The regularization tasks of the horizontal electrical dipole radiation out of a sphere with the circular aperture with dielectrical ball loading are constructed and analyzed. We discussed of the separation of the boundary conditions for scalar electrical and magnetical potentials Debaya on the ideal conductivity spherical segment and on the aperture. We use of the method of the separation variables in the spherical sys-tem coordinate. We solve auxiliary integral equations of Abel's type and select main parts of 4 functional equations by introducing two small parameters. As a result we obtain two disconnected linear algebraic systems of second kind with compact matrix operators of Fredholm's type. Some characteristics of the spherical antenna by improvement of analytical-computational method are discussed.