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re-2 Introduction

placement of reflector antennas. In addition to this the attempt has been made to use such reflectarray technology for beam scanning by integrat-ing the antenna with active phase shifters, but this is a rather complicated process. In 1999 the International Research Centre for Telecommunications and Radar (IRCTR) initiated a research program in the field of reflectarray antennas. The result of this research has led to writing this Ph.D thesis.

1.1 Research objective

The major and central problem that is investigated in this thesis refers to the design of microstrip reﬂectarray (MRA) antennas with active

devices demonstrating low cost beam scanning capabilities. The

primary focus is directed towards the solution for the phasing technique that can be achieved with the microstrip reflectarray structure. The secondary focus is to develop a platform for designing microstrip reflectarray antennas using different type of phasing techniques.

1.2 Research lines

Reﬂectarray antennas are complex antenna systems having a number of fea-tures that needs to be investigated for a successful realization. A graphical illustration of the major topics and features of reﬂectarray antennas to be investigated is provided in Figure 1.1. Attention is paid to the design and analysis of the single cell elementary radiator and the array for a successful realization of this new concept.

Reﬂectarray antenna Array architecture Primary radiator Phase diagram Phasing method Radiating part Beam scan Passive Array Active array

Figure 1.1: Research tree.

In the recent years microstrip antennas has got numerous attention due to their versatilities as primary radiator in the design of reﬂectarray

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Novelties and main results ₃

antennas. Due to the proposed complex patch geometry, numerical analysis tools for electromagnetic problems are used to predict their performance as primary radiator. Taking into consideration the three distinctive important aspects of each radiator for MRA, i.e. the radiating part, the phasing tech-nique and the phase diagram, form a fundamental approach for a successful design of an antenna element in the array environments.

The main goal of this thesis is to design reflectarray antennas with scanning capabilities of the main beam. Passive and active beam scanning are taken into consideration and numerical electromagnetic tools are used to predict the array performance. Small array antennas are developed on a thin dielectric slab and measured to validate the proposed concept. As will be motivated in the next chapter the mutual coupling issue is not considered in detail. Experimental validation in an array realized in printed circuit board technology has justified the simplification to neglect mutual coupling effect.

1.3 Novelties and main results

The approach to design a reﬂectarray antenna has led to a number of research incentives that will be addressed here. The most relevant novelties presented in this thesis are as follows:

• proposal of a new concept for a reﬂectarray antenna on semiconductor

material using optical imaging (Chapter 4);

• modelling and measuring the RF reﬂection- and transmission

coef-ﬁcients of semiconductor material under illumination of an optical source (Chapter 4);

• fast calculation of the impedance matrix using multi-node processors

Distributed ASCI Supercomputers (DAS) based on a self-developed Method-Of-Moment (MOM) algorithm (Chapter 5). In this way a full wave element analysis is presented, where a number of diﬃculties such as numerical integration, treatment of singularities could be solved in a classical way;

• addition to existing designs for variable-sized reﬂectarray antennas

based on MOM (Chapter 6);

• design procedure and measurement of a new phasing technique; the

so-called hollow patch antenna was initiated at IRCTR and has led to results given in Chapter 7;

• design procedure of active-loaded reﬂectarray antennas using hollow

patch antennas (Chapters 8 and 9);

• realization of a low cost reconﬁgurable MRA consisting of hollow patches

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4 Introduction

The main achievements of this thesis are:

• modelling and experimental validation of the reﬂection from and

trans-mission through a semiconductor material under illumination of light are presented in Chapter 4;

• a fast technique for evaluation of currents excited on the patches is

developed in Chapter 5;

• a design procedure for an elementary variable-sized patch antenna

us-ing a numerical software package has been realized and its potentials are demonstrated in Chapter 6;

• a design procedure for an elementary equal-sized hollow patch antenna

is given in Chapters 7 and 8;

• a design procedure for an elementary active hollow patch antenna and

the realization of a low cost reconﬁgurable active MRA with such an-tenna elements are described in Chapter 9.

1.4 Outline of the thesis

This thesis is organized in three parts which include the main steps for designing MRA antennas. In the first part the electromagnetic formulation of the elementary radiator is presented. The full wave formulation based on MOM is developed and studied. The second part is dedicated to the design and analysis of the different geometries for elementary radiators which allow different phasing techniques. The third part covers the aspects related to the design and analysis of passive- and active reflectarray antennas for beam scanning purposes. A brief description of each chapter is provided hereafter:

• Chapter 2 - An overview of the reﬂectarray antenna is given. The

advantages and disadvantages of such array conﬁguration are discussed in more detail. Important aspects of the antenna are presented and explained with some examples.

• Chapter 3 - This chapter gives an overview of the parameters of a

single antenna element which determine the performance of the to-tal antenna system. Some of the parameters are determined for each phasing technique given in subsequent chapters.

• Chapter 4 - This chapter introduces a new concept for the realization

of reflectarray antennas. The antenna uses semiconductor material il-luminated optically. The reflection- and transmission coefficients of the semiconductor material under illumination of light is modelled us-ing the S-T matrix. The approach was developed and presented for the first time at IRCTR. Measurements have been done to validate simulation results.

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Outline of the thesis ₅

• Chapter 5 - This chapter deals with the modelling and analysis of a

single patch antenna on an infinite ground plane. The full wave integral equations are presented using the dyadic Green’s function and solved using MOM to predict accurately the current distribution excited on the surface of the patch antenna. Once the current is known, all other parameters including the phase of the scattered field in the far zone can be determined. Computer implementation of the MOM method is discussed subsequently. The efficiency, in terms of computing time requirement, was achieved by adopting a new parallel programming using DAS systems.

• Chapter 6 - In this chapter the analysis and design of MRA at

mil-limeter wave (MMW) frequencies using a variable-sized phasing

tech-nique is explained. Critical parameters and design curves are

pre-sented. A number of arrays has been built and measurements are

performed to demonstrate the passive beam scanning.

• Chapter 7 - A new phasing technique, the “so-called hollow phasing

using slotted patch” is introduced in this chapter. Such a geometry form the basis for the realization of active reﬂectarray antennas using varactors. The dimensions of the slot are altered in both x- and y directions simultaneously to achieve the phasing while the outer patch dimensions remain the same. Design and performance parameters of such phasing technique are analysed. Measurements are done using a waveguide simulator to measure the phase and to validate the simula-tion results.

• Chapter 8 - This chapter is the second part of hollow phasing using

the slotted patch. Since the active antenna is realized at 6 GHz, this chapter determines speciﬁc aspects of the phasing mechanism at this frequency. The focus in this case is that the slot dimensions can be changed in one direction only.

• Chapter 9 - In this chapter the concept of active reﬂectarray

anten-nas at 6.0GHz is presented. The hollow patch antenna is integrated with active varactors. The capacitance of such a varactor can dynam-ically be adopted by applying different voltages. It is shown that such change in capacitance has a considerable effect on the reflected phase of the signal impinging on the hollow patch antenna loaded with a varactor device. The dimensions of the slot are kept constant for all antenna elements in the array. A new antenna geometry is designed for integration with the active device. The design aspects and parameters are studied in detail. Measurements are performed to demonstrate the proposed concept.

• Chapter 10 - Main conclusions, recommendations and open issues for

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Chapter 2

Microstrip reﬂectarray

antennas

As the name implies, a reflectarray antenna combines some of the best fea-tures of reflector- and array antennas. Due to their high efficiency and gain, reflector antennas are most often used in applications where one single main lobe pattern as fixed beam is required. The geometry of the reflector an-tenna consists of a feed illuminating the reflector surface. Usually the surface has a parabolic shape. In general, reflector antennas and antenna mounts are bulky in size and large in mass. For high-performance applications, they have huge manufacturing costs and their packaging and transportation is dif-ficult. By mechanically moving the feed, which can have often complications in many applications, some limited scanning of the main beam becomes fea-sible. As an alternative a planar reflectarray antenna has been proposed as a replacement for conventional parabolic reflector antennas. It was first inves-tigated by Berry [1]. The reflectarray antenna employs a number of isolated antenna elements without any power divider network and is in many cases printed on a flat surface [2]-[16]. Figure 2.1 shows the basic geometry of a microstrip reflectarray using patch antennas. The flat reflector, as shown in Figure 2.1, is composed of a thin slab of dielectric material having one side completely covered with a thin layer of metal (serving as a ground plane) and the other side etched with many metallic microstrip patches. A feed an-tenna illuminates the array anan-tenna, the individual elements are designed to scatter the incident field with proper phase to form a planar phase surface in front of the array aperture, as suggested in Figure 2.1. This approach is especially desirable at higher frequencies where the loss of a microstrip feed network is unacceptable. The rapid development in microstrip antenna technology has led to the use of microstrip antennas in a variety of reflectar-ray configurations. The appreciation for microstrip antennas is mainly due to their inherent compactness, lightweight and low manufacturing cost and its beam scanning capabilities once it is integrated with a controlling phase

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8 Microstrip reflectarray antennas

device. In general, the feed may be positioned at an arbitrary angle from reflectarray, but is assumed to be far enough from the reflectarray so that the incident field can be approximated by a plane wave.

Microstrip antenna element Substrate Ground plane Path delay Feed antenna

Co-phase wave front

fF P

fF P = focal distance

from feed antenna to MRA

x

z

O h

Figure 2.1: Geometry of the microstrip reﬂectarray antenna. Phase shifting elements correct for path delay, and create a co-phase wavefront at a given angle.

As indicated in Figure 2.1 the basic design principle requires that the

phase ψi of the field reflected from an element in the reflectarray be

cho-sen so that the total phase delay from the feed to a fixed aperture plane in front of the reflectarray is constant for all elements. An antenna with such a configuration is called Microstrip ReflectArray (MRA) antenna. The advantages of MRA antennas are as follows [16]:

• Surface mounting: because of its thin and ﬂat reﬂecting surface, the

antenna can be mounted more easy onto a vehicle, spacecraft, building walls or roof tops with less support structure (less mass and volume) than needed for parabolic reﬂectors in Direct Broadcast Satellite (DBS) receiver stations. The antenna can also be mounted on a conformal (i.e. curved) structure. The phase deviation caused by the curved structure can be compensated by a number of techniques which will be explained in the subsequent chapters;

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Basic microstrip reflectarray ₉

scanned in space, passive as well as active. This will be a central

theme in this thesis;

• High reliability: since the element devices of the array can be highly

decoupled from each other, the failure of a few elements will have a minor impact on the performance of such an antenna system;

• Low manufacturing cost: the reﬂectarray uses a printed microstrip

an-tenna and can be fabricated using a simple and low cost etching pro-cess. This is speciﬁcally true for the high-performance aircraft, space-craft, and satellites and missile applications where size, weight, cost, performance, ease of installation, and aerodynamics are constraints;

• Weight and compactness;

• Large aperture dimension capability: due to the fact that no power

combiner/divider is needed, the resistive insertion loss of thousands of microstrip patches in the reﬂectarray is the same as that of a single patch element;

• Mutual coupling: as extracted from literature on printed and ﬂat

struc-tures of arrays employing patch antennas, the mutual coupling eﬀect between the MRA antenna elements is low and is not considered in this thesis [16]-[21];

• Side lobe levels: The sidelobe levels of MRA with electrically large

dimensions (gain higher than 30 dB) are generally low, since the il-luminated ﬁeld coming from the feed horn is tapered. The elements on the edge of the array receive less energy compared to the center element. These eﬀects result into a strong tapering across the array aperture, which leads to low sidelobe level.

Disadvantages of MRA are:

• Narrow bandwidth: because of the resonance behaviour of the patch

element the maximum bandwidth is in the order of few percent of the resonance frequency. It is possible to increase the bandwidth by using a two or three layered stacked array [22];

• Efficiency: a high reflection coefficient and low insertion loss allow for

achieving relatively good eﬃciency for electrically large apertures. It has been shown that the eﬃciency of the antenna can be in order of 50% to 70% [3, 8].

2.1 Basic microstrip reﬂectarray

The basic geometry of a MRA conﬁguration is shown in Figure 2.1. There is a great deal of ﬂexibility in choosing the feeding method such as prime-focus,

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offset and cassegrain feeding. Linear, dual and circular polarization can be obtained. Since it is desired to form a planar phase surface in front of the aperture, one of the key feature of MRA is how the individual elements can be made to scatter with a desired phase. There are a number of different techniques to control the phase. One method is to use identical elements with variable length stubs to control the reflection phase [4, 5]. Usually this is not the optimal approach since the delay lines require space and as its length increases it becomes part of the radiating process. This unwanted radiation increases the cross polarization component [5]. A better approach was chosen by Pozar in which the compensation was done by using patches with variable sizes [8, 9]. This technique will also get attention in this thesis. Another method is by rotating the antenna element [7]. These techniques can be viewed as methods to shift slightly the resonance frequency of the patch which effects the phase of the reflected field.

The new phasing technique proposed in this thesis is the active hol-low patch phasing technique. It uses identical patches with a slot of ﬁxed dimensions loaded with active device.

2.2 Active microstrip reﬂectarray

In active phased array antennas, each radiating elements is equipped with a phase shifter. Beams are formed by shifting the phase of the signal emitted from each radiating element, to steer the beams in the desired direction. This property of active antennas can be used in many applications such as: space probe communication, weather research, radio-frequency identifica-tion, broadcasting, low-profile and low cost in-motion satellite TV reception system, earth science missions, earth based sensors for remote sensing, and application to satellite TV. Hence due to the enormous applications there is a great interest for developing advanced high gain phased arrays in many companies and universities. There is the experience that such systems are extremely expensive, electronically complex, and beyond the reach of many applications where cost constraints prevail. In some applications, only lim-ited beam steering is required; in such cases, a simplified beam scanning facility, can be selected. For this thesis work it was decided to focus on the design and analysis of a low cost array antenna with limited-scan angle,

±18◦ _{based on the active MRA concept.}

In the past different single element phasing techniques have been con-sidered for use in active MRA. Hollow patches are assumed to be easily modified for active controlling the phase shift [23]. Research has been done loading a rectangular patch with varactors at each radiating edge [24]. In [25] an aperture-coupled patch with perpendicular feeds is used. Another possi-bility is presented in [26] using a slotted patch loaded with Micro-Electro-Mechanical-System (MEMS). This thesis offers a new approach using a ca-pacitive element in combination with a hollow patch. This method shows

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Design parameters of microstrip reflectarray ₁₁

advantages compared to other techniques. For evaluating the active MRA it is important to consider the following aspects:

• Beam steering: Not only the capability of beam steering is important

but also the scanning range and the quality of the pencil beam needs to be evaluated. The sensitivity of the signal controlling the phase should receive separate attention;

• Control circuit: The complexity of the control circuit is an important

issue especially for large array antennas. The number of control signals and the method of control might become a complex issue in the design. For example if each array element requires two switches (four choices for the phase) a 5x5 array already needs 50 signals to be connected and controlled. The control unit requires additional electronics which can introduce parasites etc;

• Durability and Robustness: Durability and robustness are considered

to be advantageous for passive MRA. Integrating the MRA with ac-tive components may put a limitation on system lifetime, since these components are less robust and may lead to signal distortions.

2.3 Design parameters of microstrip reﬂectarray

In this section the most important design parameters of MRA are listed and compared to those of reﬂector antennas, if appropriate.

2.3.1 Feeding

The MRA can use feeding techniques similar to that of the reﬂector. They

have both the same subtended angle [8]. In this thesis the feeding is a

horizontally-polarized plane wave along the main axis of the array, normal to the antenna. For MRA measurements a horn- or waveguide feed is used. The feed is placed at the focal point of the antenna which is usually is at the far-ﬁeld of MRA. Hence it can be assumed that the MRA is illuminated with the plane waves.

2.3.2 Spillover and taper eﬃciencies

The efficiency of MRA is dominated by the spillover and taper efficiencies. To illustrate the spillover and taper efficiencies the following feed pattern is assumed

Gf(θ) = cosn(θ) (2.1)

where n = 2, 4, 6, 8,... For this feed pattern the spillover and amplitude taper eﬃciencies can be found in closed-form expressions. Based on the

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deﬁnitions and analysis given in [8] and [27] the spillover and amplitude taper eﬃciencies for a circular array become

ηs= 1− cos(n+1)θ0 (2.2) ηt= 2n tan2(θ0) (1− cos(n2−1)θ₀)2 (n₂ − 1)2₍₁− cosn_(θ0) (2.3)

where ηs and ηt are the spillover and taper eﬃciency, respectively and θ0 is

the subtended half-angle, defined in Figure 2.2. The aperture efficiency as function of subtended angle is depicted in Figure 2.3 for different values of

n. z fF P feed Da D_a= Aperture size θ₀ θ₀

Figure 2.2: Subtended angle of reﬂectarray.

0 15 30 45 60 75 90 0 0.2 0.4 0.6 0.8 1

Subtended half−angle [degree]

Aperture efficiency

n=8 n=6 n=4 n=2

Figure 2.3: Aperture eﬃciency for a circular MRA versus subtended half-angle.

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Design parameters of microstrip reflectarray ₁₃

As in the case of a reﬂector antenna the maximum eﬃciency is around

80% and is maximized for a selected optimum value of θ0. Although this

is the eﬃciency for a circular MRA, it still gives a good indication of the eﬃciency behaviour as function of subtended angle for non-circular MRA as will be investigated in this thesis.

2.3.3 Losses

MRA suﬀers from dielectric loss, copper loss, and surface wave excitation. The losses due to the dielectric and copper are usually higher than losses due to surface wave excitation [8]. Figure 2.4 presents the dielectric losses as function of normalized patch length at 35.0GHz. The meanings of the parameters are deﬁned in the Figure 3.1. It indicates that the losses can be several dB for thin substrates with a high-loss tangent tanδ of the dielectric, where δ is the loss angle.

−0.150 −0.1 −0.05 0 0.05 0.1 0.15 0.5 1 1.5 2 2.5

Normalized Patch Length ΔL/L₀

Loss [dB] tanδ = 0.012

h = 0.381 mm h = 0.508 mm

tanδ = 0.007

Figure 2.4: Loss for microstrip patches versus patch size for two diﬀerent

substrate thickness, h. f = 35.0GHz, resonance length L0 = 2.5mm, patch

width W = 3.3mm, εr = 2.33 [8].

2.3.4 Bandwidth

The bandwidth of the reflectarray is considered to be the frequency range in which the designed array operates within acceptable levels [27]. The band-width performance of a microstrip reflectarray can be limited by four factors [3]: microstrip patch element, element spacing, the feed antenna bandwidth, and differential spatial phase delay. According to [8] the bandwidth of MRA is mainly dominated and determined by the bandwidth of the single element. Each element of the array, independent of the phasing technique, uses the

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patch antenna within ±5% of the nominal resonance frequency. Because of

the nonlinear behaviour of the phase curve, deviations from a linear phase curve greater than a few percent, will occur due to changes in frequency. This effect limits the bandwidth of the MRA. Random phase errors can oc-cur by the processing tolerances in the flatness of the array, by the etching process and by uncertainties in the phase center of the feed. In the classical approach the bandwidth is defined at the frequencies for which the return loss is below a certain threshold, usually taken to be -10dB. However, for the MRA this is not the case. Hence in this thesis the bandwidth is connected

to the drop in gain by (±2dB) in comparison with the radiation pattern at

the center frequency.

For the evaluation of MRA most of the parameters given in the pre-vious subsections will hardly be further considered in this thesis. Also no attempt is made to obtain favourable antenna speciﬁcations concerning the elements and array structure. The main focus is to demonstrate the concept of employing reﬂectarrays for passive- and active beam scanning. The dif-ferent parameters discussed in this chapter provide background information for the evaluation of such antennas. Some of the parameters will be deter-mined and the here-given terminology is used throughout the text of coming chapters.

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Chapter 3

Single element considerations

In this thesis the array design is based on the phase characteristics of the el-ementary radiator and requires therefore detailed single element analysis. In later chapters it will be justified to design the array using single element data. Mutual coupling between array elements is presumed negligible because of sufficiently large inter-element spacing and thin substrate. The elementary radiator is microstrip antenna. Figure 3.1 illustrates the configuration of antenna element. x z y Patch in z = h Ground plane Substrate, r h L₀ W GPsize≤ λ₂0 GPsize≤ λ₂0 Fringing effect

Figure 3.1: Microstrip antenna.

Microstrip antennas, as shown in Figure 3.1, consist of a very thin metallic strip (patch) placed a small fraction of a wavelength (h << λ0,

usually 0.003λ0 ≤ h ≤ 0.05λ0, where λ0 is the free-space wavelength) above

a ground plane. The space between the patch and ground plane is ﬁlled

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16 Single element considerations

patch are ﬁnite along the length and width, based on the transmission line theory, the ﬁelds at the edges of the patch undergo fringing [27]. This is illus-trated along the length in Figure 3.1. Fringing makes the patch look wider electrically compared to its physical dimensions and need to be taken into consideration for determining the resonance frequency. In this chapter an overview on the elementary radiator and the so-called single cell parameters is given which will play a major role in realizing phase-shifting per antenna element in an array.

3.1 Numerical aspects

The single elements and array results are obtained using specific-made soft-ware and a commercial package offering a full-wave solution based on the MOM. The different phasing techniques require different modelling. For all optional techniques, the study of the sampling the patch geometry is an important issue. The dimensions and form of the geometry determine how dense the configuration needs to be sampled in space, in order to create accurate numerical results. If some parts of the geometry are small com-pared to the operational wavelength, these parts need to be sampled with high sampling rate. To reduce the run time applying non-uniform sampling becomes an important issue. Hence all models in this thesis are sampled using non-uniform meshing. The sampling issues are addressed separately for each phasing technique.

The results for the rectangular patch show that errors resulting from sampling are predictable in most cases. An error in the sampling causes a shift in the resonance frequency. It means that even though the antenna would not operate at the desired frequency, it would work at some near-by frequency and can still give the correct scan angle.

3.2 Design parameters

The basic design parameters are brieﬂy discussed in this section. These parameters play an important role in the design process of the single antenna element and array conﬁguration.

3.2.1 Patch dimensions

The rectangular patch antenna is used as antenna element in the diﬀerent phasing techniques considered in this thesis. The dimensions partly con-trol the resonance frequency for each phasing technique and determine the reﬂected phase characteristics.

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Design parameters ₁₇

3.2.2 Substrate thickness

The substrate thickness is related to the losses, phase sensitivity and phase range of the single array element. In each phasing technique there is a trade-oﬀ between the phase range and phase sensitivity. A decrease in substrate thickness yields an increase in phase range and sensitivity. The inﬂuence of substrate thickness is examined for the various phasing techniques addressed in this thesis.

Due to the large steps in discrete thickness values provided by the laminates manufacturers [28], the substrate thickness is not a major design parameter. Small adjustments of the resonance frequency or the phase sen-sitivity can not be obtained by selecting an adjusted substrate thickness.

3.2.3 Dielectric constant

Not only the free space wavelength λ0 is of importance to the propagation

properties but also the propagation inside the dielectric has to be taken into account. The wavelength inside the dielectric is given by [27]

λr=

c f√r

(3.1)

where c is the speed of light in the free space, f is the frequency and

r is the relative dielectric permittivity of the substrate. Decreasing the

dielectric constant increases the resonance frequency. The dielectric constant for microstrip arrays is chosen in the lower range [27]. The dielectric constant for the substrate is fixed throughout the thesis, unless specified differently,

at r = 2.33. At this point it can be concluded that in the design of MRA

(using commercial microstrip laminates) the dielectric permittivities and the height of the substrates are less suitable to be used as tuning parameters.

3.2.4 Ground plane dimensions

The reflection from the ground plane is an important parameter that needs to be taken into consideration while designing the reflectarrays [8]. The ground plane has a considerable effect on the reflected phase and needs to be studied carefully. The ground plane dimensions are based on an element

spacing of λ0/2 which is most often selected in array designs and is depicted

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3.3 Performance parameters

The single element performance is evaluated using parameters speciﬁed in the following subsections. Most parameters are directly obtained from sim-ulation or measurement results.

3.3.1 Far ﬁeld phase

The most important parameter needed for the design of MRA is the reﬂected phase at the broadside as function of a variable U used in the phasing tech-nique. This parameter gives the designer the ability to design an array and to predict its performance. The variable U can represent: the dimensions of the patch, the height of the substrate, the sampling or any other parameters which could eﬀect the scatter phase. The phase center of the elementary antenna at the origin is the reference phase for the phase curves presented in this thesis. For the phase curves the following aspects should be considered:

Phase range

The phase range is the complete change in phase values that can be reached

by the single element. A phase range of 360◦ ensures the largest possible

scan range.

Phase sensitivity

The phase sensitivity can be described as the steepness of the phase versus a variable. This varibale can be different for the different phasing technique. In equation form it can be described as the differential of the curve

ψsens =−

δψ

δU (3.2)

where ψ is the reﬂected phase, and U is the parameter for a speciﬁc phasing technique. The phase sensitivity is maximum at the center of the phase curve which corresponds to the resonance point. The phase sensitivity and phase error determine the bandwidth of the single element.

Phase error

The phase error is closely related to the bandwidth of a single element. It can be considered as the diﬀerence in phase caused by a shift in the frequency. The phase curve at one frequency diﬀers from the phase curve at another

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Performance parameters ₁₉

frequency and the diﬀerence between them give the phase errors. These phase errors limit the MRA bandwidth.

3.3.2 Far ﬁeld magnitude

The magnitude of the electric or magnetic ﬁeld at the far zone gives an indi-cation of the radiated power by an antenna element. The maximum radiation depends on the eﬀective area of the antenna element in its environment.

3.3.3 Bandwidth

As just suggested the bandwidth of the single element in a MRA is deter-mined by the steepness of the phase curve. A more formal definition can be the frequency range in which the phase errors are kept within a certain limit. The bandwidth for a phasing technique can be derived from the re-flected phase as function of frequency. Moreover, this describes also the range in which the spacing between the phase curves for different parame-ters is within certain boundaries. This can be then seen also as bandwidth definition of the single element. At last, the estimation of the bandwidth can be determined by studying the radiation pattern of the array for each phasing technique.

3.3.4 Cross-polarization

In MRA a linear polarized wave is assumed to excite surface currents on the microstrip antenna element. Depending on the geometry, the surface currents have a current pattern with minor components perpendicular to the polarization of the incoming wave. These components are responsible for some cross-polarization. In this thesis cross-polarization is usually measured.

3.3.5 Resonance frequency

The resonance frequency of a single microstrip antenna element is the fre-quency at which the wave ’matches’ the electrical length of the current ex-cited on the patch. At the resonance frequency the imaginary part of the surface current is zero [29]. For the microwave circuits integrated with the element the maximum power is radiated and no power is reﬂected back to the source at this resonance frequency. As was mentioned the phase curve is most sensitive to small changes in the resonance frequency and resonance length. Hence the accurate determination of these parameters plays a major role in accurate design of the antenna system.

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3.3.6 Near ﬁeld

The radiating edges [27] based on the transmission line and cavity model determine the radiation characteristics of the microstrip antenna element. Study of the near field confirms such phenomena. The surface current dis-tribution can provide an indication of the radiating edges; near field analysis quantifies the effect of the radiating edge as will be shown in subsequent chapters.

3.3.7 Surface currents

The induced surface currents determine the antenna properties [29]. In or-der to have a thorough unor-derstanding of a phase-shifting technique, study of the induced surface currents is essential. An accurate study of the surface currents can oﬀer extensive knowledge of the patch behaviour. The impor-tant parameters of the antenna can be determined by the distribution of the surface current.

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Chapter 4

RF Reﬂection and

transmission of

semiconductor material

under illumination of light

potential approach to realize a reﬂectarray is based on the use of semicon-ductor material, which material properties alter when it is illuminated by a light source. This concept is studied in this chapter. It is well known that at microwave frequencies, antenna beam steering is commonly realized using phased array antennas. Such approach is expensive and require time con-suming design procedures [30]. As the frequency increases, the complexity and costs make the realization of phased array antennas even more, demand-ing and diﬃcult. A preliminary study of implementdemand-ing a non-mechanical and low-weight antenna that can form and scan the beam is presented in this chapter.

4.1 The concept

The antenna uses a semiconductor wafer, a MMW source and an array of lasers for the optical masking (Figure 4.1). Each optical laser in the array illuminates a number of pixels in the semiconductor wafer. In the semi-conductor wafer the spatially varying density of charge carriers changes the properties of the semiconductor. The portions of the semiconductor that is illuminated with light becomes a conductor [31]. The duration of the semi-conductor at this state depends on the carrier lifetime of electrons and holes,

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22 Semiconductor material under illumination of light

from an electromagnetic wave source.

Semiconductor material Metalization (Dipole) Array of low power laser Light illumination: holographic imaging Addressing the array Look up table z y x MMW Feed source

Figure 4.1: The antenna system based on the optical technology, in this case dipoles elements are projected.

Since the optical illumination can be manipulated locally, the spatial distribution of carriers can be chosen in such a way that a reﬂected or trans-mitted electromagnetic wave can form a beam of desired shape and direction. By changing the optical masking, beam scanning in space becomes feasible [32, 33]. The antenna elements in the array conﬁguration can be dipole-or patch-like. The concept of such an antenna fdipole-or beam-scanning based on optical imaging is depicted in Figure 4.2.

Semiconductor: not illuminated Semiconductor: illuminated with light

(a) (b) (c)

Figure 4.2: Projection of microstrip reﬂectarray on semiconductor with beam

scanning capabilities over a time interval τn with diﬀerent element

geome-tries: (a) equal size; (b) variable size; (c) rotation.

Speciﬁc projections of the light source on the semiconductor correspond to each desired scan angle. Prior knowledge of the coordinates for each el-ement in the array geometry is a must and needs to be stored in advance

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Modelling the reflection and transmission coefficients ₂₃

in a look-up table for all possible elevation- and azimuth scanning angles,

θscan = θ0, φscan = φ0, respectively. Based on the data from the look-up

table, the low power lasers in the array will be addressed individually to be

on or oﬀ. The lasers that are in on state determine the optical masking. In

this way the wafer can be arbitrary masked as function of the time. Since

the duration τn of the masking depends heavily on the carrier lifetime of the

semiconductor material, the masking can be reconfigured rapidly. In this way the radiation from a MMW source can be scanned through space. In order to understand the behaviour of the semiconductor material illuminated by the light source, a silicon wafer is encapsulated between two air-filled mi-crowave (MW) or MMW waveguides and is illuminated with high power laser pulses. The wave reflected from and transmitted through semiconduc-tor material is modelled using the S-T matrix. The propagation constant in the semiconductor material depends on the density of the electron-hole pairs generated by the optical source. The generated electron-hole pair changes the conductivity of the material so that it becomes more a good conductor instead of insulator. It is demonstrated that, once a semiconductor mate-rial is illuminated with an optical source, a nearly complete reflection can occur. In order to validate the theoretical results measurements have been done. The measurements are carried out on a silicon wafer in order to get an indication of the magnitude of reflection and transmission of signals in the MMW and MW region. This property of semiconductor material can be used to realize a reconfigurable reflectarray antenna that can scan the beam of an incoming wave generated by the fixed feed.

4.2 Modelling the reﬂection and transmission

co-eﬃcients

Figure 4.3 presents the overall T-matrix that relates the input-port to the output-port of a microwave network. Based on the transmission line theory,

T

A linear two-port network κ₁ ι₁ ι₂ κ₂ ξ Γin a Waveguide b (a) (b)

Figure 4.3: (a) Two-port network for determining the reﬂection and trans-mission of a microwave device; (b) aperture waveguide with width of a and height of b.

the input reflection coefficient, Γin, and output transmission coefficient, ξ,

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compo-24 Semiconductor material under illumination of light nents via [34] Γin=S11≡ ι1 κ1 κ2=0 = T12 T22 ξ =S21≡ ι2 κ1 κ2=0 = 1 T22 (4.1)

where κ and ι are the incident and scattered waves, respectively. The conver-sion relations between the scattering matrix, S, and the transmisconver-sion matrix,

T , is given by [34] T = T11 T12 T21 T22 = S12S21−S11S22 S21 S11 S21 −S22 S21 1 S21 (4.2) and S = S11 S12 S21 S22 = T12 T22 T11T22−T12T21 T22 1 T22 − T21 T22 (4.3) For further analysis the geometry consisting of the silicon wafer of ﬁnite

length ls encapsulated by two air-ﬁlled hollow rectangular waveguides is

modelled as shown in Figure 4.4. Moreover, Figure 4.4 illustrates the S-T matrices for each waveguide section and for each transition, the correspond-ing lengths and their respective propagation constants. The T-matrices of

l1 ls l2 γ0 γg γ0 S_l2 S₂ S_s S₁ S_l1 T_l2 T₂ T_s T₁ T_l1 T

Figure 4.4: Conﬁguration of S-T matrices with the silicon wafer. the network becomes [35]

Tl1= e−γ0l1 ₀ 0 eγ0l1 (4.4) T1 = 1 2√γgγ0 γg+ γ0 γg− γ0 γg− γ0 γg+ γ0 (4.5)

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Modelling the reflection and transmission coefficients ₂₅ Ts= e−γgls ₀ 0 eγgls (4.6) T2 = 1 2√γgγ0 γg+ γ0 γ0− γg γ0− γg γg+ γ0 (4.7) Tl2= e−γ0l2 ₀ 0 eγ0l2 (4.8)

where T1 and T2 represents the interface between waveguides with diﬀerent

propagation constants. γg is the propagation constant in the silicon and will

be determined in the next section. γ0 is the propagation constant in the

air-ﬁlled waveguide and is given by

γ0 = jω2_μ 0− (π_a)2 if ω2μ0> (π_a)2 (π_a)2− ω2_μ 0 otherwise (4.9) where a is the width of the waveguide cross section. j is imaginary unit, ω is the radial frequency of the signal, 0 is the free space permittivity, μ = μ0 is the free space permeability.

4.2.1 Propagation constant in semiconductor material

The propagation constant γg of electromagnetic waves in semiconductor

ma-terial is derived from a similar procedure as used in Equation (4.9). It is

noted that the propagation constant γgin the guide diﬀers from the intrinsic

propagation constant γs of a material. γg is given by [36]

γ_g2= γ_s2+ k2_c (4.10)

where kc=(π_a) is called the cut-oﬀ wave number. The electrical properties

of a semiconductor material under illumination from an optical source will change. In general the propagation constant in a medium is given as [36]

γs=

jωμ(σ + jω) (4.11)

where σ is the conductivity of the material. The conductivity for semicon-ductor is given by [37]

σ = Nnqnμn+ Npqpμp (4.12)

where μn and μp are the mobility of electrons and holes in cm

2

Vsec. Nn and

Np are the electron and hole concentration in cm−3, which will be altered

when extra electron-hole pairs are generated. In general in thermal

equilib-rium we have Nn=Np= N0, where N0 is the intrinsic carrier concentration.

Substituting Equation (4.12) in (4.11) and combining with Equation (4.10) leads to the propagation constant in the semiconductor material. The only unknown parameter is the concentration of optically generated electron-hole pairs which will be addressed in the next subsection.

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26 Semiconductor material under illumination of light

4.2.2 Electron-hole pair generation rate

The electron-hole pair concentration generated by the optical source is de-rived from the following approach. It is shown that photons with energy

greater than the band-gap energy Eg of the material can be absorbed in the

semiconductor, thereby creating electron-hole pairs. The intensity Iv(x) is

given in the unit of _cmenergy2_sec; αIν(x) is the rate in which energy is absorbed

per unit volume. α is the absorption coeﬃcient in cm−1 and depends on the

semiconductor material and wavelength of the optical source. If we assume that one absorbed photon at energy hν creates one electron-hole pair, then the generation rate of electron-hole pairs equals [38]

dg dt =

αIν

hν (4.13)

where hν is the photon energy in eV and is related to the wavelength of the optical source via

E = hν = 1.24

λ(in μm) (4.14)

The generated electron-hole during a time interval Δτ is given as

δn(t = Δτ ) = dg

dtΔτ, in unit of

Number of electrons

cm3 (4.15)

where Δτ is duration of the pulse. Assuming that there is no spatial variation in the excess carrier concentration and that at time t = 0 the electron-hole pairs have been generated uniformly based on Equation (4.15), the time dependence of the generated electron-hole pairs can then be given as [38]

δn(t) = δn(0)e−τ nt _(4.16)

where τn is the carrier life time of electrons and holes, δn(0) is the

concen-tration of excess carriers which exist at t = 0. Note that for pure (undoped)

Si in a thermal equilibrium N0 = 1.5 × 1010 per cm3 at room temperature

while the total carrier concentration that can be generated is: 5.0 × 1022

per cm3. Electron-hole pair concentration as indicated in Equation (4.12) is

adjusted by the generated electron-hole pair given by Equation (4.16).

4.2.3 Reﬂection and transmission coeﬃcients

The overall T-matrix of the microwave network depicted in the Figure 4.4 is determined by the matrix multiplication

T = T11 T12 T21 T22 = Tl2T2TsT1Tl1 (4.17)

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Numerical results ₂₇

Inserting Equations (4.4)-(4.8) in (4.17), and after some manipulations and rearranging, the elements of the total T-matrix yields

T11= 1 4γgγ0 [(γg+ γ0)2e−γgls − (γg− γ0)2eγgls]e−γ0(l1+l2) (4.18) T12= 1 4γgγ0 [(γg2− γ02)(e−γgls− eγgls)]eγ0(l1−l2) (4.19) T21= 1 4γgγ0 [(γg2− γ02)(eγgls − e−γgls)]e−γ0(l1−l2) (4.20) T22= 1 4γgγ0 [(γg+ γ0)2eγgls − (γg− γ0)2e−γgls]eγ0(l1+l2) (4.21) Substituting Equation (4.19) and (4.21) into equation (4.1) leads to the expression for the input reﬂection

Γin=

(γg2− γ02)(e−γgls − eγgls)e−2γ0l2 (γg+ γ0)2eγgls− (γg− γ0)2e−γgls

(4.22) The transmission coeﬃcient is given as [35]

ξ = 4γgγ0

[(γg+ γ0)2eγgls− (γg− γ0)2e−γgls]eγ0(l1+l2)

(4.23)

4.3 Numerical results

Using the Equations (4.9) to (4.16), (4.22) and (4.23), the reflection and transmission coefficient of a silicon wafer under illumination of an optical source is determined. The waveguide is operating in the dominant T E10 mode. The operational frequency is 35.0GHz. The wafer is encapsulated by two air-filled waveguides. The dimension of the cross-section of the

waveg-uide is 3.5mm × 7mm. The thickness of the silicon wafer is 0.3mm. The

optical pulse has a Gaussian shape with a wavelength of 1.06μm and a pulse duration of 10ns. At this wavelength the absorption coeﬃcient of silicon is

α = 10cm−1 [38], with a typical value for the mobility of silicon μn = 1350

cm2

Vsec [37]. The reﬂection and transmission as function of time are shown in

Figure 4.5.

The parameter is the energy density of the optical source in _cmmJ2

illu-minating the semiconductor at time t = 0. The conductivity of the silicon wafer as a function of time and for diﬀerent values of the energy density of the optical source is plotted at linear and logarithmic scales in Figures 4.5(c) and 4.5(d), respectively. It is evident that this considerable change in conductivity leads to a nearly total reﬂection of the electromagnetic waves.

A carrier lifetime of τn= 10μs has been chosen. It is shown that when the

generation rate decreases, the input reﬂection also decreases. The results are in good agreement with results published [39].

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28 Semiconductor material under illumination of light 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 Time [μsec] Reflection coefficient Energy Intensity mJ/cm2 10.0 6.0 4.0 2.0 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 Time [μsec] Transmission coefficient Energy Intensity mJ/cm2 10.0 6.0 4.0 2.0 0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 2 2.5x 10 4 Time [μsec] Counductivity (S/m) Energy Intensity mJ/cm2 10.0 6.0 4.0 2.0 0 10 20 30 40 50 60 70 80 100 101 102 103 104 105 106 Time [μsec] Logarithmic Counductivity (S/m) Energy Intensity mJ/cm2 10.0 6.0 4.0 2.0 (a) (b) (c) (d)

Figure 4.5: (a) Reﬂection, (b) transmission and (c) the conductivity σ (d) the conductivity in logarithmic scales of silicon after being illuminated by an optical source for diﬀerent values of optical energy density in _cmmJ2.

4.4 Experimental results

The measurements presented in this chapter were performed at the Applied Physics department of the Faculty-Applied Sciences of Delft University of Technology. Measurements have been done to validate the theoretical re-sults and to determine experimentally the reﬂection- and transmission of electromagnetic waves incident on a piece of semiconductor material which is illuminated by an optical source. A silicon wafer with a thickness of 0.3mm is encapsulated between two waveguides. One of the waveguides had a slot on the rear side for illuminating the wafer with the laser pulse. Two de-tectors (DC to 50GHz) are used to measure the reﬂection and transmission of the MW or MMW source. A mirror and a lens are used to focus the

laser light into the waveguide. The laser was an Nd+3 _{Yttrium Aluminium}

Garnet (Y3Al5O12 or YAG) operating at an infrared wavelength of 1.06μm,

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Experimental results ₂₉

20-30ns leading to a peak power of 15MW [40]. A three-channel digital oscil-loscope, TDS784A, is used for simultaneously measuring the reﬂection and transmission and synchronizing.

4.4.1 X-band

The measurement set-up in the X-band is depicted in Figure 4.6.

Light Lens Mirror Attenuator Laser S Ch1 Ch2 Ch3 TDS 784A Detector for measuring Transmission Detector for measuring Reﬂection 20dB LNA f=9.47GHz P_max=16dBm Waveguide Silicon Coupler Slot

Input microwave signal

Reﬂection

S Synchronization

Figure 4.6: Reﬂection- and transmission measurement set up at X-band. The silicon wafer is encapsulated by two open waveguides operating in

the dominant T E10 mode and having aperture dimensions of b = 10.0mm

and a = 22.0mm. For generating the incident electromagnetic waves on the silicon wafer, a MW source at 9.47GHz with a maximum output power of 16dBm has been used. The source is connected to the hollow waveguides via a -20dB wide-band coupler. The coupler is simultaneously used for mea-suring the wave reflected by the silicon; use is made of a detector, which subsequently is connected to one of the channels of the digital oscilloscope. The transmission wave through the silicon wafer is measured by the sec-ond channel of the digital oscilloscope using another detector. The third channel of the oscilloscope is used for synchronization. The mirror and lens were used for aligning and focusing the laser light. Before switching-on the laser, the reflection caused by the silicon (high dielectric constant) and the open-ended waveguide is tuned away with a matching stub. The relative reflection- and transmission voltage before and after switching-on the laser is depicted in Figure 4.7. The straight line represents the reference voltage. The portion of the reflected pulse between 42μs < t < 70μs becomes lower than the reference signal. This phenomena could not be explained. It can be concluded that a complete reflection occurred after switching-on the laser.

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30 Semiconductor material under illumination of light 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 25 30 35 40 Time (μs) Reflected voltage (mV) Reflected pulse Reference pulse 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 25 30 35 40 Time (μs) Transmitted voltage (mV) Transmit pulse Reference pulse (a) (b)

Figure 4.7: Measured X-Band (a) reﬂection and (b) transmission pulse after the silicon is illuminated with light, the laser pulse of 20ns occurs at t=0 sec.

4.4.2 Ka-band

Figure 4.8 presents the block diagram of the measurement set-up at Ka-band and is almost similar to the measurement set-up in the X-band.

Reﬂection set-up Transmission set-up Laser Mirror Lens 10dB coupler Light 3dB coupler MMW source Adaptor 2.4 mm 2.4-3.5 mmTransition HP8474C Detector .01-33GHz Adaptor 2.4 mm 2.4-3.5 mm Transition HP8474C Detector .01-33GHz Oscilloscope Waveguide Silicon Waveguide Coupler Slot Synchronization

Figure 4.8: Reﬂection- and transmission measurement set up at Ka-band. A picture of the measurement set-up with the IRCTR AB MMW Net-Work Analyzer (NWA) system is presented in the Figure 4.9. For generating the incident electromagnetic waves on the silicon wafer, a MMW source at 32.0GHz with a output power of 3dBm is used. The source is connected to the hollow waveguides where the silicon is located via a -3dB and -10dB

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Discussions ₃₁

(a) (b)

Laser

Figure 4.9: (a) IRCTR AB mm NWA (10MHz up to 110GHz) employed as the MMW source for the measurement, (b) measurement set-up at the de-partment of Applied Physics, Faculty of Applied-Sciences of Delft University of Technology.

wide-band waveguide coupler. Moreover, both couplers are simultaneously used to measure the reﬂection wave through an adaptor and a coaxial tran-sition from 2.4mm to 3.5mm. This signal is then measured by a detector, which subsequently is connected to one of the channels of the digital os-cilloscope. The transmission wave through the silicon wafer is measured by the second channel of the digital oscilloscope using another detector through an adaptor and a coaxial transition from 2.4mm to 3.5mm. Similar to the measurement set-up in the X-band, the third channel of the oscilloscope is used for synchronization. The laser pulse is guided into the waveguide con-taining the silicon via a mirror and a lens. In this case the silicon wafer is

encapsulated by two open waveguides operating in the dominant T E10mode

having an aperture with b = 3.5mm and a = 7.0mm. Before turning-on the laser, the reﬂection caused by the silicon (high dielectric constant) is tuned away with a MMW tuner. Figure 4.10 depicts the relative transmission and reﬂection of the silicon wafer before and after the laser is switched on.

The figures present measured results for a single shot measurement, and a measurement averaged over 16 laser pulses. For clarity the average measurement is inverted. An on/off ratio of almost 20dB is measured. A complete reflection occurs after the laser is turned on. Figure 4.11 shows the comparison between simulated and measured results. A good agreement is observed.

4.5 Discussions

After examining the results given in the previous sections it can be concluded that the transmission and reﬂection is independent of the operational

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fre-32 Semiconductor material under illumination of light 0 10 20 30 40 50 60 70 80 −20 −15 −10 −5 0 5 10 15 20 Time (μs) Transmission coeficient (mV) Single shot Average 0 10 20 30 40 50 60 70 80 90 −20 −15 −10 −5 0 5 10 15 20 Time [μs] Transmitted voltage [mV] Single shot Average (a) (b)

Figure 4.10: Measured (a) reﬂection and (b) transmission pulse after the silicon is illuminated with light at Ka-band, the laser is turned on at t=0 sec. 5 10 15 20 25 30 35 40 45 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [μsec] Reflection coefficient Measurement Simulation 10 20 30 40 50 60 70 80 90 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time [μsec] Transmission coefficient Measurement Simulation (a) (b)

Figure 4.11: Comparison between the measured and simulated results, (a) reﬂection (b) transmission.

quency. In this section the eﬀect of some of the features of the semiconductor material and optical source on the overall performance of the antenna system is brieﬂy addressed. If the antenna would be used for short range commu-nications or radar applications, the system would operate at low microwave power. The following aspects should then be taken into account.

• Dimensions:

Consider a MMW collision avoidance radar sensor for short range

de-tection using a beam switching antenna with 3.0dB beamwidth of 8.8◦

and 4◦ in the azimuth- and elevation plane respectively [41]. This

Passive and active reconfigurable microstrip reflectarray antennas

Contents

Chapter 1

Introduction

1.1

Research objective

1.2

Research lines

1.3

Novelties and main results

1.4

Outline of the thesis

Chapter 2

Microstrip reﬂectarray

antennas

2.1

Basic microstrip reﬂectarray

2.2

Active microstrip reﬂectarray

2.3

Design parameters of microstrip reﬂectarray

Chapter 3

Single element considerations

3.1

Numerical aspects

3.2

Design parameters

3.3

Performance parameters

Chapter 4

RF Reﬂection and

transmission of

semiconductor material

under illumination of light

4.1

The concept

4.2

Modelling the reﬂection and transmission

co-eﬃcients

T

4.3

Numerical results

4.4

Experimental results

4.5

Discussions