84 



CALCULATION OF RADIO GAIN 



5.6.3 



Type II. Radio Gain Versus 



Receiver Height for Given Distance 



Radio gain versus receiver antenna height are 

 to be found, while ti-ansmitter antenna height, 

 wavelength, and distance are gi\'en. 



Suppose that a radar set has an antenna height 

 of 30 meters, and an antenna gain of 13.5 db. Polari- 

 zation is horizontal and the wa\'elength is 1.5 meters. 

 Assume also a recei\-er with a gain of 6*2 = 1 (or db) 

 at a distance of 100 km. 



The following calculations are made : 



1. The variation of the radio gain Pi'Px, -with 

 receiver antenna height 1h is to be found. 



2. Instead of a receiver assume a target mth 

 cross section of 50 square meters. The value of the 

 radar gain P«/Pi at the radar recei^'er is to be found 

 as a function of target height ho. 



The diffraction part of the calculation is given in 

 Section 5.7.3; the optical part in this section. The 

 results are represented in Figure 25, the two partial 

 curves for one-way transmission having been com- 

 bined into a smooth overall curve A\-hich makes pos- 

 sible the estimation of 10 log P2/P1 in the transition 

 region near the line of sight. The radar gain \-aries as 

 40 log A [equation (5)] rather than as 20 log .,4 and 

 contains a constant shift 10 log [GrilQwa/QX-)] 

 rather than 10 log GiGn. 



Radio Gain": Oxp:-Way Traxsmission 



The calculation is most readily performed by using 

 p = di/dx as the independent \'ariable and then 

 finding the corresponding -values of hi, the receiver 

 height, and A. 



1. From Figure 15 in Chapter 6 or equation (115), 

 r = 9.403. 



For n = 1, corresponding to the first maximum, 

 p is approximately l/r, since R = nr > 2. Accord- 

 ingh', we begin with p = 0.1. 



2. (It = 22.5 km (from Figure 2), and 



d 100 

 V = — = = 4.45. 



dr 22.5 



3. From equation (112), 



R = 9.58. 



4. From equation (121), 



u = -- = 62.028 



and hence 



h« = 1,861 meters. 



5. At d = 100 km, the free-space attenuation 

 (Figure 3 in Chapter 2) is 



20 log .4,, = - 115. 



6. Compute the factor 



nI 



(1 - D)2 + 4/)sin^-. 



From equation (117) 

 D = 0.980, 

 R 



n =- = 1.019, 

 r 



o = mr = (1.019) • (3.1416) = 3.19 radians, 

 -^ = 1.00 radians. 



sin= - = 0.9992. 

 9 



From Figure 12, 



20 log yl (1 - D)- + 4Z) sin^ - = 6 db. 



Hence 



20 log A = - 115 db -I- Gdb = - 109 db, and 



10 log — = - 109 db + 10 log GiG. = - 95.5 db. 



7. The foregoing values, together with results 

 obtained with other \'alues of p, are listed in Table 1. 



Table 1* 



R 



Q 

 2 



D 



Radio Gain 



Pi 

 10 log- 



Radar Gain 

 10 log ^ 



