90 



BEij. SYSTEM mcnxiciL JOrRWII. 



abo\e are sufficient to t,n\'e a reasonal)l\- comprehensive idea of the 

 general character of tlicse osciUations and their dependence on the 

 number of sections and the constants of the hUer. 



It will be observed that the current is small until a time ai)proxi- 

 mately equal to 2n/w,—n\/LiC2 has elapsed after the voltage is 

 applied. Consequently the low-pass filter behaves as though cur- 

 rents were transmitted with a finite velocity of propagation ajf/2 = 

 1/\/LiC2 sections per second. This velocity is, however, only ap- 

 parent or virtual since in every section the currents are actually 

 finite for all values of tlme>0. 



After time t = n\/LiC2 has elapsed the current oscillates about the 

 value Ik with increasing frequency and diminishing amplitude. 

 The amplitude of these oscillations is approximately 



1/k 



Vl-(2n/o:,ty 



1^' 



and their instantaneous frequency (measured by intervals between 

 zeros) 



The oscillations are therefore ultimately of cut-ofif or critical frequency 

 co,/27r in all sections, but this frequency is approached more and more 

 slowly as the number of filter sections is increased. 



Figs. 23, 24, 25, give the indicial admittance in the 100th. 500th 

 and 1000th section of the low-pass wave filter. The filter itself seldom 



CM 



ISO 



240 



300 



320 



Fig. 23 — Low pass \va\c' tiltcr. Indicial admittance^ of lUJtli section in =90). 

 Multiply ordinates by -^ C, L 



