It is always relevant to improve performance in electrodynamic systems. When solving problems on the electrodynamic characteristics of hollow coupled systems, the question is often asked about the relationship between them, about the form of the communication hole with a certain orientation of the guide axes in the system elements and its geometric dimensions. Such a system is a generator (small-sized local oscillator8 mmrange). The inclusion of a high-Q stabilizing resonator in the Gunn diode generator significantly improves its characteristics. The use of a low-quality coaxial chamber as a diode section increases the generation stability. However, this complicates the numerical calculations of the electrodynamic system of the generator due to the uncertain configuration of the communication hole, since it arises as a result of the intersection of two cylindrical volumes of a coaxial waveguide and a high-quality cylindrical resonator. In the present work, the task is determination of the shape and size of the intersection figure of two unequal radii of cylindrical volumes with axes orthogonally located in relation to each other at a distance. The resulting shape of the intersection figure in a planar approximation forms a flat ellipse. The larger diameter of the coupling ellipse depends on the diameter of the resonator, the smaller on the inner diameter of the coaxial chamber, depending on the distance between their axes. It is necessary to determine the equivalent rectangular hole of the connection. Its presence simplifies the construction of a tangent electric field at the communication hole, which is necessary for numerical calculations of the electrodynamic characteristics of the system. In this case, with constant diameters of the cylindrical resonators, the geometrical dimensions of the hole depend only on the distance between the axes. It is with this circumstance that they are dealing with the study of the connection between a cylindrical coaxial diode section and a high-Q stabilizing resonator. Unlike other circuits, where the diode is included in the waveguide section, in this case, its inclusion is made in a coaxial line.