142G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



charge exchanged during one-half period of the resonance is 



,^^ k(0) - eMl 



^1 -+- ^2 



For the present case, (16) and (17) become 



62(0 = lit) - / ^Vo(r)^l(^ - r) dr, 



J — 00 



^3(0 = f uMz.it - t) dr. 



J — GO 



Following the same procedure as before we are finally led to the block 

 diagram of Fig. 10 whose output is given by 



E,{p) = 



[Zn''\p)h(p)]* ^^p^ S^(p)Z,S-\p) 

 ^1 + C2 



Appendix IV 



THE DERIVATION OF EQUATION (24) 



Considering the method used in Section IV to derive the zeroth ap- 

 proximation, it is clear that during the switch closure the voltages e^it) 

 and €^{1) vary sinusoidally, that is. 



lo 



62(0 = 62(0) 



e^{t) = eM + 



62(0) - 63(0) 



62(0) - 63(0) 



1 — cos — 



1 — cos 



irt 



IMPULSE 

 MODULATOR 



-12 



«H 



2C,C2 



Si(p) 



Zi(p) + Z2(p) 



,(2) 

 -12 



Fig. 10 — Zeroth approximation: modified bloclv diagram for the case where A^'i 

 and A^2 are not identical. 



