BELOW THE INTERFERENCE REGION 



91 



versus /12 tor some distance is constructed. In 

 Figure 28, a set of such curves is given for the dis- 

 tance 100 km and for various transmitter heights. 

 By taking the intersection of 20 log .4 equal to — 130 



Figure 28. Radio gain versus receiver height /i-., for 

 given values of transmitter height h,. 



with the curve hi = 2, a value of Ih is obtained. 

 This value hi = 3,300 and d = 100 km represent 

 the coordinates of a point on the contour hx = 2 in 

 Figure 27. 



It is of some interest to observe the shortening 

 of the lobe for Ai = 100 meters on account of the 

 divergence which is close to unity at the tips of the 

 lobes corresponding to the low transmitter heights 

 but drops to 0.65 at the tip of the lobe for hx = 100. 

 Since for hx = 100, the formula for both antennas 

 low (A < SOX^'^) is not applicable, the lowest points 

 on the curve hx = 100 in Figure 27 were obtained 

 by applying the reciprocitj' principle to the curves 

 already obtained. The distance at which h« = 100 

 on the hx = 2 curve is the same as that at ^^hich 

 /12 = 2 on the hx = 100 curve. 



5^ BELOW THE INTERFERENCE REGION 



5.7.1 



Analysis of the First Mode 



Except for the numerical constants involved, the 

 discussion for one mode applies to all the other modes. 

 Each mode is of the form <l>(d) • /(Ai) • /(/!2), i-e., the 

 product of a distance function # by two antenna 

 height-gain functions/ (see Section 5.1.7). 



Distance 



$i(d), the distance function of the first mode, can 

 be represented as the product of two physically 



significant factors, one for free space and one for 

 the earth effect. The latter may be divided into a 

 plane earth factor and a shadow factor. 



1. Free space. It has been shown in equation (18) 

 in Chapter 2 that for doublet antennas, with matched 

 load at the receiver and adjusted for maximum 

 power transfer, the free-space gain factor Aq is 

 given bv 



A, 



4 



3X 



8^/' 



For other tjqjes of antennas in free space, this takes 

 the form 



.AoVCiViVa = yj— = 



'X 



3X /— / — 



(140) 



Under actual conditions when earth and atmos- 

 pheric effects are of importance, each mode \xi\\ be 

 considered to have Ao as one factor. 



It may also be recalled that for given power Po 

 delivered to the load, the corresponding electric- 

 field strength, under matched conditions, is given by 



E = -^yj—- (i-ii) 



Combining equations (140) and (141) gives the 

 free-space value of the electric field strength E, in 

 terms of transmitted power 



i? = 3j(5vF;VrA, 



(142) 



which is the same as equation (7) in Chapter 2 AAith 

 the addition of the transmitter gain Gx. 



2. Plane earth. The earth modifies the field by 

 absorbing and reflecting radiation. If the earth 

 were plane and perfectly conducting, the value of 

 the gain factor would be 2.4 and the electric field 

 22?o for vertical antennas several wavelengths above 

 the ground and at distances sufficiently large. The 

 imperfect conductivity of the earth produces a 

 change in the gain. Representing this effect by the 

 factor 4 1 (where Ai < 1), 



.4 = 2AoAx. 



(143) 



The plane earth factor Ax depends on distance and 

 on the electrical properties of the earth. Fortunately 

 the earth constants enter the problem in an intrinsi- 

 cally simple way, as the main effect is taken into 

 account by multiplying the distance d by a certain 

 factor which we shall denote by p', so that Ai is 

 mainly a function of p'd. The new parameter p' is 



