TIME DIVISION MULTIPLEX SYSTEMS 



201 



and let the switching between the /'"' channel and the line at the sending 

 end be represented by: 



/,,(/) = /'.(/)£;(/), (2) 



where /«;(/) is the current tlowing into the line from the /"' channel. The 

 function F j{t) has the dimensions of an admittance and, in the arrangement 

 shown in Fig. 1, is periodic in time with fundamental frequency q — 2t/T 

 radians per second, where T is the time occupied by one cycle of the switch- 

 ing operation. In the interests of economy of analysis, it is preferable for 

 our purposes to assume for Fj(i) a somewhat more general function of time 



SENDING RECEIVING 



channels: 



(J-I) 



Ui(t). 



{Eie^'^jt 



UJj <(jOo 



(J + I) 



I 



L 



ti 



LINE 



'in out 



SYNCHRONIZED AT 

 FREQUENCY q > 2 OJq 

 PHASE DIFFERENCE 



~ DELAY OF LINE 



Fig. 1— Elementary arrangement for time division multiplex system 



than is directly obtainable with the elementary arrangement of Fig. 1. 

 We shall let 



Fi(t) = Z Ami cos [(v + mq)t - 6,^]. 



(3) 



To make the results applicable to Fig. 1, we merely let ;' = 0; then by the 

 usual Fourier series analysis, 



Aoj = ao/2, Ami ~ ^mj + Kii 



m > 



doj — 0, tan 6mi = bmj/am} J 



<^mj = ™ / Fjit) cos mqt dt 



1 Jti 



bmj — ^ f Fi(0 sin mqt dt, t\ arbitrary 



(4) 



