Page 84 - Antennas for Base Stations in Wireless Communications

Base Station Antennas for Mobile Radio Systems 57

If the currents in elements 2 and 4 are much larger in magnitude than
that in element 3, the input impedance of element 3 may be substan-
tially changed even if the mutual impedance is itself relatively small.
If we use ordinary branched power dividers, the change in Z 3 and the
corresponding but different changes in other element input impedances
will result in an uncertainty in the value of I 3 relative to other element
currents. Worse, as the frequency changes the mutual impedances will
change, particularly in phase, causing the error in the relative magni-
tude and phase of I 3 to be frequency dependent. Other array excitations
to be avoided include those with large amplitude tapers across the array,
causing excessive broadening of the main beam with consequential loss
in directivity. We must also avoid any excitation function for which the
specified pattern characteristics are very sensitive to the achievement
of exact current values.
A wide range of strategies for pattern synthesis are described in the
literature, the cited references 13,14 being only a small sample. It is pos-
sible to write computer programs using iterative optimization routines
and genetic algorithms, the main problem with their use being to specify
the constraints described above and to appropriately weight the differ-
ent features of the solution. Solutions can be tested by applying a Monte
Carlo analysis; after, say, 1,000 trials using different sets of random
errors, it is possible to list the number of trials that failed because of
inadequate directivity, poor sidelobe suppression, inadequate null fill,
or any other selected parameter. The use of this method allows a robust
solution to be selected from a number of possible candidates and devel-
ops a good understanding of the need to control errors in the excitation
of a practical array.
For many years the author has used a simple computer-based synthe-
sis technique developed by his former colleague Jun Xiang, which makes
use of the superposition of patterns created by superposed excitation
functions. In the case of a base station array, we need an asymmetric
elevation pattern with adjustments made only to the first lower null
and typically three upper sidelobes, so a uniform distribution serves us
well as a starting point.
For the purpose of pattern synthesis, we are interested in the region
of the pattern within about 20° of the broadside direction, so for ele-
ments with limited directivity in the elevation plane (such as dipoles or
patches), we can concentrate on the array factor rather than working
with the complete elevation pattern.
If we excite the array uniformly, the resulting array factor is a function
of the form E = sin(nx)/nsin(x), as shown in Figure 2.10. If all currents
are cophased, the maximum of this function will be in the broadside
direction, but we can apply a linear phase shift across the aperture after
the synthesis is complete to move the maximum to the desired angle.