Introduction To Modern Planar Transmission Lines. Anand K. Verma

Introduction To Modern Planar Transmission Lines - Anand K. Verma


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href="#ulink_3b605365-ac70-508b-bf63-4763449078f7">Fig (5.7). These media are obtained just above the plasma frequency. The refractive index of the ENZ and MNZ is numerically less than unity, supporting the fast‐wave. Even a zero refractive index could be obtained. It is known as the “nihility” [B.6].

Schematic illustration of electrical grouping of the materials media in the (mu r, epsilon r)-plane.

      The DNG materials are commonly known as metamaterials. However, artificially engineered ENG, MNG, ENZ, and MNZ media also belong to the metamaterials. Even the DPS could be engineered, and called a metamaterial, to realize the controlled values of permittivity and permeability to meet the specific design requirement. One such requirement is to develop the microwave absorbers discussed in subsection (5.5.8). Several dedicated books are available on the topics of the metamaterials [B.6–B.10].

      Depending on their characteristics, several other names have also been proposed for the metamaterials [B.7, B.10]. Veselago proposed the concept and electrodynamics of the metamaterials [J.3]. The metamaterials have been synthesized by embedding either the resonating type inclusions or the C‐L type artificial transmission line inclusions in a host medium. The metamaterials could be either resonant metamaterials or nonresonant metamaterials, so the metamaterials are structured composite materials. Starting with J.C. Bose, such composite materials have a long history [J.4–J.6]. The concept of composite materials and their modeling is discussed in section (6.3) of chapter 6. The C‐L line supports the backward wave propagation. It is discussed in section (3.4) of chapter 3. A metamaterial, i.e. the DNG medium, is also called the backward wave (BW) medium, or BW material [J.7]. The normal forward wave supporting DPS medium could be called forward wave (FW) medium, or FW material.

      The physical dimensions of the resonating inclusions, or the C‐L line inclusions, are much smaller than the operating wavelengths. The metamaterials could be treated as the homogenized medium described by the parameters permittivity and permeability. The inclusions are arranged in the host medium either periodically, or nonperiodically. The periodically arranged inclusions, with a period λg/2, form another group of metamaterials known as the electronic bandgap (EBG) materials. It is discussed in chapters 19 and 20. Even the ENG and MNG materials have been artificially developed using such inclusions.

      

      5.5.2 EM‐Waves in DNG Medium

      This section considers the EM‐wave propagation in the lossless DNG medium, the concept of the negative refractive index, the basic circuit model of a DNG medium, and the lossy DNG medium.

      Lossless DNG Medium

      Maxwell's equation (4.4.11a,b) of chapter 4 could be written for a lossless (σ = 0) DNG medium by using (−|εr|) and (−|μr|) in place of their usual positive values:

      (5.5.2)equation

      Figure (5.8c) shows both the sets of the vector triplets of a DPS medium. The field vectors are rotated in cyclic order so that the power flow is maintained from left to right‐hand side, i.e. from a source located at the origin O, power flows outwardly in a positive direction. For both the phase and group velocities, the DPS medium follows the right‐hand (RH) coordinate system, so a normal DPS medium is called the right‐handed, i.e. the RH‐medium. As the RH‐system holds for both triplets, they are combined into one diagram as shown in Fig (5.8c). For a DPS medium, the directions of the vectors images and images are identical, i.e. they are parallel vectors giving the relation images. Therefore, in a DPS medium, both the phase and group velocities are in the same direction giving Скачать книгу