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Quadmode dualband bandpass filter based on a stubloaded circular resonator
EURASIP Journal on Wireless Communications and Networking volume 2019, Article number: 48 (2019)
Abstract
In this paper, a quadmode dualband bandpass filter (BPF) only using a stubloaded circular resonator is presented. The odd and evenmode resonant frequencies can be easily computed and flexibly controlled by the radius of the circle and the two sets of stubs, as all odd and evenmode equivalent circuits are halfwavelength resonators (doubleended shortcircuited uniform transmission line resonator). Introducing the resonator makes the filter be analyzed and designed easily. To further improve the isolation between the two passbands, a dualband BPF is designed by introducing the sourceload coupling technique; the simulation and test Sparameter curves show that the designed BPF has four controllable transmission zeros. The good agreement of measured data with simulation results verifies the proposed design.
Introduction
With the development of microwave and millimeterwave technology, there is an increasing need of the high performance and miniaturization of multifrequency band filter in communication systems [1].
In [2], a dualband bandpass filter (BPF) was achieved by a dualmode circular resonator; however, there were only two transmission poles in each passband. A resonator with a cross slot and unbalanced stubs has been proposed [3] for the design of dualband BPF. A dualband BPF [4] makes commonmode rejection be improved by introducing four coupled Ushaped defected ground structures below the resonators, and the differential mode is not significantly affected. In [5], some resonators were used to design dualband filter, but resonant frequencies were dependent. Unfortunately, the poor inband performance of the dualband filter is also an existing disadvantage of the revised method in [2,3,4]. Meanwhile, these solutions increase the complexity of structure and analytical method in [2,3,4,5,6,7,8,9,10].
In this letter, a stubloaded quadmode circular resonator is presented to design the dualband bandpass filter. This resonator can generate four independent resonant frequencies. The properties of the presented resonator are analyzed theoretically and simulated by fullwave simulation software.
A passband controllable dualband BPF can be formed by adding a suitable external coupling structure. To greatly improve the isolation between the two passbands, the sourceload coupling is introduced, which increases the transmission zeros between the two passbands. Finally, the dualband filter with 1.25 GHz and 2.0 GHz is presented, and the measurement results show good performance.
Methodology of the proposed resonator
Analysis of the proposed resonator
The proposed stubloaded quadmode circular resonator structure consists of a circular resonator and four shortcircuited stubs, which is shown in Fig. 1a. Due to the symmetrical structure of the resonator, the theory of odd and even modes can be used to analyze it [11,12,13].
As shown in Fig. 1b, it was clear that the equivalent circuits of odd and even mode still have a symmetrical structure feature of the resonator with doubleended shortcircuit, and the shortcircuited stub shunted at the midpoint of the resonator. Consequently, we can utilize the odd and evenmode theory to analyze its odd and evenmode equivalent circuits again. That is the main idea of our proposed method. The analytical results are shown in Fig. 2a and b, respectively.
It can be seen from Fig. 2 that the four equivalent circuits are all doubleended shortcircuited resonators in the form of a uniform transmission line. The frequencies corresponding to the four resonant modes are denoted by f_{1}, f_{2}, f_{3}, and f_{4}, respectively. According to the odd and evenmode theory, the resonant frequencies can be derived as
In the case of L_{2} ≥ L_{1}, there is a relationship existing among the four frequencies: f_{4} < f_{2} < f_{3} < f_{1}. It is not hard to find, stub L_{1} exists only in f_{3} and f_{4} and L_{2} exists in f_{2} and f_{4}. All the resonant frequencies will reduce as the radius R increases. By changing the length of the stub L_{1}, only f_{3} and f_{4} can be affected. Similarly, f_{2} and f_{4} are only affected by the length of the stub L_{2}. In order to verify the above theoretical conclusions, fullwave simulation is carried out, and the simulation results shown in Fig. 3 coincide with the theoretical analysis.
The sourceload coupling technique
According to the above analysis, the four resonant frequencies can be divided into two groups in accordance with their values, the first group including f_{2} and f_{4} forms the first passband and the second group including f_{1} and f_{3} forms the second passband. In the basis of the resonator, a dualband BPF can be designed by adding the arcshaped parallel coupling feeder. That way we can control the center frequencies and relative bandwidths of the dualband by adjusting the values of each resonant frequencies and the strength of coupling. In order to further improve the performance of the filter and enhance the isolation between the two passbands, the sourceload coupling technique is introduced.
As shown in Fig. 4 (for simplicity, get arcshaped feeder structure straightened out), both ends of the feeder that is close to each other are extended and then bent down. Sourceload coupling technique refers to the introduction of a certain resonant coupling structure between the two ports so that some signals at the source end are directly coupled to the load through the coupling structure, while the other part is coupled to the load through the resonator. When the amplitude is equal and the phase difference is 180°, the transmission zeros can be generated as shown in Fig. 4c. The position of transmission zeros can be flexibly controlled by controlling the resonant frequency and coupling size of the coupling structure. Such a way makes the design of the resonator and feeders become more convenient.
Results and discussion
Structure of the dualband BPF
Based on the proposed structure and the analysis of the resonant characteristics above, a dualband BPF in other frequency is designed. The design parameters of the filter are as follows: The center frequencies of the two passbands are 1.25 GHz and 2 GHz, respectively. The insertion losses are less than 1.5 dB, and the return losses are greater than 15 dB. The first passband has a relative bandwidth of 7 to 12%, and the second is from 10 to 15%.
According to the above performance indicators and the material of existing dielectric substrates, the F4BMX dielectric substrates with a dielectric constant of 2.65 and a thickness of 1 mm were selected. The specific design ideas are as follows:
Firstly, according to Formula (1), the radius R of the ring is calculated preliminarily so that the resonant frequency of the ring is near the central frequency of the second passband. Then, the radius R is optimized by eigenmode solution through HFSS.
Secondly, adding branch L_{1} to the model and optimizing its length makes the coupling of resonant frequencies f_{1} and f_{3} reach the required strength.
Thirdly, the resonant frequencies f_{2} and f_{4} of the ring resonator are located near the central frequency of the first passband by adding a branch L_{2} and optimizing its length in the model.
Fourth, by optimizing the length of the feeder L_{f1} and the distance between L_{f1} and the resonator g_{1}, the external coupling strength can meet the requirements of their respective passband bandwidth.
Finally, according to the theory of sourceload coupling, the length of L_{f2} is optimized, and the location of transmission zeros is determined.
The configuration of structure is shown in Fig. 5. The dimensions are determined as follows: R = 32.98 mm, L_{1} = 2.59 mm, L_{2} = 26.5 mm, W = 0.5 mm, g_{1} = 0.35 mm, g_{2} = 0.7 mm, d = 1.4 mm, L_{f1} = 27.14 mm, and L_{f2} = 3.2 mm. The shortcircuited effect is achieved with a metalized via of 1 mm diameter at the end of the shortcircuited stub.
Simulated and measured results of the dualband BPF
Figure 6 shows the simulated and measured results. The center frequencies of the two passbands are 1.25 GHz and 2 GHz, respectively. The insertion losses of the lower and upper passbands are only 0.4 dB and 0.5 dB, respectively. The measured return losses of the lower and upper passbands are 18 dB and 27 dB, respectively. These meet the needs of design targets. The error between simulation and measurement results is very small, and there is a good agreement between them. Some of these deviations may be due to machining errors and SMA connectors.
Comparison between the existing filters and the proposed filter
The comparison with the existing filters is summarized in Table 1. It can be observed that the developed filter offers many advantages in this letter, such as better performance in the return losses and passbands, lower insertion losses, independently controlling bandwidths, and simple structure. It is conducive to the realization of the filter miniaturization. But the filter still has many shortcomings in design, and better performance filters will definitely be realized in the future.
Conclusion
In this letter, a stubloaded circular resonator is proposed. Because all odd and evenmode equivalent circuits have the same structure, the resonant frequencies can be easily obtained and flexibly controlled. To further improve the selectivity of the filter, a dualband BPF is designed by introducing the sourceload coupling technique so that the BPF has four controllable transmission zeros. The measured results agree well with simulated ones, and the filter has high performance.
Abbreviations
 BPF:

Bandpass filter
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Acknowledgements
The research presented in this paper was supported by Ministry of Education, China.
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Contributions
ML is the main writer of this paper. He proposed the main idea, deduced the performance of BPF, completed the simulation, and analyzed the result. PR and TX assisted ML in designing the architecture of the resonator and measuring the performance of BPF. ZX gave some important suggestions for the design of the filter. All authors read and approved the final manuscript.
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Correspondence to Zheng Xiang.
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Liu, M., Xiang, Z., Ren, P. et al. Quadmode dualband bandpass filter based on a stubloaded circular resonator. J Wireless Com Network 2019, 48 (2019) doi:10.1186/s136380191362z
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Keywords
 Bandpass filter (BPF)
 Dualband
 Circular resonator
 Coupling