THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 



757 



For the particular case illustrated in the above figure, the delay dis- 

 tortion is given by 



When CO - 



\\'hon COT = TOJr 



Hence 



dyp/diAi = — 6r cos cor. 



dxp/do) = —br = — C?max • 



= 7r/2 



#/dco = 0. 



dyp/doi = —dmvx COS (c07r/2cOmax)- 



(6.08) 



(G.09) 



With r = 7r/2comas and br = dmax , the following relation is obtained 



— — COmax C^max — ^/max O^n 



(6.10) 



In Fig. 22 are shown the positions of the pulse echoes for the above 

 case on a numerical scale ^/ma^ , together with their amplitudes for 



6 = 5 radians. On this scale the interval between pulse echoes 



7 = 1/4/max is }i. In the same figure is shown an assumed pulse shape in 

 the absence of phase distortion, which is the same as shown in Fig. 13, 

 except that the small tail has been neglected. The peak of the pulse is 

 taken at (fmax = —0.75, and the amplitude of the resultant pulse at the 



1.00 

 0.85iJ 'bO.85 



*o.70 \transmitted pulse 



AMPLITUDES OF 

 0.39 .-'PULSE ECHOES 





 "t 'wax 



Fig. 22 — Illustrative example of cak'uhition of impulse characteristic shown 

 in Fig. 23, by method illustrated in Fig. 2()(d). 



