DESIGN OF REACTIVE EQUALIZERS 



Ui 



where /(.V-) is the rational function which approximates /"V"^^''^^'^ over the 

 useful band, F„(-^") is a Tchebycheff polynomial of order ;/ (odd), and e is 

 the coefficient of the Tchebycheff polynomial, B(x-) in Fig. 15 will be 

 modilied as sliown in Fig. 16. In this hgure it is to be noted that/f.v-), the 

 in-band approximating function, is represented as having a variety of vari- 

 ations outside the useful band. The function has been indicated in this 

 manner to emphasize that a fairly wide latitude in the choice of the behavior 

 of /(.V-) outside the useful is permittetl since €'-T^,(.v), the out-band ap- 

 proximating function, is the predominant function in this region. In addi- 

 tion, the variations of e'-F;(.v) in the in-band region have been exaggerated 

 in order to demonstrate their efTect on the combined approximating func- 

 tion, /(.v-) + e'F^f.v), over the useful frequency band. 



Fig. 17— Resultant transfer function for equalization purposes. 



Finallv, when the relation expressed bv eq. (12) is reciprocated and re- 



■^12(i.v) " 



plotted in terms of K 

 is obtained. 



, the result shown in eq. (13) and Hg. 17 



1 



fix') + e' Vlix) 



(13) 



Comparing the resultant special transfer function shown in l-"ig. 17 with 

 the transfer characteristic shown in Fig. 14, and assuming that f(x-) and 

 the coefficient of the Tchebycheff polynomial have been suitably chosen, 

 it is established contingently that the combination of functions chosen to 

 represent B{x-) produces the desired result. 



This brief derivation serves as a guide to the main {problem of choosing a 

 particular f(x-) and a particular e^F„(.T) which, when added together and 



