Antennas

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Antennas

• Hertzian Dipole
• Current Density
• Vector Magnetic Potential
• Electric and Magnetic Fields
• Antenna Characteristics

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Hertzian Dipole
Step 1 Current Density
Let us consider a short line of current placed
along the z-axis.
Where the phasor
The stored charge at the ends resembles an
electric dipole, and the short line of
oscillating current is then referred to as a
Hertzian Dipole.
The current density at the origin seen by the
observation point is
A differential volume of this current element is
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Hertzian Dipole
Step 2 Vector Magnetic Potential
The vector magnetic potential equation is
A key assumption for the Hertzian dipole is that
it is very short so
The unit vector az can be converted to its
equivalent direction in spherical coordinates
using the transformation equations in Appendix B.
This is the retarded vector magnetic potential at
the observation point resulting from the Hertzian
dipole element oriented in the az direction at
the origin.
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Hertzian Dipole
Step 3 Electric and Magnetic Fields
The magnetic field is given by
It is useful to group ? and r together
The electric field is given by
In the far-field, we can neglect the second term.
Far-field condition
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Hertzian Dipole
Step 4 Antenna Parameters
Power Density
Maximum Power Density
Antenna Pattern Solid Angle
Directivity
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Hertzian Dipole
Step 4 Antenna Parameters
Total Radiated Power and Radiation Resistance
The total power radiated by a Hertzian dipole can
be calculated by
The power radiated by the antenna is
Circuit Analysis
Field Analysis
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Hertzian Dipole - Example
Example
Electric Field
Power density
Maximum Power density
Normalized Power density
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Example
Antenna Pattern Solid Angle
Radiated Power
Radiated Resistance