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

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

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.

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:

Hertzian Dipole Step 4: Antenna Parameters Power Density: Maximum Power Density: Antenna Pattern Solid Angle: Directivity:

The power radiated by the antenna is 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

Hertzian Dipole - Example Electric Field: Power density: Maximum Power density: Normalized Power density

Example Antenna Pattern Solid Angle: Radiated Power: Radiated Resistance: