14-12] MODIFYING THE RADAR RANGE EQUATION 765 



where Pr = reflected power returned to the receiver 



Pt = power delivered to the antenna from the transmitter 



R = range to radar target 



G — antenna gain (assuming that the same antenna is used for both 

 transmitting and receiving, as is usually the case) 



X = wavelength 



a = scattering cross section of target. 



The antenna gain G can be related to the physical dimensions of the 

 antenna through the expression 



Go = -^^ (14-19) 



where A is the aperture area, Go is maximum gain at nose of beam, and mis 

 a fractional quantity relating the actual gain to that of a theoretical 

 antenna having a spherical phase front and a uniform amplitude field 

 impinging on the whole aperture. Therefore, Equation 14-18 can be 

 simplified and rearranged in terms of maximum attainable range for a 

 specified minimum usable power into the receiver (PRmin)' 



\47r(/'/i.min)X^ 



A moment's study of Equation 14-20 would indicate that the designer has 

 control over at least four variables — transmitter power, antenna size, 

 minimum usable receiver power (MDS), and frequency; with a fifth 

 variable a not quite so well understood, since it is the contribution made by 

 the target — in this case a meteorological disturbance. These targets take 

 on special significance for two reasons. First, the radiated energy may have 

 to pass through accumulations of hydrometeors, suffering attenuation 

 during its round trip as discussed in Paragraph 14-10. Then the target 

 itself always has appreciable cross-sectional area and depth; storms can 

 never be classed as point targets. If the area of a meteorological target 

 exceeds that of the intersected radar beam (a beam-filling target) and the 

 target depth exceeds half the distance occupied by the pulse as it propagates 

 through space, a can be expressed in terms oP 



a = i?^0^y- • n = ^ X volume occupied by radiated pulse at range R 



(14-21) 



9D. E. Kerr, (Ed.), Propagation of Short Radio Waves, McGraw-Hill Book Co., Inc., New 

 York, 1951. 



