478 



BELL SYSTEM TECHNICAL JqURNAL 



The determinant then becomes 



Du = 





 

 -\-jZ Zo +jZ 

 -\-jZ Zo +jZ 

 



Zo +jZ 

 +JZ Zo +jZ 

 "^ " 





 

























 

 

 





 

 

 

 





 

 

 



Zo_ +jZ 

 jZ Zo 

 

 

 

 



+jZ 



















+ iz 



+ jZ Zo +jZ 



+jZ Zo +jZ 



+yz Zo +jz 



+iZ Zo 



For a IJ X ring, n = 6 and the system shrinks to 



Zo 



+iz 





 

 



+jz 



+jz 



Zo 

 +JZ 

 

 

 







+iz 



Zo 



+iz 





 





 



+jz 



Zo 



+jz 







El 

 E, 

 Es 

 Es 



£6 



£7 



£9 



-Elo 



II 



2.2 



II— 2.3 



For the study of the effects occurring if we move off the design center, 

 we can modify the individual Ts to a length t = - ± — . Each series arm. 



assuming no Hne dissipation, and N large so— « X, is: 



'-4?(l)]-^"[l(i4) 



= jZ tan 



TT TT 



In 



^ y 1 rb tan tt/N 

 ~ ^ 1 =F tan tt/N 



JZ{1 ± 27r/iV) = JZ{1 =h A) 



II— 2.4 



Similarly, each shunt arm is: 

 Z Z 



'■-[i'<'']"'-'»[?(j'4)]"-»b-s] 



-jz . -jz 



. TT Itt cos a 1 - AV2 



Sm ;r- 003 -f 



2 iV 



^ -iZ 



II— 2.5 



-jZ 



So the shunt arm is, to a first approximation, not affected by a small shift 

 off design center. Our shunts Y thus remain —jZ and 



5 + 2F = Zo + 2jZ zL 2jAZ - 2jZ = Zo ± 2jAZ. 



