By Reinhold Pregla

ISBN-10: 0470033606

ISBN-13: 9780470033609

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Extra info for Analysis of Electromagnetic Fields and Waves: The Method of Lines (RSP)

Sample text

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 [14] and [15]. 5 are very close to those of the MoL. The differences between these and the results of [15] 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.

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