TRANSIENT OSCILLATIONS IN ELECTRIC WAVE-FILTERS 19 



The transient distortion, it is interesting to note, is, as regards fre- 

 quency, independent of the applied frequency, and ultimately attains 

 the cut-off frequency of the filter. Its envelope is ultimately 



co/co c 



\ ircoj 



k 1 - (w/co c ) 2 \ TCOc t 

 when a voltage sin cot is applied, and 



i i nr 



k l-(0>/0>c) 2 \ TTU c t 



when a voltage cos oil is applied. 



Figs. 33 and 34 show the form of the current in the 5th section 

 when sinusoidal voltages sin cot and cos cot of frequency 25 per cent 

 above the cut-off frequency of the filter are applied. The transient 

 current shown in the curves increases in frequency up to the critical 

 frequency of the filter, the oscillations being ultimately given by 



1 u/u c 2 / , 2n+l 

 r T~i — V2 — t \ cos W a — ^ 



and 



1 1 |~2" • / , 2w + l , 



k (<a/uc) 2 -l\ TUc t 4 



corresponding respectively to applied voltages sin cot and cos ut. 

 The amplitude of these transient oscillations are enormous compared 

 with the final steady state, and the curves furnish a clear illustration 

 of the fact, stated in a previous part of this paper, that the selective 

 properties of wave-filters are essentially properties of the steady state 

 only. 



Figs. 35-41 show the building-up phenomena in the band pass 

 filter, type L1C1L2C2, and are applicable also to types L1C1C2 and 

 L\C\Li when proper values are assigned to the constants and para- 

 meters. 16 The curves actually show the envelopes of the oscillations 

 which are of slowly variable frequency in the neighborhood of co m /2ir. 



A study of these curves and the formulas of Appendix III lead to the 

 following proposition, analogous to that stated above for the low pass 

 filter. 



The time T required for an alternating current of frequency u/2ir 

 within the transmission range w/2ir of a band filter to build up to its 



16 n sections of type L\C\Lt,C% are approximately equivalent to 2n sections of 

 type L1C1C2 or of type LiGL 2 . 



