Paraboloidally Shaped Antenna Possessing Pointing and Beam-Width Control

Abstract

The surface shape of a paraboloidal ree ector was recone gured using electrostatic forces of repulsion. The experiment consisted of a recone gurable electrostatically shaped ree ector and a measurement system. A set of test cases demonstrated pointing and beam-width control of the radiating surface. The surface ree ector angles of rotation µx and µy were plotted vs eight test cases. The resulting sine functions show the near-linear relationship between voltage and pointing, indicating that expected rotations are in agreement with measurements and that a simple interpretation of Coulomb’ s law dominates the behavior of the system. Nomenclature a = vector of undetermined coefe cients C = coefe cient matrix Ex = error function for rotation about the x axis Ey = error function for rotation about the y axis i; j;k = counting indices p = number of sample points in one quadrant Rx;Ry = rotation matrices xn; yn;zn = coordinates in a new reference frame z = vertical position of ith point in the (j;k)th quadrant z = new vertical position of ith point in the (j;k)th quadrant z = vector of measured displacements z (x; y) = function to be curve e tted µx = angle of rotation about the x axis µy = angle of rotation about the y axis