Circular Electric Wave Transmission 

 Through Serpentine Bends 



By H. G. UNGER 



(Manuscript received January 9, 1957) 



An otherwise straight waveguide line with equally spaced discrete supports 

 may deform elastically into a serpentine bend under its own weight. The 

 TEoi wave couples in such bends to the TMn and TEi„ waves. The general 

 solution of coupled lines with varying coupling coefficient is applied to a 

 serpentine bend by an iterative process, and evaluated for the elastic curve 

 resulting from a periodically supported line. TEoi-TMu coupling causes 

 only a small increase in TEoi attenuation. Mode conversion to TEi„ waves 

 can become seriously high at certain critical frequencies when the supporting 

 distance is a multiple of the beat wavelength. In a copper pipe of 2^ inch 

 O.D. and 2 inch I.D., the mode conversion to the TE12 wave at critical 

 frequencies near 5-mm wavelength causes a TEoi attenuation increase of 

 90 per cent and a spurious mode level of —7 db. These mode conversion 

 effects can be controlled effectively by inserting mode filters. 



I. INTRODUCTION 



In curved sections of round waveguide the TEoi - wave couples to 

 the TMu and TEi,, waves, and power is converted to these waves when 

 the TEoi wave is transmitted through bends. A form of bend which is 

 inherently present even in an otherwise straight and perfect line is the 

 serpentine bend, Fig. 1. Between discrete supports the pipe is deflected 

 by the force of its own weight. The resulting curve is well kno^\Ti from 

 the theory of elasticity. The curvature varies along the axis following 

 essentially a square law. The minimum bending radius occurs at the sup- 

 ports. For the practical example of a copper pipe of 2f-inch O.D., 2.00- 

 inch I.D. and a supporting distance of 15 ft, this minimum bending ra- 

 dius is 992 ft. A uniform bend of this radius would convert most of the 

 power incident in the TEoi wave to the TMn wave after a certain length 

 of bend. 



Fortunately a serpentine bend with the same order of bending radius 

 does not affect circular electric wave transmission as seriously as does a 



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