212 BELL SYSTEM TECHNICAL JOURNAL 



geological strata for some distance below the earth's surface, constitute 

 other important factors. An accurate mathematical evaluation of the 

 coupling between earth return circuits is difficult. Formulas have been 

 developed under simplifying assumptions as to symmetry and homo- 

 geneity, which aid in explaining and interpreting experimental results 

 and in predicting approximate values of coupling in cases where experi- 

 mental measurements are not available. 



Assuming uniformity of exposure conditions the coupling varies 

 directly with length of parallelism, except for end effects or interactions 

 between ground connections of the two lines. Increase in separation of 

 the lines diminishes the coupling but the exact relationship depends 

 upon the distribution of current in the earth which in turn depends 

 upon the frequency and the earth conductivity. In many cases differ- 

 ent strata of different conductivities are involved in the path of the 

 earth current, which adds to the difficulty of correlating experimental 

 and theoretical results. The effect of earth conductivity on coupling 

 is accentuated as the lines are more widely separated. At roadway 

 separation, large differences in earth conductivity affect the coupling 

 only moderately; but at separations of one half mile to one mile, 

 coupling values may differ by 20 to 1 or more, due to the range in 

 v^alue of earth conductivity. Irregularities in exposure conditions 

 such as changes in direction of one or both lines, crossovers, and angular 

 exposures of varying separation, are complications which frequently 

 occur in practise. 



The voltages set up in neighboring communication circuits by power 

 currents are due usually to inductive coupling but in some cases are 

 due partly or wholly to resistive coupling. It is seldom necessary in 

 practical studies to try to segregate these two components of voltage, 

 since their effects in the telephone system are not a function of the 

 phase relationships of these components to the power line current which 

 produces them. It is not unusual to speak of inductive coupling as 

 including both inductive and resistive coupling. 



Any grounded circuit in proximity to power and telephone lines 

 within an exposure brings about a certain amount of shielding through 

 the reaction of the currents induced in this conductor upon the primary 

 magnetic field set up by the residual current in the power circuit. In 

 this respect a shield wire acts like a short-circuited turn on a trans- 

 former. The effectiveness of the shielding depends upon the conduc- 

 tance of the shield wire, the manner and effectiveness of its grounding, 

 and its position with respect to the power and telephone wires. Such 

 a wire affords maximum shielding when closely coupled to either the 

 power wires or the telejihone wires, when its conductance is high, and 

 when its ground connections are of low resistance. 



