Small Antenna Design
Keeping mathematics to the absolute minimum, this guide describes the theory behind effective small antenna design while providing design techniques and examples for small antennas for different operating frequencies.
TABLE OF CONTENTS Small Antenna Design
Appendix D: The Proximity Effect
D.1 Distribution
In the late 1960s Glenn Smith analyzed the problem of what happens to the current distribution in long parallel wires that are close to one another in terms of their radius. His work was published in a Harvard technical report [1], and a paper [2] in 1972. This Appendix reworks the analysis given in the paper, makes some comments, and describes a simpler method to find the coefficients in the Fourier series for the normalized current densities.
D.1.1 Problem Formulation and Reduction to a System of Linear Equations
Figure D.1 shows the layout and notation for the geometry. The plan of attack is to develop the vector magnetic potential near wire m due to all currents, then apply a boundary condition to get the integral equation for the surface current. This requires an integration of the contribution from each element of current density, and that requires writing an expression for the distance from the source point at ( a, ? ?, z ?) on wire n to the observation point at ( r, ?, z) on wire m.
Figure D.1: Cylindrical conductors of length 2h. The transverse view shows half the length, and is not to scale. D >> Nd, where N is the number of wires.
The overall distance is R mn. Let r mn be the distance between the two points projected into an x- y plane such as is occupied by...
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