172 



SITING AND COVERAGE OF GROUND RADARS 



For a particular coverage contour, such as the 

 threshold of detection, usually taken as a signal-to- 

 noise ratio of unity, a minimum received field inten- 

 sity | E N ] may be assumed. This is related to receiver 

 noise voltages, antenna gain, and other factors of 

 design. Using | E N | for | E | and solving for d 



d 



I pt I -Ei 

 " \ I E N | 



d A 



(107) 



Because of the way in which E\ and p T are defined, 

 d , the maximum free space range, has the dimen- 

 sions of length (in miles) . It depends on the design 

 of the transmitter and receiver and on the target. 

 A may be considered a coverage factor which depends 

 on 7 and terrain effects. 



Because of the implicit character of the parameters 

 of A in equation (103), a general solution of A as a 

 function of y is not feasible. However, examination 

 of typical problems discloses that the range of varia- 

 tion of some of the factors is limited, and a method 

 of successive approximations may be readily applied. 



200 



In most cases <t> and f will vary slowly (about Ko as 

 fast) compared to 5 below 2° or 3°. At higher angles 

 the rate of change may be faster, but contribution 

 of the reflected wave at these angles is likely to be 

 unimportant. 



The method described here consists in computing 

 the lobe angles, diffraction, and divergence as though 

 the only phase shift involved was that due to path 

 difference as in Sections 15.6.4, 15.6.11 and 15.6.17. 

 The phase shifts from the apparent lobe angles thus 

 computed are then determined. The diffraction phase 

 shift is f, and the reflection phase shift is 



0' = 4, - 180°, (108) 



where </> is obtained from Figure 70. If horizontal 

 polarization is used 4> may be taken as 180°, and 

 <t>' is then zero. With curves of the phase shift 

 <t>' + t and the product f(y — 2d)Dpz plotted 

 against y the apparent lobe angles and lengths 

 computed above may be corrected to obtain the 

 actual values. The details of this method will be 

 given in the example below. 



— O.OI O.00 



0.01 



0.05 



0.06 



0.02 0.03 0.0 4 



tflN RADIANS 



Figure 72. Relative magnitude and phase of the reflected ray. 



0.07 



0.08 



