328 BELL SYSTEM TECHNICAL JOURNAL 



a transmitter to a reference antenna, designated as No. 3, which is 

 located at any desired point 3. Let £13 denote the intensity of the 

 (vertical) electric field produced at point 3 by antenna No. 1. Then 

 the current induced in the receiving branch of No. 3 will be azEu, 

 the parameter as being the receiving sensitivity of antenna No. 3. 

 The power Pn transferred from 1 to 3 is then 



Pi3 = rzaz^Eu^, 



where r^ is the equivalent resistance of the receiving branch of antenna 

 No. 3. 



Now reverse the direction of transmission; we have 



Pzi = riarEzi^. 



We now suppose that the terminal impedances are adjusted for maxi- 

 mum output and maximum transfer of power and that the power Pu 

 developed by No. 1 when transmitting is equal to the power P33 

 developed by No. 3 when transmitting. Then it follows at once from 

 the reciprocal energy theorem, that Pu = Pzu and 



ExzY ^i«i! . 

 2 



£31 / ''30:3' 



Now replace antenna No. 1 by any other antenna, designated as No. 2 ; 

 we then have from the foregoing 



E,zY _r,a.^ _ 

 Ez2 / rzdz^ 



By virtue of the terminal impedances specified, r^ = Ri and 

 ^2 = R2 where Ri and R2 are the resistances of the two antennas as 

 measured from their operating terminals. Consequently, since 

 £32 = Ezi, we have 



EuV Riar i?l/^l- 



where hi and h-z are the equivalent heights of the two antennas. 



The ratio rjn will be termed the 'relative transmission figure of 

 merit' of the two antennas No. 1 and No. 2 with respect to trans- 

 mission between any two specified points. For directional antennas, 

 the parameters cci and a^ will depend on the direction of transmission; 

 that is, the location of the receiving with respect to the transmitting 

 point. 



