F.M. Sibide1, S.N. Shabunin2, K. Burlakov3, M. Ghafourivayghan4

1-4 Institute of Radio Electronics and Information Technology, Ural Federal University n.a. the First President of Russia B.N. Yeltsin (Yekaterinburg, Russia)

1 sidibefousseny80@gmail.com; 2 s.n.shabunin@urfu.ru; 3 k.a.burlakov@urfu.ru; 4 mgafurivaigan@urfu.ru

This study presents a comprehensive investigation into novel computational methodologies for precise determination of characteristic impedance and propagation constant in multi-layer microstrip transmission line structures. The research addresses the growing complexity of modern microwave integrated circuits, which increasingly incorporate multiple dielectric layers with diverse electromagnetic properties to achieve enhanced performance characteristics. A streamlined analytical framework is developed to facilitate accurate characteristic impedance calculation in microstrip configurations incorporating arbitrary numbers of dielectric layers with varying electromagnetic material parameters, addressing a significant gap in existing analytical approaches for complex multi-layer structures. The proposed computational technique employs an innovative field formulation strategy that utilizes a single electric field vector component combined with average voltage computation, while maintaining rigorous consideration of complete transverse electromagnetic field components within a Cartesian coordinate system. This approach represents a significant advancement in computational efficiency without compromising analytical accuracy. Characteristic impedance derivation follows the fundamental voltage-current relationship established in transmission line theory, with voltage obtained through sophisticated numerical integration of electric field strength utilizing a strategically selected single vector component. Propagation constant determination employs a rigorous electrodynamic analysis framework through specialized Green's function formalism specifically adapted for stratified media configurations. The comprehensive methodological approach accommodates both shielded and unshielded microstrip geometries, including rectangular shielding enclosures that have become standard in contemporary microwave integrated circuit design. This flexibility ensures broad applicability across various practical engineering scenarios encountered in high-frequency circuit design. The heterogeneous cross-sectional architecture inherent to advanced microstrip structures is systematically incorporated through equivalent circuit models embedded within the Green's function formulation. Computational implementation was achieved through specialized algorithm development in the MATLAB environment, enabling universal propagation constant calculation across arbitrary substrate and overlay layer configurations while maintaining computational efficiency. Detailed analysis reveals substantial frequency-dependent behavior in microstrip parameters directly attributable to electromagnetic field distribution variations, providing valuable insights into dispersion characteristics of complex multi-layer structures. Extensive validation through comparative analysis with established computational tools demonstrates exceptional agreement, with characteristic impedance calculations achieving 1.5% accuracy and propagation constant determinations showing merely 0.36% deviation from conventional methods. The comprehensive methodology successfully accounts for all propagating modes within multi-layer transmission line structures, including protective overlay layers, and provides complete capability for full electromagnetic field characterization. The developed analytical framework demonstrates substantial potential for adaptation to related electromagnetic boundary value problems in microwave engineering and represents a significant contribution to the computational electromagnetics field. Finally, this study introduces a rigorous and efficient computational technique for microstrip analysis. It achieves an effective compromise between accuracy and practicality for complex, multilayer high-frequency circuits, and serves as a stepping stone for future advancements in electromagnetic modeling.

Sidibe F.M., Shabunin S.N., Burlakov K., Ghafourivayghan M. Methods for calculating characteristic impedance and propagation constant of microstrip line with multi-layer substrate. Radiotekhnika. 2026. V. 90. № 2. P. 158−170. DOI: https://doi.org/10.18127/j00338486-202602-16 (In Russian)

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