EC6602
ANTENNA
AND
WAVE
PROPAGATION
UNIT
II
APERTURE
AND
SLOT
ANTENNAS
v Radia8on
from
rectangular
apertures
v Radia8on
from
Uniform
and
Tapered
aperture
v
Horn
antenna
v Reflector
antenna
v Aperture
blockage
v Feeding
structures
v Slot
antennas
v Microstrip
antennas
–
Radia8on
mechanism
–
Applica8on
v Numerical
tool
for
antenna
analysis
APERTURE ANTENNAS
Aperture Antennas
Aperture
antennas
cons8tute
a
large
class
of
antennas,
which
emit
EM
waves
through
an
opening
(or
aperture).
These
antennas
have
close
analogs
in
acous8cs,
namely,
the
megaphone
and
the
parabolic
microphone.
The
geometry
of
the
aperture
may
be
square,
rectangular,
circular,
ellip8cal,
or
virtually
any
other
shape.
Aperture
antennas
are
most
commonly
used
at
microwave
and
the
millimeter-‐wave
frequencies.
Antennas
that
fall
into
this
category
include:
reflector
antennas,
lenses,
and
horn
antennas.
Aperture
antennas
are
very
popular
for
aerospace
applica8ons
because
they
can
be
flush-‐mounted
onto
the
spacecraX
or
aircraX
surface.
In
order
to
evaluate
the
distant
(far-‐field)
radia8on
paZerns,
it
is
necessary
to
know
the
surface
currents
that
flow
on
the
radia1ng
surfaces
of
the
antenna
aperture.
In
many
instances,
these
current
distribu8ons
may
not
be
known
exactly
and
only
approximate
or
experimental
measurements
can
provide
es8mates.
For
an
aperture
antenna
to
be
efficient
and
have
high
direc8vity,
it
has
to
have
an
area
≥λ2
A
technique
based
on
the
Equivalence
principle
allows
one
to
make
reasonable
approxima8ons
to
the
electromagne8c
fields
on,
or
in
the
vicinity
of,
the
physical
antenna
aperture
structure,
which
can
then
be
used
to
compute
far
field
antenna
radia8on
paZerns.
Field
equivalence,
first
introduced
by
Schelkunoff,
is
a
principle
by
which
the
actual
sources
on
an
antenna
aperture
are
replaced
by
equivalent
sources
on
an
external
closed
surface
that
is
physically
outside
the
antenna
aperture.
The
fic88ous
sources
are
said
to
be
equivalent
within
a
region
because
they
produce
the
same
fields
within
that
region.
Field
equivalence
principle
states
that
the
aperture
fields
may
be
replaced
by
equivalent
electric
and
magne8c
surface
currents,
whose
radiated
fields
can
then
be
calculated.
Another
key
concept
is
Huygens’
principle,
which
states
that
the
“equivalent
source
at
each
point
on
the
external
surface
is
a
source
of
a
spherical
wave”.
The
secondary
wave
front
can
be
constructed
as
the
envelope
of
these
secondary
spherical
waves
Huygens’ principle
EQUIVALENCE PRINCIPLE
It involves carrying out the far-field analysis in the outer
(unbounded) region only, which is external to the radiating
antenna. This requires the knowledge of the tangential field
components at the aperture.
Let Ea,Ha be the tangential fields over an aperture A.
These fields are assumed to be known and are produced by
the sources to the left of the screen.
The problem is to determine the radiated fields E(r),H(r) at
some far observation point.
The radiated fields can be computed with the help of the field
equivalence principle which states that the aperture fields
may be replaced by equivalent electric and magnetic surface
currents, whose radiated fields can then be calculated:
The equivalent surface currents are:
Js = ˆn × Ha (electric surface current)
Jms = −ˆn × Ea (magnetic surface current)
As long as a problem is re-formulated so that it preserves the
boundary conditions at S, it is going to produce the only one
possible solution for the Volume region Vs bounded by
Surface S. Such a re-formulated problem is referred to as an
equivalent problem.
Applying Equivalence principle in three different ways.
The open-region far-zone solutions for the vector potentials A
(resulting from Js ) and F (resulting from Ms ) are found from:
The relations between the far-zone fields and vector
potentials are:
Since,
The total far-zone electric field (due to both A and F) is found
as:
SUMMARY
Uniqueness Theorem: a solution satisfying Maxwell’s Equations
and the boundary conditions is unique.
Field equivalence principle states that the aperture fields
may be replaced by equivalent electric and magnetic
surface currents, whose radiated fields can then be
calculated
Radiation from Rectangular Aperture
The aperture field distribution is usually not known
exactly and approximations are used.
Usually, it is assumed that the field is to be determined
in half-space, leaving the feed and the antenna behind
an infinite wall S (electric or magnetic).
A rectangular aperture is
defined in the plane as shown :
“If the field is uniform in
amplitude and phase across
the aperture, it is referred to as
a uniform rectangular
aperture. “
Let us assume that the aperture field is y-polarized.
According to the equivalence principle, we assume an electric
wall at Z=0 , where the equivalent magnetic current density is
given by:
According to image theory
The only non-zero radiation integral is
To shorten the notations, let us introduce the pattern variables:
The complete radiation field is found by substituting the above
equations in
The total-field amplitude pattern is, therefore,
The principal plane patterns are:
Note that: The physical and effective areas of a uniform aperture are
equal.
Case (ii)The Uniform Rectangular Aperture in Open Space :
Now the rectangular aperture is not mounted on a ground plane. The field
distribution is the same as in previous, but now the H field must be defined, too, in
order to apply the equivalence principle with both types of surface currents,
Far-field components,
Radiation from Tapered Rectangular Aperture on a
Ground Plane
The uniform rectangular aperture has the maximum possible
effective area (for an aperture-type antenna) equal to its physical
area. This also implies that it has the highest possible directivity
for all constant-phase excitations of a rectangular aperture.
However, the directivity is not the only important factor in the
design of an antenna.
A factor that frequently comes into conflict with the directivity is
the side-lobe level (SLL).
Reduction of the SLL can be achieved by tapering( gradually
reducing the size) the equivalent sources distribution from a
maximum at the aperture’s center to zero values at its edges.
One practical aperture of tapered source distribution is the open
rectangular waveguide.
The dominant TE10 mode has the following distribution:
Far-field components,
Inference:
Ø T he lower SLL of the
tapered-source pattern is
obvious.
Ø The price to pay for the
lower SLL is the decrease in
directivity (the beam width of
the major lobe increases).
Principle plane patterns
In the E-plane, the aperture is not tapered. As expected, the E-plane principal
pattern is the same as that of a uniform aperture.
* Note the difference with that of
Uniform Aperture
The above results are approximate. Better results are obtained if the following
factors are taken into account:
