Effect of Ground Permeability on Ground Return Circuits

N account of the irregular a n d heterogeneous character of the m a j o r portion of the earth's surface a n d the consequent difficulty in choosing a c o n d u c t i v i t y to be used in a c o m p u t a t i o n of g r o u n d return circuit i m p e d a n c e it has heretofore been considered useless to t a k e i n t o consideration the possibility of an earth permeability greater unity. However, since the permeability m a y sometimes be k n o w n to be appreciably different from u n i t y a n d it is always desirable to reduce the probable error in a c o m p u t a t i o n a n d since the inclusion of t h e permeability in the formulas m a y sometimes lead to a better agreement between the theory a n d experiments it seems w o r t h while to provide formulas which include the permeability. T h e self i m p e d a n c e of a g r o u n d return circuit is Z = z + i'2co log p"ja + 4co(P + iQ), where s + i2u log p"ja is the self i m p e d a n c e w i t h a perfectly cond u c t i n g g r o u n d a n d 4 u ( P + iQ) contains the effect of the finite cond u c t i v i t y a n d permeability of t h e g r o u n d . permeability. Carson 1 has derived an infinite integral a n d series expansions for P + iQ on the basis of u n i t T h e infinite integral derived here is arrived at merely Carson's paper a n d w r i t i n g in the permeability T h e reader will be expected by going t h r o u g h wherever Carson has replaced it by u n i t y . paper will be here reproduced.