Fig. 20 Comparison of the simulated and measured frequency responses for CDBBWF

band bandstop Þlter, the conductivity is set to 30 MS/m. The increased value of 30 MS/m provides better correspondence between the measured and simulated Þlter response.

The measurement results are in good agreement with those obtained from the 3D EM simulations, and they are compared in Fig. 20.

6 Conclusions

In this paper, a miniaturized H -plane dual-band bandstop waveguide Þlter has been proposed. The Þlter has been designed using SRRs implemented as printed-circuit inserts. Therefore, the response of the single insert with SRR placed within a waveguide is analyzed to explore the impact of different design parameters on the response of the SRR.

A novel algorithm for the design of waveguide SRR has been developed to simplify and speed up the optimum design of the H -plane multi-band bandstop Þlters with independently tunable stopbands. Proposed simple design curves

provide fast computation of the resonant frequency of the SRR.

The conventional third-order dual-band bandstop Þlter has been designed using SRRs separated by the quarter-wave waveguide sections that implement immittance inverters. The inverter is miniaturized by the use of an additional insert, which provided the necessary impedance required for the reduction in the length of the quarter-wave waveguide section.

To exemplify the performance of the proposed novel algorithm and miniaturization, the third-order compact dual-band bandstop Þlter has been designed with the ability of independent control of the designed stopbands. SpeciÞed center frequencies are f01 = 8.90 GHz and f02 = 10.90 GHz, and bandwidths of both stopbands are the same and equal to 340 MHz.

The undesirable mutual coupling, caused either by the interactions between the SRRs on the insert or their interactions with the insert for miniaturization of the inverter, has been completely eliminated in two ways. First, following the proposed algorithm, the SRRs for different stopbands were modiÞed into rectangular shape to increase the interspace between them. Then, the proper position of the additional insert for inverter miniaturization has been found. Therefore, distinct stopbands can be tuned by the adjustment of the dimensions of the corresponding SRRs.

Simple equivalent electrical circuits have been proposed for all of the considered waveguide structures, to enable fast Þlter design with less computational resources.

Proposed compact dual-band bandstop Þlter using the shorter inverter is 32% smaller in length compared to the conventional dual-band bandstop Þlter using the quarter-wave inverter, while maintaining the characteristics of the conventional Þlter and low fabrication complexity. The proposed Þlter is also more compact in comparison with the Þlters having the same features presented in literature.

Compact dual-band bandstop Þlter with independent control of designed stopbands has been fabricated and measured. The measured response of the Þlter is in a good agreement with the response obtained by the 3D EM simulation. The proposed design represents a viable option for compact H - plane dual-band bandstop Þlters in waveguide technology.

Acknowledgements This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant TR32005. The authors would like to thank WIPL-D d.o.o. company for providing a free software license.

References

1.Hunter, I.C.: Theory and Design of Microwave Filters. IET, London (2006)

2.Lutovac, M.D., Toši«c, D.V., Evans, B.L.: Filter Design for Signal Processing Using MATLAB and Mathematica, 1st edn. Prentice Hall, Upper Saddle River (2001)

3.Moyra, T., Parui, S.K., Das, S.: Modeling and validation of high selective harmonic reduced bandpass Þlter using coupled resonators and defected ground structures. J. Comput. Electron. 11(4), 330Ð335 (2012)

4.Moyra, T.: Modeling of bandpass Þlter using defected ground structure and defected microstrip structure. J. Comput. Electron. 12(2), 287Ð296 (2013)

5.Chen, X., Wu, K.: Substrate integrated waveguide Þlter: Basic design rules and fundamental structure features. IEEE Microw. Mag. 15(5), 108Ð116 (2014)

6.Cameron, R.J., Kudsia, C.M., Mansour, R.R.: Microwave Filters for Communication Systems: Fundamentals, Design, and Applications, 1st edn. Wiley, Hoboken (2007)

7.Marcuvitz, N.: Waveguide Handbook, 1st edn. McGraw-Hill, New York (1951)

8.Kehn, M.N.M., Quevedo-Teruel, O., Rajo Iglesias, E.: Split-ring resonators loaded waveguides with multiple stopbands. Electron. Lett. 44(12), 714 (2008)

9.Rajo Iglesias, E., Quevedo-Teruel, O., Kehn, M.N.M.: Multiband SRR loaded rectangular waveguide. IEEE Trans. Antennas Propag. 57(5), 1570Ð1574 (2009)

10.Bassirian Jahromi, P., Rashed-Mohassel, J.: Deformed omega resonator and its application to microwave Þlter. Microw. Opt. Technol. Lett. 57(6), 1447Ð1451 (2015)

11.Odabasi, H., Teixeira, F.L.: Electric-Þeld-coupled resonators as metamaterial loadings for waveguide miniaturization. J. Appl. Phys. 114(21), 214901 (2013)

12.Monorchio, A., Manara, G., Serra, U., Marola, G., Pagana, E.: Design of waveguide Þlters by using genetically optimized frequency selective surfaces. IEEE Microw. Wirel. Compon. Lett. 15(6), 407Ð409 (2005)

13.Ohira, M., Deguchi, H., Tsuji, M., Shigesawa, H.: Novel waveguide Þlters with multiple attenuation poles using dual-behavior resonance of frequency-selective surfaces. IEEE T. Microw. Theory 53(11), 3320Ð3325 (2005)

14.Singhal, S.: Asymmetrically fed octagonal Sierpinski bandnotched super-wideband antenna. J. Comput. Electron. 16(1), 210Ð219 (2017)

15.Srivastava, D.K., Khanna, A., Saini, J.P.: Design of a wideband gap-coupled modiÞed square fractal antenna. J. Comput. Electron. 15(1), 239Ð247 (2016)

16.Jarry, P., Beneat, J.: Design and Realizations of Miniaturized Fractal Microwave and RF Filters, 1st edn. Wiley, Hoboken (2009)

17.Oloumi, D., Kordzadeh, A., LotÞ Neyestanak, A.A.: Size reduction and bandwidth enhancement of a waveguide bandpass Þlter using fractal-shaped irises. IEEE Antennas Wirel. Propag. Lett. 8, 1214Ð 1217 (2009)

18.LotÞ-Neyestanak, A.A., Seyed-Momeni, S.M., Haraty, M.R.: Improved bandwidth bandpass waveguide Þlter using Sierpinski fractal shaped irises. Prog. Electromagn. Res. 36, 113Ð120 (2013)

19.Bonache, J., Gil, I., Garcia-Garcia, J., Martin, F.: Complementary split rings resonators (CSRRs): towards the miniaturization of microwave device design. J. Comput. Electron. 5(2), 193Ð197 (2006)

20.Ortiz, N., Baena, J.D., Beruete, M., Falcone, F., Laso, M.A.G., Lopetegi, T., Marques, R., Martin, F., Garcia-Garcia, J.: Complementary split ring resonator for compact waveguide Þlter design. Microw. Opt. Technol. Lett. 46(1), 88Ð92 (2005)

21.Baena, J.D., Bonache, J., Martin, F., Sillero, R.M., Falcone, F., Lopetegi, T., Laso, M.A.G., Garcia-Garcia, J., Gil, I., Portillo, M.F., Sorolla, M.: Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines. IEEE Trans. Microw. Theory Tech. 53(4), 1451Ð1461 (2005)

22.Mrvi«c, M., Potrebi«c, M., Toši«c, D., Cvetkovi«c, Z.: E-plane microwave resonator for realization of waveguide Þlters. In: Proceedings of XII International SAUM Conference on Systems, Automatic Control and Measurements (SAUM 2014), Niš, Serbia, pp. 205Ð208 (2014)

23.Jin, J.Y., Xue, Q.: A type of E-plane Þlters using folded split-ring resonators (FSRRs). In: Proceedings of Asia-PaciÞc Microwave Conference (APMC), pp. 1Ð4 (2015)

24.Sun, H., Feng, C., Huang, Y., Wen, R., Li, J., Chen, W., Wen, G.: Dual-band notch Þlter based on twist split ring resonators. Int. J. Antennas Propag. 2014, 541264 (2014)

25.Stefanovski, S., Potrebi«c, M., Toši«c, D.: A novel design of E-plane bandstop waveguide Þlter using quarter-wave resonators. Optoelectron. Adv. Mater. Rapid Commun. 9(1Ð2), 87Ð93 (2015)

26.Mrvi«c, M., Potrebi«c, M., Toši«c, D.: Compact E-plane waveguide Þlter with multiple stopbands. Radio Sci. 51(12), 1895Ð1904 (2016)

27.Potrebi«c, M.M., Toši«c, D.V., Cvetkovi«c, Z.Ž., Radosavljevi«c, N.: WIPL-D modeling and results for waveguide Þlters with printedcircuit inserts. In: Proceedings 28th International Conference on Microelectronics (MIEL), Niš, Serbia, pp. 309Ð312 (2012)

28.Bahrami, H., Hakkak, M., Pirhadi, A.: Using complementary split ring resonators (CSRR) to design bandpass waveguide Þlters. In: Proceedings Asia-PaciÞc Microwave Conference (APMC), Bangkok, pp. 1Ð4 (2007)

29.Fallahzadeh, S., HateÞ, H., Tayarani, M., Soleiman-Meiguni, J.: A compact and low-loss bandpass waveguide resonator using higher order resonance of CSRRs. IEICE Electron. Expr. 9(3), 122Ð126 (2012)

30.Bahrami, H., Hakkak, M., Pirhadi, A.: Analysis and design of highly compact bandpass waveguide Þlter using complementary split ring resonators (CSRR). Prog. Electromagn. Res. 80, 107Ð 122 (2008)

31.Fallahzadeh, S., Bahrami, H., Tayarani, M.: A novel dual-band bandstop waveguide Þlter using split ring resonators. Prog. Electromagn. Res. Lett. 12, 133Ð139 (2009)

32.Stefanovski, S. LJ., Potrebi«c, M.M., Toši«c, D.V., Cvetkovi«c, Z.: Bandstop Waveguide Filters with Two or Three Rejection Bands. In: Proceedings of the 29-th International Conference on Microelectronics (MIEL), Belgrade, Serbia, pp. 435Ð438 (2014)

33.Fallahzadeh, S., Bahrami, H., Tayarani, M.: Very compact bandstop waveguide Þlters using split-ring resonators and perturbed quarterwave transformers. Electromagnetics 30(5), 482Ð490 (2010)

34.Stefanovski, S.L., Potrebi«c, M.M., Toši«c, D.V.: A novel design of dual-band bandstop waveguide Þlter using split ring resonators. J. Optoelectron. Adv. Mater. 16(3Ð4), 486Ð493 (2014)

35.Stefanovski, S., Potrebi«c, M., Toši«c, D., Cvetkovi«c, Z.: Fabrication parameters affecting implementation of waveguide bandpass Þlter with complementary split-ring resonators. J. Comput. Electron. 15(4), 1462Ð1472 (2016)

36.WIPL-D Microwave Pro 4.1, Circuit Solver, WIPL-D d.o.o., Belgrade. http://www.wipl-d.com (2014)

37.WIPL-D Pro 11.0, 3D Electromagnetic Solver, WIPL-D d.o.o., Belgrade. http://www.wipl-d.com (2013)

38.Hong, J.-S.: Microstrip Filters for RF/Microwave Applications. Wiley, Hoboken (2011)