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

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

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

Sommerfeld Integrals No analytic solution Oscillate Rapidly Decay Slowly Infinite

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

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

Impedance Problem

Complex Image Technique

CIT Results

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

Exact Image Theory Eliminates bad behavior of Sommerfeld Integral

Impedance Problem Superposition Induced EMF Method

Comparing Results: Z in

Comparing Results: Time

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

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

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

Questions ?

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

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

Exact Image Theory Verification of Infinitesimal Dipole Results