By Reinhold Pregla
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Extra info for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)
8). The ﬁeld vectors for the GTL equations are given by E = Ex and H = Hy . The third ﬁeld component ◦ is obtained from Ez = −jε−1 zz D x Hy . 30) Fig. 5 Solution of the GTL equations Unless otherwise stated, the formulas that we derive here are valid for the TE polarisation as well as for the TM case. 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 .
13). We see that the oﬀ-diagonal elements are zero. Therefore, we obtain two decoupled polarisations that can be treated independently. As usual in the MoL, the operators are now discretised with ﬁnite diﬀerences. The positions of the discretisation lines in a 2D-structure are shown in Fig. 8. As mentioned before, the fulﬁlment of the boundary conditions suggests determining the ﬁeld components on diﬀerent positions, which are shifted by half a discretisation distance. This is shown in Fig. 27 for a 2D-discretisation.
23 shows the MoL results for εre as a function of s/d, in comparison with those of  and . 5 are very close to those of the MoL. The diﬀerences between these and the results of  are much higher. 0 0 10 20 frequency (GHz) 30 40 MMPL4010 Fig. 0 0 a 5 10 frequency (GHz) 50 15 MMPL4020 0 b 5 10 frequency (GHz) 15 MMPL4030 Fig. 22 Dispersion diagram (a) and characteristic impedance (Reproduced by permission of Elsevier) (b) for the quasi-TEM mode in the groove guide of Fig. 20 (Reproduced by permission of Taylor & Francis) fast.
Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP) by Reinhold Pregla
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