. The Bell System technical journal . p) _ + cos <p - cos 2cp + cos 3^ M = M^) COS^ ~ These functions are tabulated in the last two columns of Table H. The coefficients .4o •■• A3 oi f(x-) are easily calculated from {he J\((p) f(<p) above by the relation of the Ak- to the Oj expressed in Table I. Thus,fix-) = - ^ ^ _ ;^ The tinal operation in the solution of the approximation problem is thechoice of the squared Tchebycheff polynomial, e-I^^), which satisties aresistance efficiency of 65 per cent. The Tchebychefif polynomial fo
. The Bell System technical journal . p) _ + cos <p - cos 2cp + cos 3^ M = M^) COS^ ~ These functions are tabulated in the last two columns of Table H. The coefficients .4o •■• A3 oi f(x-) are easily calculated from {he J\((p) f(<p) above by the relation of the Ak- to the Oj expressed in Table I. Thus,fix-) = - ^ ^ _ ;^ The tinal operation in the solution of the approximation problem is thechoice of the squared Tchebycheff polynomial, e-I^^), which satisties aresistance efficiency of 65 per cent. The Tchebychefif polynomial for ;/ = 5 is Vb{x) = 5x — ; + 16x . 748 BELL SYSTEM TECHNICAL JOURNAL Thus, Vb{x) becomes Vh^x) = 25a: 200/ + ^ 640/ + A 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 becomes1 ( - + * - ) + ( - + - ^,-8 + ). Fig. 24—Comparison of the resultant special transfer function with the transfercharacteristic of Fig. 23. This expression is the resultant special transfer function which satis-factorily approximates the transfer characteristic of Fig. 23. Fig. 24 shows aplot of these functions for comparison purposes. The squared magnitude of the transfer impedance of the network .Y isfound from the analytical expression for the special transfer function byadjusting the value of A so that KAq = 1. Therefore, Zuijx) _ . 1 Ro 1 - + + - + The elements of the network N are found from the squared magnitudeof the transfer impedance by methods standard in circuit ^ Thenetwork elements of Fig. 22 in terms of unit impedance and unit radian = Ref. 2, pp. 25-53. DESIGN OF REACTIVE EQUALIZERS 749 frequency turn out to be Ci = faradsG = faradsCs = farads f IN MEGACYCLES Li = henrysLi = henrvs.
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