WAVEGUIDE HYBRID RINGS FOR MICROWAVES 475 



puts. No matching stubs are required to achieve a fairly good standing 

 wave ratio; however, the bandwidth over which the ring operates differen- 

 tially is inherently narrower than that of the junction. The rings have con- 

 siderably higher power capacity. 



The use of hybrids, both junctions and circles, has been noted, as applied 

 to both duplexer and mixer design^. 



There follows a circuit analysis of hybrid rings, primarily of the series 

 type. The method used is to consider the annulus as a continuous Hne 

 closed on itself. The sections between series taps are then treated as being 

 made up of integral single or multiple quarter wave line sections. Equiv- 

 alent T or lattice sections are derived for 1, 2, 3, and 4 quarter-wavelength 

 sections, ignoring line dissipation. These equivalences are used to draw 

 equivalent mesh networks. The mesh networks are then solved by deter- 

 minantal methods. To study some effects of frequency shift off the design 

 center, where the mean periphery of the ring departs from an exact integral 

 number of quarter-wavelengths, the increments in the element values for a 

 quarter-wave equivalent T section are calculated and utilized. The ex- 

 ample studied is a ring of 1| X mean perimeter with 3 and 4 taps. 



The general procedure neglects possible fringing effects at the junctions. 

 It also neglects the fact that each tap embraces a length of ring which is dis- 

 tinctly more than a small fraction of a wavelength. Nevertheless, the re- 

 sults appear in every case to give a good first approximation. The writer is 

 indebted to Messrs. J. T. Caulfield and J. F. P. Martin for checking the cal- 

 culations. 



Throughout the analysis Zo represents guide impedance and Z represents 

 annulus impedance. It will be noted that the analytical match condition 

 listed is \/2 Z = Zo for the 1 J X rings. 



The variation of the method necessary to treat the case of shunt taps is 

 indicated. 



I. Circuit Analysis 



The rings studied herein are of the series type. This type is the one which 

 results when waveguide is bent in the H plane, into a circle, and tap connec- 

 tions are made to the broad outer face. This type of ring is used, for ex- 

 ample, in the "rat race" plumbing. 



Such rings may be considered on the basis that the annular slot is a trans- 

 mission line, whose characteristic impedance will here be called Z and propa- 



3E. G. Schneider, Proc. I. R. E., — August 1946, p. 528 et seq. — see page 550 ct seq. 

 and Figs. 40, 42 and 47. 



