IMPEDANCE CONCEPT AND APPLICATION 29 



If the source of electromagnetic waves is a small coil rather than 

 a small doublet, the field is 



j/,+ =^:^^^(l+^. + 4-Jsin^, (8) 



Avr \ ar cr-r 

 iir,+ = -^ — ^ 1 H cos ^. 



In this equation / is the current in the loop and S is the area. The 

 corresponding radial impedance is then : 



ar a^r 



This impedance approaches tj as r increases indefinitely. Close to the 

 loop we have approximately 



Z+ = iwtir. (9) 



The field of the internal wave having the same type of amplitude 

 distribution over equiphase surfaces as the diverging wave (8) is 



Tyo" 



'A ( , sinh ar 



E^- = -^ — ( cosh ar — sin 9, 



^ Ittt \ ar J 



a-A ( . , cosh ar , sinh ar\ . . 



Hq- = -Ti — smh ar 1 ^-^5— sm Q, 



Irr \ ar a~r- ) 



^-. aA /sinh ar u \ a 



Hr" = ■ — o cosh ar cos d. 



irr^ \ ar I 



The radial impedance to this wave is then 



, sinh ar 

 _ cosh ar 



Z-=^=. ""I- . 



'' Hd~~ . , cosh ar . sinh ar 



smh ar h — -^rr^ 



ar ah^ 



Close to the origin we have approximately 



Zr = hi^ixr. (10) 



A line doublet formed by two parallel electric current filaments 

 produces a cylindrical wave. Close to the doublet (compared with 



