NETWORK SYNTHESIS 



G35 



envelopes, between which the actual error curve oscillates. These are 

 the dashed lines in Fig. 7. 



The maximum error, in the useful intcn-val, is determined by the 

 maximum value of the envelopes, i.e.. 



2o 



n + 1 I' 



(43) 



This function is plotted in Fig. 8, for various values of n. The abscissae 

 "distortion before equalization" represent distortion relative to the 

 median loss in the useful interval, or one half the total variation in the 

 interval. (This is a function of the top useful frequency coc , relative to 

 the assigned natural mode po ; and (7) makes Wc/po a simple function of 

 2o .) The figure is convenient for estimating the values of n needed for 

 specific applications. 



The various ripples in a — a do not all have the same amplitude, (43). 

 For some values of n and 2o , the amplitudes are almost uniform; for 

 others they are quite variable. A measure of the variability in ripple 



0.1 

 0.08 



0.06 



0.05 



-' 04 



M 0.03 



5 0.01 



a 



^ 0.008 



cc 



t= 0.006 



11. 



< 0.005 



O 0.004 



O 0.003 



0.001 

 



0.2 0.3 0.4 0.6 0.8 1.0 2 3 4 5 6 



DISTORTION BEFORE EQUALIZATION IN DECIBELS 



Fig. 8 — Distortion before and after equalization — n natural modes equalizing 

 2 identical natural modes. 



