Lab 1: Radiation & Ideal Physics

Section A: Theoretical Proficiency

1. Who provided the unified theory of electromagnetism that first established light as an electromagnetic wave?

2. In a non-magnetic material medium, by what factor is the velocity of an electromagnetic wave reduced compared to its speed in a vacuum?

3. Why does the “Hairy Ball Theorem” prove that a perfectly isotropic electromagnetic radiator cannot physically exist in free space?

4. What is the “Principle of Pattern Multiplication” used in the study of antenna arrays?

5. What is the primary idealized assumption regarding the current distribution on a Hertzian dipole?

6. For a center-fed short dipole with a triangular current distribution, what is the relationship between its effective length ($L_e$​) and its physical length ($L$)?

7. What is the conventional boundary distance used to separate the near-field and far-field regions for a Hertzian dipole?

8. According to the transmission-line analogy, what is the shape of the current distribution along a thin half-wave dipole?

9. In Image Theory, how do you model a vertical Hertzian dipole located at a height ($h$) above a Perfect Electric Conductor (PEC) ground plane?

10. How does the radiation resistance of a quarter-wave monopole above a perfect ground plane compare to that of a half-wave dipole in free space?

Section B: Simulation Mastery

Approximating the Hertzian Dipole

Objective:

Use AN-SOF to approximate the theoretical properties of an infinitesimal Hertzian dipole and estimate its radiation resistance.

Exercise:

1. AN-SOF Modeling: Set the frequency to 300 MHz ($\lambda \approx 1\ \text{m}$). Draw a vertical dipole with a physical length of 0.01 meters ($0.01\lambda$).
2. Uniform Current: To approximate the uniform current distribution of an ideal Hertzian dipole, add short horizontal radial wires to both ends of the vertical dipole.
3. Analysis: Set the input power to 100 W. Open the Results > Power Budget table to find the Radiated Power ($P_r$​). Right-click the vertical wire and select List Currents > Current on Segment to find the input current magnitude ($|I_0|$).
4. Verification: Calculate the radiation resistance. Compare this value to the theoretical result for a dipole of this electrical length.