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Additional resources for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)
This is shown in Fig. 27 for a 2D-discretisation. Assuming ∂/∂y = 0, we see that the •- and the ✷-lines, respectively the ◦- and the ✸-lines, become identical. They become the straight (•- and ✷-lines) and dashed lines (◦- and ✸-lines) in Fig. 8. We then compute the corresponding ﬁeld components at the positions as stated below. Due to the discretisation, the operators become operator matrices and we combine the discretised ﬁelds in vectors. Then we obtain: • TEz modes with the components Ey , Hx , Hz computed on the bullets • in Fig.
Furthermore, when we come to describe the full 3D case we may use the same expressions. We would like to solve eq. 17). 32) Therefore the eqs. 19) show that the matrices QE and QH are determined as products of RE and RH . g. ), a product of two square matrices results in identical eigenvalues if the order of the product is reversed. Also, the corresponding 24 Analysis of Electromagnetic Fields and Waves eigenvectors are related. We will use this characteristic later. 35) In what follows, we show the steps of the analysis for the cases where we start with the electric or the magnetic ﬁeld in parallel.
109) from eq. 110). After solving this eigenvalue equation for EI , the current density S according to eq. 111) can be calculated. 2 The groove guide As a second example, the dispersion diagram and the characteristic impedance of the groove guide (Fig. 20) will be calculated. All layers are assumed homogeneous. Region I is smaller than the other regions II and III. The transformation matrix in region I is therefore of another size than the matrices of regions II and III. 113) V IIb Y II EA HA II III II III where EB = EB = EB .
Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP) by Reinhold Pregla