SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 



1407 



The problem i.s to determine the relation between K4 , the voltage 

 across R^ , and /o . 



III. METHOD OF SOLUTION 



Let us first write the equations of the system. Obviously the equations 

 will depend on the exact configuration of the networks A'': and No . For 

 simplicity we shall write them for the case where .Vi and N2 are dissipa- 

 tionless low-pass ladder networks. As will become apparent later this 

 assumption is not essential to the argument. What is essential, however, 

 is the fact that both A^i and N-> should start (looking in from the switch) 

 with a shunt capacitor C and a series inductance L„ , the element value 

 of Ln being much larger than (. Using a method of analysis advocated 

 by T. R. Bashkow,'^ we obtain, for the network of Fig. 3, the equations: 



J dii 



Rii — i'2 + Rio 



Ci 



dv2 

 dt 



t\ - l2 



> L 



^ dVn _ . _ . 



dt 



di 

 dt 



(l.a) 



C^^ = in - iA{t) (Lb) ] 

 dt 



t ^ = k - e,]A(t) (Lc) } R 

 dt 



c^' = iMt) -i,: (Ld) 



dt 



r din t 



Ln -jr = es — Vn 



at 



CdVn . / . / 

 n J, 'n In —1 



dt 



> h 



Ci -7- = li — i\ 

 dt 



T dii , j3 . / 



Lx -^ = V2 — RlIi 

 dt 



(1) 



