RA DA RAN TENNA S 227 



2.2 Relationship behveen Gain and Efeclive Area 



Figure 4 shows a radio circuit in free space made up of a transmitting 

 antenna T and a receiving antenna R. If the transmitted power 7^r had 



TRANSMITTING 

 ANTENNA 



Fig. 4 — Radio Circuit in Free Space. 



been radiated equally in all directions, the power flow per unit area at the 

 receiving antenna would be 



47r(/2 



Definition (1) gives, therefore, for the power flow per unit area at the 

 receiving antenna 



P = p,Gr = ^" (4) 



and definition (2) gives for the received power 



^« = ''■'' = '-^ (') 



From the law of reciprocity it follows that the same power is transferred if 

 the transmitting and receiving roles are reversed. By (5) it is thus evident 

 that 



KJT-Aji = QtrAt 



or 



Gt/At = Gr/Ar (6) 



Equation (6) shows that the ratio of the gain and effective area has the 

 same constant value for all antennas at a given frequency. It is necessary, 

 therefore, to calculate this ratio only for a simple and well known antenna 

 such as a small dipole or uniform current element. 



2.3 The Ratio G/A for a Small Current Element 



In Fig. 5 are given formulas' in M.K.S. units for the free space radiation 

 from a small current element with no heat loss. We have assumed that 



2 See S. A. Schelkunoff, Electromagnetic Waves, D. Van Nostrand Co., Inc., 1943, p. 133 



