Practical_Antenna_Handbook_0071639586

C h a p t e r 5 : a n t e n n a A r r a y s a n d A r r a y G a i n 153
to the broadside pattern. The peak gain of this array’s end-fire mode compared to a single
vertical is 2.3 dB—about 1.5 dB less than that of the broadside mode.
Array Factor
One nice feature about arrays is that we can build them out of just about any kind of
antenna element. From a purely mathematical viewpoint, the easiest arrays to analyze
are those comprised of isotropic radiators because the individual elements have a very
simple pattern—they radiate equally well in all directions. As a result, when two or
more isotropic radiators are combined to form an array, the resulting pattern is the array
pattern itself. The array pattern (also called the array factor) is an equation obtained from
evaluation of the geometry of the element positions, as well as the relative amplitudes
and phases of the individual element feedpoint currents. For the two-element broadside
array discussed here and shown in Fig. 5.1B, the shape of the azimuthal array pattern
is given by the equation
⎛ π ⎞
AP = cos⎜
cosθ⎟ (5.5)
⎝ 2 ⎠
I 1
r
2
I 1
= I 2
r
I 2
Array axis
r
Figure 5.2A Two-element broadside array of l/2
dipoles spaced l/2 apart on their axis.
A
where θ is the angle between the array axis and a line drawn from the center of the array
to a distant receiving antenna.
But isotropic radiators, as we saw in Chap. 3, are totally fictitious, so we are forced to
form arrays out of “real” elements: dipoles, verticals, loops, and other basic antenna
types. When we do that, the resulting radiation pattern developed by the array is the
array pattern multiplied by the radiation pattern of an individual element. For example,
if we replace the l/4 monopoles of Fig. 5.1B with l/2 dipoles, we still have a two-element
broadside driven array with l/2 element spacing. So the resulting radiation pattern will
be the array pattern of Fig. 5.1C multiplied by the inherent radiation pattern of a conventional
dipole (Fig. 3.7). Clearly, the exact orientation of the dipole elements relative to the
orientation of the array itself will make a big difference in the overall pattern. An excellent
rule of thumb is to try to use elements in such a way that their natural direction of maximum
radiation coincides with at least one of the desired directions of maximum radiation
for the array as a whole. Failure to do so will usually lead to arrays that are “temperamental”;
that is, they will tend to have patterns that are sharp and/or multilobed (often in the
wrong directions) and feedpoint impedances that are unstable and/or difficult to match.
Consider the broadside array of Fig. 5.2A, where we have replaced the verticals
with l/2 horizontal dipoles laid end to end
with centers l/2 apart. The pattern for this
array is graphed in Fig. 5.2B. Note that the directivity
of the main lobe is “sharper” or narrower
than the main lobe of Fig. 5.1C as a
result of the added directionality of the l/2
dipoles. However, the peak gain of the main
lobe relative to a single l/2 dipole is only 1.5
dB because the mutual impediances between
the two dipoles cause the feedpoint current in
each dipole to be less than it would be if the