Hyper-Frequency Wave Guides — Mathematical Theory 



By JOHN R. CARSON, SALLIE P. MEAD and S. A. SCHELKUNOFF 



F"ollowing a brief historical sketch, this paper deals with the niathc- 

 matical theory of wave transmission in two novel kinds of cylindrical 

 wave guides of circular cross section; namely, the hollow conductor and 

 the dielectric wire. These transmission systems behave as high pass 

 filters with exceedingly high critical frequencies. 



The attenuation and impedance characteristics of the hollow conductor, 

 heretofore ignored as far as the writers are aware, are given espjecial atten- 

 tion. This investigation discloses the remarkable fact that there exists in 

 this system one and only one type of wave, the attenuation of which de- 

 creases with increasing frequency, a characteristic which attaches to no 

 other type of guided wave known to the writers. 



I. Introduction 



THE object of this paper is to derive and discuss the characteristics 

 of two novel guided wave transmission systems. Structurally 

 ^ one consists simply of a straight hollow ^ conducting cylinder of circular 



cross-section. The electromagnetic wave is confined inside the cylin- 

 drical sheath and is propagated along the axis of the cylinder. The 

 other consists simply of a dielectric wire, within which the major part 

 of the electric field is confined. The mathematical theory developed 



II below does not deal with the question as to how such waves are estab- 



' lished nor with the reflection phenomena which must occur at the 



terminals and other points of discontinuity. The analysis is limited to 

 finding the types of waves which are possible in such systems, and to 

 investigating and describing their characteristics. 



The historical background of the problem is interesting. In 1897 

 Rayleigh published a paper entitled "On the Passage of Electric Waves 

 through Tubes, or the Vibrations of Dielectric Cylinders." - Dealing 

 solely with ideal cylinders of perfect conductivity he showed that for all 

 types of waves that can exist inside the cylinders there are critical fre- 

 quencies below which the waves are attenuated and above which they 

 are freely transmitted. The first paper on transmission along dielectric 

 wires was that published in 1910 by Hondros and Debye entitled 

 " Elektromagnetische Wellen an dielektrischen Drahten." ^ This 

 deals theoretically with transmission along cylinders of ideally non- 

 conducting material, somewhat along the lines followed in Section I\' 



' The term hollow means that the interior of the cylinder is electrically non- 

 conducting. 



^Phil. Mag., Vol. 43, 1897, pp. 125-132. 

 Mnn. der Phys., Vol 32, 1910, pp. 465-476. 



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