1. Input Impedance of a Vertical Electric Dipole above earth Thomas Ng, RHIT Advisor: Prof. Xiao-Bang Xu SURE Program 2004 Clemson University July 27, 2004

2. Outline Why is this hard ? Why is this interesting ? How do we do it ?

3. Historical Overview Marconi’s Wireless Telegraph 1901 Sommerfeld’s Formulation 1909 Sommerfeld-Type Integrals Lossy Earth Air Dipole h R Observation

4. Sommerfeld Integrals No analytic solution Oscillate Rapidly Decay Slowly Infinite

5. Applications Design and development of communications systems Efficiency and cost considerations Scattering Problems Mine Detection

6. Impedance Problem Induced EMF Method Sinusoidal Current Approximation Lossy Earth, ε r Air Half- Wavelength Dipole h 2*l z0z0 z1z1 z2z2

7. Impedance Problem

8. Complex Image Technique

10. CIT Results

13. Exact Image Theory Laplace Transforms performed on reflection coefficients Change order of integration

14. Exact Image Theory Eliminates bad behavior of Sommerfeld Integral

15. Impedance Problem Superposition Induced EMF Method

16. Comparing Results: Z in

17. Comparing Results: Time

18. Conclusions Varying ground conditions affect input impedance There are different ways to avoid Sommerfeld-type Integrals Accuracy and Computation Time tradeoff

19. Future Work More accurate expression for antenna current Investigate EIT method more completely

20. Acknowledgements Prof. Xiao Bang Xu Prof. Daniel L. Noneaker

21. Questions ?

22. References Shubair and Chow Sarabandi and Casciato Kraus Balanis Collins Chow, Yang, Fang, and Howard Askun and Mitra Frohmberg

23. Complex Image Technique z=0 2*l h dqdq d1d1 d2d2 Original antenna Real quasi-dynamic image Complex Images d q = l+h d 1 = l+h-j*b 1 d 2 = l+h-j*b 2

24. Exact Image Theory Verification of Infinitesimal Dipole Results