748 



BELL SYSTEM TECHNICAL JOURNAL 



Thus, Vb{x) becomes 



Vh^x) = 25a: 



200/ + 560.T^ 



640/ + 256.T 



A 



0.01 is easily found such that the resistance efficiency calculated 



from a graphical integration of 



the analytical expression for K 



1 



fix) + e' VUx) 



fix') + fvlix) 

 I Znijx) ' 



equals 65 per cent. Hence, 



Ro 



becomes 

 1 



(2.975 - 6.143x' + 7.493.r* - 3.325.r') 



+ (0.25.v' - 2.00.v' + 5.60.v' - 6.40^,-8 + 2.56x ") 



Fig. 24 — Comparison of the resultant special transfer function with the transfer 

 characteristic of Fig. 23. 



This expression is the resultant special transfer function which satis- 

 factorily approximates the transfer characteristic of Fig. 23. Fig. 24 shows a 

 plot of these functions for comparison purposes. 



The squared magnitude of the transfer impedance of the network .Y is 

 found from the analytical expression for the special transfer function by 

 adjusting the value of A' so that KAq = 1. Therefore, 



Zuijx) ' _ . 1 



Ro 1 - 1.981.v' + 1.846.v' + 0.765.v' - 2.157.v' + 0.861.v"'' 



The elements of the network N are found from the squared magnitude 

 of the transfer impedance by methods standard in circuit theory.-^ The 

 network elements of Fig. 22 in terms of unit impedance and unit radian 



=" Ref. 2, pp. 25-53. 



