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BELL SYSTEM TECHNICAL JOURNAL 



Alternatively, meshes where Zo = can be chosen. Another needed 



quantity is driving point impedance. Since h = ^ , then — = 



D Zd.p. 



-r and Zdp = -j- 

 D dn 



The resulting impedance will include an extra Zo , the 



generator impedance, to which we must match. 



It may be of interest to show how the reentrant transmission line analysis 

 can be extended to the case of hybrid rings involving shunt taps. For the 

 reiterative shunt case wx have the conditions illustrated in Fig. 4a. With 

 substitution of quarter-wave equivalences Fig. 4a becomes Fig. 4b. Clearly 

 determinants analogous to II — 2.1 et seq. can be written for this structure. 

 Alternatively we can split each Zo into two parallel impedances, each 2Zo , 

 yielding a typical symmetrical section which can be reduced to a simple 

 r or TT by well know^n transformation methods^ as shown in Fig. 4c. 



^-. 



Fig. 5 — \]/2 X ring — ^3 arm— equivalent mesh circuit. 



III. Detailed Analysis of Specific Cases of Series Type Rings 



Case A. 7J X Ring — 3 Arm — As Power Divider — Two Way 



This is most simply analyzed using equivalents from Method 1. The 

 equivalent circuit is shown in Fig. 5. It is immediately clear that: 



a. Power fed in at 5 will divide equally between Ei and £2 . 



b. Although El and E2 are in proper wavelength relationship for isolation 



relative to each other, they are effectively in series and there will 

 not be cancellation. The particular wavelength spacing is thus a 

 necessary but not sufficient condition. 

 With a voltage E at (5) we will have 



E = hZo - l2i-2jZ) 



= -h{-2jZ) + /2(2Zo) 



c. 



or 



Zo 



-^2j2 



+2jZ 



2Zo 



III— 1 



* loc. cit. page 282. 



