476 BELL SYSTEM TECHNICAL JOURNAL 



and — 7r/2 radians. The best number of sections to use is determined 

 by the total minimum phase required and can be found here quite 

 readily, as follows. Because of the comparatively small amount of 

 attenuation assumed for the total correcting network at / = 25 ~, 

 this type of network is one in which Zu consists of a resistance in 

 parallel with an approximate reactance so that we may apply for the 

 present purpose the relation (37) between maximum attenuation and 

 minimum phase of such a section. For a total maximum attenuation 

 of 10.00 napiers this relation gives for two sections a total minimum 

 phase of — 2.81 radians, which is close to the required value — 2.75 

 radians. Three sections give — 3.59 radians, showing the best number 

 to be two. (If the result with two identical sections had been a 

 negative phase considerably greater than the required value, it would 

 have been possible to proportion the total maximum attenuation at 

 zero frequency between two such different sections so as to give 

 approximately the desired total minimum phase. In such a case each 

 section could be designed from its corresponding proportion of the 

 total attenuations at the other frequencies.) 



Each of two such identical sections was designed by the formulae 

 given in Appendix IV, using attenuation data fixed by the values of 

 (a' — a)/2. Allowances had to be made at /i = 5~ and fo = 15 ~ 

 for necessary curvature in the attenuation characteristic so as to 

 obtain a physical result. It was assumed that the phase constant 

 would turn out to be satisfactory since it had already been given some 

 consideration when determining the number of sections. The fre- 

 quencies and corresponding attenuations used were 



/o = 0, ^0 = 5.00 napiers; 



/i = 5~, Ai = 3.25 napiers; 



/2 = 15~, Ao = \.78 napiers; 



/a = 25~, As = .15 napier. 

 The solution of the attenuation linear equations gave 



P2 = - 68.737; Qo = 1.1929; Qi = 2.5537 -lO-". 

 Whence 



Also, 



where R = 58.12 ohms. 



Ci = 1.1854- 10--^; 

 &2 = 1.5980-10-3. 



L,2 = 1.994 h.; 

 Rn = 114.68 ohms; 



