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Introduction To Modern Planar Transmission Lines. Anand K. Verma
Читать онлайн.Название Introduction To Modern Planar Transmission Lines
Год выпуска 0
isbn 9781119632474
Автор произведения Anand K. Verma
Издательство John Wiley & Sons Limited
1.2.2 Analytical Methods Applied to Planar Transmission Lines
Assaudourion and Rimai considered the microstrip in the quasi‐static limit. They assumed the TEM mode propagation on it. They applied, in 1952, the well‐established conformal mapping method to compute the characteristic impedance, dielectric, and conductor losses. Between the years 1954 and 1955, Cohn also used the conformal mapping method to get the design‐oriented results for the characteristic impedance, dielectric and conductor losses of the stripline. He further used the conformal mapping method to get the odd‐even mode impedances of the edge‐coupled strip lines in 1955 itself. He further obtained these results for the broadside‐coupled strip lines in 1960. Following the conformal mapping method, in 1964 and 1965 Wheeler produced more accurate and design‐oriented expressions for the computation of characteristic impedance of microstrip line. He extended his analysis to get further results in 1977 and 1978 [J.56–J.64].
In 1969 Cohn suggested another planar line, i.e. the slot line. It is a complementary structure of the microstrip line. He also presented the equivalent waveguide model of the slot line, and obtained the frequency‐dependent propagation parameters of the slot line. Next in the group of the planar lines is the coplanar waveguide (CPW) proposed by C.P. Wen. He obtained the initial quasi‐static line parameters of CPW using the conformal mapping method. Subsequently, the conformal mapping method was applied to analyze several variants of the planar lines [J.65–J.67].
Other quasi‐analytical and numerical methods were also used for the analysis of microstrip lines. For instance, in 1968 Yamashita and Mitra introduced the quasi‐analytical variational method in the Fourier domain to obtain the quasi‐static line parameters of the microstrip line. It was the prelude to the quasi‐analytical dynamic spectral domain analysis (SDA) of microstrip and other planar lines. The dynamic SDA is a full‐wave analysis method that considers the hybrid mode nature of planar lines. After a gap of nearly 10 years, Itoh used the concept of the discrete Fourier transform and Galerkin's method to get the static line parameters of suspended coupled microstrip lines, and also extended the method to suspended multiconductor microstrip structures. The Fourier domain method was significantly extended by many investigators to other planar structures such as the CPW [J.68–J.71, B.15, B.16].
In 1973 and 1974, Itoh and Mitra introduced the dynamic 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