PHASE DISTORTION AND PHASE DISTORTION CORRECTION 215 



and 



T-To= 0'(co) - 0'(O) 



(¥")■ 



- 1 



(30) 



1 + 



The variation of T — To in terms of the general parameter <ji-y[LC is 

 shown in Fig. 16. As 7" is a maximum at zero frequency and decreases 

 with increasing frequency, its variation tends to equahze the delay 

 on the cable. It will be demonstrated later that a more complicated 

 type of lattice network is available to supplement the simple lattice 

 type to improve the equalization still further. 



4 5 6 7 



VALUES OF wVlc" 



Fig. 16 — Time of building-up, T — To, for simple lattice network of n sections 



To provide partial delay equalization by means of the simple 

 lattice network, phase angle variation alone need be considered without 

 taking into account its derivatives. As pointed out above, the dis- 

 tortion a{w) of the cable phase B{w) is given by 



cr(co) = B{w) — cor zt nir, 



where r is a constant representing the slope of the required distortion- 

 less phase. In the present case n will be zero. The constant r also 

 represents the time in which the current will build up to proximate 

 steady state on the corrected cable. It is desirable, usually, that 

 this time be as short as possible, and, moreover, the smaller the value 

 of T, the smaller will be the amount of distortion to be corrected, 



