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This document describes the energy distribution within an electrically small antenna. Chu (1948) derived expressions for the "Q" of an omnidirectional antenna whose entire structure is enclosed within a sphere. Many authors have extended this technique. Because the sphere is not conformal to the structure of most linear polarized antennas, much energy is not accounted for. If the structure is surrounded by an ellipsoid of revolution, the fit is much better. Prolate spheroidal coordinates are expected to provide a much better description for a linearly polarized antenna. We derive expressions for the electromagnetic field and the Poynting vector for vertically and horizontally polarized antennas. From the expressions, we calculate the Q of an electrically small antenna. We can derive an analytic expression for the value of Q for the leading term. The leading term is a product of the inverse of the cube of the dimensionless wave number (product of the wave number and half the distance between foci of the ellipse) and a factor that depends only upon the shape. This result is reformulated so that as the shape changes, the volume and wave number remain constant. |
