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Linear Wire Antennas โContinued
EE-4382/5306 - Antenna Engineering
Perfect Ground Effects
2
Boundary Conditions
Linear Wire Antennas
Boundary Conditions on PEC
Linear Wire Antennas
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
Image Theory โ Vertical Dipole
Introduction to Antennas Slide 6
Slide 7Linear Wire Antennas
Image Theory โ Vertical DipoleFor electric field direct component (radiated),
๐ธ๐๐ = ๐๐
๐๐ผ0๐๐โ๐๐๐1
4๐๐1sin ๐1
For electric field reflected component,
๐ธ๐๐ = ๐๐ ๐ฃ๐
๐๐ผ0๐๐โ๐๐๐2
4๐๐2sin(๐2)
๐ ๐ฃ is reflection coefficient. For PEC, ๐ ๐ฃ = 1
๐ธ๐๐ = ๐๐
๐๐ผ0๐๐โ๐๐๐2
4๐๐2sin ๐2
๐ธ๐๐ก = ๐ธ๐
๐ + ๐ธ๐๐
Image Theory โ Vertical Dipole
Introduction to Antennas Slide 8
Image Theory โ Vertical Dipole
Introduction to Antennas Slide 9
In general, assuming the antenna lies at the origin, we can write that
๐1 = ๐2 + โ2 โ 2๐โ cos ๐12
๐2 = ๐2 + โ2 โ 2๐โ cos ๐ โ ๐12
For components in the far-field (๐ โซ โ)๐1 โ ๐ โ โ๐๐๐ ๐๐2 โ ๐ + โ๐๐๐ ๐
๐1 โ ๐2 โ ๐Thus we obtain
๐ธ๐ = ๐๐๐๐ผ0๐๐
โ๐๐๐
4๐๐sin ๐ [2 cos ๐โ cos ๐ ]
And the scalloping (number of total lobes) is
number of lobes โ 2โ
๐+ 1 (for โ โซ ๐)
Element Factor Array Factor
Image Theory โ Vertical Dipole
Introduction to Antennas Slide 10
The normalized power pattern is equal to
๐ = ๐21
2๐๐ธ๐
2 =๐
2
๐ผ0๐
๐
2
sin2 ๐ cos2(๐โ cos ๐)
Introduction to Antennas Slide 11
Vertical Dipole Above Ground
Introduction to Antennas Slide 12
Vertical Dipole Above Ground
Introduction to Antennas Slide 13
Vertical Dipole Above Ground
Ground Effects - Example
Introduction to Antennas Slide 14
An infinitesimal dipole of length ๐ is placed a distance ๐ from an air-conductor interface and at an angle of ๐ = 60ยฐ 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.
๐ = โ๐0, ๐0
๐
60ยฐ
+โ
โ
Ground Effects - Example
Introduction to Antennas Slide 15
An infinitesimal vertical dipole of length ๐ is mounted on a pole at a height โabove the ground, which is assumed to be flat, perfectly conducting, and of infinite extent. The dipole transmits in the VHF band (๐ = 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 80ยฐ from the vertical. What should the shortest height in meters be of the pole to achieve the desired null?