16-01-2013, 10:10 AM
Shaped patterns from a continuous planar aperture distribution
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Abstract:
A pattern synthesis procedure is developed
for a planar aperture with a circular boundary.
A &symmetric continuous distribution is
assumed and required to produce a flat-topped
beam with controlled ripple, surrounded by ring
side lobes of controlled height. With M filled-in
nulls in the shaped region, there are 2* solutions
for the aperture distribution. Sampling can yield
the excitation of a circular grid planar array.
Linear stretching extends the results to an elliptical
boundary.
Introduction
In 1985 Orchard et al. [l] introduced a pattern synthesis
procedure applicable to equispaced linear arrays, excited
so as to produce a shaped pattern (e.g. csc2 8. cos 8 or
flat-topped) with controlled ripple in the shaped region
and controlled side lobe heights in the unshaped region.
That procedure is applicable to planar arrays if one uses
it to obtain collapsed distributions and then finds a way
to spread out these distributions appropriately. Spreading
out has proved successful for sum and difference patterns
[2] and in one case for a pattern that is
csc2 8 . cos 8 in one principal plane and a pencil beam in
the other principal plane [3]. It has recently yielded
favourable results in limited circumstances for the important
case of a flat-topped beam in every &cut [4].
The spreading-out technique generally relies on a
decent guess for starting values of the two-dimensional
distribution and then use of the conjugate gradient procedure.
The guess is more difficult for collapsed distributions
that produce shaped beams, since such distributions
exhibit more variability than those associated with sum
and difference patterns. Thus the development of an independent
procedure to synthesise two-dimensional flattopped
beam patterns seems desirable.
Applications
Although sum patterns (no null-filling) are not of central
concern in this paper, it is desirable to point out that the
synthesis procedure just described is applicable to a sum
pattern consisting of a main beam surrounded by a
family of ring side lobes, each of which has a height that
can be individually controlled. We shall consider two
examples of this, the first of which has radar applications,
the second will serve as a springboard to the design of a
flat-topped beam.
Conclusions
It has been shown that Taylor’s circular aperture synthesis
technique can be extended to patterns exhibiting flattopped
beams with controlled ripple surrounded by ring
side lobes with controlled heights. The aperture distributions
are &symmetric and complex but reasonable in
their variability. Sampling for circular grid arrays is seen
to be feasible, as is extension to apertures with elliptical
boundaries.