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2024 | Buch

Basic Concepts in Electromagnetic Radiation Kapitel lesen Erstes Kapitel lesen

Electromagnetic Sources and Electromagnetic Fields

verfasst von: Gaobiao Xiao

Verlag: Springer Nature Singapore

Buchreihe : Modern Antenna

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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SUCHEN

Über dieses Buch

This book presents a modified spherical harmonic expansion method in which the electromagnetic fields and their sources are expanded with the same set of spherical vector basis functions in a similar procedure. Explicit expressions for the electromagnetic fields, potentials, energies, and the related Green’s functions are derived for the spherical modes in both frequency domain and time domain. Based on the formulation, the relationships between the electromagnetic sources, the electromagnetic far fields, and the electromagnetic near fields are clearly revealed. In particular, a nonuniform transmission line model is developed for intuitively characterizing the total radiation process. The introduction of the cutoff radius and the cutoff mode degree provides a simple reference for determining the numbers of degrees of freedom of the fields associated with sources in a bounded region. Based on the theory, an efficient hybrid method for synthesizing antenna arrays with complex footprints is proposed and demonstrated with several numerical examples. Effective algorithms are also developed for reconstructing the radiating part of the current sources.

This book is intended for researchers, engineers, and graduate students who are interested in studying the energy transfer in electromagnetic radiation, synthesis and measurement of antenna arrays, and applications of inverse electromagnetic source problems.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Basic Concepts in Electromagnetic Radiation
Abstract
This chapter will not discuss the incompleteness of the classical macroscopic electromagnetic theory. Readers who are interested in this topic may find comprehensive discussions in the literature, such as the books by Barrett T W and Rohrlich F. On the contrary, we confine our discussions within the frame of the Maxwell’s theory and try to give an intuitive interpretation to the relationship between the electromagnetic fields and the electromagnetic sources in free space. The electromagnetic fields are solutions to the Maxwell equations. They are generally characterized by some conserved dynamic quantities, of which the most commonly known ones are the electromagnetic energy, the electromagnetic power, the electromagnetic linear momentum, and the electromagnetic angular momentum. We will give a brief introduction to the fundamental notations, concepts, and principles in the classical electromagnetic theory. Detailed and systematic descriptions about the classical electromagnetic theory can be found in classical books.
Gaobiao Xiao
Chapter 2. Q Factor of a Radiator
Abstract
Q factor is a parameter for describing the resonance behavior of a resonator or an oscillator. For time harmonic resonators with higher Q factors, they may oscillate with higher amplitude and attenuate slower. The frequency range that they can oscillate tends to be narrower. However, in practical engineering, Q factors may be defined in different ways in different problems. This chapter will give a brief introduction to the commonly used definitions of Q factors for circuits and antennas.
Gaobiao Xiao
Chapter 3. Non-relativistic Radiation of a Moving Charge
Abstract
A static charge generates an electric field in the space and stores an electric energy called the Coulomb energy. A moving charge introduces an additional magnetic field in the space and stores a magnetic energy. The electric energy and the magnetic energy associated with a uniformly moving charge may be called velocity energy. The Coulomb energy and the velocity energy are considered as being attached to the charge. When the charge moves uniformly, the two energies may be dragged by the charge and cause energy fluctuation in space. When a charge is accelerated, part of the attached fields and energies may be not able to keep the pace with the charge and will be thrown away from the charge to form the electromagnetic radiative field and radiative electromagnetic energy. The concept of the electromagnetic energies of a charged particle may help us separate the macroscopic electromagnetic energy of a distributed source. In order to reveal the connection between the electromagnetic field of the charged particle and the macroscopic electromagnetic field of the distributed source, we are to derive the electromagnetic potential, field and energy of a moving charge from the Maxwell equations.
Gaobiao Xiao
Chapter 4. Spherical Harmonic Expansion
Abstract
Analytical and semi-analytical methods can be used to reveal the general principles in the electromagnetic issues, to catch the characteristic properties of a radiating system, and to predict the applicability boundaries and limitations of the numerical methods. In this chapter, we discuss the spherical harmonic expansion solutions to the fields of a bounded source in free space. We treat the three-dimensional space in vacuum as a two-port radial waveguide The spatial distributing properties of the fields on the transverse spherical surfaces and the propagation properties of the fields in the longitudinal direction are handled separately. This strategy is quite flexible for handling the discontinuities in the waveguide, like the local reflection at the interface of two waveguides. The spherical harmonic expansion expressions for the fields and potentials have been derived both in time domain and in frequency domain. The dyadic Green’s functions are rederived using a method different from that was used by Collin and Tai. The formulation is more straightforward, and the treatment of the discontinuities crossing the source point is simpler. We will show that the expansion of the static fields, the time harmonic fields, and the transient fields can be handled in almost the same manner.
Gaobiao Xiao
Chapter 5. Nonuniform Transmission Line Model
Abstract
Spherical harmonic expansion provides an effective analytical tool for evaluating the radiation property of radiators in free space. Because the spherical harmonic modes are orthogonal, we can analyze the radiation fields mode by mode and obtain the total radiation fields by summing up the contribution from those modes of significance. In this chapter, by comparing the governing equations for the transverse electric field and the transverse magnetic field of a spherical harmonic mode with the standard Telegraphers’ equations, we create an equivalent nonuniform transmission line (NTL) model for the spherical harmonic modes in both time domain and frequency domain. Similar to conventional waveguides, the equivalent NTL model consists of a propagating zone and an evanescent zone, separated by a cut-off interface with the cutoff radius. Local lumped element circuit model of the NTL is developed with nonuniform distributed inductances or capacitances. The electromagnetic radiation process in free space and in media with radially varying parameters can be illustrated more intuitively with the NTL model.
Gaobiao Xiao
Chapter 6. Pulse Radiator in Free Space
Abstract
Pulse radiator in free space is a suitable example to use for deriving the energy separation formulae because all the energies are finite and their performances with respect to the source can be examined rigorously. By analogy with the electromagnetic energy concepts in the classical charged particle theory and using the relationships derived from the Maxwell equations, the total electromagnetic energy of a pulse radiator is divided into three parts. The first part is the Coulomb-velocity energy. It disappears immediately after the source has disappeared. The second part also disappears a short while later after the source has disappeared. It is called the macroscopic Schott energy in this book because its behavior is similar to the Schott energy in the charged particle theory. The third part is the radiative electromagnetic energy which keeps propagating in free space till it encounters other sources. The energy separation formulae for time harmonic waves are also available. The results in time domain and frequency domain are completely in consistent because they are respectively derived from the time domain Maxwell equations and the frequency domain Maxwell equations directly. It is also verified with the Hertzian dipole both in frequency domain and in time domain.
Gaobiao Xiao
Chapter 7. Synthesis of Far Field Patterns
Abstract
In this chapter, we will focus on the synthesis of antenna arrays and treat the problem from a slightly different perspective. We at first to synthesize the required radiation pattern with a continuous current distribution in free space, and then spatially sample the continuous current source and realize it with discrete radiation elements. We show that the effective number of degrees of freedom (NDF) can be adopted as a useful information to obtain the direct synthesis pattern, which can be used as a very good initial value for further optimization. The sidelobe levels and the ripples in the main beams can be effectively controlled using an efficient hybrid optimization algorithm, in which the extrema of the objective radiation pattern are assigned based on the properties of the entire function while their positions are flexibly adjusted. Meantime, we investigate the relationship between the radiation pattern of the continuous current and that of the spatially sampled current and discuss the aliasing effect on the radiation pattern due to spatial sampling. Eleven examples are provided to demonstrate that the sidelobe levels and the ripples in the main beams can be controlled much more effectively with the hybrid method.
Gaobiao Xiao
Chapter 8. Electromagnetic Inverse Source Problems
Abstract
In this chapter, we give a brief introduction to the electromagnetic inverse source problems in free space. Making use of the spherical harmonic expansions discussed in the previous chapters, the NDFs of the electromagnetic fields at different spherical observation surfaces can be estimated. Effective and stable numerical methods are developed for reconstructing the current sources in domains with regular structures from their radiated fields. In the electromagnetic inverse problem, we use the concept of the effective NDF of a source and the effective NDF of the field of the source. To develop stable reconstruction algorithm, we generally consider that the two NDFs should be matched. When we talk about the effective NDF of a field, we have to associate it with a source region and specify the size and shape of the source region, as well as the distance between the field and the source region. When we talk about the effective NDF of a source, we may have to associate it with the field on an observation surface and specify the distance between them. Basically, we tend to consider the source in a bounded region and its field at the sampling surface as a pair of connected physical quantities.
Gaobiao Xiao
Backmatter
Metadaten
Titel
Electromagnetic Sources and Electromagnetic Fields
verfasst von
Gaobiao Xiao
Copyright-Jahr
2024
Verlag
Springer Nature Singapore
Electronic ISBN
978-981-9994-49-6
Print ISBN
978-981-9994-48-9
DOI
https://doi.org/10.1007/978-981-99-9449-6

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