TIME DIVISION MULTIPLEX SYSTEMS 219 



carrying energy simultaneously, as would be the case if the channels were 

 subdivisions of a common signal band, the peak value of interference would 

 probably be of more significance than the average value. 

 It is convenient to let 



i^=101ogio^' (58) 



F = -10 logio f ' W,-M doii (59) 



H is the ratio expressed in db of mean signal power in one channel to the 

 total interference power received in one channel, and F is the weighting 

 factor expressed in db. From (56), 



U = lo-'^-^'/^o (60) 



Equation (57) may be written in the form, 



a^ b^ 

 where 



a = 8.69 i/ /'".. db 



NU 

 {N - l)r" 



^ ^^^-^y (iV^r^"^'""' 



(62) 



Without the numerical factors, a and b are expressed in nepers and radians 

 respectively. 



If we regard ai and <X2 as variables, (61) determines a family of ellipses 

 in which a and b are the semi-axes. By assigning values to A'^, r, and 

 H — F we may thus represent the requirements on gain and phase variation 

 by elliptical boundaries in the (Tio-2-plane. Figure 5 shows such a diagram 

 constructed for a large number of channels each active one-fourth of the 

 time and with flat weighting. In terms of the symbols above, we have set 

 N/{N — 1) equal to unity, t = 1/4, and F = 0. Gain and phase variations 

 included within a particular ellipse produce average interference power less 

 than the amount designated on the boundary in terms of db down on mean 

 power in one channel. The requirements imposed on both gain and phase 

 variation are considerably more stringent than the corresponding require- 

 ments for carrier systems using frequency discrimination and employing 

 comparable band widths. 



Requirements on linear transmission of the line are, of course, not the 

 only considerations involved in a comparison of time division multiplex 



