A. D. Vinogradov, P. A. Mozgovoy

The article analyzes the well-known integro-differential equation of the problem of determining the current distribution on the conductor of circular single-turn loop antenna excited by a generator voltage in the form of the Dirac -function, included in an infinitely narrow gap of a thin wire of finite conductivity antenna located in free space. It is shown that this equation is incorrect in the gap region of excitation antenna Using a model of excitation antenna in the form of an electromotance (EMF) source, included in the gap of finite width, and the symbolic square wave function, where the current longitudinal angular coordinate of a point on the conductor antenna and angular width of the gap excitation reformulated integro-differential equation of the problem of determining the current distribution on a thin conductor of finite conductivity single-turn circular loop antenna located in free space. Solution of the modified integro-differential equation is obtained as a convergent Fourier series. It is shown that the well-known integro-differential equation of the problem of determining the current distribution on the conductor of circular single-turn loop antenna and its decision is "zero" approximation of the modified integro-differential equation and its solutions. Comparison of current distributions for models of the excitation antenna to the generator function and a source of EMF, included in a gap of finite width. It is shown that the current distribution, resulting in a model with a source of EMF, included in a gap of finite width, more appropriately reflects the physics of the excitation wire antenna. In particular, it noted a sharp increase in the amplitude of the current near the antenna feed points in an effort width of the gap excitation to zero, which explains the increase in static capacitance of the gap excitation of antennas tending in the limit to infinity. Noted that the well-known integro-differential equation and its solution can be used to determine the integral characteristics such as loop antenna radiation pattern and the coefficient of directed action. For the calculation of characteristics, which are taken into account in determining the local properties of loop antennas near power outlets, you must use the modified integro-differential equation. The article includes 4 figures and references to 11 information sources.