816 



BELL SYSTEM TECHNICAL JOURNAL 



terms of Legendrian harmonics is given on p. 184 of Byerly as 



vr^. = 5[ip.(,,_5(i)(i)Va.)-9(^)QJ=P.w 



Upon replacing the harmonics by their values in terms of x, — 

 Poix) = 1, 

 P,{x) = \ {^x^ - 1), 



F^ix) = I (35x4 - 30x2 _^ 3)^ 

 o 



16 



p^(x) = j2 (231x4 - 315x4 + 105x2 



3), 



and sorting out the various powers of x, values of the coefficients 

 Ai . . . An are secured, and from these the actual element values are 

 found by means of formulas developed previously. The following 

 table summarizes the results 



TABLE II 



The quantities Ko . . . Kz are the numerical coefficients of the cor- 

 responding harmonics. It will be observed that with this method of 

 determining the network parameters Zq is not quite equal to Ro. 

 When the analysis is based upon impedances instead of admittances 

 the ratio Ro/Zo should be replaced by Zo/Ro. The conductance char- 

 acteristics secured by this process are shown in Fig. 7. 



