Rand Muaffaq Hadi

DOI: https://doi.org/10.5281/zenodo.24200434

Operating a substrate integrated waveguide (SIW) only above the cutoff of its dominant mode leads to bulky filters in the low-gigahertz range. In this work, a space-filling I–H slot is etched on the upper wall of an SIW so that transmission is obtained inside the evanescent band of the guide. The slot acts as a magnetic-dipole resonator; together with the negative effective permittivity of the guide below cutoff, it creates a backward-wave band followed directly by a forward-wave band. Slots of first, second and third order are compared inside an identical footprint, the effective permittivity and permeability are extracted from the simulated scattering parameters, and a lumped-element model with analytical expressions for the lower transmission zero and both resonant modes is fitted to the full-wave response. For the third-order slot on FR4 (εᵣ = 4.3), the passband is located near 2.15 GHz, roughly 59% lower than the 5.2 GHz cutoff of the unloaded guide. A fabricated single-cell filter measures about 1.5 dB insertion loss including the SMA connectors, about 19 dB return loss, two transmission zeros and a board area of 17 × 17 mm² (0.12λ₀ × 0.12λ₀). Cascaded two- and three-cell designs with steeper skirts are also reported and compared with recent SIW fractal and metamaterial filters.

SIW filter; below-cutoff propagation; space-filling slot; double-negative medium; lumped-element model; compact bandpass filter

A space-filling I–H slot etched on the broad wall of an SIW has been shown to open a usable passband deep inside the evanescent band of the guide. Increasing the slot order within the same area lowers the passband from about 4.1 GHz to 2.15 GHz, which is roughly 59% below the cutoff of the unloaded waveguide. The extracted constitutive parameters and the dispersion curves reveal a backward-wave band immediately followed by a forward-wave band, and a compact lumped-element model reproduces the lower transmission zero and both resonant modes while linking each of them to a physical dimension. The measured single-cell filter on FR4 provides about 1.5 dB insertion loss, about 19 dB return loss, an almost linear in-band phase and a footprint of 0.12λ0×0.12λ0; cascading two or three cells sharpens the skirts considerably. Low-loss laminates and electronically tunable slot loadings will be investigated next.

[1] M. Bozzi, A. Georgiadis, and K. Wu. Review of substrate-integrated waveguide circuits and antennas. IET Microwaves, Antennas & Propagation, 5(8):909–920, 2011.
[2] D. Deslandes and K. Wu. Accurate modeling, wave mechanisms, and design considerations of a substrate integrated waveguide. IEEE Transactions on Microwave Theory and Techniques, 54(6):2516–2526, 2006.
[3] A. Iqbal, J. J. Tiang, S. K. Wong, M. Alibakhshikenari, F. Falcone, and E. Limiti. Miniaturization trends in substrate integrated waveguide (SIW) filters: A review. IEEE Access, 8:223287–223305, 2020.
[4] W. Che, C. Li, D. Zhang, and Y. L. Chow. Investigations on propagation and the band broadening effect of ridged rectangular waveguide integrated in a multilayer dielectric substrate. IET Microwaves, Antennas & Propagation, 4(6):674–684, 2010.
[5] R. Kumar and S. N. Singh. Design and analysis of ridge substrate integrated waveguide bandpass filter with octagonal complementary split ring resonator for suppression of higher order harmonics. Progress In Electromagnetics Research C, 89:87–99, 2019.
[6] Q. Lai, C. Fumeaux, W. Hong, and R. Vahldieck. Characterization of the propagation properties of the half-mode substrate integrated waveguide. IEEE Transactions on Microwave Theory and Techniques, 57(8):1996–2004, 2009.
[7] Y. Wang, W. Hong, Y. Dong, B. Liu, H. Tang, J. Chen, X. Yin, and K. Wu. Half mode substrate integrated waveguide (HMSIW) bandpass filter. IEEE Microwave and Wireless Components Letters, 17(4):265–267, 2007.
[8] X. L. Huang, L. Zhou, M. Völkel, A. Hagelauer, J. F. Mao, and R. Weigel. Design of a novel quarter-mode substrate-integrated waveguide filter with multiple transmission zeros and higher mode suppressions. IEEE Transactions on Microwave Theory and Techniques, 66(12):5573–5584, 2018.
[9] R. Asgharivaskasi, V. Mashayekhi, N. Azadi-Tinat, and M. Koohestani. Ultra-compact quad-band half-mode SIW bandpass filter for sub-6 GHz 5G applications. Scientific Reports, 15:30077, 2025.
[10] R. Moro, S. Moscato, M. Bozzi, and L. Perregrini. Substrate integrated folded waveguide filter with out-of-band rejection controlled by resonant-mode suppression. IEEE Microwave and Wireless Components Letters, 25(4):214–216, 2015.
[11] A. Parameswaran, P. Athira, and S. Raghavan. Miniaturizing SIW filters with slow wave technique. AEU – International Journal of Electronics and Communications, 84:360–365, 2018.
[12] D. F. Guan, P. You, Q. Zhang, Z. B. Yang, H. Liu, and S. W. Yong. Slow-wave half-mode substrate integrated waveguide using spoof surface plasmon polariton structure. IEEE Transactions on Microwave Theory and Techniques, 66(6):2946–2952, 2018.
[13] V. G. Veselago. The electrodynamics of substances with simultaneously negative values of ε and μ. Soviet Physics Uspekhi, 10(4):509–514, 1968.
[14] I. Gil, J. Bonache, J. García-García, F. Falcone, and F. Martín. Metamaterials in microstrip technology for filter applications. In IEEE Antennas and Propagation Society International Symposium, volume 1A, pages 668–671, 2005.
[15] R. Marqués, J. Martel, F. Mesa, and F. Medina. Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides. Physical Review Letters, 89(18):183901, 2002.
[16] F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla. Babinet principle applied to the design of metasurfaces and metamaterials. Physical Review Letters, 93(19):197401, 2004.
[17] F. Falcone, T. Lopetegi, J. D. Baena, R. Marqués, F. Martín, and M. Sorolla. Effective negative-ε stopband microstrip lines based on complementary split ring resonators. IEEE Microwave and Wireless Components Letters, 14(6):280–282, 2004.
[18] Y. D. Dong, T. Yang, and T. Itoh. Substrate integrated waveguide loaded by complementary split-ring resonators and its applications to miniaturized waveguide filters. IEEE Transactions on Microwave Theory and Techniques, 57(9):2211–2223, 2009.
[19] X. C. Zhang, Z. Y. Yu, and J. Xu. Novel band-pass substrate integrated waveguide (SIW) filter based on complementary split ring resonators (CSRRs). Progress In Electromagnetics Research, 72:39–46, 2007.
[20] W. Che, C. Li, K. Deng, and L. Yang. A novel bandpass filter based on complementary split rings resonators and substrate integrated waveguide. Microwave and Optical Technology Letters, 50(3), 2008.
[21] S. S. Karthikeyan and R. S. Kshetrimayum. Harmonic suppression of parallel coupled microstrip line bandpass filter using CSRR. Progress In Electromagnetics Research Letters, 7:193–201, 2009.
[22] Y. Dong and T. Itoh. Miniaturized substrate integrated waveguide slot antennas based on negative order resonance. IEEE Transactions on Antennas and Propagation, 58(12):3856–3864, 2010.
[23] Y. Dong and T. Itoh. Composite right/left-handed substrate integrated waveguide and half mode substrate integrated waveguide leaky-wave structures. IEEE Transactions on Antennas and Propagation, 59(3):767–775, 2011.
[24] M. Danaeian, K. Afrooz, and A. Hakimi. Miniaturization of substrate integrated waveguide filters using novel compact metamaterial unit-cells based on SIR technique. AEU – International Journal of Electronics and Communications, 84:62–73, 2018.
[25] G. Peano. Sur une courbe, qui remplit toute une aire plane. Mathematische Annalen, 36(1):157–160, 1890.
[26] J. Romeu and Y. Rahmat-Samii. Fractal FSS: A novel dual-band frequency selective surface. IEEE Transactions on Antennas and Propagation, 48(7):1097–1105, 2000.
[27] V. Sekar and K. Entesari. Miniaturized half-mode substrate integrated waveguide bandpass filters using cross-shaped fractals. In IEEE 12th Annual Wireless and Microwave Technology Conference (WAMICON), pages 1–4, Clearwater Beach, FL, USA, 2011.
[28] A. M. Hamzah, L. Audah, and N. Alkhafaji. H-shaped fractal slots based highly miniaturized substrate integrated waveguide metamaterial bandpass filters for C-band applications. Progress In Electromagnetics Research B, 86:139–158, 2020.
[29] N. Muchhal, A. Chakraborty, K. Vishnoi, and S. Srivastava. Miniaturized and selective half-mode substrate integrated waveguide bandpass filter using Hilbert fractal for sub-6 GHz 5G applications. IETE Journal of Research, 69(10), 2023. doi: 10.1080/03772063.2021.2021816.
[30] N. Muchhal, M. Elkhouly, R. Z. Vintimilla, A. Chakraborty, and S. Srivastava. Design of hybrid fractal integrated half mode SIW band pass filter with CSRR and Minkowski defected ground structure for sub-6 GHz 5G applications. Photonics, 9(12):898, 2022.
[31] R. M. Hadi. Miniaturized bandpass filter using the metamaterial half-mode technique for substrate integrated waveguide. International Journal of Computer Science Engineering Techniques, 10(5):281–286, 2026.
[32] D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Physical Review E, 71(3):036617, 2005.
[33] J.-S. Hong and M. J. Lancaster. Microstrip Filters for RF/Microwave Applications. John Wiley & Sons, New York, 2001.

Rand Muaffaq Hadi (2026). Compact Below-Cutoff Substrate Integrated Waveguide Bandpass Filters Based on Space-Filling I–H Slot Resonators. International Journal of Computer Science Engineering Techniques, 10(6), 460–466. ISSN: 2455-135X. DOI: https://doi.org/10.5281/zenodo.24200434