818 



BELL SYSTEM TECHNICAL JOURNAL 



In most designs it is desirable to make the maximum departure from 

 the ideal characteristic within the operating range as small as possible. 

 A method of doing this for the 2-branch networks has been developed. 

 The method assumes that the Zo of the filter has been taken equal to 

 the terminating impedance, which assures a correct conductance at 

 the point x = 0. The manipulation of the parameters Ai and A2 

 allows us to secure the desired value of conductance at two additional 

 points. The result is a two looped characteristic, similar, if we make 

 allowance for the difference in the assumptions regarding Zo, to that 

 already determined for this network by means of the Legendrian 

 expansion. The requirement that the maximum departure from the 

 ideal within the operating range be a minimum is equivalent to saying 

 that the amplitudes of the downward and upward loops must be equal. 

 It can be shown that a 2-branch conductance network will satisfy this 

 condition if 



27 . 

 1+^1+^0 



= (^l2 - 4.42)2. 



In view of the relations which have been developed between Ai, Ai, 



Fig. 8 — Design chart for 2-branch termination. 



