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

2. Hertzian Dipole Let us consider a short line of current placed along the z-axis. 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. Where the phasor The current density at the origin seen by the observation point is A differential volume of this current element is Step 1: Current Density

3. 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 a z 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 +a z direction at the origin.

4. Hertzian Dipole Step 3: Electric and Magnetic Fields The magnetic field is given by It is useful to group  and r together Far-field condition: In the far-field, we can neglect the second term. The electric field is given by

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

6. Total Radiated Power and Radiation Resistance : Hertzian Dipole Step 4: Antenna Parameters The total power radiated by a Hertzian dipole can be calculated by The power radiated by the antenna is Circuit Analysis Field Analysis

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

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