DELA y EQUALIZA TION OF CARRIER CIRCUITS 183 



An examination of equation (1) indicates that there are zeros at the two 

 points: 



p = —kn + j^n , and P = —kn — join 



and poles at the two points 



P = -\-kn + J0}n , and P = -\-kn — join 



■OOr 



- w 



00 - PLANE 



-COr 



kn 



kn 



+ 00 



+ p 



Fig. 3 — Plot of zeros and poles of the network of Figure 2 on the complex-frequency 

 plane. 



The first zero in equation (1) contributes a delay (defined as the derivative 

 of the phase with respect to frequency) of the form 



Ti 



dBi 



dit} 





(2) 



Similar expressions may be obtained for the other zeros and poles, the total 

 delay of the section then being equal to the sum of the delays contributed 

 by each zero and pole. 



The four zeros and poles of equation (1) may be plotted on the complex- 

 frequency plane as shown in Fig. 3, where the circles indicate zeros and the 

 crosses poles. The four points are seen to be symmetrically disposed with 

 respect to the origin. With reference to this figure, it will be noted that, 

 since w = —jp, positive real values of p correspond to negative imaginary 



