48 BELL SYSTEM TECHNICAL JOURNAL 



ceived power is the maximum power that can be transferred from the 

 receiving antenna to the first circuit of the receiver. This is 



for a short doublet. From equation (3) it follows that the ratio of 

 transmitted to useful received powers for antennas in free space is * 



For short vertical doublets above the surface of a perfectly con- 

 ducting plane this becomes, 



at distances that are large compared with the antenna heights. Here 

 RvJRo and RvJRo are the ratios given by equation (6) and Fig. 1 for 

 the transmitting and the receiving antenna respectively. When the 

 antennas are more than a wave-length above the ground these ratios 

 are substantially unity, and only one-fourth as much transmitted 

 power is required as would be if the antennas were in free space. 

 When both antennas are very near the surface of the earth, Rv/Ro — 2 

 and the same transmitted power is required as in free space. 



Part I — Vertical Antennas on the Surface of the Earth 



In this section transmission between two short vertical antennas 

 above and very near to the surface of plane earth will be considered. 

 The attenuation factor will be taken as the ratio of the received field 

 strength to that which would result if this plane surface had perfect 

 conductivity. 



In evaluating the electromagnetic field generated by a short vertical 

 antenna on the surface of an imperfectly conducting plane it is con- 

 venient to first determine the auxiliary function 11, called the Hertzian 

 potential, from which the vertical component of the electric field may 

 be obtained by means of the relationship.f 



240^x2/ , , X^ 32 \ 

 £= -^^(^l+^,^jn volts per meter. (11) 



* For half-wave antennas the right-hand side of equation (9) must be multiplied 

 by r73.2/80)2 = 0.837. 



t Bold face type is used to indicate a complex quantity. The same character in 

 light face type represents its magnitude with which the radio engineer is concerned. 

 The imaginary unit, V— 1, is represented by i. 



