Input Impedance of a Vertical Dipole Above Earth

1
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

• Marconis 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
Conclusions
Verification
Sommerfeld-Type Integrals

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

• Impedance should approach free space values as
• Antenna height increases
• Relative Permittivity of ground nears 1

Computationally Intensive because

• Slow Decay
• Infinite Interval

• No analytic solution
• Rapid Oscillation

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