162 



PROPAGATION ASPECTS OF EQUIPMENT OPERATION 



on the gain control is marked 5 db (see dotted lines 

 in Figure 3). 



Keeping the 5-db position on the gain control, 

 another signal is obtained which comes up to 

 1.8-cm line. The gain control is turned until the 

 signal is brought do\ra to the datum line. The new 

 ■setting is marked 10 db. This is repeated until 

 markings up to about 70 db are obtained. 



This calibration of (S + .V)/'.V must be corrected 

 to S/N (Figure 3) which can be done by means of 

 Table 1. For 25 db and above, the values of 

 (S + N)/N can be taken as equal to S/N. Any 

 signal voltage can then be measured in decibels 

 above the noise voltage (N) by tin-ning the gain 

 control until the signal height is 1 cm. By equation 

 (3) this is also the signal power received, in decibels, 

 above the noise power which is discussed in Sections 

 2.3.1 and 2.3.2. 



T.\BLE 1. Correction of (S + A')/iV to S/N. 



Corrected 

 db 



(f) 



Uncorrected 







.5 



10 



1.5 



20 



12..5 

 16.5 

 21 



In the calibration just described, the pip on the 

 scope is supposed to be proportional to the received 

 signal strength. In a set functioning normally, this 

 is ju.stified, but occasionally defects in the set may 

 destroy the linearity. The existence of a linear rela- 

 tion can be tested by means of a signal generator. 



7-2 FREE SPACE — HIGH-ANGLE 



COVERAGE 



7.2.1 Maximum Range Formulas 



In free space, the gain factor ,4 has the value 

 3X/8xd (for maximum power transfer between 

 doublets). Equations (3) and (5) in Chapter 5 

 then take the simple forms : 



One-way, radio gain: 



P, 



P 

 Two-way, radar gain: 



1 \87rd/ 



IGttct /'3XY 

 1)>^ " \8^/ 



(4) 



Pi 



(5) 



If Pn is replaced by the minimum detectable power 

 of the i-eceiver, P^in, and Pi by the peak power Pp 

 of the transmitter, the maximum range is given by: 



One-way, 





(6) 



Tivo-ivay, 



"max 



\ 



Pj^ G'2X2 . ^^ 



256 TT^ 



(7) 



^^^ Deviation from Maximum of Beam 



For an antenna whose direction is fixed, the 

 ecjuations in Section 7.2.1 apply onl.y to points on 

 the axis of the beam. Denoting hy fir) the ratio of 

 gain in a direction at an angle r from the axis of the 

 beam to the gain at the axis and by 2 to the beam 

 width between half-power points, then 



/(r) = exp - 0.692(T/ro)l 



(8) 



Accordingly, for pomts ofT the axis, G must be 

 multiplied hy fir) before substitution in the formulas 

 of Section 7.2.1. 



SCANNING RATE R P M 



Figure 4. Scanning loss as a function of scanning 

 speed and beamwidth. 



7.2.3 



Performance Figure 



Equations (6) and (7) for dmax depend on the 

 performance figure defined in Section 7.1.2. The 

 quantities which appear in the perfonnance figure 

 can be measured. The one which offers most diffi- 

 culty is Pmin, the minimum detectable power, which 

 has been discussed in Section 2.3. In Tables 3 and 4 at 



