1. Introduction

Waveguides, due to their low insertion loss and high power handling capabilities at microwave and millimeter-wave frequencies, are the transmission line commonly used for transmitting or propagating or guiding the signals of these frequencies from one point to another. The propagation characteristics of a guiding structure are generally represented by its dispersion characteristics. The dispersion characteristics are the study of structure supported frequency for a given phase propagation constant, and most commonly being plotted as the supported angular frequency ω (¼ 2π f, f being frequency) against the phase propagation constant β. Therefore, the dispersion characteristics are also known as ω � β characteristics. The dispersion (ω � β) characteristics of a waveguide is a hyperbola that has a cutoff frequency, more specifically a lower cutoff frequency. All the signals having

category of gyro-devices, for the broadband amplifier namely the gyro-travelingwave tube (gyro-TWT) the growth rate of the TM-mode vanishes at higher frequencies [6]. The models are also restricted to circular waveguide and the analyses

Metal- and Dielectric-Loaded Waveguide: An Artificial Material for Tailoring the Waveguide…

In this section, we will explore two variants of dielectric-loaded structure: (i) the

This model (model-1) includes a metallic circular waveguide of inner radius rW, inner wall of which is containing a dielectric lining of inner radius rL and relative permittivity ε<sup>r</sup> for the full length of the waveguide [7]. (Here, the waveguide is considered to be infinitely long and there is no reflection of the traveling signals

circular waveguide with dielectric lining on metal wall (Figure 2), and (ii) the circular waveguide with dielectric coaxial insert (Figure 3) for their dispersion characteristics and the tailoring of these characteristics with change of the relative

are carried out in cylindrical ð Þ r; θ; z system of coordinates.

2.1.1 Circular waveguide with dielectric lining on metal wall

2.1 Dielectric-loaded circular waveguide

DOI: http://dx.doi.org/10.5772/intechopen.82124

permittivity of the dielectric material.

Circular waveguide with dielectric lining on metal wall [7].

Circular waveguide with dielectric coaxial insert [7].

Figure 2.

Figure 3.

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#### Figure 1.

ω � β dispersion characteristics of a circular waveguide showing the waveguide cutoff frequency and phase and group velocities.

frequencies above this lower cutoff frequency are allowed to propagate through the waveguide, and the signals having frequencies below this frequency will face a high reflection. Because of this characteristics a waveguide is inherently a high pass filter. The waveguide supports two kinds of velocities namely the phase velocity and the group velocity. The phase velocity at a chosen frequency is the one with which the signal of constant phase travels, which is represented by the slope of a line joining a chosen frequency point on ω � β dispersion characteristics to the origin (point representing zero frequency and zero phase propagation constant), i.e. mathematically given as ω=β. The group velocity at a chosen frequency point is the one with which the energy in signal travels, which is represented by the slope of the ω � β dispersion characteristics at the chosen frequency point, i.e. mathematically given as dω=dβ (Figure 1). Thus, one can control the supported phase and group velocities in a waveguide by tailoring its dispersion characteristics. Such tailoring can be achieved by loading the waveguide by metal and/ or dielectric in to the smooth wall waveguide [1–5]. The characteristics (propagation or dispersion) of the conventional (smooth wall) waveguide changes with the metal and/or dielectric loading, and the same cannot be generated naturally. Therefore, the metal- and/or dielectricloaded waveguide may be considered as artificially created material or artificial material. In part of the chapter to follow, a number of circular waveguide models containing various metal and/or dielectric loading are considered (Section 2). The electromagnetic boundary conditions (Section 3) and the dispersion relations (Section 4) of these loaded waveguides are outlined. Further, the dispersion characteristics of all the considered loaded waveguides are discussed with their sensitivity against variation in structure (geometrical) parameters (Section 5). Finally, the conclusion is drawn (Section 6).

#### 2. Structure models

Although, the considered structures being a single conductor structure support TE (Ez ¼ 0) as well as TM (Hz ¼ 0) modes, they are being analyzed for the TE modes. The structures excited in these modes are of the interest for a specific class of vacuum electronic fast-wave devices, specifically the gyro-devices. In the

Metal- and Dielectric-Loaded Waveguide: An Artificial Material for Tailoring the Waveguide… DOI: http://dx.doi.org/10.5772/intechopen.82124

category of gyro-devices, for the broadband amplifier namely the gyro-travelingwave tube (gyro-TWT) the growth rate of the TM-mode vanishes at higher frequencies [6]. The models are also restricted to circular waveguide and the analyses are carried out in cylindrical ð Þ r; θ; z system of coordinates.
