Tables of Phase Associated with a Semi-Infinite Unit Slope of Attenuation

HE method described by Bode2 for the determination of the phase associated with a given attenuation characteristic or the reactance associated with a given resistance characteristic has proved to be an extremely useful laboratory and design tool. In this method the attenuation (or real) characteristic, plotted versus the log of frequency, is approximated by a series of straight lines. The phase (or imaginary component) is then determined by summing up the individual contributions of each elementary straight line segment to the total phase (or imaginary component). The most elementary straight line characteristic which can be used to construct a given straight line approximation is that in which the attenuation plotted against the log of frequency is constant on one side of a prescribed frequency, / 0 , and has a constant slope thereafter. Such a characteristic has been called by Bode a "semi-infinite constant slope" characteristic. 3 A semi-infinite unit slope of attenuation or one in which the attenuation changes 6 db per octave, or 20 db per decade is shown in Fig. 1. The phase associated with this attenuation characteristic is plotted in Fig. 2.4 The independent variable was chosen as///o for values of / less than/o and/o// for values of / greater than f 0 to keep it finite for all values o f / and in order to show the phase plotted exactly as it is given in the tables to follow. The phase associated with a semi-infinite constant slope of 1 For a complete discussion of minimum phase see Hendrik W.