Antenna Theory EELE 5445
Transcript of Antenna Theory EELE 5445
Dr. Mohamed Ouda Electrical Engineering Department
Islamic University of Gaza
2013
Antenna Theory
EELE 5445
Lecture3: Radiation from Infinitesimal Source
Radiation from an infinitesimal dipole
Definition: The infinitesimal dipole is a dipole whose length Δl is
much smaller than the wavelength λ of the excited wave, i.e.
The infinitesimal dipole is equivalent to a current element IΔl, where
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Magnetic vector potential
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Power density and overall radiated
power of the infinitesimal dipole
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Duality in Maxwell’s equations
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DUAL QUANTITIES IN
ELECTROMAGNETICS
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Radiation from an infinitesimal
magnetic dipole
Using the duality theore for obtaining the vector potential
and the field vectors of a magnetic dipole (magnetic current
element) ImΔl
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Equivalence between a magnetic
dipole and an electric current loop First, we prove the equivalence of the fields excited by the
following sources:
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If the boundary conditions (BCs) for E1 and E2in are the same
and the excitations of both fields fulfill
then both fields are identical i.e.,
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Consider a loop [L] of electric current I.
The integral on the left side is the electric current I. M is assumed
non-zero and constant only at the section Δl , which is normal to
the loop’s plane and passes through the loop’s centre. Then,
The magnetic current Im corresponding to the loop [L] is obtained
by multiplying the magnetic current density M by the area of the
loop A[L] , which yields
Thus, a small loop of electric current I and of area A[L] creates EM field
equivalent to that of a small magnetic dipole (magnetic current
element) Im Δl.
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Field vectors of an infinitesimal loop
antenna By substitution
The far-field terms show the same behaviour as in the case of an
infinitesimal dipole antenna.
The radiated power can be found to be
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Radiation zones – introduction
Reactive near-field region
This is the region immediately surrounding the antenna, where the
reactive field dominates and the angular field distribution is different
at different distances from the antenna.
where D is the largest dimension of the antenna
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For the infinitesimal dipole
This approximated field is purely reactive ,H and E are in phase
quadrature
Since we see that:
(1) Hφ has the distribution of the magnetostatic field of a current
filament IΔl (remember Bio-Savart’s law);
(2) Eθ and Er have the distribution of the electrostatic field of a dipole
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The field is almost purely reactive in the near zone is obvious
Its imaginary part is
The radial near-field power flow density Pr has negative
imaginary value and decreases as 1/r5
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The near-field Pθ power density flow component is also
imaginary and has the same order of dependence on r but it is
positive:
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Radiating near-field (Fresnel)
region
This is an intermediate region between the reactive near-field
region and the far-field region, where the radiation field is
more significant but the angular field distribution is still
dependent on the distance from the antenna.
In this region,
For most antennas, it is assumed that the Fresnel region is
enclosed between two spherical surfaces
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The fields of an infinitesimal dipole in the Fresnel region are
obtained by neglecting the higher-order (1/r)n-terms:
The radial component Er is still not negligible, but the
transverse components(Eθ and Hφ ) are dominant
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Far-field (Fraunhofer) region Only terms 1/ r are considered when . The angular field
distribution does not depend on the distance from the source any
more. The field is a transverse EM wave.
For most antennas, the far-field region is defined as
The far-field of the infinitesimal dipole is obtained as
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Important features of the far field
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Far-field approximation
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