COUPLED WAVE THEORY AND WAVEGUIDE APPLICATIONS C)77 



stant strength couplings is much greater than when high discriminations 

 are required. Fig. 1.3 shows a (hstribution wliich i)ro(hi('es about 20 db 

 discrimination from QJ-k = 1 to 3.25. Eight coujolings arranged with the 

 Tchebj'sheff amplitude taper for 20 db discrimiuation would i)roduce 

 that discrimination from 6/w = 1.05 to 5.95. 



It is possible to obtain directivity or mode discrimination at smaller 

 d/ir values than made available with uniform coupling. This situation is 

 analogous to the superdirectivity problem in antenna design, with similar 

 results — the lobes of spurious response are increased. In particular, if 

 the coupling near the ends of the third array of Fig. 4 is made larger than 

 the coupling in the center region, making "c" a negative quantity, the 

 first peak in discrimmation occurs at d/ir less than one, and the first 

 minmaum in discrimination becomes less than 13 db. 



B}^ implication, emphasis has been placed on obtaining both mode dis- 

 crimination and directivity simultaneously. However, by employing a 

 relatively short coupling length it is apparent that the discrimination 

 associated with 



may be kept small when the directivity associated with 



is in suitable range for good discrimination. Consequently, one can de- 

 sign a directional coupler with little mode discrimination. Conversely, 

 when using a relatively small number of point couplings, the mode dis- 

 crimination in the forward wave may be good when the directivity is 

 poor. 



TIGHT COUPLING THEORY* 



We now consider the case in which a significant amount of power is 

 taken from the driven transmission line by the line coupled to it. To 

 simplify the problem the coupling is assumed uniform along the length 



* An analysis of coupled transmission lines was given by W. J. Albersheim," 

 and the effects of coupling between waves on certain particular forms of trans- 

 mission media were analyzed by Meyerhoff' and Krasnushkin and Khokhlov.*" 

 The treatment given here is intended to be more general and is believed to de- 

 scribe the effects of wave coupling under a greater variety of conditions. 



