# 8.6 Waveguides

Earlier in Chapter 2, we considered two families of transmission lines, namely those that support transverse-electromagnetic (TEM) modes, and those that do not. Transmission lines belonging to the TEM family (Fig. 2-4), including coaxial, two-wire, and parallel-plate lines, support E and H fields that are orthogonal to the direction of propagation. Fields supported by lines in the other group—often called higher-order transmission lines—may have E or H orthogonal to the direction of propagation k ˆ, but not both simultaneously. Thus, at least one component of E or H is along k ˆ.

Among all higher-order transmission lines, the two most commonly used are optical fiber and the metal waveguide. As noted in Section 8-3, a wave is guided along an optical fiber through successive zigzags by taking advantage of the total internal reflection at the boundary between the (inner) core and the (outer) cladding (Fig. 8-20(a)). Another way to achieve internal reflection at the core’s boundary is to have its surface coated by a conducting material. Under the proper conditions (we shall elaborate later) a wave excited in the interior of a hollow conducting pipe, such as the circular or rectangular waveguides shown in Figs. 8-20(b) and (c), undergoes a process similar to that of successive internal reflection in an optical fiber, resulting in propagation down the pipe. Most waveguide applications call for air-filled guides, but in some cases, the waveguide may be filled with a dielectric material used to alter its propagation velocity or impedance, or it may be vacuum-pumped to eliminate air molecules in order to prevent voltage breakdown, thereby increasing its power-handling capabilities.

# Figure 8-20 Wave travel by successive reflections in (a) an optical fiber, (b) a circular metal waveguide, and (c) a rectangular metal waveguide.

(a) Optical fiber

Figure 8 20-a Full Alternative Text

(b) Circular waveguide

(c) Rectangular waveguide

Figure 8-21 illustrates how a coaxial cable can be connected to a rectangular waveguide. With its outer conductor connected to the metallic waveguide enclosure, the coaxial cable’s inner conductor protrudes through a tiny hole into the waveguide’s interior (without touching the conducting surface). Time-varying electric field lines extending between the protruding inner conductor and the inside surface of the guide provide the excitation necessary to transfer a signal from the coaxial line to the guide. Conversely, the center conductor can act like a probe, coupling a signal from the waveguide to the coaxial cable.

# Figure 8-21 The inner conductor of a coaxial cable can excite an EM wave in the waveguide.

(a) Coax-to-waveguide coupler

(b) Cross-sectional view at x = a/2

For guided transmission at frequencies below 30 GHz, the coaxial cable is by far the most widely used transmission line. At higher frequencies, however, the coaxial cable has a number of limitations: (a) in order for it to propagate only TEM modes, the cable’s inner and outer conductors have to be reduced in size to satisfy a certain size-to-wavelength requirement, making it more difficult to fabricate, (b) the smaller cross section reduces the cable’s power-handling capacity (limited by dielectric breakdown), and (c) the attenuation due to dielectric losses increases with frequency. For all of these reasons, metal waveguides have been used as an alternative to coaxial lines for many radar and communication applications that operate at frequencies in the 5–100 GHz range, particularly those requiring the transmission of high levels of radio-frequency (RF) power. Even though waveguides with circular and elliptical cross sections have been used in some microwave systems, the rectangular shape has been the more prevalent geometry.