FUNDAMENTAL PROBLEMS AND LIMITATIONS 



is defined as the ratio of received power P2, delivered 

 to a load matched to the receiving antenna, to 

 power Pi, suppHed to the transmitting antenna, with 

 both antennas adjusted for maximum power transfer. 

 Thus 



P'l 



Radio gain = 



Pi 



which is equal, in the decibel scale, to 



10 log, 



radio gain in decibels. 



(5) 



(6) 



The attenuation is the reciprocal of the gain. Since 

 P2/P1 < 1, the gain in decibels is necessarily a nega- 

 tive quantit^^ The attenuation in decibels is a 

 positive quantity equal in magnitude to the gain in 

 decibels. 



The radio gain can be taken as the product of 

 physically significant factors. Among these are the 

 gains (?i and G'2 of the transmitting and receiving 

 antennas respectively ; and A- which accounts for all 

 other influences modifying the transmission of power. 

 A is called the gain factor. 



P-y 



Radio gain = — ^ = GiG^A'. 

 Pi 



(7a) 



The radar problem involves double transmission 

 over the path as well as the reradiating properties of 

 the target, lQira/9\-. 



Radar gain = — = fnCi->A'' ( 1 



Pi ' V 9XV 



(7b) 



where a is the radar cross section of the target and X 

 is the wavelength. 



adjusted for maximum power transfer. .4o = 3\/8ird 

 where d is the distance between doublets. .4^ is the 

 path gain factor which includes all additional influ- 

 ences modifying the transmission of power. 



These factors may also be related to the field 

 strength, E, at any point in space by 



E = Eo^GiA 



and 



V(Ti/i^ 



E 



A 



'4o PoVG'i 



(9) 

 (10) 



Here Ea is the free-space field at a point in space 

 set up by a doublet transmitter and Eo'^fn is the 

 free-space field of a transmitter with antenna 

 gain r/i. 



The primary function of this book is to show how 

 the factors A and Ap may he calculated, taking into 

 account all contributory influences which modify 

 their magnitudes. 



'■^•^ Radio Gain of Doublet Antennas 

 in Free Space 



This is the fundamental and simplest case of 

 transmission of radiant energy, against which other 

 transmitting combinations may be compared. Two 

 doublet antennas (for which the gains, by definition, 

 are unity) are set up in free space in a manner which 

 insures the maximiuii transfer of power to the re- 

 ceiver circuit, i.e., the doublets are parallel to each 

 other, ha\'e a common eriuatorial plane, and the 



-.r^n 



From " \1KJ 



Transmitter Circuit^ 



T 



To 

 ReceWer Circuit 



Figure 3. Doublet antenna.? in free space. 



The gain factor, .4, ma3r also be split into two receiver circuit impedance is matched to that of the 

 factors, so that receiving antenna (see Figiu-e 3). Then for free 



(8) space. 



-4 = .4o.4^. 



Here Ao is the free-space gain factor for doublet 

 antennas (see Sections 1.2.7, 2.1.3, 2.2.2, and 5.1.2) 



Free-space gam = — = ,4o- = -— 1 , 

 Pi \ Sird/ 



(11) 



