(BQ) Part 2 book "Advanced engineering electromagnetics" has contents: Circular cross section waveguides and cavities, spherical transmission lines and cavities, scattering, integral equations and the moment method, geometrical theory of diffraction, diffraction by wedge with impedance surfaces,.and other contents. | CHAPTER 9 Circular Cross-Section Waveguides and Cavities INTRODUCTION Cylindrical transmission lines and cavities are very popular geometrical configurations. Cylindrical structures are those that maintain a uniform cross section along their length. Typical cross sections are rectangular, square, triangular, circular, elliptical, and others. Whereas the rectangular and square cross sections were analyzed in Chapter 8, the circular cross-section geometries will be discussed in this chapter. This will include transmission lines and cavities (resonators) of conducting walls and dielectric material. CIRCULAR WAVEGUIDE A popular waveguide configuration, in addition to the rectangular one discussed in Chapter 8, is the circular waveguide shown in Figure 9-1. This waveguide is very attractive because of its ease in manufacturing and low attenuation of the TE0n modes. An apparent drawback is its fixed bandwidth between modes. Field configurations (modes) that can be supported inside such a structure are TEz and TMz . Transverse Electric (TEz ) Modes The transverse electric to z (TEz ) modes can be derived by letting the vector potentials A and F be equal to A=0 (9-1a) ˆ F = az Fz (ρ, φ, z ) (9-1b) The vector potential F must satisfy the vector wave equation 3-48, which reduces for the F of (9-1b) to ∇ 2 Fz (ρ, φ, z ) + β 2 Fz (ρ, φ, z ) = 0 (9-2) When expanded in cylindrical coordinates, (9-2) reduces to 1 ∂ 2 Fz 1 ∂Fz ∂ 2 Fz ∂ 2 Fz + 2 + + + β 2 Fz = 0 2 2 ∂ρ ρ ∂ρ ρ ∂φ ∂z 2 whose solution for the geometry of Figure 9-1, according to (3-70), is of the form (9-3) Fz (ρ, φ, z ) = [A1 Jm (βρ ρ) + B1 Ym (βρ ρ)] ×[C2 cos(mφ) + D2 sin(mφ)] A3 e −j βz z + B3 e +j βz z (9-4) 483 484 CIRCULAR CROSS-SECTION WAVEGUIDES AND CAVITIES y r e, m f x a z Figure 9-1 Cylindrical waveguide of circular cross section. where, according to (3-66d), the constraint (dispersion) equation is 2 2 βρ + β z = β 2 (9-4a) The constants A1 , B1 , C2 , D2 , A3 , B3 , m, βρ
