wavp:guide as a commuxicatiox mkdium 1203 



rn - — i oe + — ^ e — r- e (21) 



(^1 - ro) (n - r.) 



It is informative to note that (ri — ra) is always positive and is e(|ual to 



Via -/3)2 + 4aua,i 



We are usually interested in the ratio of the power in the x-modctothe 

 signal power Pi and the ratio of the reconverted energy P„ to the signal 

 ]ioAV(n- Pi . These ratios are given by the following exi)ressions 



P„ _ (n + /3) ^r,+a)z _ (/•2 + /3) (n+aU _ . /orjN* 



Pi " (ri - r,) ' W^=^) " ^^^^ 



[1 - e-'-'-'''-] (23) 



Px (ri - r.) 



Thus, we have explicit solutions for the iniiform transmission medium 

 containing mode conversions. 



In order to make the most general study of these relations, we shall 

 express the mode conversion coefficients in terms of the heat loss coeffi- 

 cient in the signal mode — i.e., as the ratio au/dih . This is natural enough 

 phj'sically, for Ave are interested in the relative magnitudes of the heat 

 loss and mode conversion effects. It is found that knowledge of the ratios 

 a\x!a\h , 0x1 Qu and axh/cbih enables us to completely determine Pi/Pi 

 and Pn Pi in terms of the distance parameter e""""'. The latter is the 

 heat loss in the signal mode, another familiar physical characteristic. 



characteristic conditions in bare round waveguide 



In order to use the theoretical relations derived iii the preceding sec- 

 tion, we need to know typical values of the parameters. In particular, 

 we need to know the magnitude of typical conversion coc^fficicnts au 

 and values of the heat loss coefficients a-iu and Oxh for the modes of 

 interest. 



One set of heat loss coefficients wliicli is of immediate interest may be 

 made up fiom the calculated values for the 5-inch diameter round wave- 

 guide used in waveguide experiments at Holmdel. Table V shows the ratio 

 of attenuation coefficients for several modes in this fine. The circular 

 electric wave TEoi has the lowest attenuation coefficient (absolute value 



* When using these relations, it is helpful to note that (ri + Tt) = -(a -f- 0) 

 at all times. Hence (rj -|- a) = -(rj -}- /3) and (r^ + a) = -(r, -|- /3). 



