Theory and Design of Microwave Filters

A waveguide is a structure which directs the propagation of an electromagnetic wave in a particular direction by confining the wave energy. Waveguides normally consist of hollow metallic pipes with uniform cross-section. The use of dielectric rods as waveguides is also common and these will be discussed in Chapter 7. Waveguide resonators are useful elements in filter design as they generally have much higher Q factors than coaxial or other TEM resonators.
There are distinct differences between waveguides and TEM transmission lines. A transmission line has a minimum of two conductors and supports the TEM mode of propagation, which has zero cut-off frequency. There is no minimum size for the cross-section of a TEM line in order for signal propagation to occur, other than that determined by dissipation losses. On the other hand, a waveguide has only one conductor consisting of the boundary of the pipe. The waveguide has a distinct cut-off frequency above which electromagnetic energy will propagate and below which it is attenuated. The cut-off frequency of the waveguide is determined by its cross-sectional dimensions. For example, a rectangular cross-section waveguide must have a width at least greater than one-half of the free space wavelength for propagation to occur at a particular frequency.
Furthermore, propagation in waveguides occurs with distinct field patterns, or modes. Any waveguide can support an infinite number of modes each of which have their own cut-off frequency. Also, both the characteristic impedance and the propagation constant of a waveguide are functions...