108 PEI.I. SYSTl.M JI.CH.XU.II. Jul KX.IL 



Whence Kb ;.-, = !, (119) 



and A'.,, fi = ^=-^'={=. (120) 



where /i and /» are llie lower .iiid u|)|)i-r i-ul-ulT freciuencies, respec- 

 tively, and /.I/ V/,/.j of the structures of 1-ij;. 4(1. 



From (IK)) and (120) 



/c^^-±=-^.(a:^-_)= ^(.^---y. 



(121) 



Therefore, wiieii the relationships between the constants of the two 

 structures of Fij;. 4!t satisfy equations (,119), (120) and (121), the 

 structures will have the same mid-series image impedance character- 

 istics. Explicit relations for the values of Ci', Li and L/ nray be 

 obtained from equations (119), (120) and (121) as follows: 



C/ = Cu (122) 



Ai' = /-.4 (123) 



'•'■=t(7:-/;)- 02*' 



("on.sc(|ueniK , if the lonslants and cut-off frequencies of a conHuenl 

 structure are known, the constants of a structure of the .3-1' form 

 having an identical mid-series image imix-dance characteristic can be 

 derived from equations (122). (123) and (124). 



llliistralion No. 2 -Negative hiditctance in Series Arm of One 

 Structure. Consider next the filter sections listed as 3 4 (confluent 

 structure) in Table II and 1' 4 in Table III. It will be shown that, 

 under proper conditions, their mid-shunt image impedance charac- 

 teristics may be made ecpial at all fretjuencies. (By reference to the 

 above tables, both sections ha\i' mid-slumt im()edaiice characteristic 

 No. 14 of Fig. 8). 



I'rom e(|ualion (7) 



lV=l-,r... + l",. (12.5) 



where K, = l/;^,, 1^=1, ,^5 and y, = \,Zi. 



