RADAR CROSS SECTIOIN AND GAIN 



19 



later stages is much less amplified by the system 

 than the noise from the early stages. 



In equipment specifications, the noise figure is 

 usually expressed in the decibel scale as decibels 

 above thermal noise. Actual noise figures vary from 

 a few decibels above thermal noise in the very high- 

 frequency [VHF] region (receivers built a few years 

 ago often have appreciably higher noise figures) to 

 larger values for microwave receivers. 



^■*-^ Sensitivity of Radar Receivers 



It is by no means true for radar receivers that 

 ■Pmin= Pno', as a matter of fact, P^ia>>Pno- That 

 is, the minimum discernible power considerably 

 exceeds the noise level. 



The largest single additional loss in radar recep- 

 tion is scanning loss which is relate to the rotation 

 of the antenna (one or several revolutions per 

 minute). As an example, for one particular radar 

 which has a bandwidth Af = 2 mc, this loss is from 

 10 db to 12 db. 



In case the antenna does not rotate, there is no 

 scanning loss. This fact would seem to be of limited 

 operational importance, since it would usually be 

 necessary to locate the target (a plane, for example) 

 by scanning. 



Another loss, closely connected with scanning 

 loss, is sweep-speed loss. This loss is due to the fact 

 that practical targets, such as airplanes, reflect 

 rapidly varying amounts of power to the radar 

 receiver, these amounts depending on the precise 

 orientation of the target at the moment when the 

 radar beam sweeps over it. Consequently, sweep- 

 speed loss will depend on the speed of rotation of the 

 antenna, on the distance of the target from the 

 antenna, and, to some extent, on the beamwidth 

 and the nature of the target. The overall figure 

 for this loss on the same radar used to illustrate 

 scanning loss is about 4 db for targets 200 miles 

 from the radar. 



In addition to these losses, careful experiments 

 with the radar used as an example above have 

 indicated that there is an operator loss of about 

 4 db for even experienced operators. This might be 

 thought of as a loss due to the difference between 

 laboratory and field conditions. 



Statistical consideration about the extent of noise 

 fluctuation and about the fact that a target need 

 not be seen on every sweep lead to further small 



losses which total, for the radar under discussion, 

 2db. 



Summarizing for the case of the radar of the above 

 example, the minimum detectable power is about 

 34 db above kTAf or about 8 X W^'^ watt, not 

 12 db above kTAf or 8 X 10"'^^ watt, as w^ould be 

 indicated from the noise level alone. This amounts 

 to 22 db or a factor of 166; that is, the actual min- 

 imum discernible power is 166 times that calculated 

 from noise alone. It will be seen in the results of 

 the next section that the maximum range of a radar 

 set varies with the inverse fourth root of the min- 

 imum discernible power. Consequently, a calcula- 

 tion of the maximum range of the radar of the 

 example, which assumed that the minimum dis- 

 cernible power was equal to the noise power, would 

 give a range too great by a factor of VlQQ = 3.59. 

 Since this would be a serious error, it shows the 

 importance of a very careful consideration of radar 

 receiver sensitivity in calculations of this type. 



2 4 RADAR CROSS SECTION AND GAIN 

 ^•*' Radar Cross Section 



The total scattering of a target may be described 

 by the use of a parameter (having the dimensions 

 of an area) called a scattering cross section. This 

 concept has already been presented in the latter part 

 of Section 2.1.2, where both scattering and absorp- 

 tion cross sections of doublets were discussed. The 

 scattering cross section S is defined by 



Wi 



(39) 



w'here Ps is the total power scattered by the target 

 irrespective of its angular distribution and IF,- is 

 the incident power per unit area. 



The scattering cross section S, which gives in- 

 formation about the total scattered energy, is not 

 directly useful in radar work because in such applica- 

 tions one is interested only in that fraction of the 

 total scattered power which is scattered in the direc- 

 tion of the radar; that is, one wants a parameter 

 involving the scattered power per unit area at the 

 receiver instead of the total scattered power. If 

 the target is an isotropic scatterer. 



Wr 



