Page 81 - Antennas for Base Stations in Wireless Communications

54 Chapter Two

b. Because the electrical length of the array increases with frequency, it
is often assumed that the elevation-plane directivity of the antenna
will also increase with frequency. However, the directivity/frequency
relationship is determined by the chosen spacing. The usual specifi-
cation requirement is to achieve the largest possible minimum direc-
tivity across the required frequency band. This leads to the choice of
the largest acceptable inter-tier spacing consistent with acceptable
grating lobes, so the directivity may fall with frequency at the upper
band edge. Errors in element currents will tend to be higher at band
edges than at band center, and the attenuation of the feed system
will increase with rising frequency. To ensure that all these effects
are understood and taken into account in the array design, the gain
budget should be established for the band-edge frequencies as well
as for the center frequency (see also item e).
c. A typical array specification will require the first null below the
horizon to be filled to at least −18 dB and the two sidelobes above
the main beam suppressed to at least −20 dB relative to the main
beam. This will result in a beam shaping loss of about 0.3 dB.
d. This factor accounts for the difference between the intended radiat-
ing currents, used in the computation of directivity, and those real-
ized in practice. This difference may be as small as 0.2 dB, but is
often larger, especially at the band edges.
e. The max /mean ratio of the azimuth pattern can most easily be
understood by considering an idealized pattern in which the antenna
uniformly illuminates a 90° azimuth quadrant. Compared with the
power necessary to provide a given field strength over a complete
360°, the quadrant antenna will require only one quarter of the input
power. The ratio of the area of the whole circle to that of the quadrant
pattern is 4. In a general case, if we plot the azimuth pattern in terms
2
of relative field, the power in each direction is proportional to the E
(i.e., the radius squared) and the area inside the curve is the integral
2
of r over 360°. For any azimuth pattern plotted on a relative field
scale, the numerical value of the max /mean power ratio is the ratio
of the area of the outer circle (E = 1) to that of the azimuth pattern
plotted within it. This relationship is true for any number of tiers
in the array, and we can obtain its total directivity by multiplying
the (numerical) directivities in the azimuth and elevation planes,
calculated separately. Any tendency for the azimuth beamwidth to vary
with frequency will cause a change in max /mean ratio that will in turn
impact the gain/frequency behavior of the array. The highest array
gain will be obtained if the azimuth beamwidth is kept close to the
specified minimum value at all frequencies in the operating band.