. The Bell System technical journal . l limit to the reduction of A 0 below e^o. Referring to Figs. 13 and 14, it is apparent that A = —. Thus, .4o is a direct measure of the impedance level over the useful band, and must not be made too small if the highest practical level of responseis to be attained. 8 Ref. 2, pp. 53-79. Ref. 3, pp. 26-34. ^ - + ^ - + - 1 64v - -f - 7x 734 BELL SYSTEM TECHNICAL JOURNAL where e is an arbitrary constant. Figure 19 shows the plot of the squaredTchebycheff polynomial, eWn{x), for the values of » = 5, and e = 6 = 0.
. The Bell System technical journal . l limit to the reduction of A 0 below e^o. Referring to Figs. 13 and 14, it is apparent that A = —. Thus, .4o is a direct measure of the impedance level over the useful band, and must not be made too small if the highest practical level of responseis to be attained. 8 Ref. 2, pp. 53-79. Ref. 3, pp. 26-34. ^ - + ^ - + - 1 64v - -f - 7x 734 BELL SYSTEM TECHNICAL JOURNAL where e is an arbitrary constant. Figure 19 shows the plot of the squaredTchebycheff polynomial, eWn{x), for the values of » = 5, and e = 6 = , while Fig. 20 shows a j)lot of the transfer function expressedin eq. (18). It is to be noted that the oscillatory behavior with equal maxima andminima of squared Tchebycheff polynomials for values oi x 1 make their use particularlysuitable as the solution of the approximation problem for low-pass filtersand impedance matching networks. It is now apparent that these same. Fig. 18—Tchebycheff polynomial, F„(.t), for w = 5. properties validate their use as the out-band approximating function forreactive Another useful property of squared Tchebycheff polynomials as ap-proximating functions for low-pass filters and impedance matching net-works is the inclusion of the specification of the tolerance as a factor in thetransfer function. The allowable db deviation over the useful band is relatedto e by € = e - 1, where ap is the maximum pass-band loss in nepers. Thus, the appropriatechoice of e always realizes the specified tolerance over the useful band. 2 When better tolerances are required and when the network configuration is notrigidly specified, Jacobian elliptic functions, rather than TchebychefT polynomials, mightbe employed. DESIGN OF REACTIVE EQUALIZERS 735 However, it is imi)ortaiit to observe that a given value of e automaticallydetermines l)()th the pass-band tolerance and the rate of cut-oflF in the out-band region. Hence, if a
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