# Galerkin's Spectral Method in the Analysis of Antenna Wall Operation
## 6 Conclusions  
Printed antennas have been some of the most innovative areas of antenna technology for a dozen or so years. They are increasingly used in antenna arrays. However, the dielectric substrate used promotes the excitation of surface waves, which, propagating along the dielectric plane, disrupts the normal operation of the antenna. Therefore, an important issue is the choice of method for their analysis. Among the methods of analyzing microstrip antennas, the method of integral equations is considered to be the most accurate. Commonly used methods for constructing approximate solutions of antenna theory equations are direct methods, consisting in reducing an integral equation or a system of integral equations to a system of linear algebraic equations. Many methods of algebraization are known, with the vast majority being, in fact, different variants of one general scheme, which in the technical literature has been assumed, following [PERSON], to be called the method of moments. The method of moments offers many effective computer-implementable algorithms for solving integral equations, which is why it quickly became almost mandatory in solving problems of radiation and diffraction of electromagnetic waves on thin wires, and phenomena related to antenna radiation and coupling between them. Planar, multilayer, periodic dielectric structures are currently widely used in millimeter and microwave antenna technology, mainly due to their frequency and polarization selectivity properties. Antenna arrays most often consist of repeating metal radiation elements placed on or buried in a dielectric multilayer medium. Changes in the size and shape of individual antenna elements enable effective modeling of its spectral characteristics; these changes can be additionally modeled by selecting geometric and physical parameters of the dielectric layered substrate and coating. Generalized spectral analysis of the unconstrained antenna case is particularly convenient when using the window function due to the full Floquet harmonic system used in solving the problem. The proposed sequence of successive solution steps should lead to a strictly numerically convergent solution. According to the procedure given above, it is practically necessary to determine partial and global transmission matrices in order to determine the scattering matrix. In the case of specific antenna structures, various modifications of the above analysis are used to obtain faster convergence of the applied numerical procedure and to reduce the requirements of the memory capacity used by the numerical program. The selection of the number of K harmonic cutoffs included in the numerical calculations and their order in the field distribution series, is extremely important from the point of view of the effectiveness and accuracy of the procedure. The presented procedure for solving the scattering of the electromagnetic field on the antenna system is an original solution.  
This research was funded by Military University of Technology University Research Grant No.051/2025.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The author declare no conflict of interest.