Analysis of Electromagnetic Fields and Waves: The Method of by Reinhold Pregla

By Reinhold Pregla

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Example text

The matrices RE and RH are symmetric (but not Hermitian in the case of complex elements): RE,H = RtE,H . Therefore, we have QH = QEt , which is also true for the submatrices. 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.

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. [7]), 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.

The chosen position of the plane is arbitrary. Therefore, the eigenmode connected with any plane can be calculated correctly. If we formulate the eigenvalue problem for the field in plane B of Fig. 13, we can determine the mode for the slot in this plane. It is clear that the strips in the neighbouring interfaces have an influence on this mode. However, this influence must be considered in a proper way. The computation of the field distribution is a difficult numerical task. It will be shown how this problem can be solved in an accurate way.

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