Effect of Ground Permesbility on Ground Return Circuits Sais deat titel inte arse ON S25 shite a toogesexs ha of the ‘uajos portion uf He wus usleee an the eoasequent dic in chonsing. 4 eonducsivigy to he abe fm commana a rsa feturn cenit inypedarce his heesofre Ine eilered ten 1 she inia consideration the pesibiity ofan ears peewebilty greater than ey. “However, eer the pevenbiity iy séneies ht Evol epneiably diferent Sos ny rd 1 fey devia to reduce the pre eeor it a computation and since the inclusion 1 fhe perimeatiligy in the terms mye sere inns Ie tb wetter fageerotnt Letween the chevry al rsyeriner i seems worth while tt prvi fnalas rien ince the peemeabilics, “The ell asks 6 1 gvound recurs circu ie Za sb Bolog te Laat Wy where 2-1 i2a wie ie Ie sll anperaace witk a peefet'y vom Seti ground ane Auf? + £0) costsine te oet of the Hite com ‘duetvity and. permealssiy of the ground. Catsen® has derived ininive itegee! ail seiewrsymasiona fou 2 | Qo che lao anit esmeabiliee, The insite iacyea! derive hen is arrived at merely by going tvougi Cavson's taper snd serine fn Ihe permessiity ‘wherever Can has replaced it iy arity. Therealer will be expected Tohave a copy ef Carson's yet tl a Hot all of the ten Bs eae wl bt here repredce equations (24) and (21) Tespetivey ace the nese ite Sacer formulas for sei an mul inypelance. Kquations (A) and (0) repectively are the new asympsnie asl onavergent series firme for P aad G0 The functions o sad Focusing ha oyustious (C) ae fhmetions of the permeability Since tome of them ane defined by fries aul thie computations cnmomently rather inven, enough "ola R. Caen, Bal eae Tao dora ey 1h of then ave tabled for valves of w feom 1 9 1. to provide forthe Computation of Pand 0 for values of 7, up t02 Equation (1! is change lu there i 2 new definition for « = teas Since curl ~~ (0)}uHfeqations (2) al (8) sit to thee lee hand side. he sest change sin the snslicaion ef the Boundary conditions [Ac the wire w/the geound Zan fy must be continwous. The eave ae else for Pn ard gt new bom have the fase LAPT ie = te 4 a, 1 63 hence ay a as a9) ay fee oar react teil! |e eo ta meh alae 1 dee 0. By = dolog Sp + Sten [EP cone ey, “The puincipal steps ia che derivation of enuation (18) ae piven in Appendix “The new definition uf P+ Qs P+io= if Replacing é by ¢# and assuming that oie a real quantity thie ree en gee ‘where R is uted to indicste chat the real pare i ca be taken, ‘The asymptotic expursion is easiest desved by expwaling 1A(¥H# — Th) into an ascending power series in rad integrating JPorcoeio—4---], a ° the leading It is worth noticing that when + is ao large that on! eras ia P are of impertance a] tnhel st + Gh +) Pa tet ti ti At power fms thy + fa) V2s dav ie small in comparison with in ovens of gw — 1's 2 convenient Whew y= 1 stall a er “Thief eaily arrived be wring form of sain aes “The expansive is alwolutely convergent for all values of ea LETT + en wet aaa feel Ts bette +) = 26 4 Fe(low | ie + 29) = 83208 1B tt) ote soe Tes = SZ eunses | ote pa By Ee] HD eae a ea eae Sets | See bt abe ae | 5) else payee BE aS Wing © = HG Ff) = ae we have thea, eR fo) ~ (1A) = 9 mes Cann's P= i with « ~ ated “The problem is now reduced to the talious proemlare of éiferen tlasng Mle) and senarating real and iaaginary. parte tie foreach, pier of The hilt sles are given in Appendix IT. The rele Fe het wee i the fn poy (3)"em 108-4] an DE FCoE, reo or totssay + | HEH A+ malar 2) >See ahd nde “Funtionetl” page 1 98 nePRCT OF GsOUND PRRMBARITITY m 3) sino (5Ysane- +] rene 2) oot ae?) smtoe2) = whee = 0 TJ — Cavan’ F and the per rcbigy fs eomtaned inthe funevien: mean ‘The definitions of the me and wile found ia Append tl. “The lalde of sumerieal value should sue for ost needs. TABLE a eLe SuSTEN TECHNICAL sowaNAL “ i SEa i i os] i ASHES oe ii ee — BI iia i zB: a cs) Hi i ui aa EEE SEEUC EE Tt te EE “The curves show the effect of x = 17 on the mutual impedance between two parle! poound eetutn eco with the wires ying en {Regu ae dashed portions of thr vas were not compute Avvesone 1 vubtated ito (10 give qvetion: (1, (ar = Pais} wf an if ° ate) costes = 3 (7) 08 are ve Jan fs, tia iat lon =o iter sat [een tat tog Awessvix TT “The eureveitng assis has been emeiesably shortened by sting each gy Lp beeen the # being an ever iateger "The iuvere power of ¢ all eee ost, in equation (2), sea shove pe ipa mn {Se g-wn [Se Ras ad bonne Babee ahaglg = ¢ (eget — fey'y)