Electromagnetic Field Evaluation of Dipole Antennas in Half-Space

1. Electromagnetic Field Evaluation of Dipole Antennas in Half-Space Robert Daniels Penn State University Clemson University SURE Program Advisor: Prof Xiao Bang Xu

2. Outline • Background Information • The Sommerfeld problem for dipole antennas • Exact Image Theory and the Sommerfeld problem • Applications • Results

3. Background • Infinitesimal Dipole • Arbitrary Length Linear Dipole • Diffracted and Direct Field Portions • Radiation Pattern of Dipole Antenna • Numerical Integration (e.g. Gaussian Quadrature)

4. Calculating the Electromagnetic Field Strength of Infinitesimal Dipoles Radiating in Half-Space • The situation • Why this calculation is important • The first solution: Arnold Sommerfeld

5. Numerical Integration in Sommerfeld Solution • Example integrals in diffracted portion of solution • Several methods have been devised to evaluate integrals of this type • Note that these integrals have no closed form solution so they must be evaluated numerically

6. Four Main Problems with these Solutions • (1) Dispute between several asymptotic techniques and their advantages • (2) Lack of universal solution for all values of distance between source and observation • (3) Slow convergence of numeric calculation in integrals • (4) In some instances, asymptotic techniques still don’t converge

7. Introducing Exact Image Theory • Introduced in the early 1980s • Method of representing diffracted field sources from complex images • Example: (image sources for perfect conductor)

8. EIT in Sommerfeld Problem • EIT improves the convergence of Sommerfeld Integrals • Uses a Laplace transform on reflection coefficients • Compact form of diffracted portion of field

9. Numerical Integration and EIT • Ability to numerically integrate significantly improved • Gaussian Quadrature necessary

10. Results for Infinitesimal Dipole • Note the improved results in calculation time

11. Soil Moisture Content and Dipole Radiation • The different moisture contents in soil contribute a great deal to electric field calculation

12. EIT in Linear Dipole Antennas • Superposition of Infinitesimal Dipoles

13. Arbitrary Length and Orientation Dipole Antennas • We are able to construct plots like this:

14. Radiation Patterns • Notice the impact of different soil moisture content levels on radiation pattern for a vertical half-wave dipole

15. Conclusions • EIT Applied to Sommerfeld Integrals provides various advantages • Differences in the earth boundary can contribute a great deal to antenna radiation

16. Future Work • Exact representation of current distribution on linear antennas instead of sinusoidal approximation • Analysis of new antenna configurations that can be derived from infinitesimal dipoles

17. Acknowledgements • Professor Xiao Bang Xu • Professor Daniel Noneaker • Applied Electromagnetics Group

18. Evaluating Highly Oscillatory Integrals • if distance between source and observation is large • standard asymptotic techniques (steepest descent method) • If distance between source and observation relatively small • Alternate asymptotic techniques available in literature (methods in dispute)