1378 THE BELL SYSTEM TECHNICAL JOUKNAL, NOVEMBER 1956 



V. DISCUSSION OF RESULTS 



«ai 



The dimensioiiless results of Section IV may easily be scaled to any >. \\ 

 desired operating wavelength, and the attenuation constants and guides 

 wavelengths expressed in conventional units. If Xo is the free-space wave- 

 length in centimeters, then the guide diameter d in inches, the attenua- 

 tion constant a in db/meter, and the guide wavelength X^ in centimeters 

 are given by the following formulas: 



din = 0.12532 (M(Xo)cn. 



«db/m = 



vAgjcm — 



5457.5 (aa) 



(|8oa)(Xo)cm 



(i8oa)(Xo)cm 



,< 



ta 



Table II lists the guide diameters and the conversion factors for a and 

 Xg for the three values of /Soa used in Section IV, at frequencies corre- 

 sponding to free-space wavelengths of 3.33 and 0.54 cm. The table also 

 lists the number of propagating modes in a perfectly conducting guide 

 as a function of jSoa (different polarizations are not counted separately). 



When helix waveguide is used to reduce mode conversions, an im- 

 portant parameter is the ratio of the attenuation constant of any given 

 unwanted mode to the attenuation constant of the TEoi mode. The 

 theoretical attenuation constants of the TEoi mode at Xo = 5.4 mm in 

 copper guides of various sizes are listed below: 



Table II — Conversion Factors for Attenuation Constants and 

 Guide Wavelengths in Various Waveguides \ 



