Abstract

1. Approximate Current on a WireA Differential Equation MethodAdam Schreiber, Yuriy Goykhman, SURE 2004Faculty Research Advisor: Dr. Chalmers Butler • Results • 0.4 λ • 0.8 λ • 1.0 λ • Error • Lengths that Do Not Converge • Region around 0.5 λ • Region around 1.5 λ • Odd multiples of 0.5 λ • Reasons for Error • Initial delta function approximation • Accuracy of evaluating • Almost singular matrices at non-convergent lengths • Future Work • Increase efficiency/speed • Extend algorithm to bent/curved wires • Improve numerical integration methods • Conclusion • Provides good approximations for current on wires, although not near lengths that are odd multiples of 0.5 λ • Can be adjusted to improve speed and increase accuracy • Perhaps, can be fixed for lengths near odd multiples of 0.5 λ • 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 method’s 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 • KR approximates the • delta function • Differential Equation • Pulse Test • Evaluate the Differential Equation at m points • Creates N equations in I(z) • Changes intervals from (-h, h) to (zm - Δ/2, zm + Δ/2) • Triangle Expansion • Replaces I(z) with N unknowns • We now have N equations with N unknowns • Matrix Equation • Solution Method • Generate tri-diagonal matrix • Find I0 with J0 = 0 • Generate a new right hand side • Find Ip • Repeat the above 2 steps till convergence • Compare results with integral equation data • Convergence Rate