LOBE-ANGLE METHOD 



141 



Intermediate points in the lobe may be formed by 

 assigning fractional values to ?i. The corresponding 

 path-difference angle S may be calculated in the 

 following manner. Suppose it is desired to find 

 intermediate points on the fourth lobe. The values 

 of n for this lobe raijge from n = 6 to n = 8, with 

 the maximum at n = 7. It follows that a change of 



as gi\-en in equation (46) in Chapter 5, in which 

 K = {F2/Fi)pD and p = 1. The value of D may 

 be read from Figures 11 and 12, usuig the assigned 

 value of n\ and the relation y' = nX/4A/. The 

 proper value of rfi to be used in equation (63) in 

 Chapter 5 to determine the antenna-pattern angle ;' 

 may be read from Figure 9. 



300 



200 



100 



T)X 



0.5 0.6 



D 



Figure U. Contour.? of 7' as a function of D and n\. 



0.8 



2 in n corresponds to a change of 27r in 5. Thus if 

 71 = 6.5, 5 = (0.5/2) (2 tt) = 7r/2 = 90°. For hori- 

 zontal polarization fi ( = 8 + cf)') reduces to 8, 

 since 4>' = 0- The distance from the transmitter 

 base to this intermediate point in the lobe is equal to 



5.6.7 



d 



VGA ^j (1 - KY + iK sin= (^^ , (43) 



Correction for Low Angles 



The method outlined in Sections 6.6.2 to 6.6.6 

 depends upon the assumption that 7' — > ;/- or di ^ 0. 

 This assumption gives good results when n is a large 

 number but serious errors are involved for small 

 values of n. The method described in this paragraph 

 is designed to avoid this difficult}. The procedure 



