本論文之多頻帶濾波器之通帶由一低通濾波器以及兩組半波長步階式阻抗共振器組成，使用散佈式耦合技術減少頻帶間的負載效應，且帶通濾波器的每兩個通帶由一組半波長步階式阻抗共振器控制，由於使用散佈式耦合技術因此不需要額外的匹配電路來設計帶通濾波器的電路。使用了半波長步階式阻抗共振器可以相較於傳統半波長共振器的電路面積縮小，將四個通帶分別設計在3、4、5、6 GHz，論文中分別以三種不同低通濾波器使用以RO4003C，介電係數3.55，厚度0.8mm的板材來驗證設計之可能性。

第一個電路當中的低通濾波器為步階式阻抗低通濾波器，在通帶內的反射損耗從0 GHz至2 GHz皆大於20 dB，且有一個接近2 GHz的3-dB截止頻率為1.93 GHz，截止帶大於20 dB的範圍從 2.66 GHz 至9.32 GHz。

第二個電路中的低通濾波器是基於第一個電路的低通濾波器增加一段並聯的傳輸線來增加零點；第三種低通濾波器則為以串聯兩組由一對耦合線連接一開路殘段結構當成一單位所組成的低通濾波器。第二個電路在通帶內的反射損耗從0 GHz至1.85 GHz皆大於10 dB，且3-dB截止頻率為1.93 GHz，截止帶大於20 dB的範圍從 2.68 GHz 至6.86 GHz。第三種低通濾波器的3-dB通帶從0 GHz 至 1.9 GHz，通帶內的反射損耗從0 GHz 至 1.85 GHz 皆大於10 dB，截止帶大於20 dB之範圍從2.86 GHz 至 9.85 GHz

The passband of the multi-band filter of this paper consists of a low-pass filter and two pairs of half-wavelength stepped impedance resonators. Distributed coupling technique is used to reduce the loading effect between the passbands, and every two passbands of the band-pass filter are controlled by a set of half-wavelength stepped impedance resonators. The use of half-wavelength stepped impedance resonators can reduce the circuit size compared to traditional half-wavelength resonators. The frequency of the passbands is designed in 3,4,5 and 6 GHz. In the paper, three different low-pass filters are fabricated on Rogers RO4003 substrate with a relative dielectric constant of 3.55, a thickness of 0.8 mm, and a loss tangent of 0.0027 to verify the possibility of the design.
The low-pass filter in the first circuit is a stepped impedance low-pass filter. The return loss in the passband is greater than 20 dB from 0 GHz to 2 GHz, and there is a 3-dB cutoff frequency close to 2 GHz at 1.93 GHz. The cutoff band is greater than 20 dB from 2.66 GHz to 9.32 GHz.
The low-pass filter in the second circuit is based on the band-pass filter of the first circuit by adding a shunt transmission line to increase the transmission zeros. The third type of the low-pass filter is a low-pass filter composed of two series circuit of a pair of coupled lines connected to an open stub structure as a unit. The return loss of the second circuit in the passband is greater than 10 dB from 0 GHz to 1.85 GHz, and the 3-dB cutoff frequency is 1.93 GHz. The cutoff band is greater than 20 dB from 2.68 GHz to 6.86 GHz. The third low-pass filter has a 3-dB passband from 0 GHz to 1.9 GHz, and the return loss in the passband is greater than 10 dB from 0 GHz to 1.85 GHz. The cutoff band is greater than 20 dB from 2.86 GHz to 9.85 GHz.

[1] D. M. Pozar, Microwave Engineering, 4th ed. New York: Wiley, 2012.
[2] J.-S. Hong and M. J. Lancaster, Microstrip Filter for RF/Microwave Application. New York: Wiley, 2001.
[3] J. Lee and Y. Lim, "Design of a microstrip multi-band bandpass filters using the filter synthesis method," 2012 42nd European Microwave Conference, pp. 463-466, Nov. 2012.
[4] M. Awida, A. Boutejdar, A. Safwat, H. El-Hennawy and A. Omar, "Multi-Bandpass Filters Using Multi-Armed Open Loop Resonators with Direct Feed," 2007 IEEE/MTT-S International Microwave Symposium, pp. 913-916, Honolulu, HI, Jun. 2007.
[5] A.Kumar and D. K. Upadhyay, "A Compact Planar Quint-Passband Lowpass-Bandpass Filter Using Open-End Folded Stub CRLH-TLs," 2021 Advanced Communication Technologies and Signal Processing (ACTS), pp. 1-5, Dec. 2021.
[6] R. Gómez-García et al., "Dual-band lowpass/bandpass periodic-type microstrip filter with Long-Term-Evolution (LTE) service mitigation," 2014 IEEE 5th Latin American Symposium on Circuits and Systems, pp. 1-4, Feb. 2014.
[7] H. Issa, H. El-Halabi, D. Awde, L. Ezzeddine, A. El-Hawary and B. El-Ibrahim, "Compact Dual Band LowPass-BandPass Filter," 2020 7th International Conference on Electrical and Electronics Engineering (ICEEE), Antalya, Turkey, pp. 198-201, May. 2020.
[8] C. -. Chen, T. -. Huang and R. -. Wu, "Design of Dual- and Triple-Passband Filters Using Alternately Cascaded Multiband Resonators," in IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 9, pp. 3550-3558, Sept. 2006.
[9] Y. . -L. Lu, C. . -Z. Hua and T. . -J. Liu, "A novel dual-band bandpass filter with C-section loaded resonators," 2015 Asia-Pacific Microwave Conference , pp. 1-3, Sept. 2015.
[10] Y. Chang, C. Kao, M. Weng and R. Yang, "Design of the Compact Dual-Band Bandpass Filter With High Isolation for GPS/WLAN Applications," in IEEE Microwave and Wireless Components Letters, vol. 19, no. 12, pp. 780-782, Dec. 2009.
[11] P. Deng, J. Tsai and R. Liu, "Design of a Switchable Microstrip Dual-Band Lowpass-Bandpass Filter," in IEEE Microwave and Wireless Components Letters, vol. 24, no. 9, pp. 599-601, Sept. 2014.
[12] S. Zeng, J. Wu and W. Tu, "Compact and High-Isolation Quadruplexer Using Distributed Coupling Technique," in IEEE Microwave and Wireless Components Letters, vol. 21, no. 4, pp. 197-199, April 2011
[13] F. Zhang, Y. Gao, B. Liu and J. Xu, "A Compact Sharp Roll-Off Microstrip Lowpass Filter With Ultra-Wide Stopband," 2020 International Conference on Microwave and Millimeter Wave Technology (ICMMT), pp. 1-3, Sept. 2020.
[14] F. Zhang, S. Liu, P. Zhao, M. Du, X. Zhang and J. Xu, "Compact ultra-wide stopband lowpass filter using transformed stepped impedance hairpin resonator," 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, pp. 2227-2228, July. 2017.
[15] Z. Wang, F. Zhang, Y. Gao, Y. Wang, Y. Zhang and J. Xu, "A Microstrip Lowpass Filter With Miniaturized Size and Broad Stopband," 2019 8th International Symposium on Next Generation Electronics (ISNE), pp. 1-3, Oct. 2019.
[16] T. K. Rekha, P. Abdulla and T. A. Nisamol, "Compact Microstrip Lowpass Filter with Ultra-Wide Stopband," 2018 Asia-Pacific Microwave Conference (APMC), Kyoto, Japan, pp. 1351-1353, Nov. 2018.
[17] Q. He and C. Liu, "A Novel Low-Pass Filter With an Embedded Band-Stop Structure for Improved Stop-Band Characteristics," in IEEE Microwave and Wireless Components Letters, vol. 19, no. 10, pp. 629-631, Oct. 2009
[18] M. Alyahya, M. Aseeri, H. Bukhari, H. Shaman, A. Alhamrani and A. Affandi, "Compact microstrip lowpass filter with ultra-wide rejection-band," 2017 International Conference on Wireless Technologies, Embedded and Intelligent Systems (WITS), pp. 1-4, April. 2017,
[19] L. Li, Z. -F. Li and J. -F. Mao, "Compact Lowpass Filters With Sharp and Expanded Stopband Using Stepped Impedance Hairpin Units," in IEEE Microwave and Wireless Components Letters, vol. 20, no. 6, pp. 310-312, June 2010.
[20] Min-Chieh Kang and Jen-Tsai Kuo, "Multi-path design for stepped-impedance low-pass filter to create transmission zeros and wide rejection band," 2006 Asia-Pacific Microwave Conference, pp. 1691-1696, Dec. 2006.
[21] Rui Li and Dong Il Kim, "A new compact low-pass filter with broad stopband and sharp skirt characteristics," 2005 Asia-Pacific Microwave Conference Proceedings, pp. 3 , Dec. 2005.
[22] N. Junsong, C. Liu, Z. Chen and B. Shirong, "A compact elliptic-function low-pass filter using stepped-impedance coupled microstrip resonators," 2014 International Conference on Information Science, Electronics and Electrical Engineering, 2014, pp. 1557-1561,
[23] R. Li, D. I. Kim and C. M. Choi, "Compact Structure With Three Attenuation Poles for Improving Stopband Characteristics," in IEEE Microwave and Wireless Components Letters, vol. 16, no. 12, pp. 663-665, Dec. 2006, doi: 10.1109/LMWC.2006.885617.
[24] P. R. Geffe, Simplified Modern Filter Design. NewYork: John F. Rider,1963, sec. Appendix 4.