1228 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



other modes, none of which appears by itself to be very strongly coupled 

 to TEoi . 



Of course if Ave had a single normal mode of the compensated guide, 

 with a field pattern independent of distance along the guide, it might 

 well be possible to calculate the field distribution and the dielectric losses 

 approximately, without reference to the telegraphist's equations and 

 regardless of the permittivity of the dielectric. However, we do not have 

 a single normal mode of the compensated guide, but rather a mixture of 

 modes. The field pattern varies along the guide as the modes phase in 

 and out; and it is not easy to conclude from this picture what the actual 

 dielectric losses will be. 



Finally it should be remembered that we have said nothing about the 

 possible effect of a dielectric compensator on eddy current losses in the 

 waveguide walls. If one attempted to use a compensator of small physical 

 size and correspondingly high permittivity, the resulting perturbation 

 of the electric field might very well increase the eddy current losses in 

 the wall adjacent to the compensator. On the other hand, the increase 

 would probably be negligible for a compensator made out of a foam di- 

 electric. 



II. APPLICATION 



2.1 Properties of Unijormly Coupled Transmission Lines 



We shall now apply the preceding theory to the calculation of TEoi . 

 mode coupling in gentle bends. To describe propagation in a curved 

 w^aveguide in terms of the modes of a straight guide requires, in general, 

 the solution of the infinite set of equations (37) ; but we can give an ade- : 

 quate approximate treatment by considering just two modes at a time, 

 one mode of each pair always being TEoi . Furthermore we need consider 

 only the forward waves, since the relative power coupled from the for- 

 w^ard waves into the backward waves is quite small. 



The differential equations representing the forward waves on two uni- 

 formly coupled transmission lines are: 



dao . , . „ 



"1- + ToQo + iKGi = 0, 



dz , ^ 



(58) 



. dax 

 iKtto + -7- + Ti«i = 0- 

 dz 



In these equations ao{z) and ai{z) are the amplitudes of the forward' 

 traveling waves, normalized so that | Oo |^ and | Oi |' represent power flow 

 directly. We may think of the subscript as always referring to the TEoi 



