Calculation of attenuation in wave guides

摘要

This paper, based on work carried out in 1941?1942, furnishes tables and curves giving (a) field equations for rectangular and circular wave guides, and (b) attenuation constants of wave-modes likely to be met in practice in these guides. The text explains the derivation of the tables and curves. It should be noted that the approach to the problem uses waveengths to describe both the frequency (?e) and the guide itself (?cr). Wavelengths refer always to the dielectric which fills the guide. The free-space wavelength is not used at all. Field amplitudes (Table 1) are expressed in terms of power carried by a wave. To obtain comprehensive formulae, the concept ?characteristic density? of energy, or power, is introduced. Other factors determining field amplitudes enter into the equations in the form of field impedances. A general formula (Table 2) is produced for the attenuation constant ?wcaused by losses in the wall-metal. This formula applied to any mode of wave in rectangular or circular guide, and the values coefficients, which are to be used in a particular case, are given in the table. The curves shown in Fig. 1?4 are of a general character, and may be used for any size of guide and at any frequency. Figs. 1 and 2 deal with the attenuation constant ?w of air-filled copper guides the transmitting region. Fig. 1 shows attenuation of H01, H11 and E11-modes in a rectangular guide, and Fig. 2 shows attenuation of the lowest modes in a circular guide. The curves show the relationship between a quantity (?wD3/2), which is independent of the actual values of linear dimensions, and the ratio ?e/D which is the only term influenced by frequency. Fig. 3 gives the attenuation constant ?d due to loss in the dielectric filling of a guide, and shows the relationship between a quantity (?d??cr), again independent of the values of linear dimensions, and ratio ?e/?cr through which the frequency affects the attenuation. The curves are drawn for a few loss-angles, ?, of the dielectri-nc and are applicable to any wave-mode in any guide, in both the transmitting and attenuating regions. Fig. 4 is a counterpart to Fig. 3, showing the values of phase constant ? instead of attenuation constant ?d.