Analytical Techniques for Solving of Electromagnetics Problems

In this paper we consider electromagnetic problems occurring in modern theoretical and engineering researches and main analytical techniques for their solution. Based on Maxwell equations the wave equations of electromagnetic field components are derived in current research. The equations are obtained in a general form, which allows to take into account losses in the medium and two types of sources including charges and external currents. Wave equations are presented in the time domain. An equivalent technique is developed for the frequency domain. In this case the general electromagnetic problem was reduced to the solution of Helmholtz equations. Both types of Helmholtz equations were found theoretically, including homogeneous and inhomogeneous expressions. Formulated electromagnetic problems were solved by means of scalar and vector potentials. This method allows to take into account volume and surface distributions of charges and external currents. Presented in the paper general analytical techniques can be widely applied for solving of various mathematical problems occurring in the processes of electromagnetic waves propagation in dielectric media and radio engineering systems. As a result of applying the proposed method, a polarization device was developed. The output phase difference of the device is 90°±2.0°. Isolation of linear polarization on frequency does not fall below 32 dB. The maximum value of the ellipticity factor is 0.42 dB.