Generalized integral operators for unifying 2.5D AND 3D electromagnetic modeling of microwave composite structures by the method of moments


Аuthors

Klyukin D. V.*, Slobodyanenko A. A.**, Kuksenko S. P.***

Tomsk State University of Control Systems and Radioelectronics, 40, Lenin str., Tomsk, 634050, Russia

*e-mail: dmitrii.v.kliukin@tusur.ru
**e-mail: sepwood@gmail.com
***e-mail: sergei.p.kuksenko@tusur.ru

Abstract

Microwave devices are used a lot in the field of aerospace engineering. They are used in complex composite structures (for example, high-speed interconnects on printed circuit boards, microwave integrated circuits, scattering objects and antenna arrays). The characteristics of these structures are largely determined by their geometry and material properties. Designing such devices relies heavily on electromagnetic simulation based on numerical methods. Among these, the method of moments (MoM) is widely used, since it reduces systems of integro-differential equations to systems of linear algebraic equations. In practice, two main MoM-based approaches are employed: so-called 2.5D formulations for planar multilayer structures, and fully 3D formulations for arbitrary three-dimensional geometries. For three-dimensional composite structures, we use the EFIE–PMCHWT (Poggio–Miller–Chang–Harrington–Wu–Tsai) formulation, which combines electric- and magnetic-field integral equations for conducting and dielectric regions. For planar multilayer configurations, we employ mixed-potential integral equations (MPIE) with dyadic Green’s functions tailored to layered media. We present the results of the generalization of integral operators, which allow the unification of 2.5D and 3D approaches to the electrodynamic modeling of composite structures using the method of moments. The unified formulation is validated on three representative examples: a microstrip transmission line, an inductive coil, and a low-pass filter. For each structure, S-parameters computed with the generalized operator framework are compared against reference results obtained from independent commercial electromagnetic software. The simulated responses exhibit the expected frequency behavior and show good agreement with the external data over the operating bands. These results confirm the correctness of the proposed unified approach and demonstrate its suitability for implementation in computer-aided design tools for the analysis and optimization of composite microwave structures.

Keywords:

computational electrodynamics; method of moments; EFIE; MFIE; EFIE-PMCHWT; MPIE

References

  1. Gadzhiev E. V. Elektronnyi zhurnal «Trudy MAI», 2014, no. 76, available at: https://trudymai.ru/published.php?ID=50113 (accessed 15.01.2026).
  2. Ovchinnikova E. V., Rybakov A. M. Elektronnyi zhurnal «Trudy MAI», 2012, no. 52, available at: https://trudymai.ru/published.php?ID=29558 (accessed 15.01.2026).
  3. Azarov A. V. et al. Elektronnyi zhurnal «Trudy MAI», 2023, no. 128, available at: https://trudymai.ru/published.php?ID=171392 (accessed 15.01.2026).
  4. Surovtsev R. S., Gazizov T. R. Elektronnyi zhurnal «Trudy MAI», 2015, no. 83, available at: https://trudymai.ru/published.php?ID=62204 (accessed 15.01.2026).
  5. Balanis C. A. Advanced Engineering Electromagnetics, 2nd ed., John Wiley & Sons, New York, 2012, 1045 p.
  6. Kozlov K. V., Volkov A. P., Starovoytov E. I., Popov E. V. Elektronnyi zhurnal «Trudy MAI», 2022, no. 122, available at: https://trudymai.ru/published.php?ID=164200  (accessed 06.12.2025).
  7. Denisenko D. V. Elektronnyi zhurnal «Trudy MAI», 2014, no. 73, available at: https://trudymai.ru/published.php?ID=48568  (accessed 06.12.2025).
  8. Grigor'ev A. D. Metody vychislitel'noi elektrodinamiki (Methods of Computational Electrodynamics), Moscow, Fizmatlit, 2013, 430 p.
  9. Makarov S. N. Antenna and EM Modeling with MATLAB, John Wiley & Sons, New York, 2002, 288 p.
  10. Gibson W.C. The Method of Moments in Electromagnetics, Chapman & Hall/CRC, Boca Raton, 2008, 272 p.
  11. Yla-Oijala P., Taskinen M., Sarvas J. Surface integral equation method for general composite metallic and dielectric structures with junctions. Progress in Electromagnetics Research. 2005, vol. 52, pp. 81–108.
  12. Michalski K. A., Zheng D. Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory, IEEE Transactions on Antennas and Propagation, 2002, vol. 38, no. 3, pp. 335–344.
  13. Rao S., Wilton D., Glisson A. Electromagnetic scattering by surfaces of arbitrary shape, IEEE Transactions on Antennas and Propagation, 1982, vol. 30, no. 3, pp. 409–418.
  14. Umashankar K., Taflove A., Rao S.M. Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric bodies. IEEE Transactions on Antennas and Propagation. 1986, vol. 34, pp. 758–766.
  15. Rao M., Cha C.C., Cravey R.L., Wilkes D.L. Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness. IEEE Transactions on Antennas and Propagation. 1991, vol. 39, pp. 627–631.
  16. Michalski K.A. The mixed-potential electric field integral equation for objects in layered media. Arch. Elektr. Ubertragung. 1985, vol. 39, pp. 317–322.
  17. Michalski K.A., Mosig J.R. Multilayered media Green's functions in integral equation formulations. IEEE Transactions on Antennas and Propagation. 2002, vol. 45, no. 3, pp. 508–519.
  18. Pan S. Modelling of Interconnects in 3DIC Based on Layered Green's Functions. Missouri University of Science and Technology, 2015.
  19. Simsek E., Liu Q.H., Wei B. Singularity subtraction for evaluation of Green's functions for multilayer media. IEEE Transactions on Microwave Theory and Techniques. 2006, vol. 54, no. 1, pp. 216–225.
  20. Ling F., Jin J.M. Discrete complex image method for Green's functions of general multilayer media. IEEE Microwave and Guided Wave Letters. 2000, vol. 10, no. 10, pp. 400–402.
  21. Aksun M.I. A robust approach for the derivation of closed-form Green's functions. IEEE Transactions on Microwave Theory and Techniques. 2002, vol. 44, no. 5, pp. 651–658.
  22. Kipp R.A., Chan C.H. Complex image method for sources in bounded regions of multilayer structures. IEEE Transactions on Microwave Theory and Techniques. 2002, vol. 42, no. 5, pp. 860–865.
  23. Hua Y., Sarkar T.K. Generalized pencil-of-function method for extracting poles of an EM system from its transient response. IEEE Transactions on Antennas and Propagation. 1989, vol. 37, no. 2, pp. 229–234.
  24. Medgyesi-Mitschang L.N., Putnam J.M., Gedera M.B. Generalized method of moments for three-dimensional penetrable scatterers //Journal of the Optical Society of America A. – 1994. – Т. 11. – №. 4. – С. 1383-1398.
  25. Klyukin D. V., Mochalov D. M., Kuksenko S. P. Doklady TUSUR, 2024, vol. 27, no. 1, pp. 23–34, available at: https://journal.tusur.ru/ru/arhiv/1-2024/o-sposobah-vychisleniya-poverhnostnyh-singulyarnyh-integral... (accessed 06.12.2025).
  26. Klyukin D. V. Doklady TUSUR, 2024, vol. 27, no. 4, pp. 13–22, available at: https://journal.tusur.ru/ru/arhiv/4-2024/ob-ispolzovanii-kvadratur-gaussa-v-vychislenii-poverhnostny... (accessed 06.12.2025).


Download

mai.ru — informational site MAI

Copyright © 2000-2026 by MAI

 Вход