ANTENNAS 357 
with angle @ measured from the dipole axis. See also 
equation (15) and Figure 11 (for n = 1). 
In the vertical plane, the beam is much narrower. 
If @ is the angle from the vertical and B = 90° — @ 
is the angle from the (horizontal) broadside direc- 
tion, the field in the vertical plane (6 = 90°) is given 
Spacing 
n infinitely 
I I PLAN VIEW close 
le 
Figure 29. Broadside array, elements perpendicular 
to paper. 4 N 
Spacing = — 
2 
elements 
n=5 
Spa cing=4 
5 elements 
n=9 
n=l3 
n=|7 
Spacing = A 
4 elements 
Figure 30A. Effect of array length for broadside with 
element spacing s=}/2. (From Radio Engineers’ c 
Handbook by Terman.) GC) 
° 
For center-fed half-wave dipoles, from equation (3) a 
= a 
ae, 601 cos ( 5) cos a) om < 
d sin 0 , Figure 30B. Effect of element spacing for broadside 
for array length L =3A. (From Radio Engineers’ 
The patterns for the equatorial plane are illustrated Handbook by Terman.) 
in Figures 380A and 30B. Figure 30A shows the in- 
crease in directivity with increasing number of 40 
elements. Figure 30B illustrates the effect of element xX) PPT ttt TY 
spacing on*the production of side lobes. Figure 31 = 8 35/5 | 
gives the gain for various spacings and array lengths. E 5 20 r-Element HH 
From this it appears that s = 5\/8 is approximately @s spacing} _ oo 
the optimum spacing. panes SEBBEEES’/4 
2. Broadside: pattern factor and beam width. For oo ane 
‘ : 3 oa 
illustration, suppose that the antenna consists of a a 
vertical array of m horizontal center-fed dipoles $3 
spaced s apart with all fed in phase to give a broad- iY ° v. 
side beam strongly directive in the vertical plane. om 5 v2 
For this arrangement the field strength in the ou 4a 
horizontal plane is given by m times equation (27), % 2 4 6 B 10 l2 14 16 
that is, Array Length In Wave Lengths 
cos ( cos a) Figure 31. Gain for broadside array of doublets as a 
Ehorizontal = m 601 2 (28) function of array length and spacing. (From Radio 
d sin 6 Engineers’ Handbook by Terman.) 
