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BELL SYSTEM TECHNICAL JOURNAL 



gation constant P. The transmission line is closed upon itself. Series con- 

 nections are made by the waveguide connections. The waveguide outlets 

 are assumed, by virtue of their lengths and/or terminations, to present wave- 



Fig. 2a — Series type hybrid ring as re-entrant transmission line. 



Z TANH ^ 

 o \^A^ 



Z TANH ^ 



AAAr 



SINH PI 



WHICH FOR A 



LOSS-FREE 



LINE IS: 



+ jZTAN^ +jZTAN^ 



AA/W — I WV-^^ 



-jz 



jSINBl SINBl 



Fig. 2b — T Network equivalent to a line section. 



° WV 



+ jz 



AAA/ — ° 

 -^jz 



iZ 



- A 



3A 



o WV 



-JZ 



A/V\ o 



-jz 



•+iZ 



LENGTH = /I 



^ DERIVED FROM EQUIVALENT LATTICE 



Fig. 2c — Networks equivalent to particular lengths of loss — free line. 



* For this case the T becomes indeterminate. However, the needed equivalence can be 

 proved by using the equivalent lattice. If we call Za and Zb the respective series and 

 shunt arms of the T, then the equivalent lattice has series arms = Za and diagonal arms 

 Za + 2Zb . 



guide characteristic impedance to the ring; this will herein be called Zq. 

 Diagrammatically, the situation is as in Fig. 2a. In the course of the fol- 

 lowing, the line sections will be replaced by equivalent networks, assumed 

 non-dissipative. 



