14-19] MODIFYING THE RADAR RANGE EQUATION 783 



X = wavelength of transmission 



c = velocity of transmitted energy, customarily taken as the 

 velocity of light in vacuum 



0„ = horizontal beamwidth, defined by the half-power points 



Wrf = RF attenuation losses in the system 



fr = repetition frequency 



h = aircraft altitude 



K = Boltzmann's constant (1.38 X IQ-^^ joule /C°) 



T = absolute temperature (°K) 



B = receiver bandwidth 



(NF) = RF noise figure. A typical value for this parameter is about 

 12 db 



a^ = back-scattering cross section of earth's surface 



Gg = antenna gain at a depression angle 6 



a = round trip atmospheric attenuation. 



As noted earlier, for uniform mapping the returned power should be 

 independent of the depression angle d. If we use the customary expression 

 for the cosecant-squared beam given in Equation 14-31 and add a factor a 

 to account for the change in atmospheric attenuation with range, the 

 signal-to-noise ratio becomes 



PAVG^'dVltFe, 



liiTry/rh'KTBCNF) 



a^Gl CSC 6 (14-34) 



where Ge, is the antenna gain in the direction ^o- The signal-to-noise ratio 

 will still be dependent on the depression angle to some extent. 



Using the expression for antenna gain given in Equation 14-32, where a 

 term has also been included to account for atmospheric attenuation, 

 Equation 14-33 becomes 



P..oXW..G„ jJ^,J ^j4_35) 



2{4Ty/r¥KTB(N¥) 



Thus the signal-to-noise ratio is now independent of the depression angle. 

 Of course this is an ideal condition since, as already noted, the scattering 

 cross section o-° will be a function of the type of terrain being mapped. 



