IMPEDANCE CONCEPT AND APPLICATION 29 



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

 a small doublet, the field is 



£„+ = - -'—. 1 H sm ^, 



^^^ a^SIe-"' (, , 1 , 1 \ . , 



He+ = —j 1 + — + -2-2 sm ^, (8) 



Hr^ = -^^ — 1 -\ cos ^. 



In this equation / is the current in the loop and 5 is the area. The 

 corresponding radial impedance is then : 



77+ 1+- 



ar 0-r 



This impedance approaches j? as r increases indefinitely. Close to the 

 loop we have approximately 



Zr+ = ioofxr. (9) 



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

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



_ 7](t'^A ( . sinh (jr\ . ^ 



tL^ = ^r — cosh ar sin B^ 



lirr \ f'' / 



_-r a'^A I . , cosh ar , sinh ar\ . 



He~ = -Ti — sinh ar 1 5-^^— ) sin 



2irr \ ar a-r- 



_ a A /sinh ar u \ o 



Hr = — 7. ■ • — cosh ar cos 6. 



wr- \ ar J 



The radial impedance to this wave is then 



, sinh ar 

 „ cosh ar 



He~ . , cosh ar . sinh ar ' 

 sinh ar \- 



ar a'^r'- 



Close to the origin we have approximately 



Zr~ = liuinr. (10) 



A line doublet formed by two parallel electric current filaments 

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



