IMPEDANCE CONCEPT AND APPLICATION 27 



Usually it is only one of the entire set of three-dimensional imped- 

 ances that is of particular importance, the preferred direction being 

 frequently the direction of the wave under consideration. When the 

 ratios involved in the above definitions are unequal, it is expedient to 

 resolve the field into component fields for which the ratios are equal. 

 We shall now consider some special examples. 



The field of the spherical electromagnetic wave emitted by a Hertzian 

 doublet is known to be 



E0+ = — 1 H h -T^, sm ^, 



47rr \ ar a~r~ ] 



£,.=l«£Z.7i+l\eos.. (7) 



l-wr^ \ QY 



7V=^^7l+l)si„9, 



47rr \ ar 



where : // is the moment of the doublet in ampere-meters, r is the 

 distance from the doublet, d the angle made by a typical direction in 

 space with the axis of the doublet, and ^p is the angle between two 

 planes containing the doublet, one of which is kept fixed for reference. 

 The radial impedance of this wave is 



P 1+^ + 4-. 



_ £9 _ ar 0-r 



ar 

 In a non-dissipative medium this becomes 



ipr 



At a distance large compared with the wave-length, the radial im- 

 pedance to the spherical wave emitted by a doublet is substantially 

 equal to the intrinsic impedance of the medium. Very close to the 

 doublet (compared with the wave-length) the radial impedance is sub- 

 stantially a capacitive reactance; in fact, we have approximately 

 Zo+ = l/iooer. 



Reversing the sign of o- in (7), we obtain a spherical wave traveling 

 toward the origin. At first sight, this inward bound wave appears to 

 be the natural mate to the outward bound wave. Two such waves 

 move in opposite directions in the same sense in which two plane 



