1252 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



perimental helices were known to be impei-fect, and in a smaller diameter 

 of helix, losses within 15 per cent of the theoretical values for perfect 

 copper pipe were achieved. These results lead us to regard the helical 

 line as a verj- promising medium for circular electric waves. 



SURFACE ROUGHNESS 



Since frequencies on the order of 50,000 mc are desirable for low-loss 

 waveguide use, it was recognized that roughness of the surface at the 

 waveguide walls might appreciabh^ increase the heat loss in a practical 

 waveguide. The first approach to this problem was made by VV. A. 

 Tyrrell using sections of 5 diameter copper pipe from the experimental 

 line. Tyrrell measured the heat-loss coefficients of the pipe when used as 

 a resonant cavity at 9,000 mc in lengths on the order of 4 to 8 feet. Care- 

 fully selected resonant conditions were employed to avoid bringing the 

 unused modes of propagation into resonance at the same time that the 

 circular electric wave was resonated. Whereas Tyrrell observed that the 

 heat loss coefficient in the pipe as originallj^ drawn was about 21 per cent 

 higher than the value computed using the measured dc conductivity, he 

 found that rotary* grinding and polishing the inner surface of the guide 

 reduced the excess loss to about 12 per cent. Tyrrell also observed that 

 commercially drawn brass and 2S aluminum tubing of approximately the 

 same dimensions showed measured losses 11 per cent and 20 per cent 

 respecti^'ely greater than the ^'alue predicted from the measured dc 

 conductivity'. Therefore, the indication from Tj'rrell's work was that 

 surface roughness did indeed account for increased losses even at 9,000 

 mc, and that the excess losses could be reduced either by polishing the 

 surface or through the use of lower conductivities (which have the effect 

 of increasing the skin depth). 



A parallel approach to the measurement of surface-roughness effects 

 was made bj' A. C. Beck and R. W. Dawson, also at 9,000 mc.^ Beck 

 and Dawson used small wire samples as the center conductor of a coaxial 

 cavityf and found that commercially drawn copper, aluminum and sil- 

 ver wires showed loss values 10 per cent and 15 per cent higher than those 

 expected from the measured dc conducti^'ity. By mechanically polishing 



* Because the wall currents for the circular electric wave are circumferential, 

 the longitudinal surface scratches produced by drawing are in the worst possible 

 orientation. Polishing was carried out in a rotary manner so that the current would 

 not cross the scratches so induced. 



t In a coaxial, the currents are longitudinal, as are the scratches from drawing, 

 so the measurements in the coaxial would be expected to show somewhat less 

 excess loss due to surface roughness than the measurements made in circular-elec- 

 tric waveguide cavities. 



