726 



BELL SYSTEM TECHNICAL JOURNAL 



squared magnitude of the transfer impedance in this problem to be written as 



Zuiju) 



Ro 



1 



1 + 5iaj2 + ^2 co^ + • • • + 5„ w='" ' 



(7) 



where the n constants Bi ■ ■ ■ Bn are related to the )i elements of the network 

 bv the relation 



Zuijw) _ Zu/Ro 



(8) 



Ro 1 + Z22/R0 



Since the desired transfer characteristic e~" determines the variation of the 

 polynomial i?(a)-) = 1 + Bico'- + • • • + B„m'"', a major factor in the design 



nji^jT^-^ji^w — nm^ 



-(n-1) 



Z=R+jx 



REACTIVE NETWORK N 

 Fig. 9 — General form of the coupling networks of Figs. 6 and 7. 



T }l1 }\2 722 ii 



2 = R+jx 



Zl= ^2 



Fig. IC — Output circuit of Fig. 6 with Cn included as part of N'i 



^22 }l2 }l1 



Fig. 1 1— Input circuit of Fig. 7 with C„ included as part of N'. 



is the choice of the real coefficients, Bi • • • B„ , by a suitable method of 

 polynomial approximation. 



The necessary and sufficient conditions for physical realizability place a 



• • Zio( jut) 



restriction on the B's of eq. (7). The sulticient condition that —^ — 

 represent the squared magnitude of the transfer impedance of a physical 



