POWER TRANSMISSION. RECIPROCITY 



15 



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X{METERS) 

 Figure 3. Free-space gain for doublets P2/P1 = (3X/87rd)2 = _^2^^ (Adjusted for maximum power transfer.) 



and from equation (14) the power delivered to the 

 load circuit of the receiving doublet is given by 



I2O7 



watts. 



(17) 



Hence the ratio of the received power (to the load 

 circuit) to the output power for maximum power 

 transfer is 



^ = (^Y = A,. (18) 



Pi \87rd/ 



The ratio P2/P1 = Ao- (as used here) is called the 

 free-space radio gain for matched doublets or for 

 short the free-space gain, since all objects, including 

 the earth, are supposed remote from both doublets. 

 This free-space gain, ^o = SX/Sird. On the decibel 

 scale, it takes the form 

 P2 



10 logi, 



Pi 



= 20 log .4o 



= 18.46 - 20 logio -^decibels. (19) 



A 



The nomogram. Figure 3, gives a convenient 

 means of calculating the free-space gain for doublets 

 adjusted for maximum power transfer. 



22 POWER TRANSMISSION. RECIPROCITY 



' '^ Radio Gain 



The formulas in Section 2.1 apply to doublets in 

 free space. This section considers the modifications 



that must be made in the formulas when the re- 

 striction of free space is removed. In actual trans- 

 mission problems, ground reflection, reflection from 

 elevated layers of the atmosphere, diffraction by 

 earth curvature and by obstacles, and refraction by 

 the atmosphere must be considered. In Chapters 5, 

 6, and 7 special forms of gain are discussed and 

 separate gain factors are introduced to take care of 

 each effect. For the present a factor that will be 

 called the path-gain factor, Ap, representing the 

 product of all these special factors vAW be used. 

 Af\s defined by 



E = EoA, 



(20) 



where E is the absolute value of the actual field 

 strength and Eo is the absolute value of the free- 

 space field strength that would exist at the same 

 distance d from the doublet transmitter in free space. 

 Replacing Eo mth EoAp, equation (17) for the 

 received power, becomes 



p _ Eo-Ap- 3X- 



1207r Sir 



(21) 



while the power output as given by equation (16) 

 remains unchanged, so that 



replaces equation (18) as the ratio of received 

 power to output power for maximum power transfer 

 between doublets. The quantity defined by (22) 

 is the free-space gain and A is the gain factor. 



