COUPLED WAVE THEORY AND WAVEGUIDE APPLICATIONS 



713 



and (44). Assuming a coupling length .To of two wavelengths in the line 

 with the smaller phase constant, it follows that /8i//32 is about 1.18 show- 

 ing that a phase-constant difference of 18 % is required. This phase-con- 

 stant difference is quite readily attainable in the wa\'eguide structure of 

 Fig. 50(a). The two modes coupled together are given slightly different 

 cut-off wavelengths in the coupling region, and may be tapered to the 

 standard wa\'eguide size outside the coupling region. The desired phase- 

 constant difference can also be obtained in two identical metallic guides 

 by inserting a piece of dielectric into one of the guides in the coupling 

 region as sketched in Fig. 50(b). Although rectangular waveguides are 

 used in Fig. 50 to illustrate the method of obtaining frequency inde- 

 pendent transfer characteristics, the approach is general and may be 

 applied to an}' form of single or multi-mode transmission line. 



SECTION A-A 



(a) Cb) 



Fig. 50 — Examples of structures in which flat transfer loss may be obtained 

 despite coupling loss variations. 



In either dominant-mode directional couplers or in multi-mode cou- 

 pled-wave devices such as the one illustrated in Fig. 1, one may obtain 

 much more frequency selecti^•ity than occurs incidentally due to the 

 f requeue}^ sensitivity of the coupling elements used. This may be done 

 by coupling two transmission lines which have the same phase constant 

 at one frequenc}^ but unequal phase constants at other frequencies. 

 Then, as shown by equation (31), the midband transfer loss may be set 

 at any desired \'alue by adjusting the integrated coupling strength ex 

 at midband (where /3i — (So = 0), and at other fre(iuencies where (^i — 

 02) ^ 0, the transfer loss will increase. For the particular case of ex = 7r/2 

 (fixed) for which complete power transfer occurs when /3i = 02 (and as- 

 suming ai = ao or both as are negligible). Fig. 51 shows the shape of 

 the filter characteristic, Eo* versus (0i — 0-i)f2e. This plot is valid for 

 any form of transmission line. 



A very simple configuration for realizing such a frequency-selective 

 filter involves coupling between two hollow conductor waveguides, one 



