878 BELL SYSTEM TECHNICAL JOURNAL 



place, the over-all reliability of the radian tables is ± .000015 radian. 

 Since the function tabulated was constructed by a series of straight line 

 approximations to the true phase, interpolation to get the phase for values 

 of ///o or/o// between those given in the tables in problems where this is 

 necessary, will result in the same accuracy as that given for the tabulated 

 values. 



Murlan S. Corrington'^ of Radio Corporation of America has computed 

 the phase in radians for the semi-infinite unit slope of attenuation of Fig. 1 

 for approximately 100 values of ///o using equations 15-9 and 15-11 of 

 Bode's "Network Analysis and Feedback Amplifier Design" and has given a 

 table of these values to five decimal places. Where the values of Table III 

 difi"er from Corrington's values, his value is given as a superscript. Since 

 his approach is the more exact one, it is assumed that where a difference 

 exists, his value is correct. The differences have a maximum value of one 

 figure in the fifth decimal place which is consistent with the accuracy of 

 ± .000015 radian given for Table III. However, linear interpolation of 

 Corrington's values to get the function to three figures in///o, which preci- 

 sion in //'/o is really needed to utilize five figure accuracy in B, will result 

 in errors considerably larger than those of Table III for the higher values of 

 ///o. 



Acknowledgment 



The writer wishes to thank Miss J. D. Goeltz who carried out the calcula- 

 tions of the basic Tables and of the illustrative examples of this paper. 



APPENDIX 



Use of Tables I to IV' in Determining Phase from Attenu.a.tion or 

 Reactance from Resistance 



The first step in determining the phase associated with a given attenua- 

 tion characteristic using the tables described in the basic paper is to plot 

 the attenuation as a function of log frequency to a suitable scale. Such an 

 attenuation characteristic is illustrated in Fig. 4a. The attenuation char- 

 acteristic is then approximated by a series of straight lines such as are shown 

 in dotted form. The number of straight lines used will depend upon the 

 accuracy desired in the resultant })hase. As a rule, an apjn'oximation to the 

 attenuation which does not depart by more than dz .5 db will give a resultant 

 phase which does not depart by more than ± 3° from the true phase. 



If we now examine the straight line attenuation apj^roximation of Fig. 4a, 



'Murlan S. Corrington, "Tabic of the JntcKral - / • dl" K.C.A. Review 



IT Jo I 



September, 1946, page 432. 



