COUPLED WAVE THEORY A.ND WAVEGUIDE APPLICATIONS 717 



If one of the transmission lines (Fig. 54) is round and the other is 

 rectangular and if their cross-sectional dimensions are set for equal phase 

 constants, then the power in one of the two polarizations of the lound 

 line may be transferred to anj^ desired extent to the rectangular guide, 

 and power in the other polarization of the round guide will pass the 

 coupling region undisturbed. Two such rectangular-rod to round-rod 

 coupling configurations arranged in cascade along the round-rod, with 

 the two rectangular rods coupled in planes at 90° to each other, consti- 

 tutes a means for independently connecting to the two polarizations of 

 the round-rod. This type of de\'ice depends upon the fact that the phase 

 constants of the two polarizations of round-rod are identical, whereas 

 the two phase constants for the rectangular rod are different. Thus a 

 wave interference occurs in the transfer characteristic for one of the 

 polarizations, and for suitable values of (/5i — ^i)/c (see Fig. 18) the 

 power transferred in this polarization can be made small. 



SU.MMAKY 



Two approaches to a theoretical description of the behavior of two 

 coupled waves have been presented. One, based on the assumption of 

 negligibly small coupling, is applicable in cases where very little power 

 is transferred between the coupled waves. The other, a solution based 

 on uniform coupling between waves in the coordinate of propagation, is 

 valid for any magnitude of total coupling. 



The loose coupling theory shows how to taper the coupling distribution 

 in order to minimize the length of the coupling interval required for a 

 given degree of directivity and/or for a given magnitude of mode im- 

 purity. In particular, it is possible to shape the coupling distribution so 

 as to discriminate sharply against one or more undesired modes in a 

 coupled-wave arrangement involving just a few modes. (See Figs. 7 and 

 15 for examples). 



The theory indicates that significant exchange of power takes place 

 provided that the attenuation and phase constants of the coupled waves 

 are ecjual, or provided that the difference between the attenuation con- 

 stants and the difference between the phase constants are small compared 

 to the coefficient of coupling. A suitable difference between either the 

 attenuation constants or the phase constants of two coupled waves is 

 sufficient to prevent appreciable energy exchange (equations 29-32 and 

 35-36). 



It follows that substantially single-mode propagation is possible in a 

 multi-mode structure even though geometrical effects tending to cause 

 coupling between modes are present. A gradual transition in the boundary 



