1240 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



of (1) the ratio of the conversion coefficient (ai^) to the true dissipation 

 coefficient* in the signal mode (ai/,), (2) the ratio of the heat-loss coeffi- 

 cient of the unnsed-mode to that for the signal-mode (a^h/aik) , and (3) 

 the length of the transmission line specified in terms of decibels of heat 

 loss to the signal wave. For a given ratio of conversion-loss to heat-loss, 

 the same ratio of signal-power to reconverted-wave power will be present 

 for a long low-loss waveguide as for a short high-loss waveguide. This 

 makes it important to determine the ratio of conversion-loss to heat-loss 

 for waveguides of several nominal attenuation coefficients and to predict 

 these effects theoretically insofar as it is possible. 



Another result of this analysis is plotted in Fig. 20, which shows the 

 ratio of the signal power to the power in the unused mode at the end of 

 the line, with transmission-line heat loss as the abscissa. These curves 

 have been plotted for a fixed magnitude of conversion loss coefficient 

 (au) equal to 50 per cent of the true heat loss coefficient (aih) and for 

 ratios {axh/ciih), heat loss in the unused mode to heat loss in the signal 

 mode, between 2 and 100. These values are typical of solid round wave- 

 guide without mode filters. It is interesting to note in Fig. 20 that the 

 magnitude of the unused mode power relative to the signal mode power 

 reaches very nearly a constant value in a transmission line length of only 

 ^2 to 1 db, except for extremely low ratios axh/am . Physically what is 

 happening is that the unused mode power becomes dissipated through 

 heat loss about as rapidly as it is created by mode conversion, after an 

 initial short transmission line length. 



Fig. 21 shows the ratio of signal power to reconverted wave power as 

 a function of transmission line length for the same conditions described 

 in connection with Fig. 20. A heat loss ratio on the order of 2 to 10 is 

 typical of important modes in solid round waveguide without the addi- 

 tion of mode filters,! and Fig. 21 shows that the ratio of signal-to-recon- 

 verted wave power for such a medium becomes poorer than 20 db for 

 transmission line lengths longer than 1.5 to 2 db. Although there is some 

 uncertainty as to the precise interpretation which may be placed on the 

 signal power to reconverted wave power calculated in this manner, since 

 the time relations in connection with a definite modulation method are 

 not included, it seems evident that a solid copper tube without mode 



* There is a v(M-y sigiiifieaiit difiereiice between the effects of signal power loss 

 to other modes through conversion and signal power loss due to dissipation in the 

 waveguide walls. However, it does not matter here whether the latter be due to 

 surface roughness, chemical impurity or just the theoretical minimum heat loss 

 for ideal copper. Therefore, all of the heat loss effects are combined into the single 

 coefficient, au • 



t See the appendix for further discussion. 



