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8/13/2019 Antennas-9 - Travelling Wave Antennas
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Dr.-Ing. Getahun Mekuria
Department of Electrical and Computer Engineering (ECE)
Addis Ababa Institute of Technology (AAiT)
Addis Ababa University (AAU)
ECEG 6308
Analysis and Design of Antenna
Travelling Wave Antennas
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Travelling Wave Antennas
• Antennas with open-ended wires where the currentmust go to zero (dipoles, monopoles, etc.) can be
characterized as standing wave antennas or resonant
antennas.
• The current on these antennas can be written as a sum
of waves traveling in opposite directions (waves which
travel toward the end of the wire and are reflected in the
opposite direction).
• For example, the current on a dipole of length l is
given by
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Travelling Wave Antennas
• For example, the current on a dipole of length l isgiven by
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Travelling Wave Antennas
• The current on the upper arm of the dipole can bewritten as
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Travelling Wave Antennas
• Traveling wave antennas are characterized by matchedterminations (not open circuits) so that the current is
defined in terms of waves traveling in only one direction
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Example of a Travelling Wave Antenna
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Travelling Wave Antennas
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• Consider a segment of a traveling wave antenna (anelectrically long wire of length l lying along the z-axis).
• A traveling wave current flows in the z- direction.
Where:
the attenuation constant
the phase constant
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Travelling Wave Antennas
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• If the losses for the antenna are negligible (ohmic lossin the conductors, loss due to imperfect ground, etc.),
then the current can be written as:
• The Magnetic Vector potential is given by:
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Travelling Wave Antennas
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• And the Far Field Electric Field Strength is given by:
•
And •
Where
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Travelling Wave Antennas
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• The if we assume that the phase constant of theantenna is the same as an unbounded medium ( = k),
then
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Travelling Wave Antennas
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• Then the Travelling Power Density is given by:
• And the Radiated Power can be given as:
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Travelling Wave Antennas
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• And the Radiation Resistance is then:
•
Where C i(x) is the cosine Integral given by:
• The radiation resistance of the ideal traveling wave
antenna (VSWR = 1) is purely real just as the inputimpedance of a matched transmission line is purely
real.
• A plot of the radiation resistance of the traveling wave
segment as a function of segment length.
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Travelling Wave Antennas
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•
A plot of the radiation resistance of the traveling wavesegment as a function of segment length.
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Travelling Wave Antennas
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• The Radiation Intensity is also given by:
• The normalized pattern function can be written as
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Travelling Wave Antennas
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• The polar plots for different values of length:
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Travelling Wave Antennas
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• The polar plots for different values of length:
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Travelling Wave Antennas
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•The approximate angle of the main lobe for the travelingwave segment is found by determining the first peak of
the function in the normalized pattern function.
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Travelling Wave Antennas
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•Directivity
• The Maximum Directivity, is then
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Travelling Wave Antennas - Examples
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•V-Travelling Wave Antenna
• V-Antenna Radiation Pattern
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Travelling Wave Antennas - Examples
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•Rhombic Travelling Wave Antenna
• Rhombic Antenna Radiation Pattern