linear wire antennas continued - empossible
TRANSCRIPT
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Linear Wire Antennas βContinued
EE-4382/5306 - Antenna Engineering
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Perfect Ground Effects
2
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Boundary Conditions
Linear Wire Antennas
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Boundary Conditions on PEC
Linear Wire Antennas
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Image Theory
Slide 5
Virtual sources (images) are introduced to account for reflections. They also need to satisfy boundary conditions. We will assume infinitesimal dipoles for infinite ground plane.
Linear Wire Antennas
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Image Theory β Vertical Dipole
Introduction to Antennas Slide 6
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Slide 7Linear Wire Antennas
Image Theory β Vertical DipoleFor electric field direct component (radiated),
πΈππ = ππ
ππΌ0ππβπππ1
4ππ1sin π1
For electric field reflected component,
πΈππ = ππ π£π
ππΌ0ππβπππ2
4ππ2sin(π2)
π π£ is reflection coefficient. For PEC, π π£ = 1
πΈππ = ππ
ππΌ0ππβπππ2
4ππ2sin π2
πΈππ‘ = πΈπ
π + πΈππ
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Image Theory β Vertical Dipole
Introduction to Antennas Slide 8
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Image Theory β Vertical Dipole
Introduction to Antennas Slide 9
In general, assuming the antenna lies at the origin, we can write that
π1 = π2 + β2 β 2πβ cos π12
π2 = π2 + β2 β 2πβ cos π β π12
For components in the far-field (π β« β)π1 β π β βπππ ππ2 β π + βπππ π
π1 β π2 β πThus we obtain
πΈπ = ππππΌ0ππ
βπππ
4ππsin π [2 cos πβ cos π ]
And the scalloping (number of total lobes) is
number of lobes β 2β
π+ 1 (for β β« π)
Element Factor Array Factor
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Image Theory β Vertical Dipole
Introduction to Antennas Slide 10
The normalized power pattern is equal to
π = π21
2ππΈπ
2 =π
2
πΌ0π
π
2
sin2 π cos2(πβ cos π)
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Introduction to Antennas Slide 11
Vertical Dipole Above Ground
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Introduction to Antennas Slide 12
Vertical Dipole Above Ground
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Introduction to Antennas Slide 13
Vertical Dipole Above Ground
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Ground Effects - Example
Introduction to Antennas Slide 14
An infinitesimal dipole of length π is placed a distance π from an air-conductor interface and at an angle of π = 60Β° from the vertical axis, as shown in the figure. Sketch the location and direction of the image source which can be used to account for reflections. Be very clear when indicating the location and direction of the image.
π = βπ0, π0
π
60Β°
+β
β
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Ground Effects - Example
Introduction to Antennas Slide 15
An infinitesimal vertical dipole of length π is mounted on a pole at a height βabove the ground, which is assumed to be flat, perfectly conducting, and of infinite extent. The dipole transmits in the VHF band (π = 50 MHz) for ground-to-air communications. In order for the transmitting antenna to not interfere with a nearby radio station, it is necessary to place a null in the dipole pattern at an angle 80Β° from the vertical. What should the shortest height in meters be of the pole to achieve the desired null?