An important feature of microwave waveguides and resonators is heat losses. The latter determine, in particular, the transient time, knowledge of which is indispensable for designing digital microwave devices (Kiang, 1991). Waveguides with low attenuation are required to create highly effective radio-relay, space and tropospheric-scatter communication facilities and to design measuring equipment (including that operating at the millimetre waveband and infrared). High-quality resonators are widely used in radio engineering (tunable oscillators with high frequency stability), in applied physics (wavemeters, equipment for measuring dielectric coefficients and permeabilities of substances and for micro wave heating etc.), in electronics (gyrotrons, orotrons, free electron lasers etc.) and in unique physical experiments (for instance, experiments on detecting gravitational waves).

This Chapter deals with the theory of regular waveguides with impedance walls. Spectral problems for normal modes have been formulated. General character istics of different types of normal modes (eigenmodes, associated modes) have been considered. Calculation of attenuation coefficients of the eigenmodes for the case of small losses is discussed. General expressions for attenuation coefficients are obtained with the aid of the perturbation technique. Applicability cases for different variants of the perturbation method are analysed in detail (energy-perturbation method, perturbation technique for solving the dispersion equation). Their modifications are described for cases when classic schemes of the method are not usable (degenerated modes of D-multiplicity, models of waveguides with unclosed infinitely thin metal surfaces). Typical principal errors in attenuation coefficient calculation are analysed. Computational peculiarities of different approaches are pointed out, as well as the expediency of their application for different cases. General principles are illustrated by specific examples (rectangular and circular waveguides, coaxial and microstrip lines).

This chapter is dedicated to the diffraction of plane waves by finitely conducting comb-shaped structures. Finite conductivity is taken into consideration by means of impedance boundary conditions. Periodic structures of comparatively simple configuration (array of halfplanes, symmetrical and nonsymmetrical lamellar gratings, echelettes) are examined as well as structures with complicated shape profiles. Highly effective numerical methods are described for the latter which are universal in relation to the structure configuration. Approximate formulae and numerical results are given for a linear (per period) power of heat losses. Its dependence on the angle of incidence, wave length and configuration of the unit cell is analysed. For the case of H-polarisation considerable attention is paid to the effect of abnormally small dissipation (the losses in a periodical structure may be smaller than those in a smooth surface of the same material). For E-polarised waves this does not occur. The physical mechanism of the absorption anomalies is analysed, and their practical use in reducing attenuation in microwave waveguides and resonators is discussed.

This Chapter deals with the electromagnetic fields in systems with corrugated surfaces: waveguides, resonators and horns. Special attention is given to the investigation of dissipation characteristics: attenuation coefficients of different modes in corrugated waveguides and Q-factors of eigenoscillations in resonators with corrugated walls. Application of corrugated surfaces of both step shape and smooth is considered. When a period of the structure is small compared with the wavelength, a method of equivalent impedance-boundary conditions is used. Low-loss corrugated waveguides and millimetre waveband high-quality resonators with a rare spectrum of eigenoscillations based on the effect of abnormally small absorption in periodic structures are described. A rigorous method of calculation of electrodynamic characteristics of corrugated horns, which are highly effective feeds for microwave antennae, is considered.

The expressions for current-density distributions in a microstrip line with a strip of finite thickness is discussed. Equations are shown.