to the topics discussed in other chapters. The chapter 4 commences with a basic review of the electromagnetics and elementary electrical properties of the material medium, such as linearity, nonlinearity, homogeneity, inhomogeneity, anisotropy, and losses. It further covers the topic of the circuit modeling of a medium. The known topics of Maxwell's equations in the differential form, as well as in the vector‐algebraic form are presented. The wave propagation is discussed not only in the isotropic and conducting media but also in the anisotropic, uniaxial, gyroelectric, and biaxial media. The complex media are encountered by the wave propagating in the metamaterials. While reviewing the wave polarizations, the Jones matrix description of polarization states is also discussed. It is needed to follow the contemporary developments in the metasurfaces. Chapter 4 ends with the concepts of isofrequency contours and isofrequency surfaces, and the dispersion relations in the uniaxial medium.
Chapter 5 reviews both the normal and polarization‐dependent oblique incidence of the waves at the interface of two media. It also presents the equivalent transmission line model of the wave's incidence at the interface of two media. The model can be extended to more number of layers. The formulation has many applications. The model is used for instance in chapter 20 on the EBG surface. The chapter 5 also presents the basic electrodynamics of the engineered metamaterials and formulate the basic characteristics of the wave propagation in the metamaterials. It also discusses some important directions for applications of metamaterials. However, the realization of the bulk metamaterials, metalines, and metasurfaces are followed up in the chapters 21 and 22.
Chapter 6 covers a review of the electrical properties of the natural and artificial dielectric media. It also presents various static and frequency‐dependent models of the mixture media. The artificial dielectric medium finds its application in modeling the metamaterials. The Lorentz, Drude, and Debye models applicable to the frequency‐dependent permittivity are discussed. Chapter 6 further discusses the interfacial polarization and its circuit model. This important topic is usually not discussed in popular textbooks. The modeling of the substrates, using the single term Debye and Lorentz models, as well as the multi‐term and wideband Debye models are elaborated. These models help to get the causal effective permittivity of the planar lines of the substrates, useful in the time‐domain analysis of pulse propagation on the planar lines. Finally, the chapter ends with a novel concept of artificial metasubstrate.
Chapter 7 comprehensively treats basic waveguide structures. It begins with the classification of the modal EM‐fields, and the sources of their generation. The waveguides are analyzed using the scalar electric and magnetic potentials. The spectral domain analysis (SDA) method discussed in chapter 16 is based on these scalar potentials. The concept of the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC) with boundary conditions are introduced. The analysis of the rectangular geometry of the waveguides formed with these surfaces is presented. Thus, apart from the usual all metallic walls, i.e. the PEC based waveguides, all PMC and two PEC and two PMC walls waveguides are also discussed. The dielectric slab waveguides and surface‐waveguides are also presented. The concept of the odd/even mode analysis is introduced. These concepts are used in the book for the analysis of symmetrically coupled planar lines in chapters 11 and 12. The simple and powerful transverse resonance method (TRM) is introduced to get the propagation characteristics of the dielectric‐loaded waveguides and the multilayer surface‐waveguides. Finally, chapter 7 ends with the contemporary substrate integrated waveguide (SIW) developed in the environment of the planar technology.
Basic Planar Lines and Resonators
The planar line structures – microstrip, CPW, and slot line are discussed in chapters 8–10, respectively. The chapters 11 and 12 cover the theory of the coupled transmission lines and their realization and analysis in the planar technology environment. The theory of resonating structures and planar lines version of the resonators are discussed in chapters 17 and 18, respectively. The fabrication technologies – MIC, MMIC, MEMS, and LTCC used in the planar lines and components are reviewed in chapter 13.
The microstrip is the most commonly used planar line in planar technology. It is in the inhomogeneous medium supporting the hybrid‐mode that is approximated as the dispersive quasi‐TEM mode. However, at the lower frequency, it is treated in the nondispersive static condition. Chapter 8 introduces the concept of medium transformation from the inhomogeneous medium to the homogeneous medium using Wheeler's transformation for the lossy microstrip medium. The results on the static microstrip line parameters are summarized. The dispersion law is discussed to get the dispersion model of microstrip. Some other dispersion models are also summarized. The losses and their computation are presented in detail. Finally, chapter 8 ends with the circuit model of the microstrip line giving the complex frequency‐dependent characteristic impedance and propagation constant. The circuit model explains the behavior of the low‐frequency dispersion due to the finite conductivity of the conductors. Several topics are covered for the first time in a book form. The derivations of some frequently used expressions are provided.
The coplanar waveguides (CPW) and the coplanar stripline structures (CPS) and their variations are discussed in chapter 9. The approach used in this chapter is based on the detailed derivation of the results using the conformal mapping method. Usually, the available books only summarize the results of the conformal mapping method. However, chapter 9 briefly presents the conformal mapping method as applied to the CPW and CPS. The characteristics of the modes, dispersion, and losses are presented in detail. The results are also presented for the synthesis of the CPW and CPS line structures. Finally, the circuit models of the lossy CPW and CPS are given to get the frequency‐dependent complex characteristics impedance and propagation constant.
The modeling of the third important planar line, i.e. the slot line is presented in chapter 10. The modeling process is based on the unique waveguide model of Cohn. The model provides the frequency‐dependent characteristic impedance and propagation constant of the slot line, supporting the hybrid mode. The waveguide model of the slot line treats the hybrid‐mode as a linear combination of the TE and TM modes. The equivalent waveguide model is further extended to the multilayer and shielded slot line structures. The chapter ends with the closed‐form integrated model of the slot line to compute
