WIAS Preprint No. 543, (1999)

On the Computation of Eigen Modes for Lossy Microwave Transmission Lines Including Perfectly Matched Layer Boundary Conditions


  • Hebermehl, Georg
  • Heinrich, Wolfgang
  • Hübner, Friedrich-Karl
  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301
  • Tischler, Thorsten
  • Zscheile, Horst

2010 Mathematics Subject Classification

  • 35Q60 65F15 65N22


  • Microwave device simulation, Maxwellian equations, PML boundary condition, finite-volume method, eigenvalue problem




Design of microwave circuits requires detailed knowledge on the electromagnetic properties of the transmission lines used. This can be obtained by applying the Maxwellian equations to a longitudinally homogeneous waveguide structure, which results in an eigenvalue problem for the propagation constant. Using a finite-volume approach we get an algebraic formulation. In the presence of losses or absorbing boundary conditions its system matrix is complex. A method is presented which avoids the computation of all eigenvalues to find the few propagating modes one is interested in. Special attention is paid to the so-called Perfectly Matched Layer boundary conditions.

Appeared in

  • COMPEL, Vol. 20 (2001), No. 4, pp. 948-964

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