594 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



system has a maximum allowable transmission loss which, if exceeded, 

 results in either poor quality or poor reliability. Reasonably accurat( 

 predictions of transmission loss can be made on paths that approximate 

 the ideals of either free space or plane earth. On many paths of intere.-;t . 

 however, the path geometry or atmospheric conditions differ so much 

 from the basic assumptions that absolute accuracy cannot be expected; 

 ne^'ertheless, worthwhile results can be obtained by using two or more 

 different methods of analysis to "box in" the answer. 



The basic concept in estimating radio transmission loss is the loss 

 expected in free space; that is, in a region free of all objects that might 

 absorb or reflect radio energ3^ This concept is essentially the inverse 

 square law in optics applied to radio transmission. For a one wave- 

 length separation between nondirective (isotropic) antennas, the free 

 space loss is 22 db and it increases by 6 db each time the distance is 

 doubled. The free space transmission ratio at a distance d is given by: 



T. = (srf) »* <"" 



where : 



Pr = received powder! 



}■ measured in same units 

 Pt = radiated power j 



X = wavelength in same units as d 



gi (or gr) = power gain of transmitting (or receiving) antenna 



The power gain of an ideal isotropic antenna that radiates power uni- 

 formly in all directions is unity by definition. A small doublet whose 

 over-all physical length is short compared with one-half wavelength has 

 a gain oi g = 1.5 (1.76 decibels) and a one-half wave dipole has a gain 

 of 2.15 decibels in the direction of maximum radiation. A nomogram for 

 the free space transmission loss between isotropic antennas is given in 

 Fig. 1. 



When antenna dimensions are large compared with the wavelength, 

 a more convenient form of the free space ratio is^ 



— ^ = ^^ (lb) 



Pt (\dy- 



where Ai,r = effective area of transmitting or receiving antennas. 



Another form of expressing free space transmission is the concept of 



