Input Impedance of a Vertical Dipole Above Earth

1. Introduction Input impedance is an important parameter in an array of applications. However the computation of input impedance is often hampered by the presence of Sommerfeld-type integrals. Here we compare two methods devised to avoid the direct evaluation of Sommerfeld integrals in impedance calculations z2 Half-Wavelength Dipole 2*l z1 z0 Air h Lossy Earth, εr • Electric field expression contains vector-valued Green’s function…: • …which is a Sommerfeld Integral: • Approximation of spectral function with sum of exponentials…: • allows for analytic solution: Applications • Design of Comm. Systems • Efficiency and Cost • Scattering Problems • Mine Detection Input Impedance of a Vertical Dipole Above Earth Thomas Ng, Advisor: Prof. Xiao-Bang Xu, Clemson University SURE Program 2004 Input Impedance Problem Comparing Results • Induced EMF Method yields impedance expression • Sinusoidal current approximation for simplicity • Sommerfeld-type integrals present in electric field expression Background Complex Image Technique • Marconi’s wireless telegraph sparked interest in field propagation mechanisms • Zenneck proposed surface wave propagation along the air / earth interface • Sommerfeld investigated in 1909, finding problematic integrals in electric field expression Calcula R Observation Dipole h Air Lossy Earth Sommerfeld-Type Integrals Verification Conclusions Computationally Intensive because: • Impedance should approach free space values as: • Antenna height increases • Relative Permittivity of ground nears 1 • Varying ground conditions affect input impedance • There are different ways to avoid Sommerfeld-type Integrals • Accuracy and Computation Time tradeoff • No analytic solution • Rapid Oscillation • Slow Decay • Infinite Interval Future Work Exact Image Theory • More accurate current expression • Complete investigation of EIT • Electric field expression separated into direct and diffracted fields • Laplace Transforms performed on reflection coefficients • Change order of integration • Introduces decaying term in integral: • Eliminating Sommerfeld integral behavior Acknowledgements • Prof. Xiao-Bang Xu • Prof. Daniel L. Noneaker • Clemson University • NSF