230 BELL S YSTEM TECH NIC A L JOURNA L 



2.4 The General Transmission Formula 



Transmission loss between transmitter and receiver through the radio 

 circuit shown in Fig. 4 was given by ecjuation (5). By substituting the 

 relation (12) into (5) w-e can obtain the simple free space transmission 

 formula: 



Ph = Pt 4^" watts (13) 



Although this formula applies to free space only it is believed to be as useful 

 in radio engineering as Ohm's law is in circuit engineering. 



2.5 The Reradialion Formula 



One further relation, the radar reflection formula is of particular interest. 

 Consider the situation illustrated in Fig. 6. Let Pt be the power radiated 



REFLECTING OBJECT 

 (As= PROJECTED AREA IN 



DIRECTION OF RADAR) 

 RADAR ' 



At.Gt 



TRANSMITTER 



h- 



Ar,Gr 

 Fig. 6 — Radar with Separate Receiving and Transmitting Antennas. 



from an antenna with effective area A t, As the area of a reflecting object at 

 distance d from the antenna and Ph the power received by an antenna of 



effective area ^k . By equation (13) the power striking As is — — — — . If 



this power were reradiated equally in all directions the reflected power flow 



at the receiving antenna would be — — 3—— but since the average reradiation 



is larger toward the receiving antenna, the power flow per unit area there is 



usually K J ,J^f where A' > 1. It follows from (2) that 

 4Trd*\^ 



r> T^r PtAtArAs (..s. 



Formula (14) shows clearly why the use of large and efflcient antennas will 

 greatly increase the radar range. 



Formula (14) applies to free space only. Application to other conditions 



