R. Vahldieck

Accurate analysis of scattering from multiple waveguide discontinuities using the coupled-integral equations technique

A Coupled-Integral-Equations Technique (CIET) for the analysis of multiple discontinuities and bifurcations in rectangular waveguides is presented. A set of coupled integral equations for the tangential electric field over the planes of the discontinuities are derived and then solved by the moment method. Basis functions, which include the edge conditions and mirror images in the walls of the waveguide, are used to accelerate convergence of the numerical solution. One or two basis functions are sufficient to accurately determine the reflection and transmission properties of H-plane discontinuities and bifurcations. Reflection and transmission properties of N discontinuities are computed accurately from a single matrix of the order of 3N x 3N instead of cascading the individual generalized scattering matrices whose dimensions increase rapidly as the distances between the discontinuities decrease.

Edge-conditioned vector basis functions for the analysis and optimization of rectangular waveguide dual-mode filters

The reliable computer-aided design of narrowband dual-mode filters is usually hampered by extensive CPU-time and memory requirements of commercially available software packages. This paper introduces a new concept within the coupled-integral-equations-technique (CIET) which takes into account all edge conditions simultaneously and, therefore, permits the analysis and optimization of such filter components in a timely fashion. A 12.3 GHz four-pole dual-mode filter in rectangular waveguide is chosen as design example. Comparison with HPs HFSS shows good agreement, whereas the mode-matching technique (MMT) did not converge with up to 600 modes. The CIET routine converges with up to 23 edge-conditioned vector basis functions and up to 1750 modal summation terms. Due to its speed, the new approach can also be used for a Monte-Carlo-based tolerance analysis which shows a manufacturing accuracy of 0.02 mm for this critical dual-mode filter example.

Low-Insertion-Loss Fin-Line Filters for Millimetre-Wave Applications

A design theory is described for low-insertion-loss fin-line filters with fin-line gap widths over the total height of the waveguide housing. The theory includes both higher order mode propagation and the finite thicknesses of the dielectric and the metallic fins. An evolution strategy synthesis method yields optimum design data for three- and five resonator-type fin-line filters with several substrate thicknesses. The midband frequencies chosen are about 13, 34, 66, and 75 GHz. Measured minimum insertion-losses in the passband are about 0.2 dB (13 GHz), 0.5 dB (34 GHz), and 1.9 dB (65 GHz) for three-resonator-type filters as an example.

A combined mode-matching and coupled-integral-equations technique for the design of narrow-band H-plane waveguide diplexers

This paper focuses on a new concept in diplexer design, namely a combination of the standard mode-matching technique (MMT) with the coupled-integral-equations technique (CIET), the latter being used only for the synthesis and analysis of the individual channel filters. Several major advantages are associated with this approach. First, for a full-cycle analysis of a diplexer configuration, the combined method reduces the CPU time significantly compared to ordinary MMT. Secondly, the number of basis functions in the CIET can be reduced during optimization without a shift in frequency as matrix sizes do not depend on the number of modes. In standard MMT algorithms, a reduced number of modes is usually associated with a (sometimes remarkable) shift towards lower frequencies. Thirdly, the CIET-at almost no additional computational cost-allows the extraction of the generalized scattering matrix so that the results are easily interfaced with mode-matching calculations of other components.

Global edge-conditioned basis functions from local solutions of Maxwell's equations

A new set of edge-conditioned basis functions for the moment method solutions of electromagnetic problems is introduced. The basis functions are themselves solutions to the differential forms of Maxwells equations and satisfy the local boundary conditions at metallic wedges. Numerical results using this new set are presented and compared with available data for a ridged rectangular waveguide to demonstrate its adequacy. An efficient technique to compute integrals of rapidly oscillating and singular integrands is also presented.

Accurate analysis of periodic structures with an additional symmetry in the unit cell from classical matrix eigenvalues

Dispersion diagrams of periodic structures with an additional symmetry in the unit cell are investigated by the example of a parallel-plate waveguide loaded with irises of zero thickness. The propagation constants of the Floquet modes are determined from the classical eigenvalues of a non-Hermitian matrix.

Fast and efficient mode-matching analysis of ridged circular waveguide polarizers

A fast and efficient mode-matching technique is applied to the analysis and design of polarizer components in ridged circular waveguide technology. Two different structures (the septum polarizer and the longitudinal-ridge polarizer) are investigated with respect to the validity of approximating the rectangular-cross-section septa by conically shaped ridges in theory. Measurements of two different prototypes demonstrate, first, that the axial ratio response is not potentially critical to this approximation and, second, that some differences occur with respect to return loss and isolation performance, but that these difference have only been encountered beyond the 25 dB margin. A CPU time comparison with HFSS results in a ten-minutes-versus-three-hours advantage of the mode-matching technique.

A comparative study of two integral-equation formulations of TE modes in circular ridged waveguide

We present and compare two integral-equation formulations of the TE eigenvalue problem of a ridged circular waveguide. In the E-formulation, an integral equation for the tangential electric field Eo. is derived and solved by the moment method using basis functions which include the edge conditions. The H-formulation relies on an integral equation for the axial magnetic field Hz, which is also solved by the moment method and basis functions with edge conditions. Spurious roots are encountered in the E-formulation whereas the H-Formulation is free from spurious roots but requires larger matrices. Results from both formulations are compared with previously published data and analytic results for limiting cases, excellent agreement is demonstrated.

Scattering properties of asymmetric rectangular iris in a circular waveguide using edge-conditioned basis functions

The scattering properties of asymmetric rectangular irises in circular waveguides are accurately determined from an integral equation formulation using basis functions which include the edge conditions. The inclusion of the edge conditions results in a reduction of the size of the matrix as compared to the standard mode-matching technique. Numerical results are presented and compared with previously published data and measurements to demonstrate the accuracy of the approach.

Accurate solution of waveguide model of microstrip discontinuity with the use of basis functions with edge conditions

The problem of scattering from a microstrip step discontinuity is analyzed by an integral equation technique with the use of basis functions that include the edge conditions. The presence of magnetic walls in the waveguide model of the microstrip line makes it more convenient to expand the tangential magnetic field at the interface, instead of the tangential electric field as in the case of metallic waveguides. The problem of relative convergence is not encountered as the modes of the two waveguides enter only in the computation of the inner products that are tested for convergence. Results for the reflection coefficient and the magnetic field at the interface are presented and compared with available data to demonstrate the accuracy and efficiency of the approach.