TABLES OF PHASE 



873 



The derivative of (1) above, however, proves to be quite simple and easy 

 to evaluate. It is given by Bode as: 



dB 1 - 

 -— = — log 



dXc TTXc 



I — Xc 



= l{'^hh-)^^^<'- 



(2) 



(2a) 



It therefore seemed that since the phase had already been computed by the 

 Mathematical Research Group of the Bell Telephone Laboratories, Inc., at a 



xc 





Xc+AX 



■^0 





Fig. 3 — Element of Fig. 2 for///o < 1 expanded qualitatively. 



considerable number of points, using the infinite series expansion of (1) 

 above the function in the regions between known values of phase could be 

 constructed by assuming the intervening curve of phase as a function of 



a; = - to be a series of straight lines having the slope given by (2) above 



over intervals Ax of x made sufficiently small that the resultant straight 

 line approximation would approach the true phase curve to the desired 

 degree of accuracy for the table contemplated. 



