358 : PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
by 
E vertical = GOL, 2 (29) 
with 
20 27 , 
= —scos@ = — ssinB. 
mime Paria 
The maximum value of equation (29), corresponding 
to @ = 90° and B = 0°, is equal to 
Evnax Sema (30) 
The relative field strength is then 
a ee 
Evertical Sin 2 
Emax is a j (31) 
m sin — 
2 
The beam width in the vertical plane is determined 
by the angle between the half-power points, or the 
angle between the points where the field strength is 
0.707 of the maximum. Thus, equation (81) is set 
equal to 0.707 and 6 determined. The beam width is 
equal to 28°. 
To illustrate, let s = 4/2. For m = 2,3,4,8;12,16 
dipoles in the array, the corresponding beam widths 
are 60°, 36.4°, 26.4°, 12.8°, 8.5° and 6.3°. A few field 
patterns are illustrated in Figure 30A and gains are 
shown in Figure 31. 
3. Colinear array (see Figure 32). 
cophased currents, equally spaced, 
For n equal 
- na 
STs 
Ey = Le (6, ¢) ) (82) 
Pie: 
sin 2 
where 
2a 
a= yp OCG (83) 
Figure 32. Cophased colinear half-wave dipoles. 
For center-fed half-wave dipoles, from equation (3), 
Tw 
cos ( cos a) 
pe a COL SAENZ (34) 
d sin 0 
The patterns for various array lengths and spacings 
are given in Figure 33. 
If s = d/2, equation (32) for half-wave dipoles 
reduces to equation (18). 
n=l6 { 
we he 
Spacing= — 
2 i} 
n=6 
Spacing=) 
n=4 I 
wo 
Spacing=5. 
n=3 
Midpoint Spacing s=A/2 
Effect of Array Length 
Array Length=3\ 
Effect of Element Spacing 
foi yo eulq . 
Figure 33. Cophased colinear half-wave dipoles. (From 
Radio Engineers: Handbook by Terman. ) 
Unidirectional Broadside 
and Colinear Arrays 
If-an array is backed up with a similar array, the 
latter may serve to concentrate the radiation in one 
direction, provided the currents in the arrays are 
properly adjusted in magnitude and phase. Patterns 
