Reflections from Circular Bends in Rectangular Wave Guides -- Matrix Theory

A N U M B E R of investigators have studied the propagation of electro^ magnetic waves in a bent pipe of rectangular cross-section, the bend being along an arc of a circle. H. Buchholz 1 , S. Morimoto 2 , and W. J. Albersheim 3 have employed Bessel functions to express the field in the bend. The form assumed by the field when the radius of curvature of the bend becomes large has been obtained by K. Riess 4 and R. E. Marshak 6 who use approximations suited to this case. M a r s h a k also obtains expressions for various reflection and transmission coefficients. A discussion of the subject using rather simple but approximate analysis is given on pages 324-330 of a text book 6 by S. A. Schelkunofif. T h e Bessel function approach is also sketched in the same section. Here we study the disturbance produced when a wave goes around a circular bend (of some given angle) in a rectangular wave guide, the guide being straight on either side of the bend. Especial attention is paid to the dominant mode reflection coefficients gfo and doi corresponding to H-bends and E-bends, respectively. As equations (4.2-6) and (4.4-4) show, these reflection coefficients (which are of the nature of voltage rather than power reflection coefficients) vary inversely as the square of the radius of curvature of the bend when the bend is gentle. T h e substance of (4.2-6) has been given by Marshak" for the important case in which only the dominant mode is propagated a n d the angle of the bend not too small.