Topic description

The numerical simulation of electrically large structures (structure significantly larger than the electromagnetic wavelength) remains a significant computational challenge, particularly for particle accelerator components. Particle accelerators usually consist of long chains of radio-frequency (RF) cavities. The electromagnetic characterisation of the cavity chains is essential for the design phase and during operation. While finite element methods (FEM) allow for the calculation of fields within individual components, directly simulating entire resonator chains is often very difficult due to the enormous number of degrees of freedom required.

The Chair of Electromagnetic Field Theory is developing a computational scheme that combines Model-Order Reduction (MOR) [1] with concatenation to enable efficient electromagnetic simulation of large electromagnetic structures. Implemented within the NGSolve finite element libraries [2], this approach reduces models of individual segments to compact state-space representations and then couples these reduced models at their internal ports by enforcing field continuity conditions. The result is a combined system that accurately captures the electromagnetic behavior of the complete structure while often requiring only a fraction of the computational resources needed for direct simulation.

The methodology builds upon the state-space concatenation (SSC) approach [3], previously implemented using the Finite Integration Technique (FIT), and extends it to high-order finite element discretisations within the NGSolve framework. Figure 1 illustrates different analysis options for single-segment and multi-segment assemblies.

As a simple application example, Figure 2 shows a two-cell pillbox cavity geometry. The two cells, highlighted in different colours, are initially treated as independent segments, each analysed and reduced separately before being concatenated into a single model. In this example, the first cell is reduced from 149,662 to 111 degrees of freedom, and the second from 146,948 to 110, both achieving reduction of degrees of freedom of three orders of magnitude. These reduced models are then coupled at their common facet through the concatenation procedure, yielding a combined system of just 218 degrees of freedom. A subsequent reduction step further reduces this to 202 degrees of freedom. Figure 3 compares the S-parameter magnitude and phase from these reduced models against reference results from CST Studio Suite, demonstrating excellent agreement across in the analysed frequency range.

The simulation framework is currently under active development, with planned capabilities including:

• Automatic port eigenmode computation
• Multimode network matrices
• Field reconstruction from reduced models
• Eigenfrequency analysis of concatenated structures

Literature

[1] T. Flisgen, J. Heller, T. Galek, L. Shi, N. Joshi, N. Baboi, R. M. Jones, and U. van Rienen, Eigenmode compendium of the third harmonic module of the European X-ray Free Electron Laser, Phys. Rev. Accel. Beams 20, 042002, 2017, doi: https://doi.org/10.1103/PhysRevAccelBeams.20.042002
[2] T. Wittig, R. Schuhmann, and T. Weiland, Model order reduction for large systems in computational electromagnetics, Linear algebra and its applications, vol. 415, no. 2-3, pp. 499-530, 2006
[3] J. Schöberl, C++ 11 implementation of finite elements in NGSolve, Institute for Analysis and Scientific Computing, Vienna University of Technology, 30, 2014, ngsolve.org/_static/ngs-cpp11.pdf

Topic description

Future wireless systems will utilise frequency ranges from 100 GHz to 1 THz and enable a wide range of applications, including sensor technology, imaging, high-data-rate communication and high-precision positioning. Due to their high speeds, compound semiconductor transistors based on indium phosphide are promising components for monolithically integrated electronic circuits in the above-mentioned applications.

Frequently considered properties of such transistors are their cut-off frequencies f_T und f_max. At these frequencies, the short-circuit current gain and unilateral power gain of the transistor are one. The cut-off frequencies are typically determined directly by scattering parameter measurements on the wafers for different bias points. Figure 1 shows a typical measurement setup. On-wafer scattering parameter measurements require suitable calibration methods with which the measured scattering parameters can be corrected and shifted to reference planes that are as close as possible to the transistor. Parasitic effects, such as unwanted coupling between measuring probes, the excitation of surface waves in the substrate, and unwanted coupling to neighbouring structures on the wafer, make it difficult to calibrate the scattering parameters. In particular, it is often not possible to reliably determine f_max.

Simulation studies are being conducted at the Chair of Electromagnetic Field Theory to determine the influence of these parasitic effects on the determination of the cut-off frequencies of the transistors. Figure 2 shows a typical 3D model that allows the calculation of electromagnetic fields on the on-wafer measuring station. Scattering parameters can then be derived from the simulated electromagnetic fields, which are calibrated as in the measurements. Such field simulations can significantly increase our understanding of parasitic effects. Furthermore, improved methods can be proposed and investigated that allow reliable determination of the transistor characteristics.

As part of the project, the Chair of Electromagnetic Field Theory is working closely with the Ferdinand Braun Institute, the Physikalisch-Technische Bundesanstalt and other European metrology institutes through the joint Lab Electromagnetic Fields.

Literature
[1] A. Kanitkar, R. Doerner, T. K. Johansen, W. Heinrich and T. Flisgen, On-Wafer 16-Term Calibration for Characterization of InP HBTs Featuring Sub-THz f_max, 55^th European Microwave Conference (EuMC), Utrecht, Netherlands, 2025, pp. 687-690, doi: 10.23919/EuMC65286.2025.11235132
[2] A. Kanitkar, R. Doerner, T. K. Johansen, W. Heinrich and T. Flisgen, Influence of On-Wafer Parasitic Effects on Mason’s Gain of Down-Scaled InP HBTs, 54^th European Microwave Conference (EuMC), Paris, France, 2024, pp. 252-255, doi: 10.23919/EuMC61614.2024.10732142
[3] A. Kanitkar, R. Doerner, T. K. Johansen, W. Heinrich and T. Flisgen, Mason’s Gain of Down-Scaled InP HBTs with Two-Setups: Effects of Probes and Frequency Extenders, 17^th German Microwave Conference (GeMiC), Karlsruhe, Germany, 2026 (zur Publikation angenommen)

Topic description

Catalysis is a central principle of chemistry in which a catalyst accelerates chemical reactions without undergoing any permanent chemical change. Catalysis forms the basis of numerous industrial processes – from the production of fertilisers and plastics to energy conversion. Understanding catalytic mechanisms makes it possible to develop more efficient, sustainable and economical chemical processes. Determining the material properties of catalysts plays a major role in this.

As part of the project, the Chair of Electromagnetic Field Theory is working closely with the Conductivity and Catalysis Lab (ConCat) at TU Berlin. The overall goal is to measure temperature-dependent electrical catalyst properties such as permittivity and dielectric loss angle using the apparatus shown in Figure 1. The central component is the copper-coloured cavity resonator at the top right. Its half cell is shown in Figure 2. With the aid of a network analyser connected to the resonator via the red coaxial cable, a large number of electromagnetic resonances can be excited and characterised in the resonator. The frequency and quality factor of each resonance depend on the materials present in the resonator. In addition, the material sample in the cavity resonator can be heated by hot gases flowing through the quartz glass tube shown.

As a very first approximation, the influence of the material samples on the resonance frequencies and quality factors can be estimated using analytical formulas. To better understand this influence, the Chair of Electromagnetic Field Theory performs numerical field calculations of the cavity resonator. Figure 3 shows a three-dimensional field model of the resonator (here with two ports for excitation) in cross-section. The figure shows the magnitude of the electric field of the TM₀₂₀-type resonance, which oscillates here at approximately 6.33 GHz. This resonance is particularly important for measuring material properties because it has high field energy in the area of the material sample (not shown).

The numerical field calculations performed enable a better understanding of the data measured at ConCat, so that the material parameters can ultimately be measured with greater reliability.

Literature
[1] M. Eichelbaum, R. Stößer, A. Karpov, C.-K. Dobner, F. Rosowski, A. Trunschkea und R. Schlögla, The microwave cavity perturbation technique for contact-free and in situ electrical conductivity measurements in catalysis and materials science, Phys. Chem. Chem. Phys., 2012, 14, 1302–1312, doi: 0.1039/c1cp23462e
[2] P. Kraus, E. H. Wolf, C. Prinz, G. Bellini, A. Trunschke und R. Schlögl, Towards automation of operando experiments: A case study in contactless conductivity measurements, Digital Discovery, 2022, 1, 241, doi: 10.1039/d1dd00029b