IDEAL FILTERS 



243 



8 9 10 II 12 13 14 15 16 17 18 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 17 — Attenuation characteristic of a band pass filter. 



of modifying the theoretical spacings for the transition factors has 

 been to introduce peaks of loss near the band edges. The shortened 

 intervals adjoining the cut-offs produce tanh djl curves which rise 

 rapidly beyond these points to maxima slightly greater than unity, 

 instead of approaching unity monotonically. 



Having thus located the critical frequencies, we may readily com- 

 plete the design of the filter in lattice form. 



The formulation of the transfer-constant expression results in 



tanh - 



K, 



fa' 



1 



f 



1 



^H- 



h' 



1 



where /„ and /& represent the cut-offs, and the other /'s intervening 

 critical frequencies in order of magnitude, as shown by Table IV. 



A suitable form for the image impedance must next be obtained and 

 since it is normally determined by requirements with which we are 

 not now concerned, we will adopt the simplest possible expression, 

 namely 



Zi = K- 



Vl -flfa'^1 -f/f^ 



if 



where K^ is determined from the condition that Z j = 600 ohms when 



