I. INTRODUCTION
Miniaturized RF/microwave bandpass filters (BPFs) are highly desirable for the satellite and mobile communication systems [Reference Hsieh and Chang1, Reference Deng, Zhao, Zhang, Chen and Wang2]. In recent years, many different resonators, such as Y-shaped resonator [Reference Song and Xue3] and inductance-loaded Y-shaped resonator [Reference Song and Xue4], stepped -impedance resonators [Reference Wang, Wang, Wang and Guo5–Reference Alkanhal8], multiple slotline resonators [Reference Song, Pan and Xue9], half-mode substrate-integrated waveguide resonator [Reference Chen, Song, Hu and Fan10], dual-line coupling structure [Reference Song and Xue11–Reference Song and Xue13], rectangular dual spiral resonator [Reference Bukuru, Song, Ren and Zhao14], spiral resonators [Reference Song, Mo, Hu and Fan15, Reference Song, Zhang, Zhuge and Fan16], etc. have been used to design the BPFs. In addition, the dual-mode resonators have been applied to design the compact BPFs and other components because of the advantages of compact size, low cost, and simple circuit structure [Reference Liu17–Reference Chen, Yum, Li and Xue23]. A compact superconducting dual-mode BPF with shunt capacitive loading structure was proposed in [Reference Liu17]. The central frequency of the proposed resonator is reduced by 27% due to the loaded structures. In [Reference Chiou, Wu and Kuo18], a dual-mode dual-band ring resonator BPF was implemented. The entire circuit occupies <30% of the area of a traditional ring resonator filter by employing several microwave C-sections. In [Reference Tu and Chang20], a miniaturized dual-mode resonator filter with right-crossed slots was introduced. The fundamental resonance is perturbed by the right-crossed slots, which makes the proposed square patch resonator more compact. In [Reference Mao and Tang24–Reference Cheng, Xu and Zhang30], some modified hexagonal loop resonators are designed to obtain compact filters, which have better frequency selectivity and out-of-band rejection.
In this paper, a compact dual-mode BPF using hexagonal loop resonator with capacitive loading structure is presented. The frequency selectivity and out-of-band rejection can be improved by the two inherent transmission zeros (TZs). The self-capacitance and electrical length of the loop resonator can be enhanced owing to the loaded structure, which leads to a size reduction. To verify the validity of the proposed filter, a dual-band BPF prototype is designed, fabricated, and measured.
II. ANALYSIS OF THE HEXAGONAL LOOP RESONATOR BPF
Figure 1(a) shows the structure of the proposed dual-mode BPF, which has been constructed by a hexagonal loop resonator with a capacitive loading structure. The circuit size of the hexagonal loop resonator will be reduced greatly by the capacitive loading structure [Reference Hong and Lancaster31]. The capacitive loading structure is realized by using six identical arms with interdigital fingers inside each arm of the resonator. Each of the identical arms may be considered as a microstrip open-loop element [Reference Feng, Che and Xue32]. A corner patch perturbation is applied to adjust the coupling between the two degenerate modes of this dual-mode resonator. The resonance frequency of the dual-mode resonator can be tuned by changing the length L 2 of each interdigital finger arm, the gap S 1 between the coupled strips, as well as the number of capacitive interdigital fingers (as shown in Fig. 1(a)). The resonator is fed by a pair of perpendicular 50 Ω feed lines and each feed line is connected to a V-shaped coupling arm. The external quality factor was decided by the gap W 3 between the resonator and coupling arms.
Fig. 1. (a) Layout, (b) topology, and (c) simplified equivalent circuit diagram of the proposed dual-mode filter.
Figure 1(b) shows the topology of the proposed dual-mode filter, in which the dark circles represent the two degenerate modes and the empty ones represent the input and output, respectively. The black dots represent the odd and even modes; the empty ones represent the input and output, respectively. The denotation “+” represents that there is positive coupling between two elements, while the denotation “−” represents a negative coupling. According to Mo et al. [Reference Mo, Yu and Zhang28], there is no cross-coupling between two degenerate modes and the doublet filtering configuration produces one TZ in the left side of passband.
Figure 1(c) shows the simplified equivalent circuit diagram of the proposed dual-mode filter, in which there are two different transmission paths between input and output. According to Feng et al. [Reference Feng, Che and Xue32],
$${\theta _1} = {\theta _2} \pm n\pi \;(n = 1,3,5, \ldots )\;(0\;{\rm\lt} {\theta _2}{\rm\lt }2\pi )\infty \;{\rm stopband},$$
when n = 1, f = f tz , θ 1 = θ 2 + π, two different transmission paths produce one TZ in the right side of passband.
In Fig. 1(c), θ 1 = θ (L 1, f), θ 2 = θ (L 2, f). Let ΔL = L 1 – L 2, Δθ = θ (△L, f). Keep Δθ = π, with the decrease of ΔL, f tz will increase. The frequency response of the proposed resonator with varied feed position L 4 is shown in Fig. 2. It can be seen that two TZs can be observed, and the location of TZ in the upper stopband can be adjusted greatly by altering L 4, whereas that in the lower stopband changes slightly. From Fig. 1(a), it is evident that with the increase of varied L 4, ΔL will decrease, which will lead to the increase of the frequency of TZ in the upper stopband. So the frequency selectivity can be tuned properly by changing L 4.
Fig. 2. Frequency response of the proposed BPF with varied L 4.
Figure 3(a) shows the frequency response of the proposed BPF with different gap S 1. It can be seen that the central frequency of the passband can be adjusted by altering S 1. Hence, the self-capacitance and electrical length of the hexagonal loop resonator can be increased with the increased S 1. Figure3(b) illustrates the frequency response of proposed BPF with different length L 2. It can be seen that the central frequency of the passband can also be changed by tuning L 2. Meanwhile, the passband bandwidth of the BPF almost keeps constant. Hence, the suitable circuit structure of the presented BPF can be obtained by changing the length of interdigital finger arms and the size of capacitive interdigital finger structure. That is to say, the resonant frequencies can be controlled independently by changing the size of capacitive loading structure.
Fig. 3. BPF can be changed by varying (a) S 1 and (b) L 2.
As can be seen from Fig. 4(a), the bandwidth of the proposed BPF can be changed with the varied L 3. Figure 4(b) shows the simulated-mode splitting characteristics with different perturbation size L 3. As can be seen from Fig. 4(b), the mode splitting between the two degenerate modes will increase when the perturbation size L 3 increases, which contributes to the expansion of bandwidth.
Fig. 4. (a) Frequency response of the proposed BPF, (b) simulated two resonant frequencies with varied L 3, where the resonator dimensions are: L 1 = 3, L 2 = 3.4, L 3 = 2.6, L 4 = 6.5, L s = 1.7, W 0 = 11.52, W 1 = 1, W 2 = 0.6, W 3 = 0.1, W 4 = 0.4, W 5 = 1.11, S 1 = 0.3 mm.
III. FILTER DESIGN AND EXPERIMENTAL RESULTS
To verify and demonstrate the proposed circuit, a dual-mode BPF using hexagonal loop resonator with a capacitive loading structure has been designed, simulated, and optimized. The filter is designed to meet the following specifications: f 0 = 1800 MHz, FBW = 2%, RL < −20 dB, one TZ located at 1750 MHz. For the responses with the TZ in the lower stopband located at normalized frequencies of the complex s-plane s 1 = −2.81j with an in-band return loss of 20 dB, the corresponding coupling matrix is computed as
$$\left[ {\matrix{ 0 & { - 0.5991} & {1.1287} & 0 \cr { - 0.5991} & {1.6153} & 0 & {0.5991} \cr {1.1287} & 0 & { - 1.4313} & {1.1287} \cr 0 & {0.5991} & {1.1287} & 0 \cr}} \right],$$
where matrix elements M (i, j) = 1, 2, 3, 4 denote the input, odd mode, even mode, and output, respectively. The TZ in the upper stopband is produced by transversal signal interaction theory, so it cannot be obtained directly by coupling matrix. According to [Reference Hong33], the desired design parameters can be found: f odd-mode = 1771 MHz, f even-mode = 1826 MHz, Q e,odd-mode = 139, Q e,even-mode = 39.
The commercial software HFSS is used for simulating and optimizing the presented filter. The final sizes and parameters of this filter are: L 1 = 3, L 2 = 3.4, L 3 = 2.6, L 4 = 6.5, L s = 1.7, W 0 = 11.52, W 1 = 1, W 2 = 0.6, W 3 = 0.1, W 4 = 0.4, W 5 = 1.11, and S 1 = 0.3. The optimized dual-mode BPF is constructed on a substrate Taconic RF-35 with a relative dielectric constant of 3.5, thickness of 0.508 mm, and loss tangent of 0.0018. The total area of the proposed dual-band BPF is 0.2λ g × 0.23λ g , where λ g is the guided wavelength at the center frequency of passband.
Figure 5 shows a photograph of the fabricated BPF. The BPF was measured using an Agilent 8757DE8363B network analyzer. Figure 6 gives the simulation and measurement results of the fabricated dual-mode BPF. Measured results show that the fabricated dual-mode filter is centered at 1.8 GHz with fractional 3 dB bandwidth of 2%. The simulated and measured minimum insertion losses are 0.58 and 1.6 dB, respectively. Both the simulated and measured in-band return losses are >20 dB. Two TZs near the two sides of the passband, which located at 1.75 and 2.5 GHz, are observed simultaneously in simulated and measured results. The attenuation of the lower stopband is >17 dB, while that of the upper stopband is >25 dB up to 2.9 GHz. Some slight difference between the simulated and measured results could be attributed to the fabrication errors and circuit loss, including conductor, dielectric, radiation, and two Small A Type connector losses.
Fig. 5. Photograph of the fabricated BPF
Fig. 6. Simulated and measured results of the proposed filter.
To further demonstrate the performances of the filters, the comparisons of measured results for several hexagonal loop resonator filter structures [Reference Mao and Tang24–Reference Mo, Yu and Zhang29] are shown in Table 1. Compared with the structures in [Reference Mao and Tang24–Reference Mo, Yu and Zhang29], the proposed dual-mode BPFs have smaller size while keep good frequency selectivity and out-of-band rejection at the same time.
Table 1. Comparison with some hexagonal loop resonator filter structures.
IV. CONCLUSION
This paper has presented a compact dual-mode BPF using hexagonal loop resonator with shunt capacitive loading structure. Dual-mode resonance is achieved by adjusting the size of corner patch perturbation. Good frequency selectivity and out-of-band rejection can be achieved owing to two inherent TZs of the hexagonal loop resonator. Size reduction of the BPF can be realized by adjusting the size of capacitive interdigital finger structure. The simulated and measured results show that the proposed compact filter has the advantages of compact size, high skirt selectivity, and low cost.
ACKNOWLEDGEMENTS
The work for this grant was supported by the National Natural Science Foundation of China (Grant No. 61271026), by the Research Fund of Shanghai Academy of Spaceflight Technology and by the National Fund under Grant No. 9140A21010214HT05.
Kaijun Song (M'09–SM'12) received the M.S. degree in Radio Physics and the Ph.D. degree in Electromagnetic Field and Microwave Technology from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2005 and 2007, respectively. In 2011, he received the “New Century Excellent Talents in University Award” from Chinese Ministry of Education. In 2014, he received the academic and technical leaders in Sichuan Province. Since 2007, he has been with the EHF Key Laboratory of Science, School of Electronic Engineering, UESTC, where he is currently a full Professor. From 2007 to 2008, he was a postdoctoral research fellow with the Montana Tech of the University of Montana, Butte, USA, working on microwave/millimeter-wave circuits and microwave remote-sensing technology. From 2008 to 2010, he was a research fellow with the State Key Laboratory of Millimeter Waves of China, Department of Electronic Engineering, City University of Hong Kong, on microwave/millimeter-wave power-combining technology and ultra-wideband (UWB) circuits. He was a senior visiting scholar with the State Key Laboratory of Millimeter Waves of China, Department of Electronic Engineering, City University of Hong Kong in November 2012. He has published more than 150 internationally refereed journal papers. His current research fields include microwave and millimeter-wave/THz power-combining technology; UWB circuits and technologies; microwave/millimeter-wave devices, circuits and systems; and microwave remote sensing technologies. Prof. Song is the Reviewer of tens of international journals, including Scientific Reports, IEEE Transactions, and IEEE Letters.
Yu Zhu was born in Anhui, China, in 1992. He received his B.E. degree in Electrical Information Engineering from Southeast University Chengxian College in 2014, and now he is trying to obtain his Master degree in Electrical Engineering from the University of Electronic Science and Technology of China (UESTC). His current research interests include millimeter-wave techniques with a focus in RF/microwave passive.
Minghua Zhao received the M.S. and Ph.D. degrees in Electromagnetic Field and Microwave Technology from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2006 and 2009, respectively. Since 2009, he has been with the EHF Key Laboratory of Science, School of Electronic Engineering, UESTC, where he is currently an Associate Professor. His current research fields include microwave and millimeter-wave/THz devices, circuits theory, and systems application.
Maoyu Fan was born in Chongqing, China, in 1991. She received the Bachelor of Science degree in Physics from the University of Electronic Science and Technology of China (UESTC) in 2014, and is currently working toward the Master degree in the School of University of Electronic Science and Technology of China. Her current research interests include electromagnetic, metamaterials and microwave/millimeter-wave devices, circuits, and systems.
Yong Fan received a B.E. degree from Nanjing University of Science and Technology, Nanjing, Jiangsu, China, in 1985, and an M.S. degree from the University of Electronic Science and Technology of China, Chengdu, Sichuan, China, in 1992. He is a senior Member of Chinese Institute of Electronics. From 1985 to 1989, he was interested in microwave-integrated circuits. Since 1989, his research interests include millimeter-wave communication, electromagnetic theory, millimeter-wave technology, and millimeter-wave systems. He has authored or coauthored over 90 papers, 30 of which are searched by SCI and EI.
