# An Empirical Formula for Resonant Frequency Shift due to Jerusalem-Cross FSS with Substrate on One Side

## Keywords:

Empirical formula, Jerusalem-cross frequency selective surface, least-square curve fitting, shifted resonant frequencies## Abstract

An empirical formula for calculating the shifted resonant frequencies of Jerusalem-cross frequency selective surfaces (FSSs) with different substrates is derived based on extensive calculations made on widely varying in shifted dual resonant frequencies for substrates with different relative dielectric constants and thickness. The coefficients in the empirical formula were determined by using least-square curve fitting technique to fit 672 sets of shifted resonant frequencies obtained by the HFSS simulator. Numerical results of shifted resonant frequencies obtained from the empirical formula are generally in good agreement with those calculated by the HFSS simulator and measurement. The average error in the shifted resonant frequencies is less than 5 percent. The empirical formula thus provides a simple, inexpensive, and quick method for obtaining optimum geometrical parameters of a dual-band Jerusalem-cross FSS with a substrate consisting of different dielectric constants and thickness for arbitrarily specifying two resonant frequencies.

## References

B. A. Munk, R. J. Luebbers, and R. D. Fulton, “Transmission through a 2-layer array of loaded slots,” IEEE Trans. Antennas Propagat., vol. AP22, no. 6, pp. 804-809, Nov. 1974.

M. A. Hiranandani, A. B. Yakovlev, and A. A. Kishk, “Artificial magnetic conductors realized by frequency-selective surfaces on a grounded dielectric slab for antenna applications,” IEE Pro.- Microw. Antennas Propagat., vol. 153, no. 5, pp. 487-493, Oct. 2006.

F. Yang and Y. Rahmat-Samii, “Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications,” IEEE Trans. Antennas Propagat., vol. 51, no. 10, pp. 2691-2703, Oct. 2003.

J. Liang and H. Y. David Yang, “Radiation characteristics of a microstrip patch over an electromagnetic bandgap surface,” IEEE Trans. Antennas Propagat., vol. 55, no. 6, pp. 1691-1697, June 2007.

D. Sievenpiper, L. Zhang, R. F. Jimenez Broas, N. G. Alex´opolous, and E. Yablonovitch, “Highimpedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech., vol. 47, no. 11, pp. 2059-2074, Nov. 1999.

Y. Zhang, J. von Hagen, M. Younis, C. Fischer, and W. Wiesbeck, “Planar artificial magnetic conductors and patch antennas,” IEEE Trans. Antennas Propagat., vol. 51, no. 10, pp. 2704-2712, Oct. 2003.

X. L. Bao, G. Ruvio, M. J. Ammann, and M. John, “A novel GPS patch antenna on a fractal hiimpedance surface substrate,” IEEE Antennas Wireless Propagat. Lett., vol. 5, pp. 323-326, 2006.

H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propagat., vol. 52, no. 9, pp. 2403-2414, Sep. 2004.

R. F. J. Broas, D. F. Sievenpiper, and E. Yablonovitch, “A high-impedance ground plane applied to a cellphone handset geometry,” IEEE Trans. Microw. Theory Tech., vol. 49, no. 7, pp. 1262-1265, July 2001.

A. P. Feresidis, G. Goussetis, S. Wang, and J. C. Vardaxoglou, “Artificial magnetic conductor surfaces and their application to low-profile highgain planar antennas,” IEEE Trans. Antennas Propagat., vol. 53, no. 1, pp. 209-215, Jan. 2005.

H. Li, S. Khan, J. Liu, and S. He, “Parametric analysis of Sierpinski-like fractal patch antenna for compact and dual band WLAN applications,” Microw. Opt. Technol. Lett., vol. 51, no. 1, pp. 36- 40, Jan. 2009.

M. Hosseini and S. Bashir, “A novel circularly polarized antenna based on an artificial ground plane,” Progress Electromagn. Research Lett., vol. 5, pp. 13-22, 2008.

H.Y. Chen and Y. Tao, “Bandwidth enhancement of a U-Slot patch antenna using dual-band frequency selective surface with double rectangular ring elements,” Microw. Opt. Technol. Lett., vol. 53, no. 7, pp. 1547-1553, July 2011.

H. Y. Chen and Y. Tao, “Performance improvement of a U-slot patch antenna using a dual-band frequency selective surface with modified Jerusalem cross elements,” IEEE Trans. Antennas Propagat., vol. 59, no. 9, pp. 3482-3486, Sep. 2011.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys., vol. 7, no. 1, pp. 37-50, 1967.

M. Philippakis, C. Martel, D. Kemp, M. C. S. M. R. Allan, S. Appleton, W. Damerell, C. Burton, and E. A. Parker, “Application of FSS structures to selectively control the propagation of signals into and out of buildings,” ERA Technology, Leatherhead, Surrey, U.K., Tech. Rep., 2004.

M. Gustafsson, A. Karlsson, A. P. P. Rebelo, and B. Widenberg, “Design of frequency selective windows for improved indoor outdoor communication,” IEEE Trans. Antennas Propagat., vol. 54, no. 6, pp. 1897-1900, June 2006.

G. I. Kiani, L. G. Osslon, A. Karlsson, and K. P. Esselle, “Transmission of infrared and visible wavelengths through energy-saving glass due to etching of frequency-selective surfaces,” IET Microw. Antennas Propagat., vol. 4, pp. 955-961, 2010.

G. I. Kiani, L. G. Osslon, A. Karlsson, K. P. Esselle, and M. Nilsson, “Cross-dipole bandpass frequency selective surface for energy-saving glass used in building,” IEEE Trans. Antennas Propagat., vol. 59, no. 2, pp. 520-525, Feb. 2011.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. J. Wilhelm, “The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces,” IEEE Trans. Antennas Propagat., vol. 53, no. 1, pp. 8-17, Jan. 2005.

J. McVay, N. Engheta, and A. Hoorfar, “High impedance metamaterial surfaces using Hilbertcurve inclusions,” IEEE Microw. Wireless Compon. Lett., vol. 14, pp. 130-132, 2004.

J. Bell and M. Iskander, “A low-profile archimedean spiral antenna using an EBG ground plane,” IEEE Antennas Wireless Propagat. Lett., vol. 3, pp. 223-226, 2004.

F. Costa, S. Genovesi, and A. Monorchio, “On the bandwidth of high-impedence frequency selective surfaces,” IEEE Antennas Wireless Propagat. Lett., vol. 8, pp. 1341-1344, 2009.

R. Mittra, C. H Chan, and T. Cwik, “Techniques for analyzing frequency selective surfaces - A review,” Pro. IEEE, vol. 76, no. 12, pp. 1593-1615, Dec. 1988.

B. A. Munk, Frequency Selective Surfaces - Theory and Design. John Wiley & Sons, Inc., New York, 2000.

R. Dickie, R. Cahill, H. Gamble, V. Fusco, M. Henry, M. Oldfield, P. Huggard, P. Howard, N. Grant, Y. Munro, and P. de Maagt, “Submillimeter wave frequency selective surface with polarization independent spectral responses,” IEEE Trans. Antennas Propagat., vol. 57, no. 7, pp. 1985-1994, July 2009.

F. R. Yang, K. P. Ma, Y. Qian, and T. Itoh, “A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuits,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 8, pp. 1509-1514, Aug. 1999.

C. N. Chiu, C. H. Kuo, and M. S. Lin, “Bandpass shielding enclosure design using multipole-slot arrays for modern portable digital devices,” IEEE Trans. Electromagn. Compat., vol. 50, no. 4, pp. 895-904, Nov. 2008.

M. S. Zhang, Y. S. Li, C. Jia, and L. P. Li, “Signal integrity analysis of the traces in electromagneticbandgap structure in high-speed printed circuit boards and packages,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 5, pp. 1054-1062, Nov. 2007.

K. Sarabandi and N. Behdad, “A frequency selective surface with miniaturized elements,” IEEE Trans. Antennas Propagat., vol. 55, no. 5, pp. 1239-1245, May 2007.

T. Kamgaing and O. M. Ramahi, “Design and modeling of high-impedance electromagnetic surfaces for switching noise suppression in power planes,” IEEE Trans. Electromagn. Compat., vol. 47, no. 3, pp. 479-489, Aug. 2005.

T. K. Wu and S. W. Lee, “Multiband frequency selective surface with multiring patch elements,” IEEE Trans. Antennas Propagat., vol. 42, no. 11, pp. 1484-1490, Nov. 1994.

T. K. Wu, “Four-band frequency selective surface with double-square-loop patch elements,” IEEE Trans. Antennas Propagat., vol. 42, no. 12, pp. 1659-1663, Dec. 1994.

H. L. Liu, K. L. Ford, and R. J. Langley, “Design methodology for a miniaturized frequency selective surface using lumped reactive components,” IEEE Trans. Antennas Propagat., vol. 57, no. 9, pp. 2732-2738, Sep. 2009.

R. R. Xu, H. C. Zhao, Z. Y. Zong, and W. Wu, “Dual-Band capacitive loaded frequency selective surfaces with close band spacing,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 12, Dec. 2008.

G. I. Kiani, K. L. Ford, K. P. Esselle, A. R. Weily, C. Panagamuwa, and J. C. Batchelor, “Single-layer bandpass active frequency selective surface,” Microw. Opt. Technol. Lett., vol. 50, no. 8, pp. 2149-2151 Aug. 2008.

G. I. Kiani, K. L. Ford, K. P. Esselle, A. R. Weily, and C. J. Panagamuwa, “Oblique incidence performance of a novel frequency selective surface absorber,” IEEE Trans. Antennas Propagat., vol. 55, no. 10, pp. 2931-2934, Oct. 2007.

B. A. Munk, P. Munk, and J. Pryor, “On designing Jaumann and circuit analog absorbers (CA absorbers) for oblique angle of incidence,” IEEE Trans. Antennas Propagat., vol. 55, no. 1, pp. 186-193, Jan. 2007.

A. K. Zadeh and A. Karlsson, “Capacitive circuit method for fast and efficient design of wideband radar absorbers,” IEEE Trans. Antennas Propagat., vol. 57, no. 8, pp. 2307-2314, Aug. 2009.

A. Itou, O. Hashimoto, H. Yokokawa, and K. Sumi, “A fundamental study of a thin wave absorber using FSS technology,” Electron. Commun. Jpn., vol. 87, pt. 1, pp. 77-86, 2004.

A. Itou, H. Ebara, H. Nakajima, K. Wada, and O. Hashimoto, “An experimental study of a wave absorber using a frequency-selective surface,” Microw. Opt. Technol. Lett., vol. 28, pp. 321-323, 2001.

G. I. Kiani, A. R. Weily, and K. P. Esselle, “A novel absorb/transmit FSS for secure indoor wireless networks with reduced multipath fading,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 378-380,2006.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations. Hoboken/ Piscataway, NJ: Wiley-IEEE Press, 2006.

R. Baggen, M. Martinez-Vazquez, J. Leiss, and S. Holzwarth, “Comparison of EBG substrates with and without vias for GALILEO/GPS applications,” In Proc. EuCAP 2007, 2nd European Conf. Antennas Propagat., Edinburgh, UK, 2007.

Y. Fan, B. L. Ooi, H. D. Hriston, and M. S. Leong, “Compound diffractive lens consisting of Fresnel zone plate and frequency selective screen,” IEEE Trans. Antennas Propagat., vol. 58, no. 6, pp. 1842-1847, June 2010.

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary-condition in the finitedifference time-domain algorithm for FSS structures,” IEEE Trans. Antennas Propagat., vol. 42, no. 9, pp. 1317-1324, Sep. 1994.

J. L. Volakis, T. Ozdemir, and J. Gong, “Hybrid finite-element methodologies for antennas and scattering,” IEEE Trans. Antennas Propagat., vol. 45, no. 3, pp. 493-507, Mar. 1997.

T. W. Leonard and J. W. Cofer, “A new equivalent circuit representation for the Jerusalem cross,” in Proc. IEE Int. Conf. Antennas Propagat., London, England, vol. 2, pp. 65-69, 1978.

R. J. Langley and A. J. Drinkwater, “Improved empirical model for the Jersalem cross,” IEE Proc., vol. 129, Pt. H., no.1, pp. 1-6, Feb. 1982.

M. Hosseinipanah and Q Wu, “Equivalent circuit model for designing of Jerusalem cross-based artificial magnetic conductors,” Radioeng., vol. 18, no. 4, pp. 544-550, Dec. 2009.

T. Cwik, R. Mittra, K. Lang, and T. K. Wu, “Frequency selective screens,” IEEE Antennas Propagat. Soc. Newslett., vol. 29, no. 2, pp. 5-10, Apr. 1987.

T. K. Wu, “Dielectric properties measurement of substrate and support materials,” Microw. Opt. Technol. Lett., vol. 3, no. 8, pp. 283-286, Aug. 1990.

L. B. Wang, K. Y. See, J. W. Zhang, B. Salam, and A. C. W. Lu, “Ultrathin and flexible screen-printed metasurfaces for EMI shielding application,” IEEE Trans. Electromagn. Compat., vol. 53, no. 3, pp. 700-705, Aug. 2011.

L. H. Lafara, Computer Method for Science and Engineering. New York: Hayden, 1973, pp. 148- 157.

H. Y. Chen, T. H. Lin, and P. K. Li, “Fast design of Jerusalem-cross parameters by equivalent circuit model and least-square curve fitting technique,” Appl. Comput. Electromagn. Soc. J., vol. 30, no. 7, pp. 717-730, July 2015.

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*33*(07), 730–740. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/9061