Introduction
Microwave bandpass filters (BPFs) with compact size, high selectivity, and individually controllable passbands are highly required in modern multi-service wireless communication systems. Therefore, high-performance multi-band BPFs have aroused wide concern. So far, various multi-band BPFs have been proposed to meet different applications [Reference Gong, Xiong, Zhang, Wang, Sun, Zhao, He, Ji, Zhang and Bo1–Reference Xu17]. As a straightforward method, combining several individual resonators or BPFs with a careful arrangement is a practical approach to design multi-band BPFs [Reference Gong, Xiong, Zhang, Wang, Sun, Zhao, He, Ji, Zhang and Bo1, Reference Zhu, Xu, Kang and Wu2], but it usually suffers from larger circuit dimensions. To reduce the circuit area, defected ground structure (DGS) is introduced in dual-/tri-band BPFs design [Reference Xiao, Sun and Xu3–Reference Hejazi and Ali5]. Generally, DGS technology can provide the advantage of controllable resonant frequencies by changing the DGS resonator's shape or size. However, DGS technology will increase the fabrication complexity, and it is difficult to integrate with planar circuits. For the merits of simple structure, multi-mode resonators (MMRs) are widely used to design multi-band BPFs [Reference Liu and Xu6–Reference Li, Zhang, Feng and Fan10]. However, mutual interferences between resonant modes are inevitable usually. Therefore, BPFs with fully independent and controllable passbands using MMRs are difficult to realize. Recently, multi-passband planar filters based on transversal multi-path structures have drawn a lot of attention [Reference Gómez-García, Sánchez-Renedo, Jarry, Lintignat and Barelaud11–Reference Wang, Xiong, Gong, Zhang, Li and Zhao14]. In [Reference Gómez-García, Sánchez-Renedo, Jarry, Lintignat and Barelaud11–Reference Sánchez-Soriano Miguel and Gómez-García13], by introducing intentionally constructive interference, high-selectivity filtering characteristics are achieved. However, DC suppression and the circuit dimensions should be solved and reduced. In [Reference Wang, Xiong, Gong, Zhang, Li and Zhao14], a miniaturized dual-band BPF with high selectivity, controllable bandwidth, and wide stopband is realized, but the design procedures are tedious and complex. Besides, multipath propagation concept is proposed to design multi-band BPFs [Reference Yang, Wu, Zhu, Wang and Liang15–Reference Xu17].
In this paper, a dual- and tri-band BPF with individually controllable passbands based on multipath-embedded resonators are presented. The dual-band BPF consists of two cascaded double open-ended stub-loaded terminal-shorted resonators (DOESL-TSRs) with a common via-hole connected along the symmetric plane of the filter. Based on the DOESL-TSR, an open-ended stub is added to construct a triple open-ended stub-loaded terminal-shorted resonator (TOESL-TSR), which can be employed to design a tri-band BPF. The resonant characteristics of DOESL-TSR/TOESL-TSR are analyzed by the numerical calculation method. Descriptions of the mechanism of multipath propagation are provided based on the simulated current density distributions. The proposed filters are of compact size, controllable passbands, center frequencies (CFs), and bandwidth (BWs). Multiple transmission zeros (TZs) are generated due to the mixed electric and magnetic coupling canceling effect and virtual ground effect, which result in high selectivity. Besides, the filters are of extendable channels, which can be easily extended to design dual-, tri-, and even quad-band BPFs. Due to the fully independent and controllable passbands, the proposed filters can be easily applied to design electronically tunable dual-, tri-, and quad-band filters. Finally, two filters are designed and fabricated, and the measurement results are in good agreement with the prediction ones.
Dual-band BPF analysis and design
The configuration and the coupling structure of the proposed dual-band BPF, respectively, are depicted in Figs 1(a) and 1(b). It shows that the dual-band BPF is formed by two DOESL-TSRs with a common via-hole connected along the symmetric plane of the dual-band BPF. The filter provides two resonant paths at 2.5 and 5.6 GHz, as shown in Fig. 2.
Fig. 1. Proposed dual-band BPF: (a) configuration and (b) coupling structure.
Fig. 2. Resonant path of the dual-band BPF.
Figure 3 illustrates the ideal transmission line model of the DOESL-TSR. In Fig. 3, the parameters Yn and θn (n = 1, 2, 3, 4) denote the characteristic admittances and electrical lengths of the DOESL-TSR, respectively. For simplicity, Y 1 = Y 2 = Y 3 = Y 4 = 0.01S, and the reference frequency f 0 for electrical length calculation is set to 2.5 GHz. Then, according to the resonant condition, we have
where Y in represents the input admittance from the left side of the DOESL-TSR. According to the transmission line theory, we have
Numerical calculation method is adopted to solve equation (1). As shown in Fig. 4(a), resonant frequencies versus varied θ 3 are plotted. It can be found that f 1 will shift down, significantly, as θ 3 increases from 60 to 90°, while f 2 shifts down slightly. Similarly, resonant frequencies versus varied θ 4 are also given, as shown in Fig. 4(b). It can be observed from Fig. 4(b), f 1 remains almost unchanged as θ 4 increases from 30 to 50°, while f 2 shifts down dramatically. Therefore, it indicates that two resonant frequencies f 1 and f 2 can be easily controlled by adjusting the parameters θ 3 and θ 4.
Fig. 3. Ideal transmission line model of the DOESL-TSR.
Fig. 4. Resonant frequencies versus various (a) θ 3 and (b) θ 4.
Figures 5(a) and 5(b) show the simulated frequency responses in Advanced Design System (ADS) with varied L 31 and L 41 for each resonant path. To evaluate the effects of L 31 and L 41 on two passbands, the parameters (L 1, W 1), (L 2, W 2), (L 32, W 32), and (L 42, W 42) are fixed. As an example, the first passband (path 1) will shift to lower frequency while the second passband (path 2) remains almost unchanged as L 31 increases from 3.0 to 4.8 mm. Similarly, the second passband will shift to lower frequency while the first passband remains almost unchanged as L 41 increases from 6.0 to 6.8 mm. It can be found that each passband can be tuned in a wide frequency range without affecting the performance of the other passband. Therefore, each passband can be implemented individually by adjusting the parameter L 31 or L 41. The current density distributions of the dual-band BPF are plotted in Fig. 6, which also indicate that two resonant paths are created. It is clearly observed from Figs 6(a) and 6(b) that the first and the second passbands at 2.55 and 5.55 GHz are generated by two resonant paths. It can also be found that there are no interactions between the resonators. Therefore, the passbands do not interfere with each other.
Fig. 5. ADS simulated frequency responses versus various (a) L 31 and (b) L 41.
Fig. 6. Dual-band BPF current density distribution at (a) 2.55 GHz and (b) 5.55 GHz.
Tri-band BPF analysis and design
By adding an open-ended stub, a TOESL-TSR is constructed based on the DOESL-TSR, where the TOESL-TSR can be used to design a tri-band BPF. The configuration and the coupling topology of the proposed tri-band BPF are depicted in Figs 7(a) and 7(b), respectively. The ideal transmission line model of TOESL-TSR is shown in Fig. 8, where the parameters Yn and θn (n = 1, 2, 3, 4, 5) represent the characteristic admittances and electrical lengths of the TOESL-TSR, respectively. The resonant condition can be expressed as:
where Yin denotes the input admittance from the left side of the TOESL-TSR. According to the transmission line theory, we have
Fig. 7. Proposed tri-band BPF: (a) configuration and (b) coupling topology.
Fig. 8. Ideal transmission line model of the TOESL-TSR.
Therefore, the resonant modes of the TOESL-TSR can be derived by setting Im(Yin) = 0. Similarly, the real roots of equation (5) can be solved by using the numerical calculation method.
Figures 9(a)–9(c) show the simulated frequency responses with varied L 31, L 41, and L 51 for each resonant path. To evaluate the effects of L 31, L 41, and L 51 on three passbands, the parameters (L 1, W 1), (L 2, W 2), (L 32, W 32), (L 42, W 42), and (L 52, W 52) are fixed. As can be seen, the first passband (path 1) will shift to lower frequency while the second passband (path 2) and the third passband (path 3) remains almost unchanged as L 31 increases from 3.0 to 4.0 mm. Similarly, the second passband will shift to lower frequency while the first passband and the third passband remain almost unchanged as L 41 increases from 9.5 to 10.3 mm. As L 51 increases from 5.8 to 6.2 mm, the third passband will shift to lower frequency while the first passband and the second passband remain almost unchanged. It can be found that each passband can be tuned in a wide frequency range without affecting the performance of the other passband. Therefore, each passband can be implemented individually by adjusting the parameter L 31, L 41, or L 51. In order to clarify the multipath mechanism further, the current density distributions of the tri-band BPF are given in Fig. 10, which indicate that three resonant paths are created. It is clearly observed from Figs 10(a), 10(b), and 10(c) that the first, second, and third passbands at 2.55, 3.7, and 5.8 GHz are generated by three resonant paths. It can also be found that there are no interactions between the resonators.
Fig. 9. ADS simulated frequency responses versus various (a) L 31, (b) L 41, and (c) L 51.
Fig. 10. Current density distributions of the tri-band BPF at (a) 2.55 GHz, (b) 3.7 GHz, and (c) 5.8 GHz.
Results and discussion
For experimental validation, a dual-band and a tri-band BPF are designed, fabricated, and measured. The filters are implemented on a Rogers 4003C substrate with ɛr = 3.38, thickness of 0.508 mm, and loss tangent of 0.0027. The circuit parameters of the dual-band BPF are as follows (unit: mm): L 1 = 1.4, L 2 = 0.7, L 31 = 3.5, L 32 = 12.3, L 41 = 5.0, L 42 = 3.3, W 1 = W 2 = 0.4, W 31 = 0.3, W 32 = 0.4, W 41 = 0.2, W 42 = 0.15, g 1 = 0.175, and g 2 = 0.4. The overall size of the dual-band BPF occupies only 18.19 mm × 4.9 mm (excluding the feed lines), which corresponds to 0.26λg × 0.07λg, where λg is the guided wavelength at 2.595 GHz. Similarly, the circuit parameters of the tri-band BPF are also given as follows (unit: mm): L 1 = 0.85, L 2 = 0.5, L 31 = 3.9, L 32 = 12.8, L 41 = 9.52, L 42 = 1.1, L 51 = 5.8, L 52 = 1.6, W 1 = W 2 = 0.4, W 31 = 0.3, W 32 = 0.4, W 41 = 0.1, W 42 = 0.7, W 51 = 0.15, W 52 = 0.4, g 1 = g 3 = 0.2, and g 3 = 0.4. The overall size of this tri-band BPF occupies only 23.4 mm × 4.7 mm (excluding the feed lines), which corresponds to 0.33λg × 0.066λg, where λg is the guided wavelength at 2.545 GHz.
The frequency responses of the two filters are characterized by using an Agilent vector network analyzer N5244A. Figure 11(a) shows the measurement and electromagnetic (EM) simulation results of the dual-band BPF, which are in good agreement with the prediction ones. It can be observed from Fig. 11(a), the measured CFs are located at 2.595 and 5.75 GHz, respectively, with 3 dB FBWs of 15 and 12.8%. The minimum insertion losses (ILs) are 1.58 and 2.42 dB. Four TZs are generated in out-of-band, which improves the selectivity of the filter. Figure 11(b) shows the measurement and EM simulation results of the tri-band BPF, where the measurement results are in good agreement with the prediction ones. The measured CFs are located at 2.545, 3.775 and 5.95 GHz, respectively, with 3 dB FBWs of 9.8, 9.3 and 5.5%. The measured results show that the IL within the third passband is about 5 dB. As shown in Fig. 12, the frequency responses versus varied g 3 are given. As g 3 gets increased from 0.4 to 0.475 mm, the IL will deteriorate to 4.7 dB. As can be seen, small change in g 3 (only 75 μm) will deteriorate the IL rapidly. In this design, the bandwidth of the third passband can be tuned by changing the gap coupling of g 3. With the increase in g 3, the bandwidth will become smaller. Therefore, the IL will get larger. As can be seen, six TZs are located at 2.3, 3.14, 3.3, 4.73, 5.56, and 6.65 GHz, which improve the passband selectivity. The band-to-band isolations of the tri-band BPF are 41.6 and 29.5 dB, respectively.
Fig. 11. Measurement and simulation results of the proposed (a) dual-band BPF and (b) tri-band BPF.
Fig. 12. Frequency responses of the tri-band BPF versus various g 3.
Due to the periodic characteristic of transmission line, the inherent harmonic passbands will exist in out-of-band, as shown in Figs 11(a) and 11(b). An effective and simple method to suppress the harmonics to obtain wide stopband is presented in Figs 13(a) and 13(b), in which a T-shaped structure is loaded at the left feedline of the dual- and tri-band filters. As can be seen, TZ is generated due to the virtual ground effect and can be used to suppress the unwanted harmonic passband. For the proposed dual- and tri-band filter, its upper stopband with the 20 dB rejection level can extend to 10 GHz. Table 1 summarizes a comparison between this study and some reported multi-band BPFs. The proposed filter is of compact size, individually controllable passbands, multiple TZs, high band-to-band isolation, etc.
Fig. 13. Frequency responses of (a) dual-band BPF with and without T-structure loaded and (b) tri-band BPF with and without T-shaped structure loaded.
Table 1. Comparison with other tri-band BPFs
ICP, individually controllable passband; NG, not given.
λ g is the guided wavelength at the CF of the first passband.
Conclusion
A dual-band and tri-band BPF with individually controllable passbands based on multipath-embedded resonators are presented in this paper. The numerical calculation method is adopted to analyze the resonant frequencies. In order to clarify the multipath mechanism, the current density distributions of two filters are given. The filters are of compact size, multiple TZs, and individually controllable passbands, which make the proposed filters attractive in multi-service wireless communication systems.
Yang Xiong was born in Huaihua, Hunan province, China, in 1990. He received his Ph.D. degree from Nankai University, Tianjin, China, in 2018. Now, he is a microwave and millimeter-wave circuit engineer with Southwest China Institute of Electronic Technology.
Wei Zhang was born in Leshan, Sichuan province, China, in 1993. He received his B.E. degree and M.E. degree from Nankai University, Tianjin, China, in 2015 and 2018, respectively. Now, he is an assistant engineer with Chongqing Acoustic-Optic-Electronic Company, China Electronics Technology Group Corporation.
Yue-Peng Zhong received his B.E. degree from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2017 and now is studying for an M.S. degree at the Southwest China Institute of Electronic Technology. His research interests include electromagnetic theory and microwave circuits and systems.
Li-Tian Wang was born in Tianjin, China. He received his Ph.D. degree from the Nankai University, Tianjin, China, in 2020. His main research interests include multimode microwave filters, microstrip multiplexers, HTS bandpass filters, planar transversal bandpass filters, microwave substrate-integrated waveguide filters, and tunable bandpass filters design.
