Then we shall describe the method of representing electric currents on the AA ribbons. As basis functions, we shall use functions, exponentially changing along the ribbons and having features on the edges of the ribbons. The parameters of the exponent describing the changes in current along the ribbon correspond to the excitation parameters. The feature of the current on the edges of the ribbon has power 
. Let’s write expressions for basis functions of the current:
— for ribbons parallel to the X axis:
 |
(4) |
— for ribbons parallel to the Y axis:
 |
(5) |
Solution for the diffraction problem in this configuration consists of determining the amplitudes of the basis functions of the current and then determining the scattered field. To determine the amplitudes of the basis current functions, we shall use the power balance equation, which in our case can be written as follows:
 |
(6) |
where 
, S is the surface, which includes elements with unknown currents; Pr is the power on the inputs of receiving modules. Using the thin plane approximation [1], transform (6) to the following:
 |
(7) |
To determine 
we shall use the Green tensor function representation for the space waveguide with planelayer dielectric filler. By integrating (7), we get the quadratic form, which is then reduced to the system of linear algebraic equations relative to the amplitudes of basis functions of the current
 |
(8) |
where Zij is the mutual resistance of basis functions with numbers i and j.
We shall designate the basis current function paralles to the X axis “belongs to the X class” and the basis current function parallel to the Y axis “belongs to the Y class”. For mutual resistances Zij the following expressions are valid:
 |
(9а) |
 |
(9б) |
 |
(9в) |
 |
(9г) |
where
