Antennas-9 - Travelling Wave Antennas

ECEG 6308 Analysis and Design of Antenna

Travelling Wave Antennas Anten nas

Dr.-Ing. Dr.-Ing. Getahun Getahun Mekuria Mekuria Department of Electrical and Computer Engineering (ECE) Addis Ababa Institute of Technology (AAiT) Addis Ababa University (AAU)

Travelling Wave Antennas •

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 Antennas with open-ended wires where the current must 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  2

Travelling Wave Antennas •

For example, the current on a dipole of length l is given by 

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Travelling Wave Antennas •

The current on the upper arm of the dipole can be written as

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Travelling Wave Antennas •

Traveling wave antennas are characterized by matched terminations (not open circuits) so that the current is defined in terms of waves traveling in only one direction

Example of a Travelling Wave Antenna 5

Travelling Wave Antennas •

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Consider a segment of a traveling wave antenna (an electrically 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 6

Travelling Wave Antennas •

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If the losses for the antenna are negligible (ohmic loss in 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 •

 And the Far Field Electric Field Strength is given by:

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 And

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Where

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Travelling Wave Antennas •

The if we assume that the phase constant of the antenna 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 input impedance of a matched transmission line is purely real.  A plot of the radiation resistance of the traveling wave 11 segment as a function of segment length.

Travelling Wave Antennas •

 A plot of the radiation resistance of the traveling wave segment as a function of segment length.

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Travelling Wave Antennas •

The Radiation Intensity is also given by:

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The normalized pattern function can be written as

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Travelling Wave Antennas •

The polar plots for different values of length:

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Travelling Wave Antennas •

The polar plots for different values of length:

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Travelling Wave Antennas •

The approximate angle of the main lobe for the traveling wave segment is found by determining the first peak of the function in the normalized pattern function.

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Travelling Wave Antennas •

Directivity

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The Maximum Directivity, is then

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Travelling Wave Antennas - Examples •

V-Travelling Wave Antenna

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V-Antenna Radiation Pattern

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Travelling Wave Antennas - Examples •

Rhombic Travelling Wave Antenna

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Rhombic Antenna Radiation Pattern

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