In this paper, we present a tri-band filter design using tri-mode T-shaped branches connected by λ/4 transmission lines. By analyzing the input admittance of a T-shape branch with commensurate electrical lengths, three resonant modes with two transmission zeros between are found and design formulas are derived. The filter can be regarded as a combination of three bandpass filters with only one set of coupling elements. To realize different bandwidths for each, the admittance slope of each resonating mode is set as required. A genetic algorithm is used in solving related equations to obtain the impedance of each line in a T-shape branch, followed by a final optimization. A three-pole tri-band filter having passbands of 0.6-0.9, 1.35-1.65 and 2.1-2.4 GHz, is designed, fabricated and measured with low passband insertion losses of < 0.7 dB and high rejection of > 60 dB between the passband regions. As a generalization, necessary to achieve a tri-band filter with arbitrary passbands, a non-commensurate version of the T-shape branch is introduced. An example filter design is given with the passbands asymmetrically located at 0.7-1, 1.65-1.95, and 2.2-2.3 GHz. This technique is able to achieve good design flexibility with respect to bandwidth ratios. This is validated by studying the maximum impedance variations of a T-shape branch when the bandwidth ratios vary.
2. Mokhtaari, M., J. Bornemana, K. Rambabu, and S. Amari, "Coupling matrix design of dual and triple passband filters," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 11, 3940-3945, Nov. 2006.
3. Quendo, C., E. Rius, A. Manchec, Y. Clavet, B. Potelon, J.-F. Favennec, and C. Person, "Planar tri-band filter based on dual behaviour resonator (DBR)," Proc. Eur. Microw. Conf., 269-272, Oct. 1995.
4. Liu, Y. and W.-B. Dou, "A dual-band filter realized by alternately connecting the main transmission-line with shunt stubs and shunt serial resonators," IEEE Microw. Wireless Compon. Lett., Vol. 19, No. 5, 296-298, May 2009.
5. Chen, X.-P., K. Wu, and Z.-L. Li, "Dual-band and triple-band substrate integrated waveguide filters with chebyshev and quasielliptic responses," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 12, 2569-2578, Dec. 2007.
6. Zhao, H. and T. J. Cui, "Novel triple-mode resonators using split-ring resonator," Microw. Opt. Technol. Lett., Vol. 49, No. 12, 2918-2922, Dec. 2007.
7. De Paco, P., O. Menendez, and J. Marin, "Dual-band filter using non-bianisotropic split-ring resonators," Progress In Electromagnetics Research Letters, Vol. 13, 51-58, 2010.
8. Wu, G.-L., W. Mu, X.-W. Dai, and Y.-C. Jiao, "Design of novel dual-band bandpass filter with microstrip meander-loop resonator and CSRR DGS," Progress In Electromagnetics Research, Vol. 78, 17-24, 2008.
9. Wang, X.-H. and B.-Z. Wang, "Compact broadband dual-band bandpass filters using slotted ground structures," Progress In Electromagnetics Research, Vol. 82, 151-166, 2008.
10. Wu, M.-S., Y.-Z. Chueh, J.-C. Yeh, and S.-G. Mao, "Synthesis of triple-band and quad-band bandpass filters using lumped-element coplanar waveguide resonators," Progress In Electromagnetics Research B, Vol. 13, 433-451, 2009.
11. Chen, F. C. and Q. X. Chu, "Tri-band bandpass filters using stub loaded resonators," Electron. Lett., Vol. 44, No. 12, 747-749, Jun. 2008.
12. Lin, W.-J., C.-S. Chang, J.-Y. Li, D.-B. Lin, L.-S. Chen, and M.-P. Houng, "A new approach of dual-band filters by stepped impedance simplified cascaded quadruplet resonators with slot coupling," Progress In Electromagnetics Research Letters, Vol. 9, 19-28, 2009.
13. Chen, C. F., T. Y. Huang, and R. B. Wu, "Design of dual-and triple-passband filters using alternately cascaded multiband resonators," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 9, 3550-3558, Sep. 2006.
14. Lee, C. H., C. I. G. Hsu, and H. K. Jhuang, "Design of a new tri-band microstrip BPF using combined quarter- wavelength SIRs," IEEE Microw. Wireless Compon. Lett., Vol. 16, No. 11, 594-596, Nov. 2006.
15. Hsu, C.-I. G., C.-H. Lee, and H.-K. Jhuang, "Design of a novel quadband microstrip BPF using quarter-wavelength stepped-impedance resonators," Microw. J., Vol. 50, No. 2, 102-112, Feb. 2007.
16. Chen, F. C. and Q. X. Chu, "Design of compact tri-band bandpass filters using assembled resonators," IEEE Trans. Microw. Theory Tech., Vol. 57, No. 1, 165-171, Jan. 2009.
17. Lin, X. M. and Q. X. Chu, "Design of triple-band bandpas filter using tri-section stepped-impedance resonators," Proc. Int. Microw. Millimeter Wave Tech. Conf., 798-800, Apr. 2007.
18. Chen, Y.-C., Y.-H. Shieh, C.-H. Her, and C.-I. G. Hsu, "Tri-band microstrip BPF design using tri-section SIRs," IEEE AP-S Int. Symp. Dig., 3113-3116, Jun. 2007.
19. Hsu, C.-I. G., C.-H. Lee, and Y.-H. Hsieh, "Tri-band bandpass filter with sharp passband skirts designed using tri-section SIRs," IEEE Microw. Wireless Compon. Lett., Vol. 18, No. 1, 19-21, Jan. 2008.
20. Chu, Q. X. and X. M. Lin, "Advanced triple-band bandpass filter using tri-section SIR," Electron. Lett., Vol. 44, No. 4, 295-296, Feb. 2008.
21. Ma, Z., T. Shimizu, Y. Kobayashi, T. Anada, and G. Hagiwara, "Novel compact dual-band bandpass filters using composite resonators to obtain separately controllable passbands," Asia-Paciffic Microwave Conference Proceedings, Vol. 3, 1814-1817, FR4B-4, Dec. 2006.
22. Hong, J.-S. and M. J. Lancaster, Microstrip Filter for RF/Microwave Applications, Wiley, New York, 2001.
23. Holland, J. H., Adaption in Natural and Artificial Systems, MIT Press, Cambridge, MA, USA, 1992.
24., , Ansoft Serenade 8.7, Ansoft Corporation.