Mun:u. ixiHcr.txci: i\ ifirr. iii.ir.Rs 



107 



Zi' K.iZ\,\-\-K B Ziii, 

 ami Z:' — KiZ\\, 



wluTc A.',i L\',L\,Kit (.'i t'l' .iiul A', I.i' L\. 

 Vnm\ (lOG) 





in wliiih 



/?- 



Lt_ iLx 



(lOH) 

 (109) 

 (110) 



(ilU 

 (112) 



¥ 



T ^c, -^ 2C, ?c, 

 '000000^ — II — o- — '"O'OOOW^ — II 1 — 1|- 







Fig. 49 — Two Structures Having Equal Mid-Series Image Impedances, One of 

 Which Contains a Negative Inductance in Its Shunt Arm 



From (107) and (111) 



Z,^ = R'+i{Z^A+Z,Br = l/iZ',^ + {l+K/2)R- + l/-lZ-s (113) 

 where K = ZiAZiB/R' = Li/Li = Ci/Ci. ^ (114) 



Now from (106) and (108) 



(z\r- /Ka-" 



(Z;')= = Z,'Z.' + ^'" = (^"-A-.,AV)ZL.+ 



(^-a-«av)a-/?--+Y> 



(115) 



Since, by postuiation, in I'ig. lU, Z\=Zi'. we ina\- eciiiate tliecoet'ti- 

 cients of (113) and (llo). This gives 



1 _Ka' j. j. 



K (KaK 



1+|=(^_^„^,)^. 



and 



1 _K^ 

 4 4 ■ 



(116) 

 (117) 

 (118) 



