TRANSIENT OSCILLATIONS IN ELECTRIC WAVE-FILTERS 45 



where 



Ki= characteristic impedance, as seen from terminals of 

 initial or zero-th section, 



K2 = characteristic impedance, as seen from terminals of last 

 or sth section, 



r = propagation constant per section, 



Zi, Z 2 = terminal impedances, 



■£1 



a K1+Z1 1 



Kx-Zx 



and 



XV 2 — Z.1 



P2 



X2 + Z2 



Ki, K2, Zi, Z 2 , and consequently a, p x , p 2 are, of course, functions of 

 the operator p. 



The corresponding indicial admittance A n (t) is given by the integral 

 equation 



C r * A ' m "tm)- (2) 



By aid of (1) the right hand side of (2) can be expanded as 



e -nT e -( 2s -n)T e -tf s+n) T g -(^- n )r 



a pKr + " P2 ~wr +<7plp2 ~~wr +afHpl ~wr 



e ~(4s+n)T 



(3) 



Now if a m (t) denotes the indicial admittance in the wth section of an 

 infinitely long periodic structure, when the e.m.f. is applied directly to 

 the sending end terminals, it follows from (2) and (3) that 



e-P<a m (t)dt = e - w -. (4) 



