Tables of Phase of a Semi-Infinite Unit Attenuation Slope

Five and seven place tables of the integral B(xc) =1 r~Xe 7T Jx=0 7T Ji=0 log 1 + x dx 1 -- X X which gives the phase associated with a semi-injinite unit slope of attenuation, are now available in monograph form. The usefulness of this integral and its tabulation are discussed. H. W. Bode1 has shown that on the imaginary axis, the values of the imaginary part of certain functions of a complex variable may be obtained from the corresponding values of the real part, and vice versa. This theorem was immediately recognized as a powerful tool in the communications and network fields. The most generally useful function which was given by Bode for use in applying this theorem to the solution of communications problems, is the phase associated with a semi-infinite unit slope of attenuation. This is given by the integral 2 (1) where: B(xc) is the phase in radians at frequency fc, and fn = the frequency at which the semi-infinite unit slope begins The usefulness of Integral (1) is illustrated by some of the communication problems which stimulated its accurate tabulation. 1 Bode, H. W., Network Analysis and Feedback Amplifier Design, D. Van Nostrand Co., Inc., New York, 1945, Chap. XIV. 2 Ibid: Chap. XV, pp. 342-343.