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Overall summary of antenna and propagation
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Maxwell’s Equations: Equations that describe electromagnetic fields, useful in the description ofpropagation. Most useful ones (in the case of propagation in free space) are:
If the only fields are H x and E z:
Which is effectively saying:
Rate of change of magnetic/electric field with respect to distance ∝ electric/magnetic field.
Generally, waves are radiated when charges accelerate, this is used both intentionally in the case of
antennas, or unintentionally in the radiation of energy from wave guides e.g. ladder line, coax, etc.
Near Field/Fraunhofer Zone: Area around antenna where energy is reactively stored in the local
magnetic/electric field. Defined as the radius:
2
2L
R=
λ
Where L is the diameter of the smallest sphere which encloses the antenna.
,Far Field/Fraunhofer Zone: Zone where radiation acts effectively like a plane wave. Easy to
understand in terms of phase error.
Radiation coming from the edge of the antenna has a phase error e p which may cause interference
at the receiver. If r is large enough, e p becomes small enough to be negligible.
λ
Using Pythagoras and accepting as an acceptable max e p, we can define the start of the far field
16
as:
Comparisons between a simulation of the near and the far field pattern can be seen below:
,Poynting Vector: Cross product of the E and H fields, describes the flow of power at any point in
space.
S= E× H
Average power density over a period is also:
Where is the phase of the final vector.
Hertzian Dipole: Theoretical dipole made of an infinitely small (compared to the wavelength) piece
of wire. It is assumed that the current distribution across the wire is constant and changing
sinusoidally in time. This is a useful model for basic analysis and shows how in the far field the
reactive components of an antenna disappear.
Isotropic Antenna: Theoretical antenna which radiates uniformly in all directions. Power density is
Spherical Coordinates: System that uses azimuth φ , elevation θ , and radius r to describe a point
instead of x y and z.
Useful in describing the directivity and/or gain of an antenna. The total power emitted by an
antenna is (using spherical coordinates)
2π π
PT =∫ ∫ P ( θ , φ ) sin θ dθ dφ
0 0
, Directivity: Measure of how well an antenna focuses power in a certain direction, evaluated as the
ratio of the power density seen in a particular direction as compared to the same density seen from
2
2L
an isotropic antenna. Assuming measurements are done in the far field ( r ≫ ):
λ
The maximum value of directivity is known as the boresight directivity/gain, which the rest of the
values are typically normalised to.
Gain: Directivity but with added efficiency.
Effective Area: The “area” presented by an antenna that is used to “capture” an incoming power
density.
Link Budget: Quantification of the amount of power seen at a receiver when a transmitting antenna
transmits. Generally the received power will be:
P Rx=PTx ( ) λ 2
4 πr
G Rx GRx
( ) is defined as the free space loss of the system.
2
λ
Where
4 πr
Radiation Intensity: A measurement of power density that is distance independent. Measured in
Watts per unit Steradian, where a steradian is a squared radian and a sphere has 4 π steradians in
total.
2
U =r S rad =r
2
( P Tx D Tx
4πr
2 ) =
PTx DTx
4π
Including spherical coordinates:
PTx DTx (θ , φ )
U=
4π
For an isotropic source:
PTx
Uo=
4π
And thus, the directivity in radiation intensity is
U (θ , φ)
DTx ( θ , φ )=
Uo
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