THE ELECTRIC DOUBLET IN FKEE SPACE 



13 



terms in equation (1) containing r"^ Thus the 

 radiation field for the element dl of the doublet maj- 

 be written : 



607r7rf/ sin e 



dEs = 



dH^ = 



— volts per meter, 

 ^r (2) 



Idl sin e dEt, 



2\r 120ir 



amperes per meter. 



The other components are relatively negligible 

 except near the antenna or near ground for low 

 antennas. The electric field dEg is perpendicular 

 to the radius vector r and lies in the r,z plane, and 

 the magnetic field dH,f, is perpendicular to r and to 

 dEg. It will be noted that E/H = 1207r ^ 376.7 

 ohms. This is the impedance of free space in the 

 mks rationalized system of units, the ohms of the 

 electrical engineer. 



Equation (2) describes the radiation field of a 

 differential element of the doublet. To get the 

 radiation field of the whole doublet, these equations 

 must be integrated o\'er the length I. This gives 



60 TT sin 6 



E, = 



//. 





Idl 



\r 



volts per meter. 



(3) 



Eg/120'ir amperes per meter. 



Equation (3) may be written in exactly the form 

 of equation (2) by introducing the effective length, L, 

 of an antenna, which is defined as the length that a 

 straight wire carrying current constant over its 

 length would have if it produced the same field as 

 the antenna in question. Calling the current meas- 

 ured at the input point /,-, 



L = :ldll 



1/2 



Idl 



h 



meters, 



(4) 



and hence 



E, = 



60ir/,Lsin I 



\r 



volts per meter, 



E^ = 



1207r 



(5) 



amperes per meter, 



so that equations (5) are the same as equations (2) 

 with 7;L replacing / Idl. For a short dipole or 



doublet the current varies linearly from 7, at the 

 midpoint to zero at each end so that from equation (4) 

 L = 1/2 for a doublet. 



The power per unit area, W (that is, the power 

 flowing through a unit area normal to the direction 



of propagation), is represented by Poyn ting's 



vector and is given by the product EgH^ times the 



sine of the angle between Eg and 77^. This angle is 



90 degrees. Con.sequentl}^ 



W = EH watts per square meter, 



E-' 

 W = 7o^ watts per square meter, (6) 



E = Vl207rT'F volts per meter. 



To find P, the power output of the doublet, W" is 

 integrated over a large sphere concentric with the 

 source. Using equations (5), 



E-d- 



45 

 and (7) 



3V5VP 



P = 



watts 



E = 



d ' 



where d is wi-itten in place of r. The subscripts d and 

 4> have been dropped at this point because the 

 E and 77 referred to in equations (7) are the fields 

 in the equatorial plane, where sin 6 = 1. 



As the antenna is part of a circuit, it is often con- 

 venient to think of the radiated power as being 

 dissipated in a fictitious resistance called the radia- 

 tion resistance, defined by 



R, = — ^ ohms, 



(8) 



where P is the radiated poorer and 7,- the rms input 

 current. For the doublet, 



Rr = SOtt- ( - y ohms, (9) 



whei'e L is the eftective length given by equation (4) . 



2.1.2 



Reception by an Electric Doublet 



When an electromagnetic wave falls upon an 

 antenna, a current is induced in the antenna and 

 power is abstracted from the wave. If the antenna 

 is connected to a load, the power abstracted is 

 dissipated in two ways: (1) by absorption in the 

 load (reception), and (2) by reradiation from the 

 antenna (scattering). 



In this classification, the power dissipated by the 

 antenna itself (due to its ohmic resistance) is ignored 

 because this loss is likely to be negligible compared 

 with the power dissipated through reradiation. 

 Hereafter, power absorbed by the load will be called 

 received jjower and power reradiated by the antenna 



