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Antennas: from Theory to Practice
4. Antenna Basics
Yi HUANG
Department of Electrical Engineering & Electronics
The University of Liverpool
Liverpool L69 3GJ
Email: [email protected]
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Objectives of this Chapter
• Study the basic theory of antennas
• Understand how radio waves are generated
by antennas
• Identify the most important antenna
parameters from both the field point of view
and the circuit point of view.
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4.1
Antennas to Radio Waves
• For a single frequency case
Eliminating H, we have
Thus in a open space
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This equation gives the radiated electric field from a
time varying current J (the time factor is omitted
here) and is the very foundation of the antenna
theory – it reveals how the antenna is related to
radiowaves
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Radiation from a current source IDl
η is about 377 ohms in free space
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– The electric field is always greater than the magnetic
field;
– When βr >1, the ratio of |E/H| = η
– When βr <1, as the distance increases, the electric
field reduces at a much faster rate (60 dB/decade)
than the magnetic field (40 dB/decade).
– When r is fixed, br =1 is still an important point,
– The electric field first reduces as b (or frequency)
increases to the point br =1 and then changes to
increase with b (or frequency) after this point
– the ratio of E/H reduces first as b increases to about
br = 1; it then becomes a constant for br > 1.
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Antenna far field
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Major features of the far field
– Just one E field component and one H field component
– a local plane wave?
– Both fields are inversely proportional to the distance r;
– The ratio of E/H is , the intrinsic impedance
– E and H fields are orthogonal to each other and the
cross product of these two is the power density
function which is inversely proportional to the distance
square r2:
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Antenna near field
Simulated near field around a dipole antenna
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Major features of the near field
The region βr <1 for is normally called the reactive
near field. The field changes rapidly with distance.
From its power density function, we can see that
– It contains both the radiating energy (the real part)
and reactive energy (the imaginary part – it does not
dissipate energy which is like a capacitor or
inductor). The latter is normally dominant in this
region.
– It has components in r and f directions. The former is
radiating away from the source and the latter is
reactive.
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Antenna near and far fields
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4.2
Antenna Parameters from the Field Point of
View
• Radiation Pattern
– a plot of the radiated field/power as a function of
angle at a fixed distance which should be large
enough to be considered in its far field
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– The half-power beamwidth (HPBW) of the main
lobe, also called the 3dB beamwidth; or just the
beamwidth (to identify how sharp the beam is);
– The 10 dB beamwidth or first null beam width
(FNBW) (another one capture the main beam
shape);
– The first side lobe level (expressed in dB, relative
to the peak of the main beam);
– The front to back ratio (the peak of the main lobe
over the peak of the back lobe, another attempt to
identify the directivity of the antenna).
– Null positions (sometimes used for anti-interference
and positioning).
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When the patterns are plotted in the logarithmic scale (dB plot),
both the normalised field and power patterns are the same
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• Directivity
– a measure of the concentration of radiated power in
a particular direction. It is defined as the ratio of the
radiation intensity in a given direction from the
antenna to the radiation intensity averaged over all
directions.
Pt is the total radiated power in W, and U is radiation intensity in
W/unit solid angle, linked to the averaged radiated power density
Sav
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Example 4.1
The radiated power density of the electrically short current
element is given earlier as:
Determine the directivity of the antenna as a function of the
directional angles, find the maximum directivity and
express it in decibels.
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• Gain
– the ratio of the radiation intensity in a given direction
from the antenna to the total input power accepted by
the antenna Pin divided by 4p:
• Radiation Efficiency
– the ratio of the radiated power to the input power
accepted by the antenna:
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Example 4.2
If the efficiency of the antenna in Example 4.1 is 50%,
VSWR at the antenna input is 3 and the input/supplied
power is 1 W, find:
a). the power gain;
b). the total radiated power
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• EIRP
– Effective isotropic radiated power, or EIRP, is the
amount of power that would have radiated by an
isotropic antenna to produce the peak power density
observed in the direction of maximum antenna gain:
• Effective Aperture and Aperture Efficiency
– The effective aperture Ae is less than the physical
aperture Ap, the aperture efficiency is defined as
the ratio of these two:
and directivity
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Example 4.4
The directivity of a pyramidal horn antenna of aperture
width a and height b is
Find its aperture efficiency. If the power density around the
antenna is 1 W/m2, find the received power.
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• Polarisation
– The antenna polarisation is the same as the polarisation
of its radiating wave: linear or circular in practice.
– Two orthogonally polarised antennas cannot
communicate with each other.
• Antenna Temperature
– The radiation from different sources is intercepted by
antennas and appears at their terminals as
TB is the brightness temperature of the radiation source
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• Antenna factor (AF)
– the ratio of the incident electric field E to the induced
voltage V0 at the antenna terminal when it is
connected to a load/cable (50 ohms by default)
• Radar Cross Section (RCS)
– the ability of a target to reflect the energy back to the
radar and it is the ratio of the backscattered power to
incident power density
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4.3
Antenna Parameters from the Circuit Point
of View
• Input Impedance
– Antenna input impedance (Za) is the impedance
presented by an antenna at its terminals or the ratio
of the voltage to current at its terminals
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• Radiation Resistance
– the equivalent resistance which would dissipate the
same amount of power as the antenna radiates when
the current equals the input current at the terminals:
RL is the loss resistance of the antenna.
To match with the source impedance, the condition is:
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• Reflection Coefficient, Return Loss and VSWR
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• Radiation Efficiency
• Matching Efficiency
• Total Efficiency
source supplied
power
This has taken the feed-antenna mismatch into account
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• Bandwidth
It can be defined by a number of things, such as the VSWR
return loss, gain, or even 3dB beam width!
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Summary of antenna main parameters
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