SWITCHED NETWORK FOR TIME MULTIPLEX SYSTEMS 



1405 



;C 



fr = 



Fig. 2 



277- 



r = 



2f. 



77 



CJq 



7r\ri 



Resonant circuit. 



by a current source h which is shunted by a one ohm resistor. N2 is also 

 terminated at its terminal pair (1) by a one ohm resistor R^ which is the 

 load resistor of the system. The switch S is periodically closed for a dura- 

 tion T. The switching period is T. Thus if the switch is closed during the 

 interval (0, r) it will be closed during the intervals (nT, nT + r) for 

 n = 1, 2, 3, • • • . The inductance t is selected so that the series circuit 

 sho^vn on Fig. 2 has a resonant frequency fr = 1/2t; i.e., the time r 

 during which the s^\-itch is closed is exactly one-half period of the circuit 

 of Fig. 2. 



The switch S acts as a sampler and, as a result of the well-known modu- 

 lating properties of sampled systems, the sampling period T must be 

 chosen such that the frequency l/2r is larger than any of the frequencies 

 present in the signals generated by /o . Furthermore, in order to eliminate 

 all the sidebands generated by the switching, N2 must have a high in- 

 sertion loss for all frequencies above 1/2 T cps. 



In the analysis that follows networks Ni and A^2 will be assumed to be 

 identical: it should, however, be stressed that this assumption is not 

 necessar}?- for the proposed method of analysis.* This assumption is 

 made because in the practical situation which motivated this analj'sis 

 Ni and A'^2 were identical since transmission in l^oth directions was re- 

 cjuired. 



In order for the system under consideration to achieve the maximum 

 degree of multiplexing, the closure time r of the switch will be taken as 

 small as practically possible and the switching period T as large as pos- 

 sible (consistent with the bandwidth of the signals to be transmitted). 

 As a result the ratio t/T is very small, of the order of 10~" or less in prac- 

 tical cases. Consequently the resonant frequency /r of the series resonant 

 circuit sho^^^l on Fig. 2, is many times larger than any of the natural 

 frequencies of Ni and A^2 • 



* The modifications required for the case where -Vi is not identical to N2 are 

 given in Appendix IV. 



