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Publication# Analytical Methods for the Study and Design of Integrated Switched Oscillators and Antennas for Mesoband Radiation

Abstract

This thesis was carried out within the framework of a scientific cooperation project entitled “Application of High Power Electromagnetics to Human Safety” developed by the EPFL, the National University of Colombia and Los Andes University, Colombia. The project was funded by the Swiss Agency for Development and Cooperation (SDC) through the EPFL Centre Coopéation & Développement (CODEV). The Scientific Cooperation aimed at the study and development of techniques for the generation of high power electromagnetic signals for the disruption or preemptive activation of Improvised Explosive Devices (IEDs) during humanitarian clearance activities. The results and conclusions of the thesis will be applied to the construction of a resonant radiator, which can be used for securing humanitarian demining operations in Colombia. The thesis is devoted to the analysis of a specific type of resonant radiators known as Switched Oscillators (SWO). An SWO is a radiator constituted by a high voltage charging circuit that drives a quarter-wave transmission line resonator connected to an antenna. An SWO can produce high-amplitude, short duration, electromagnetic fields, with a moderate bandwidth, when compared to the main resonance frequency. The outcome of the thesis can be also be used in electromagnetic compatibility applications, for the production of resonant, high power electromagnetic fields, with the aim of testing the immunity of electronic systems against Intentional Electromagnetic Interference (IEMI) attacks. The thesis is divided in three parts. The first part deals with the electrostatic design of an SWO. A method for producing an optimized design of the electrodes forming the spark gap of the SWO is presented. The method is based on the generation of a curvilinear coordinate space on which the electrodes are conformal to one of the coordinate axis of the space. Laplace equation is solved in the interelectrodic space, obtaining an analytical solution for the electrostatic distribution. Furthermore, using appropriate mathematical manipulations, we derive an analytical expression for the impedance of the transmission line formed by the proposed electrodes. The second part of the thesis is devoted to the analysis of SWOs in the frequency domain. An original analysis approach, based on the chain-parameter technique, is proposed in which the SWO and the connected antenna are described using a two-port network using which a transfer function between the input voltage and the radiated field is established. A closed form expression of the resonance frequency of the SWO is also obtained. The developed technique makes it possible to study the response of an SWO when connected to an arbitrary antenna with a frequency-dependent input impedance. The final part of the thesis presents the construction and test of an SWO prototype. The prototype design is based on the theoretical developments presented in the first two parts of the thesis. The realized SWO is experimentally characterized using different antennas. It is characterized by an input voltage of 30 kV and a resonance frequency of 433 MHz. Radiated electric fields using monopole antennas were in the order of 10 kV/m at a distance of 1.5 m. The prototype is used for testing the validity of the electrodynamic model for the analysis of SWOs connected to frequency dependent antennas. Different monopole antennas connected to the SWO are considered and the radiated fields are measured and compared with theoretical calculations. It is shown that the developed theoretical model is able to reproduce with a good accuracy the behavior of the SWO connected to a frequency dependent antenna.

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Transmission line

In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are lo

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In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather

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Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar example

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Gabriela Quintero Diaz De Leon

Formal research on Ultra-wideband (UWB) technology started in the U.S. in 2002; where its definition was formulated and the frequency allocation in that country established. However, the first ultra-wideband transmission was done during the confirmation of Maxwell's equations by Heinrich Hertz in 1886, the first ever reported radio transmission. Sparks or very short pulses were sent and received at a distance away from its source. UWB antennas have existed since those times, but technology has been mostly focused on the transmission of continuous wave narrowband signals. The largest problematic encountered in today's UWB antennas is that characterization methods were, since the beginning, meant to describe narrowband antennas. The frequency characteristics of these antennas are constant over their operational bandwidth, hence they can be fully characterized in the frequency domain. UWB antennas, on the other hand, are meant to transmit pulsed signals. Analyzing them only in the frequency domain is not enough to fully evaluate their performance, as pulse distortion is an important parameter that should be controlled. An extended literature review is included in the first part of this thesis, where the available UWB antenna characterization methods are evaluated. Many limitations were encountered, showing that the available techniques do not analyze simultaneously the most important parameters of an UWB antenna. A new characterization method is proposed: the System Fidelity Factor (SFF). Its main purpose is to incorporate frequency, time and space characteristics of a two-antennas system to compare UWB antennas in an efficient way. This is achieved with the correlation between the received and the input pulses, quantifying the distortion produced by the system. The SFF is an interesting tool because both simulations and measurements can be done in a simple and straight-forward manner, using tools that are commonly available in any antenna lab. Any combination of antennas can be analyzed and the free-space channel can be easily replaced with any other environment. Several UWB antennas were designed and used to prove the efficiency of the SFF. A good agreement between the proposed simulation techniques and the measurements was achieved. The antennas are novel designs specially developed for UWB applications under the American or European regulations. The last part of the thesis presents these antennas and analyzes them using the SFF to compare their performance.

The power system has been used for communication purposes for many decades, although it was mainly the power utility companies that used low bit rates for control and monitoring purposes. In the last ten years, however, the deregulation of the power and telecommunication markets has spurred the idea of using and commercializing the power networks for a range of new communication applications and services. The idea has been developed and implemented into both, narrowband and broadband systems, which are defined in terms of the operation frequency band. Depending on the frequency band, the systems over powerlines can be: Narrow-band. They use frequencies ranging from 3-148.5 kHz in Europe, with the upper frequency extending up to 500 kHz in the United States and Japan. In Europe, this frequency range is standardized by CENELEC Standard EN 50065. Broadband. The used frequency range is 1-30MHz; 1-15MHz for outdoor systems and 15-30MHz for indoor systems. In this frequency range, the standardization situation is still unclear and there exist no regulations. The developed applications and systems use different parts of the power network: medium voltage (MV) and low voltage (LV) cabling for outdoor applications and building cabling for indoor applications. These cables are designed and optimized for power transmission at frequencies of 50/60Hz and represent a hostile medium for transmissions at higher frequencies. This thesis concentrates on electromagnetic compatibility (EMC) aspects and some optimization issues of the broadband systems, currently known as Powerline Communications (PLC) or Broadband Power Line (BPL). The work presented here was preformed in the framework of the European project OPERA (http://www.ist-opera.org/). A short description of the project is given in Chapter 1. The second chapter presents the basis, introduction, description and state of the art of the topics of interest for this thesis. That chapter is divided into three parts. Each of these parts starts with a short introduction to the topic to be addressed. The introductions are intended for those not familiar with the topic at hand and they can be skipped by those already knowledgeable of it. The first part of Chapter 2 gives an overview and introduction to telecommunication issues relevant to the thesis, as well as the general technical specifications of the OPERA system. The second part deals with the transmission medium which, for the case of PLC, is the power system. The fundamentals and the different components of the PLC system are given there and the state of the art regarding the transmission channel is presented. The third part deals with the EMC and standardization issues related to the technology. The main contributions of the thesis are presented in chapters 3 to 7. The PLC technology distinguishes itself from other technologies in that it uses already existing, ubiquitous wiring, so that no new infrastructure is needed. On the other hand, using a channel designed originally for other purposes means that it is not optimized for the frequencies and applications of interest for broadband transmission. If PLC is to compete with other technologies, these problems have to be well understood and solved, so that the system can be optimized by taking into account the parameters and constrains of the already existing medium. Although the PLC system is being improved continuously, there are still concerns about emissions, immunity and standardization. These issues are important since PLC operates in an environment already populated by other services at the same frequencies, so that fair co-existence is needed. Moreover, the PLC modem has a combined mains and telecom port and, as a consequence, the standards for conducted emissions from those two types of ports are not directly applicable. In addition, the symmetry of the cables used is low and, therefore, emissions are higher than, for example, emissions from twisted pair cables used in xDSL. A good understanding of emissions and immunity in PLC systems is therefore of great importance for the optimization of the system and for EMC standardization to be based on objective technical criteria. Even if the basic phenomena are essentially the same as for any other wire transmission system, the complexity and variability of the topologies of existing structures is so large that simple, straightforward solutions are often not applicable. Emissions from the cabling are primarily due to the common mode signals. Part of the energy in this mode is injected by the imperfectly balanced output stages of the PLC modems themselves. In addition, the common mode appears at punctual imbalanced discontinuities and distributed asymmetry along the PLC signal path in the power cables. Chapter 3 presents the work performed to improve our understanding of the sources of the common-mode current and the parameters that influence its behavior, including related measurements and simulations. For the purpose of this study, a model house was built at the EPFL's test site. Different cablings were used to study the influence of different parameters on the behavior of the common-mode current since it is the main source for both types of emissions, conducted and radiated ones. The influence of different parameters such as the cable terminations, the symmetry of the termination, the height of the conductors above the ground, the presence of power outlets, switches, empty and occupied sockets and the topology, are analyzed. The data are also used to test two methods used to simulate the differential-to-common-mode conversion and the conducted emissions, namely the transmission line model and the full wave approach provided by the Method of Moments through the Numerical Electromagnetic Code (NEC). In Chapter 4, problems related to PLC immunity testing are treated. We show that the conversion of the differential mode to the common mode is coupled with the reverse conversion by reciprocity. Due to the low symmetry of PLC cabling, part of the injected common mode test signal is converted into a differential mode signal that interferes with the wanted signal at the input of the modem being tested. Depending on the actual symmetry of the Coupling-Decoupling Network (CDN), not specified in the standards, the immunity test may yield erroneous results due to the effect of this differential mode component. Working under the assumption that the CDN is built to exhibit a symmetry similar to that of PLC networks as inferred from its longitudinal conversion loss, we estimate the differential mode disturbance level that the modems should withstand from a narrowband interferer. The bit error rate induced by the presence of the disturbing differential mode current from the CDN is also estimated, for a total physical channel transmission rate of 200 Mbps, to be of the order of 1×10-5 to 5×10-5. Since these rates can be handled by error correcting coding and MAC ARQ procedures, it is concluded that the modems are not likely to suffer any severe performance degradation due to immunity testing if the CDN exhibits a symmetry similar to that of PLC networks. Simulating the complete PLC network or any significant part of it using numerical techniques such as the method of moments proves to be of limited practical use due to the fact that PLC networks extend over many wavelengths. The transmission line approximation, on the other hand, although more efficient and sufficiently accurate for differential mode calculations, is not directly applicable to simulate the EMC behavior since it neglects the antenna-mode currents that are significant contributors to the radiated emissions. Chapter 5 presents a novel approach to evaluate the antenna-mode currents using a modified transmission line theory, thus making this numerically efficient technique applicable to the estimation of emissions in PLC. An integral equation describing the antenna-mode currents along a two-wire transmission line is derived. It is further shown that, when the line cross-sectional dimensions are electrically small, the integral equation reduces to a pair of transmission line-like equations with equivalent line parameters (per-unit-length inductance and capacitance). The derived equations make it possible to compute the antenna mode currents using a traditional transmission line code with appropriate parameters. The derived equations are tested versus numerical results obtained using NEC and reasonably good agreement is found. Another important EMC issue related to PLC is the mitigation of emissions. Chapter 6 describes a technique that has been proposed to achieve a reduction of emissions associated with indoor PLC networks through the introduction of a 180° out-of-phase replica of the PLC signal into the unused neutral-ground circuit. A modification to this technique is proposed based on the selection of the appropriate amplitude and phase of the auxiliary signal, allowing a higher degree of field attenuation. A way of implementing this technique is proposed and studied, namely the integration of a required antenna into the PLC modems themselves. The measured fields very close to the modem allow the determination of the magnitude and phase of the compensation voltage. The proposed implementation should be used only to handle customer complaints, when emissions should be lowered at locations where PLC signals might cause unwanted interference or when additional capacity is required and it can be obtained through the gained signal to noise margin. Although, in principle, due to nonalignment of the wanted and the compensation field directions, minimizing one component of the field may result in an increase of the other components, we show that the application of the technique results in an overall average reduction of 10-20 dB of all the field components in the region of interest. In the same Chapter 6, we address the more general issue of the application of mitigation techniques' gained emissions margin to increase the overall throughput of PLC systems. We show that an increase in the signal power (made possible by the inclusion of mitigation techniques) leads to a considerable increase in the PLC channel capacity. Using a number of simplifications, we show that the capacity of the channel can indeed be increased by up to 66 Mbps for mitigation efficiencies of only 10 dB. We also present the results of laboratory measurements aimed at studying, under controlled conditions, different characteristics of notching in OPERA PLC modems, such as total and effective notch width, notch depth, maximum notch depth, etc. These measurements show that it is possible to obtain attenuations of up to about 45 dB for notches in all frequency bands, 10MHz, 20MHz and 30MHz. What differs for these three bands is the minimum number of carriers that need to be notched to obtain that maximum attenuation. This is an important point, since, to implement notches that have the required depth and width, one must know how many subcarriers to suppress and how deep these need to be reduced. High density PLC deployment requires the increase of overall system data rate. To achieve the higher data rates, frequency reuse in these systems is needed. In Chapter 7, we present the idea for using so-called blocking filters as a possible solution for a frequency reuse. Experimental data obtained on a real distribution network show that the use of blocking filters can, in certain cases, ensure high enough RF separation of the LV feeders belonging to the same substation. In some cases, even with the possibility to design and integrate effective blocking filters, the system needs to provide additional synchronization mechanisms for frequency reuse.

The design and minaturization of microwave circuits involves the analysis and optimization of a large varity of structures, which, in general, are based on arbritrary objects embedded in also arbritary media. The most common situation is found when optimizing terminal antennas, whose main constraint is the antenna's volume, which must be fitted into a specified space, which in general is the phone or laptop case. This kind of antennas can also include stratified media, oblique metallizations, dielectric objects, waveguide components, in their definition making their analysis more difficult from the numeric point of view. The complete treatment of this kind of problems has been performed traditionally using Finite Differences or Finite Elements software, while it is more rare to find Method of Moments implementations for the solution of this kind of general problems. The Method of Moments has a certain number of advantages as the inclusion of radiation conditions or stratified media in the Green's function of the problem. Due to this it is possible to mesh only the surfaces or boundary conditions that are not included in the Green's function definition, obtaining, for instance, a more natural radiation boundary condition compared to other fullwave methods. The other big concern is the optimization of this kind of structures. In general the structures we are dealing with in this work can have very irregular shapes, in order to fit within the required volume constraints. The traditional optimizations techniques based on the gradient or conjugated gradient are not efficient when optimizing functions containning multiple minima and a large search space, which is the case in the optimization of terminal antennas. When miniaturizing terminal antennas or just a simple microstrip filter, the number of unknowns can be very large, and the different optimization variables can vary within wide limits in the search space. In this situation the Genetic Algorithms are ideal for seeking the global optimum solution of our problem. This work covers the analysis and optimization of microwave circuits, including antennas and filters in microstrip and waveguide technologies, paying more attention to the implementation of the Method of Moments (MoM) in conjugation with the Mixed Potential Integral Equation (MPIE) and Electric/Magnetic Field Integral Equation (EFIE/MFIE). The work has been split into 3 main goals: The analysis of 3 dimensional structures in stratified media, including arbritary shaped dielectric bodies using the Method of Moments, (MPIE,EFIE,MFIE). The analysis of shielded environments and more precisely the analysis of retangular waveguide cavities with the Method of Moments. The implementation of several optimization techniques, emcompassed in the frame of genetic algorithms, for the design and miniaturization of terminal antennas and microstrip filters. Some relevant examples linked to the efficiency and accuracy of the different methods and techiques explained in this work are included in each chapter, yielding to practical results suitable to be used in real life design problems. The main contributions of this work can be summarized as follows: In Chapter 2 we have developed the interpolation of 3D Green's function to the general solution of dielectric objects embedded in multilayered media. The interpolation method itself is preceeded by a spectral extraction of the quasi-static terms. This technique, very often applied in complex images techniques, has been applied to our specific Green's function problem yielding very good results in terms of accuracy and Green's function computation time. Another contribution, also emcompassed in Chapter 2, is the integration of the static part of the field dyadic G̿EM, performed by splitting the field dyadic into TM and TE components, allowing then an analytical integration of the dyadic terms in stratified media. In the frame of shielded environments in Chapter 3, the most important contribution is the extension of Ewald's acceleration technique to full electric and magnetic problems, allowing the acceleration of the field dyadic G̿EM and thus permit the extension of the MoM to the simulation of arbritary metallic shapes coupled to apertures through Ewald's approach. In Chapter 4 the most important contribution is the implementation of a Bayesian optimiser based on the estimation of probability made by dependencies trees. The dependency tree based method found in [1] and later in [2] has been adapted to the terminal antenna miniaturization yielding to excellent results in optimisation time and quality of the solution provided by the optimiser. Our implementation of the dependency tree method was found to be better than the traditional method used in this kind of problems. Chapter 4 contains also an implementation of the growing cells method presented in [3] for the specific problem of optimising pseudo periodic structures, like microwave filters, yielding to a powerful interpolating method which accelerates the optimisation process of microwaves devices whose fitness response is very time consuming.