46 BELL SYSTEM TECHNICAL JOURNAL 



antenna.* If the antenna is placed above and perpendicular to a 

 perfectly conducting plane and the antenna current is maintained the 

 same, the electric field will be twice as great f or 



£ = 2£. = H^. (2) 



To maintain the current constant, however, it is now necessary to 

 deliver more power to the antenna. 



For a short doublet antenna in free space the radiation resistance is 

 i?o = SOTr^H^IX"^ and hence the effective value of the received field 

 strength is given as a function of the radiated power by J 



If this antenna is placed perpendicular to and very near a perfectly 

 conducting plane the field strength pattern will be unchanged in the 

 upper hemisphere but there will be no field below the perfectly con- 

 ducting plane. The power that was required to produce the field in 

 the lower hemisphere, which because of symmetry is half the total, is 

 no longer radiated so that the same field strength will be produced by 

 half the power, ff or 



E=l^. (4) 



a 



If the transmitting antenna is removed so far from the ground that 

 the reaction of the currents in the ground on the antenna current is 

 negligible its radiation resistance is the same as if the ground were not 

 present. The receiving antenna, however, still "sees" the image 

 of the transmitting antenna in the ground. At a distance large 

 compared with the height above ground, the transmitting antenna and 



* The units are volts, amperes, meters and watts. H is the effective height of 

 the antenna as defined in the most recent "Report of the Standards Committee" 

 of the I.R.E. (1933). 



t Under the hypothetical conditions taken by Sommerfeld, namely the antenna 

 half in the ground and half in the air, the field is the same above a perfectly con- 

 ducting plane as in free space. When the antenna is entirely above a perfectly 

 conducting plane the field is the same as it would be if the plane were replaced by the 

 image of the antenna in it. That is, the field is the sum of two equal components, 

 one due to the antenna itself and the other due to its image. At distances large 

 compared with the height of the antenna above the plane these two components are 

 in phase and their sum is equal to twice either of them. 



J For half- wave antennas the numerical factors in equations (3), (4) and (5) are 

 respectively 7.0, 9.9 and 14.0. 



tt Let El be the received field strength in free space produced by a power Pi and 

 let £2 be the field strength for an antenna perpendicular to and very near a perfectly 

 conducting plane produced by a power P2. Then £2 = -Ei when Pj = Pi/2, and by 

 equation (3), £2 = £1 = 3V5V-Pi/<i = 2)^S-^2Pijd, which is equivalent to equa- 

 tion (4). 



