Problems on Antenna Theory
(1)
The electric field produced by an arbitrary time harmonic current distribution may be expressed as
where is the free space
dyadic Green’s function given by the expression
=
under the integral
sign.
In the above expression stands for the free
space scalar Green’s function given by
=
Determine the expression for the far-zone field due to a very small (electrically) antenna possessing a
uniform current distribution (i.e, a Hertz dipole) oriented along the z –
direction by using the expression provided above and making the necessary
far-field approximations. You should clearly state the conditions for the
existence of the far-zone fields under which the related approximations can be
made.
Hint:
(a) One may use the symmetry property of and use
instead of
in expressing the integral for
in a form which will
simplify the integrand.
(b) When the far-zone conditions prevail, one may omit “some” of the
differentiations coming up in the evaluation of the field entities.
Given:
=
,
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Consider an isotropic and
inhomogeneous medium. Prove
that, in “geometrical optics”, in the zero wavelength limit, the E-field is
perpendicular to the to the ray, which determines the
direction of propagation of the wave front.
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Using the tools of Geometrical
Optics, determine the equation for the surfaces of a microwave lens antenna
having an index of refraction larger than unity. The lens should be capable of
convertinf a spherical wavefront into a planar one, and vice versa. The focal
point of the lens, measured along the axis of symmetry, lies at a distance F from the
apex. Use the polar coordinates in expressing the equation of the surface of
the lens.
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Derive the expression for the transformation of
polarization of the E-field of an incoming wave in undergoing reflection from a
perfectly conducting reflector in using the aperture
field integration technique. Comment
on the underlying assumptions.
( given : aXbXc =
b(a.c)-c(a.b) , where a,b,c are vectors )
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A plane wave is incident on the the concave
side of a
paraboloidal reflector antenna.
The equation representing the reflector surface
is given by
x2 + y2 = 4 f z
where f stands for the focal length.
The E-field of the incident wave given by
a)
Determine
the expression for the surface current density Js induced on the reflector surface
using the “Physical Optics” (
b)
Briefly
discuss the underlying assumptions of the
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A parabolic reflector is illuminated by means
of a feed antenna. The E-field of the wave incident on the reflector is given
by
where C is a
constant proportional to the square root of the power radiated by the feed and
the subscript ‘f’ indicates the coordinate variables with respect to the feed.
The expression for the unit normal to the reflector is given by
Using the Geometrical Optics approach, determine the expression
for the E-field distribution over the focal plane of the reflector; specifying
the aperture E-field amplitude, phase and polarization ( expressed in terms of the unit vectors of the feed
system).
.)
Given
: ; sin 2A = 2
sinAcosA
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