Approximate Current on a Wire A Differential Equation Method Adam Schreiber, Yuriy Goykhman, SURE 2004 Faculty Research Advisor: Dr. Chalmers Butler

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Approximate Current on a WireA Differential
Equation MethodAdam Schreiber, Yuriy Goykhman,
SURE 2004Faculty Research Advisor Dr. Chalmers
Butler

• Results
• 0.4 ?
• 0.8 ?
• 1.0 ?
• Error

• Abstract
• This method is an attempt to seek a faster and
  more efficient way of determining the current on
  a wire antenna. The differential equation is
  derived from the integral equation for
  determining the current on a wire. An algorithm
  for solving the second order differential
  equation is developed. This method provides good
  approximations, and the methods error is a
  function of the length of the wire.
• Importance
• Applications Wire Antennas, Antenna Arrays, Wire
  Like Coupling
• Replace Integral Equation Method Faster, More
  Efficient
• Derivation
• Integral Equation
• Approximation
• Justification

• Pulse Test
• Evaluate the Differential Equation at m points
• Creates N equations in I(z)
• Changes intervals from (-h, h) to (zm - ?/2, zm
  ?/2)
• Triangle Expansion
• Replaces I(z) with N unknowns
• We now have N equations with N unknowns
• Matrix Equation