WAVEGUIDE HYBRID RINGS FOR MICROWAVES 



479 



Therefore, determinants II — 2.2 and II — 2.3 can be used by merely consider- 

 ing Zo + J2AZ as a special value of Zq. 



As is well known,"' '^ the current solutions are obtained by writing in an 

 external column the driving voltages, opposite their associated meshes, 

 as is done at the right of II — 2.2. In the present case the number of driving 

 voltages is usually one, never more than two; so the column will be zeros, 

 save for one (or two) meshes. The current in any mesh is a fraction having 

 D as denominator, and as numerator the minor formed from D by substitut- 



Z:Pl 



Zo Z;Pi; 



z;PL. 



Zo 



z;Pin 



Fig. 4a — Re-entrant line with shunt taps. 



Fig. 4b — Re-entrant line with shunt taps— T networks as line equivalents. 



AVv — I — VW 



2Zr 



(4). 



Fig. 4c — Element ty-pical single shunt tapped section. 



ing the e.m.f. column in the column corresponding to the mesh where the 

 current is desired, i.e., column n if h is desired. 



Since D is common to all mesh current expressions, questions of relative 

 power division between branches or of null balance can be handled by 

 operations performed entirely with the numerator minors. 



Some slight advantage in evaluating the numerator minors is gained by 

 proceeding where possible so as to make /i or In the desired current. 



5 E. A. Guillemin, ''Communication Networks," Vols. I and II. Books published by 

 John Wilev and Sons Inc., New York, N. Y. 



«L. Silberstein, "Synopsis of Applicable Mathematics." Book published by D. 

 Van Nostrand Co., New York, N. Y. 



