Page 273 - Maxwell House

Chapter 5 253

number by only increasing the element separation to a certain extent and then optimizing the
magnitude and phase distribution over array. But this should be done with caution. One
unwanted effect of greater separation is the potential appearance of a grating lobe while the
main beam is steered. Figure 5.5.2a and 5.5.3b clearly demonstrates this effect when the beam
is steered beyond 48° with = 0.6. The good news is that the main beam narrows as the
⁄
electrical length of linear array equal to L / = N increases (compare Figure 5.5.2a and
⁄
5.5.2b where the number of radiators is the same).
Looking at the plots in Figure 5.5.3b, we can come to the conclusion that assembling arrays

a) b)

Figure 5.5.3 Patterns of linear array with Huygens’s radiator for a) = 0.25 and
⁄
⁄
b) = 0.6, < 0
from more directive elements than Huygens’ radiator better suppresses grating lobes. It is true,
but the practical implementation of this idea is far from trivial. First, we know (see (5.55)) that
the radiator directivity is proportional to its effective aperture . Unfortunately, theoretical
analysis shows that an effective aperture of an electrically small with respect to

wavelength antenna, is limited such that its directivity cannot exceed 1.8 or 4.8 dBi [15]. Note
that Huygens’ radiator belongs to the same class of elemental antennas and has the higher
directivity D = 7.07 dBi since the composition of two elemental radiators that enhances its
directivity. In general, any element of higher directivity and thus greater should occupy
physically larger space. If so, the inter-spacing must be expanded, which shifts the possible
grating lobe peak closer to the main beam and thereby requires the element of greater
directivity. Therefore, the array element directivity, inter-spacing and scan performances are
the area of trade-off.

As we found in Section 5.4.5 the first grating lobe in the pattern of uniformly spaced linear
array arrives at the elevation angle − = −cos − = ±2. Remember that

the wave phase constant = corresponds to some real or fictional electromagnetic wave
⁄

traveling along the antenna structure with some equivalent phase velocity . Therefore, the

pattern is free from grating lobes if >
or < 1 �cos + /� = 1 �cos + / �. For example, our goal is to
⁄
⁄
⁄

scan the main beam of the antenna while / = 1 within the angular sector of 60°, i.e. from