854 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



term, n sections are used in both the series and shunt arms. The constant 

 resistance structure permits the complete equaUzer to be formed by a 

 cascade of such networks without interaction effects. This provides a 

 loss characteristic given by 



Loss = ko -\- ki cos 2^ + ^2 cos Ayp + ^3 cos 61/^ + 



(22) 



where ^ is the phase of the individual all-pass section which goes from 

 to 90 degress between and 8.5 mc. The /c's are adjusted by means of 

 the dual adjustable resistors. Note that each term of the series is repre- 

 sented by a corresponding equalizer. 



Application of this mop-up polynominal to a large number of L3 

 deviation characteristics indicates that considerably less range than 

 the maximum ±2.78 db will be required for most of the cosine terms. 

 Fig. 9 illustrates this convergence of the series for the eight largest 

 amplifier manufacturing variations. This and other studies show that 

 after the first three harmonics the range may be reduced. It can be 

 shown, ^ for example, that if the system gain deviations are finite within 

 the range of interest (interval of convergence) the coefficients of the 

 approximating polynominal will decrease in magnitude linearly pro- 

 portional to the number of the terms, that is, the nth coefficient will be 

 smaller than some constant divided by n. If the deviation characteristics 

 are continuous and hence have finite first derivatives, then the coeffi- 

 cients of the apprximating polynominal will decrease as the square of 



77.15 

 0.868 OJ 



I n SECTIONS ^ k 



121.3 



■vw- 



x 



308.6 



75 75 





45 3 0.868 0. 



308.6 



^^M^^Y'm-^ " SECTIONS 



OHMS, /iH»/y>UF 



Fig. 8 — Circuit of a cosine equalizer without dissipation correction. 



