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Modeling a Dipole Above Earth

Modeling a Dipole Above Earth. Saikat Bhadra Advisor : Dr. Xiao-Bang Xu Clemson SURE 2005. Overview. Objective Problem Background & Theory Results Problems in the EIT Model Concluding Remarks. Objective. Accurate modeling of a dipole Linear Antenna Lossy Earth Material Properties

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Modeling a Dipole Above Earth

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  1. Modeling a Dipole Above Earth Saikat Bhadra Advisor : Dr. Xiao-Bang Xu Clemson SURE 2005

  2. Overview • Objective • Problem Background & Theory • Results • Problems in the EIT Model • Concluding Remarks

  3. Objective • Accurate modeling of a dipole • Linear Antenna • Lossy Earth • Material Properties • Scientific Model • K. Sarabandi, M. D. Casciato, and I. KohEfficient Calculation of the Fields of A Dipole Radiating Above an Impedance Surface

  4. Solving Electromagnetic Problems • The Emag Bible : Maxwell’s Equations • Available in integral and differential forms • Vector Potential • Links Magnetic and Electric Fields

  5. Non-flat & non-Euclidean surfaces Time Varying Layered Materials Antenna Environment Inhomogeneous Materials Location : Austin, TX

  6. Simplifications • Simplify math and assume : • Flat Earth Model • Two Layers • Upper half space – “air” • Lower half space – lossy earth • Euclidean (rectangular) geometry • Infinitesimal Vertical Dipole • Superposition to extend to finite dipoles

  7. Observation Point Dipole Free Space Impedance Half Space Electric Field • In this type of problem, two fields are involved • Direct Electric Fields • Fields due to antenna radiating • Solution in closed form & well documented • Diffracted Electric Fields • Fields from antenna that are reflecting off the lower surfaces • Subject of research since 1909

  8. Original Solution – Diffracted Fields • Arnold Sommerfeld (1909) • Sommerfeld Integrals • Non-analytic • Numerical integration difficult • Requires asymptotic techniques • Valid for certain regions • Convergence difficult

  9. Original Solution – Diffracted Fields cont’d

  10. Exact Image Theory Solution • Sarabandi, Casciato, Koh (2002) • Source Equation :

  11. EIT Formulation • Separate diffracted and direct components • Reflection Coefficients transformed using Laplace transform • Bessel function identities

  12. Observation Point Direct Dipole Free Space Diffracted Impedance Half Space EIT Solution – Diffracted Fields

  13. EIT Solution • Integral Advantages • Rapidly Decays • Non-Oscillatory • Easy numerical evaluation after exchange of integration and differentiation

  14. Dipole Dipole Dipole Dipole Dipole Dipole Exact Image Theory Observation Point Direct Free Space Diffracted Impedance Surface

  15. Finite Length Dipoles • Sarabandi’s model uses infinitesimal dipole • Finite dipole can be approximated by a sum of infinitesimal dipoles • Superposition Principle

  16. Calculating Input Impedance • Induced EMF Method : • Current distribution assumed to sinusoidal • Transmission line approximation • Inaccurate when dipole comes close to half space

  17. Numerical Techniques • Gaussian Integration • Useful in many emag problems • Handles singular integrands better • More accurate than rectangular, trapezoidal, and Simpson’s rule • Integral Truncation • Can’t numerically evaluate an infinite integral • Vectorized Code

  18. Results • Computational time varies with antenna location • Frequency independence • Asymptotically approaches original antenna impedance

  19. Results cont’d

  20. Problems of the EIT Model • Recall the breakdown of electric field into diffracted and direct components • Diffracted fields should go to zero if the half-space is removed • There is no longer any surface for waves to bounce off of • Numerical Results disagree • Currently finding theoretical errors of the model

  21. Problems of the EIT Model cont’d

  22. Concluding Remarks • EIT model could be promising but problems need to be solved • Research Applications • Antenna Design • Integral Equations & Numerical Methods

  23. Future Work • Solve the EIT model problems • Extend the problem to dipoles of arbitrary orientation • Develop more accurate model of current distribution • Investigate different source models

  24. Acknowledgments • Dr. Xu • Dr. Noneaker

  25. Questions?

  26. Environmental Variables • Time varying • Inhomogeneous Materials (x,y) • Water • Grass • Concrete • Layered Materials (z) • Trees, Grass, Soil • Non-flat surfaces • Amorphous (non-Euclidean) geometries • Mutual Coupling

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