*The aim of this work is to suggest a variant of constructing of a receiving AA providing a wide band of operating frequencies and wide sector of operating angles simultaneously. Then, develop a mathematical model of the suggested AA. Based on the constructed mathematical model, conduct a series of numeric experiments to discover the main properties of the AA.*

The AA in question is a multilayer periodic ribbon structure located in an environment with planelayer dielectric filler above a metallic surface (fig. 1).

Into gaps of the metallic ribbons of the AA, active elements can be directly included, such as optoelectronic converters, the first link of the input device of the receiving module of the AS. In this work, the specific implementation of the active elements is not studied and the AA is considered loaded on the lumped resistances, which are the input resistances of these elements.

*Mathematical model of the multilayer antenna array.* The analysis of characteristics of the multilayer AA in this work comes to solving of an external boundary value problem of electrodynamics. In the process of solving, the boundary value problem turns into the integral equation relative to current on the metallic elements of the construction, which then after representing the current in a specific basis, comes to a system of linear algebraic equations relative to the amplitudes of the basis current functions. The antenna array is periodic with periods *Т _{x}* and

*Т*on

_{y}*X*and

*Y*axis respectively. It is excited by a plane homogenous wave propagating in the negative direction of the

*Z*axis. The direction of wave propagation is defined by the

*θ*and

*φ*angles of the spherical coordinate system corresponding to the source Cartesian one. In the general case, the extraneous field can belong to the neither

*E*-waves, nor

*H*-waves. However, it can always be decomposed into

*E*and

*H*components and solve the problem separately for each excitation type. Thus, we will consider that the structure is excited either by

*E*, or

*H*-wave and in the process of scanning, the polarization of the extraneous field remains unchanged. Orientation of the scanning plane is defined by the azimuth angle

*φ*, the angle of scanning in this plane is angle

_{0}*θ*.

_{0}Fig.1

The following expressions relate the excitation parameters to angles, which characterize the direction of propagation of the corresponding waves.

H-waves: |
(1) |

E-waves: |
(2) |

The expressions (1) and (2) describe the field of the incident wave in the free space. To account for the planelayer dielectric filler, we will use (to describe the combination of dielec-tric layers in the space waveguide) the irregular long line model. The irregular line in question is composed of several homogenous parts, wave resistances of which are equal to the characteristic resistances of Floke harmonics in the corresponding dielectric layers. Let’s consider a dielectric filler composed of *N*+1 layers with known dielectric permittivitties *ε _{i}*.

*N*+1 layer is free space on which the extraneous field is given in the form of a plane homogenous wave incident to the structure. If the planelayer dielectric filler is present, the relation between the extraneous field in layer

*M*and the extraneous field in free space is defined by the following expression:

(3) |

where is the extraneous field in free space; is the element of the transmission matrix, describing the layers with numbers greater than *М*; *R* is the reflectivity coefficient for the layer *М*-1; z' is the coordinate counting from the joint between layers *М*+1 and *М*.