SDA to obtain dispersion characteristics of the slot line, and also microstrip line. Jansen extended the dynamic SDA to analyze the higher order modes in the microstrip. The method is very powerful and analytically elegant. It has been used and improved by other researchers in the field of planar resonators, antenna, and line structures. Other powerful methods, such as the method of moments, finite elements, finite‐difference time‐domain method, and so on have also been developed to analyze the 2D and 3D complex planar structures. The contemporary EM‐Simulators are based on these numerical methods. The closed‐form models for faster computation of the static and frequency‐dependent line parameters of planar lines have also been developed by several investigators. The closed‐form models of lines, discontinuities, and so on helped the development of the Circuit Simulators [J.72–J.75, B.15, B.16].
1.3 Overview of Present Book
The book presents a seamless treatment of the classical planar transmission lines and modern engineered planar lines using the concept of the engineered electromagnetic bandgap (EBG) structures and metamaterials. The modern EBG and metamaterials based planar lines are the outcome of the classical researches in the artificial dielectrics and concept of homogenization of mixing of inclusions in the host medium. Gradually, the modern microwave planar transmissions became a complex medium of wave propagations on the 1D lines and 2D surfaces. It demanded serious considerations of wave–matter interactions, especially in the engineered materials by the microwaves researchers and engineers. It demanded a physical understanding of various electromagnetic phenomena taking place in the artificially engineered complex medium. It also required the analytical and circuit modeling of the planar transmission lines under the complex environment. The present book: Introduction to Modern Planar Transmission Lines (Physical, Analytical, and Circuit Models Approach) addresses these problems from the very basics, making it suitable for the early comers to the fields. However, the detailed treatment of topics could be also useful to more experienced professionals and engineers. The numerical methods used in the analysis of the planar structures and basis of the EM‐simulators are more specialized topics beyond the scope and line of thought followed in the present book.
The key concept used throughout the book is the modeling, physical, analytical, and circuit, of the planar structures. However, what is the meaning of modeling itself? Scientific modeling is a process of understanding the unknown with the help of known. The reverse is not possible. The method of analogy is a great tool in such a modeling process. The growth of electromagnetic field theories at different stages has evolved from the previously known results of the gravitational field. Likewise, the gradual development of the transmission line theory has used the analogy of heat flow. These are two important illustrative examples discussed in the previous section. The experimental observation and the experimental verification of the theoretically predicted results are further contributors to the modeling process. The scientific modeling process has been examined in depth by the modern educationists [B.17]. The reader can observe such a modeling process in the development of models for the complex planar medium exhibiting unique properties.
1.3.1 The Organization of Chapters in This Book
The chapters of this book are organized into four distinct groups as follows:
1 Introductory transmission line and EM wave theory.
2 Basic planar lines and Resonators: Microstrip, CPW, Slot lines, Coupled lines, and Resonators.
3 Analytical Methods: Conformal mapping method, Variational method, Full‐ wave SDA, and SLR formulation.
4 Contemporary engineered planar structures: Periodic planar lines and surfaces, Metamaterials – Bulk, 1D metalines, 2D metasurfaces.
The group i reviews the transmission line and the EM‐theory to assist the reader to follow the rest of the chapters with ease. The groups ii and iii form the classical transmission lines, and the group iv is the modern transmission lines and surfaces. The book presents a seamless treatment of the classical planar transmission lines and the modern engineered planar lines and surfaces using the concept of EBG and metamaterials. The modern EBG and metamaterials based planar lines are the outcome of the classical researches in the artificial dielectrics and concept of homogenization of mixing of inclusions in the host medium. The topics of the chapters are selected to provide comprehensive coverage of the needed background to understand the functioning of both the classical and modern lines and surfaces. Each chapter follows a uniform style. The topics within a chapter start with simple concepts and move to a higher complexity level. Likewise, the chapters are also arranged from the simpler to complex.
The distribution of the chapters among the groups is discussed below. The key features of the chapters are also summarized.
Introductory Transmission Line and EM‐Wave Theory
The six chapters, chapters 2–7, on the transmission lines and various aspects of the EM‐theory are introduced in the book before even commencing with the microstrip in chapter 8. These topics provide the essential background to follow smoothly the topics covered in this book. It could be useful in understanding the analysis and modeling of the planar line structures, the EBG based lines, and surfaces, and also the metamaterials and metasurfaces. Moreover, the topics discussed may also help to understand the modern publications in these fields. The usual undergraduate textbooks on the EM‐theory do not cover all the topics. However, the reader's familiarity with the transmission line and EM‐theory is assumed. The reader interested in a more detailed study of these topics can follow the references given at the end of the chapters. Some contents of the chapters are highlighted below.
The chapters 2 and 3 on transmission lines are written as a review. However, it goes beyond a regular review, although it starts with the familiar notion of oscillation and wave propagation on lines. Usually, the available textbooks present the transmission line equations and wave equations for the uniform lines only, without any source. The present book covers the transmission line equations and wave equations with a source, and the analysis of the multisection transmission lines is also introduced. Such formulation is used in the chapters 14 and 16 to obtain the Green's functions of planar transmission lines used with the variational method and full‐wave spectral‐domain analysis (SDA) method. The chapter on the transmission line adequately covers the concept of dispersion in the wave supporting medium. Also, the impact of the reactive loading of the line on the nature of wave propagation is discussed. Such treatment prepares a reader for the periodically loaded engineered lines and surfaces, both as the bandgap medium and homogenized metamaterial medium. These topics are discussed in chapters 19–22. Chapter 3 covers various parameters used for the characterization of a line section. Understanding of this topic is essential for understanding the microwave components design, the results obtained from EM‐simulation, and to develop the circuit models.
Chapters 4 and 5 cover the wave's propagation in the material medium. Again, primarily it is a review of the EM‐theory. However,
