THE ii-v METHOD 



135 



ence loci are found from equation (98) in Chapter 5 

 and equation (13) in Chapter 6, giving 



h 



1 - q\ \- q) 



(46) in Chapter 5] are constructed and their inter- 

 sections with path-difference contours corresponding 

 to the assumed vahies of fi/2 determine points on 

 the lobes. 



and 



d 



= 'Kr^) 



6.5.2 



Construction of Lobes 

 (Horizontal Polarization) 



Intersections of the path-difference loci with the 

 range curves determine points on the lobes. 



In this method, the divergence factor D is con- 

 sidered to be the independent variable. Dividing 



D5999.08X) 7.0 6.0 



5.0 ^i> 035 4v0 



3.0 D=.9 2.7 



Figure 6. Curves of constant-divergence factor D and path difference parameter U. (Radiation Laboratory.) 



6.5 

 6.5.1 



THE u-v METHOD 

 Outline of Method 



both sides of equation (46) in Chapter 5 by d^ gives 

 d 



do I 



sm- 







This method makes use of the generalized coordi- 

 nates u = hi/hi and v = d/rfy described in Section 

 5.5.8. The curves of constant-divergence factor D 

 and path-difference parameter R are plotted on the 

 same sheet in Figures 4, 5, and 6. The divergence where 

 lines are shown in full and the path-difference curves 

 are dotted. Envelopes of constant sin^(n/2) [equation 



, = V fr'i — xl (1 - A')- -f 4A- si 

 dr dx ^ 2 



= VG^do ^'(1 



n 



KY + 47v sin= ^ , 



(21) 



, do 



fln = — < 



Ox 



