Formulas for Antenna Patterns in Time Domain and for the Primitive Impulse Response Function of Linearly Polarized Field of Plane Aperture

In this letter, we present a novel time-domain analytic formula for the elementary radiator antenna pattern of a metal plane surface with infinite conductivity. The formula is presented as a function of time and the integration angle. The formula refers to a flat metal aperture without regard to its shape. We also describe a novel equation for the primitive impulse response function (PIRF) of a circular aperture in the form of an elliptic integral of the second kind. We explain that this equation refers to a flat aperture of any shape. We also show that these results are in good agreement with the numerical simulation by a finite integration technique.