By Reinhold Pregla
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Additional info for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)
However, not the same this is when we compute the magnetic ﬁeld component Hy . Looking at eq. 10), we see that the operator z ][Et ] contains the expression εxy Ey to calculate Hy . Since the product [RE discretisation points are shifted in this case, we must ‘move’ the results of the product to obtain it at the correct position. For this purpose, we introduce 49 basic principles of the method of lines electric wall magnetic wall, ABC electric wall x magnetic wall, ABC electric wall 3 2 1 magnetic wall, ABC y E x , ε xx , ε yx H y , µ xy , µ yy E y , ε xy , ε yy H x , µ xx , µ yx E z , ε zz H z , µ zz HD 1 2 3 MMPL2100 Fig.
Usually the layers have equal width. However, it is also possible to model structures where the width of the layers is varied. This was ﬁrst described for the analysis of microstrip structures with ﬁnite metallisation thickness – . The transformation matrix partition technique was introduced there to describe the ﬁelds in the regions between the strips. In this section, the GTL equations will be adapted to be best suited for eigenmode calculation. For that reason, the transformation matrix partition technique will be generalised so that this technique can also be used for in homogeneous layers.
Eq. 63) If matrices QE,H have the form given in eqs. 64) From eq. 60), considering eq. 65) where Γh2 , ThE,H and Γe2 , Te are the eigenvalues/eigenvectors of QhE,H and Qe , respectively. 68) 2 For general matrices QE,H , the eigenvalues and eigenvectors ΓE,H and TE,H must be determined numerically. The general solution of eq. 69) What we would like to obtain from eq. 69) is a relation between the transverse electric and magnetic ﬁelds at interfaces A and B. In the generalised transmission line equations, the derivative of the transverse E ﬁeld 33 basic principles of the method of lines is proportional to the transverse H ﬁeld and vice versa.