Linearly polarized field of a flat aperture

The article analyzes a flat circular aperture and proposes to use a new analytical expression that describes the radiation pattern of an elementary radiator of an antenna aperture depending on time and integration angle. The formula presented in the paper can be applied to any flat section of the aperture without taking into account its shape. A new equation for the antiderivative function of the impulse response of a circular aperture is presented in the form of an elliptic integral of the second kind. It is shown that the theoretically calculated results are in good agreement with numerical simulations. In the analysis of the numerical model, the method of finite integration in the time domain (FIT) was used. Due to the requirement of a large computational resource, the numerical model was simplified.