1424 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



a potential 63(0) and that at ^ = the current v through the inductance 

 ( is zero. 



The network equation is 



dt 



ir-\-lf ir 



dt = 0. 



Now tV(0) = and di,{0)/dt = [e.,(0) - c,{0)]/(. Let 2/(C = wo', then 

 diM/dt = coo'C[e2(0) - e8(0)]/2. 

 Using Laplace transforms, 



(p^ + Uo^)Ir{p) = piriO) + 



'■c 



dirjO) 



dt ' 



(40) 



Irip) = "^ [^2(0) - eM] -^ 



■p- + wo- 



hence 



• (,^ r ^2(0) - ^3(0) . ^ 

 %r\t) = (jOqC sni COol 



(41) 



and 



q{t) - f irif) dt = C- 

 Jo 



eM - cM 



[1 — cos wnt]. 



If 27r/wn = 2r, i.e., r = Tr\/(C/2, which means that the duration of the 

 switch closure is a half -period of the resonance of the tuned circuit, then 



..,. tCIsM- eM] . ^t 

 ir{t) = sni — , 



T Z T 



( 



q{t) 



Ch(0) - ^3(0)] 



1 — cos — 



T 



It is clear then that, during the period r, the charge transferred onto the 



1 



Ir(P) " ? ? 



coi In(P) + In(P) 



Fig. 9 — Resonant circuit excited b.y current sources 7„ and /,/ 



