TIME DIVISION MULTIPLEX SYSTEMS 215 



second harmonic. Components 2 and 3 are shifted —72° and +72° respec- 

 tively and 4 and 5 are shifted — 144° and +144° in relation to the phase of 

 component 1. As shown in {b), the five vectors combine in the form of a 

 closed polygon giving a resultant of zero amplitude. Similar vector dia- 

 grams for reception in the third, fourth, and fifth channels are shown in 

 (c), {d), and (e). The appropriate diagrams for transmission in channels 2, 

 3, 4, and 5 and receiving in any channel can be obtained from {a) — {e) 

 by cyclic permutation of the channel numbers, i.e., transmission in 1 and 

 reception in 2 corresponds to transmission in 2 and reception in 3, etc. 



Production of crosstalk by phase and amplitude distortion in the trans- 

 mission medium is illustrated by (/), Fig. (4), which shows the resultant 

 component received in channel 2 when signal is transmitted in channel 1 

 and an imperfect line is used to connect the transmitting and receiving 

 terminals. The vector 1 is taken as the reference amplitude and phase. 

 The gain characteristic of the line is assumed to be one db low at the side 

 frequency producing vector 2, one db too high for vector 3, 0.5 db low for 

 vector 4, and with no error for vector 5. The phase curve is assumed to 

 depart from a straight line by —1°, —1°, —4°, +3° at the side frequencies 

 from which components 2, 3, 4, 5 respectively are derived. The vector 

 polygon fails to close and the resultant represents an unwanted signal 

 received in channel 2 at a level 25 db below the wanted signal received in 

 channel 1. 



We may make an estimate of the accuracy of the equalization required 

 in the general case by writing the transfer impedance Z{iu) in the form : 



Z(to) = p(co)Zoe~'"'"~''^'"^ (39) 



where j8(aj) represents the departure of the phase shift from a straight line 

 and the variation from flat gain is given by 



g(co) = 20 logio p(co) (40) 



The expression (39) may be rewritten as: 



Z(i<o) = [1 + z(io;)]Zog"'"'", (41) 



where 



z{io:) = p(w)e"''^*"^ - 1 (42) 



If we assume that the switching function is of the general form (34), we 

 calculate from (14) the general relation: 



