Synthesis and Design of Generalized Strongly Coupled Resonator Quartet Combline Filters with Redundant Resonance

doi:10.12142/ZTECOM.202601012

ZTE Communications ›› 2026, Vol. 24 ›› Issue (1): 88-96.DOI: 10.12142/ZTECOM.202601012

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Synthesis and Design of Generalized Strongly Coupled Resonator Quartet Combline Filters with Redundant Resonance

Xiong Zhi’ang¹, Fan Jiyuan¹, Zhao Ping¹(), Zhou Jinzhu¹, Shen Nan², Wu Qingqiang²

^1.Xidian University, Xi’an 710071, China
^2.ZTE Corporation, Shenzhen 518057, China

Received:2024-03-20 Online:2026-03-25 Published:2026-03-17
About author:Xiong Zhi'ang received his BS degree from Jiangxi University of Science and Technology, China in 2021, and the master's degree from Xidian University, Xi'an, China in 2024. His current research interests include mixed electric and magnetic coupling filters and modeling and optimization of microwave passive filters.
Fan Jiyuan received his BS degree from Nanjing University of Posts and Telecommunications, China in 2022 and his master's degree from Xidian University, China in 2025. His current research interests include mixed electric and magnetic coupling, as well as the synthesis and tuning of multiband filters and multiplexers.
Zhao Ping (aoing56@gmail.com) received his BS degree from Nanjing University, China in 2012, and PhD degree from The Chinese University of Hong Kong, China in 2017. From 2017 to 2019, he was a post-doctoral researcher with the École Polytechnique de Montréal, Canada. He joined the National Key Laboratory of Antennas and Microwave Technology, Xidian University, China in 2020. Since 2024, he has been with the State Key Laboratory of Electromechanical Integrated Manufacturing of High-performance Electronic Equipments, Xidian University, where he is currently an associate professor. His research interests include coupling matrix synthesis techniques for coupled-resonator networks, analytical computer-aided tuning (CAT) algorithms for microwave and millimeter-wave filters, and diplexers with applications in cellular base stations and satellites. He is also interested in modeling and optimization of passive RF components and computer-aided design techniques, such as the homotopy method, artificial neural networks, and machine learning techniques.
Zhou Jinzhu received his PhD degree from Xidian University, China in 2011. He is currently a professor with the State Key Laboratory of Electromechanical Integrated Manufacturing of High-performance Electronic Equipments, Xidian University. He is also the Director of the Department of Electronic Packaging and the Deputy Director of the Xi'an Key Laboratory of Intelligent Instrument and Packaging Test, Xidian University. He received the Outstanding Youth of Shaanxi Province in 2022. His research interests include microwave filter tuning, RF microsystem, smart skin antenna, and machine learning. He has published over 60 papers and holds 40 patents issued. Dr. Zhou received the National Science and Technology Award (2021 First Prize), the Science and Technology Progress Award of China Electronics Society (2022 First Prize), the Shaanxi Province Science and Technology Award (2015 First Prize), and the National Defense Science and Technology Award (2019 Second Prize). He also received four Best Paper Awards for the research of smart skin antenna and automatic microwave filter tuning in the International Conference of the 2010 IEEE International Conference on Mechatronics and Automation (ICMA), the Asia International Symposium on Mechatronics (AISM 2015), the AISM 2017, and the 2021 IEEE International Conference on Electronic Packaging Technology (ICEPT), respectively.
Shen Nan received his BS degree from Northwestern Polytechnical University, China in 2004 and MS degree in electromagnetic field and microwave technology from the same university in 2007. He is currently with ZTE Corporation, where his research focuses on filters, multiplexers, and antennas.
Wu Qingqiang received his BS degree from Xidian University, China in 2019, and MS degree in electromagnetic wave and microwave technology from the National Key Laboratory of Antennas and Microwave Technology, Xidian University in 2021. He is currently with ZTE Corporation, where his research focuses on filters and multiplexers.
Supported by:
the National Natural Science Foundation of China(62471366)

Abstract

Abstract:

This article proposes a generalized strongly coupled resonator quartet (GSCRQ) filter along with its synthesis approach. By introducing out-of-band reflection zeros (RZs), the proposed GSCRQ can generate a transmission zero on each side of the passband without negative couplings. The coupling coefficients in this coupling structure change with the positions of the out-of-band RZs. Thus, the GSCRQ configuration admits flexible design solutions. For GSCRQ coaxial combline filters, all couplings can be implemented as inductive couplings, simplifying the design and manufacturing process. In this article, a 6-2 filter in the GSCRQ configuration is synthesized and designed. The simulated results of the designed filter agree very well with the theoretical characteristics.

Key words: filter synthesis, generalized strongly coupled resonator quartets (GSCRQ), out-of-band reflection zero, transmission zero

Xiong Zhi’ang, Fan Jiyuan, Zhao Ping, Zhou Jinzhu, Shen Nan, Wu Qingqiang. Synthesis and Design of Generalized Strongly Coupled Resonator Quartet Combline Filters with Redundant Resonance[J]. ZTE Communications, 2026, 24(1): 88-96.

Figures/Tables 15

Figure 1 Topology of quartets. Black nodes represent resonators, and solid lines represent couplings

Figure 2 Iterations of Remez-like algorithm in solving the equi-ripple function for the 7th-order filter with an out-of-band RZ: (a) the first iteration; (b) the second iteration; (c) the third iteration; (d) the fourth iteration

Table 1 Coefficients of F(s), P(s), and E(s) of seven-poles with one upper TZ and one lower TZ

sⁱ, i =	F(s) (F₂₂(s))	P(s)	E(s)
0	0.373 8j	1.700 0	0.868 3 + 3.731 5j
1	0.422 9	0.110 0j	2.769 1 +12.801 1j
2	5.464 5j	1.000 0	4.956 1 + 24.638 4j
3	2.012 0		6.466 5 + 30.408 0j
4	13.070 5j		5.796 9 + 28.889 2j
5	2.613 9		4.560 8 + 16.045 3j
6	8.137 5j		1.973 3 + 8.137 5j
7	1.000 0		1.000 0
ε_R = 1.000 0		ε = 0.445 8

Figure 3 Synthesized response of the 7th-order filter with an out-of-band RZ

Figure 4 Topology with quartet: (a) 7-2 (7 RZs and 2 TZs) filter with an out-of-band RZ; (b) 6-2 filter; (c) 7-2 filter

Table 2 Rotation sequence to the filter in Fig. 4a

Rotation sequence	Elements to be annihilated	Pivot [i, j]	Rotation sequence	Elements to be annihilated	Pivot [i, j]
1	M_S₇	[7, 6]	16	M₃₇	[7, 6]
2	M_S₆	[6, 5]	17	M₃₆	[6, 5]
3	M_S₅	[5, 4]	18	M₃₅	[5, 4]
4	M_S₄	[4, 3]	19	M₄₇	[7, 6]
5	M_S₃	[3, 2]	20	M₄₆	[6, 5]
6	M_S₂	[2, 1]	21	M₅₇	[7, 6]
7	M₁₇	[7, 6]	22	M₅_L	[5, 6]
8	M₁₆	[6, 5]	23	M₆_L	[6, 7]
9	M₁₅	[5, 4]	24	M₄₆	[5, 6]
10	M₁₄	[4, 3]	25	M₄₇	[4, 5]
11	M₁₃	[3, 2]	26	M₅₇	[5, 6]
12	M₂₇	[7, 6]	27	M₃₅	[4, 5]
13	M₂₆	[6, 5]	28	M₃₆	[3, 4]
14	M₂₅	[5, 4]	29	M₄₆	[4, 5]
15	M₂₄	[4, 3]	30	M₃₄	[3, 4]

Figure 5 Frequency responses of three filter designs: the 7th-order filter with an out-of-band reflection zero (solid), 6th-order traditional filter (dashed), and 7th-order traditional filter (dotted)

Figure 6 Frequency responses with different out-of-band RZ locations: sout=-8.26j (solid), sout=-6.7j (dashed), and sout=-3.5j (dotted)

Figure 7 7-2 filter topology with different out-of-band RZ locations: (a) sout=-6.7j; (b) sout=-3.5j

Figure 8 (a) Electromagnetic model of the 6th-order filter with GSCRQ; (b) synthesis results of GSCRQ of the 6-2 filter with one out-of-band RZ

Table 3 Zeros and poles of VF results for S11

k	poles	zeros
1	-0.692 7 + 0.104 7i	0.001 0 + 0.072 2i
2	-0.556 11-0.675 5i	-0.000 1-0.530 2i
3	-0.481 2 + 0.805 7i	-0.000 5 + 0.657 6i
4	-0.180 53-1.073 5i	-0.000 7-0.889 7i
5	-0.156 41 + 1.149 1i	0.000 3 + 1.000 2i
6	-0.009 1-11.503 2i	0.000 0-11.503 1i
7	1.132 2 + 14.087 9i	1.664 5 + 13.927 9i
8	-26.468 1 + 3.616 4i	26.542 8 + 3.463 7i

Figure 9 Incorrect phasing de-embedding: (a) amplitude and phase of the phase factor α; (b) S11 and S22 after phase removal

Figure 10 Correct phase de-embedding: (a) amplitude and phase of the phase factor α and (b) S11 and S22 after phase removal

Figure 11 Simulated results using High Frequency Structure Simulator (HFSS) and ideal synthesis responses of the filter

Table 4 Dimensions of the filter in Fig. 8

Resonator ID	T₁	T₂	T₃	T₄	T₅	T₆	T₁₂	T₂₅	T₅₆
Final/mm	4.70	3.55	9.10	4.7	3.55	4.70	1.70	2.00	2.00
Dimension	d₁₂	d_{25_1}	d_{25_2}	d_{34_1}	d_{34_2}	H_port
Final/mm	1.77	7.55	7.55	6.40	11.43	6.32

References 13

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Synthesis and Design of Generalized Strongly Coupled Resonator Quartet Combline Filters with Redundant Resonance

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