##### Abstract

The prediction of the interaction of objects with electromagnetic waves is important in the design, production and testing processes in engineering. Method of Moments (MoM) can be used to analyze behavior of complex structures. First of all, geometry of the structure is discretized in this method and then basis functions are defined on the geometry. Final step is to test the integrals via test functions. As a result, these methods find the solution of the Maxwell equations on the structure. Electromagnetic waves on the structure and Radar Cross Section (RCS) calculations can be done with solutions of Maxwell equations. If it is required to find the solutions of the equations for several frequencies, this method is applied for each frequency. Time and memory requirements are high if the investigated structure is complex; the number of discretization elements is high or the number of analysis frequencies increases.
Elements that discretize the structure can be grouped as volume and surface elements. It is already shown that Shifted Frequency Internal Equivalence (SFIE) principle can use the volume components of impedance matrix at a frequency for another one with some basic algebraic manipulations. Therefore, increasing the ratio of the volume components would also increase the efficiency of SFIE method. In addition, SFIE is more advantageous if the number of frequencies increases.
This thesis investigates the performance of SFIE method in homogeneous and non-homogeneous lossy media. The aim is to widen the area that SFIE can be used and to make SFIE closer to real modeling. Imaginary component of electrical permittivity in dielectric media affects conductivity hence loss in structure. Changing loss coefficient changes the distribution of electromagnetic waves and this modifies RCS plots.
In this thesis, an imaginary electrical permittivity coefficient is defined and skin effect phenomenon is studied for different parameters. Afterwards, wide band study is done where SFIE is advantageous. In wide band studies differences between MOM and SFIE are calculated with respect to observation angle and frequency for RCS, and difference plots regarding frequency are drawn for electromagnetic waves. Finally; to be able to show distribution of differences on the structure, difference between MOM and SFIE results of each discretizing element is calculated. Then effect of frequency, conductivity and size of the structure on difference is shown.