1216 THE BELL SYSTEM TECHNICAL .TOURXAL, NOVEMBER 1954 



FREQUENCY IN MEGACYCLES PER SECOND 



Fig. 4 — Round guide diameter versus frequency for attenuation of 13.2 db/ 

 mile (0.25 db/100 ft.). 



link application, the waveguide size is definitely too large for long- 

 distance application. In the vicinitj^ of 50,000 mc, however. Fig. 3 shows 

 that the reciuired waveguide size is on the order of 2", and this is com- 

 parable to the size of the present standard 8-pipe coaxial cable. From 

 these simple calculations, it is evident that carrier frecjuencies in the 

 vicinity of 50,000 mc or more are ver}- desirable for long-distance wave- 

 guide applications in order to minimize the size of the wa\'eguide. 



Other reasons for wanting a high carrier fref]iiency arise from a con- 

 sideration of bandwidth. Any hollow conductor waveguide has a cutofT 

 characteristic of the form sketched in Fig. 5. Above cutoff the group 

 velocity approaches asymptotically to the velocity in an unbounded 

 medium composed of the dielectric used in the waveguide. Because the 

 group velocity varies across the frecjuencj' band, a signal being trans- 

 mitted in a waveguide will experience delay distortion; the components 

 transmitted at /o ± A/ (Fig. 5) would be delaj-ed compared with their 

 relation at the input to the line. When this delay is 180° a baseband sig- 

 nal of frequency A/ would be severely distorted regardless of the mod- 

 ulation method, and this condition msiy be regarded as an upper limit to 

 the usable bandwidths in the waveguide unless correction for delaj' 

 distortion is employed. This particular type of phase distortion has 

 been anah^zed in unpuljlished papers, first b}' D. H. Ring and later by 

 S. Darlington. The work of Darlington leads to the following relation 

 between the parameters of the waveguide and the baseband width /b 

 associated with the 180° phase difference noted above: 



, 304/"-(l - vV" , , 



