WAVEGUIDE HYBRID RINGS FOR MICROWAVES 



481 



so 



and the mesh impedance at S is 



Therefore an impedance match is secured if 



V2Z = Zo. III- 



d. For a voltage e slI Ei , the current at E2 may be obtained from 



2Zo -27Z 



-2iZ Zo 



and is 



eZo 



m— 3 



2Zo + 4Z' • 



Under the impedance match condition -\/2Z = Zo , this is e/4Zo which is 

 just half the current which could be drawn through a load Zo connected to a 

 source Zo with internal voltage e. Therefore, the ''loss" from jEi to E2 

 is 6 db. 



Case B. 1\\ Ring — 4 Arms — As Power Divider and Null Device 



As power divider — Two Way (Fig. 6). Using the determinantal method, 

 let £1 be in mesh 1. Then D is in mesh 4, E2 in mesh 5 and 5 in mesh 6. 

 Zo = for meshes 2 and 3. Then the determinant of II — 2.3 and its minor 

 for mesh 5 (£2 in Fig. 6) with voltage apphed at Ei , are respectively, from 

 II— 2.3: 



III— 3 



III— 4 



Upon expansion ^5 is found to be 0. Therefore, by adding outlet Z>, we 

 have isolated branch Ei from branch E^ . (Compare with case A.) Since 



