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Scientific Reports volume 14, Article number: 26722 (2024 ) Cite this article 5g Coaxial Isolator
In this paper, a novel compact bandpass filter (BPF) with a wide out-of-band rejection is proposed. It can achieve broadband characteristics by combining hollow bowtie-type spoof surface plasmon polaritons (SSPPs) with complementary H-type defected grounded structures (DGSs) through aperture coupling. Compared with the conventional SSPP unit cells, the hollow bowtie-type structure exhibits much better slow-wave characteristics. The introduced slant antenna type port-coupling can produce a very strong high-performance rejection outside the high frequency stopband. Simulation results show that the SSPPs-DGS-based BPF has an excellent band pass characteristics in a broadband range with − 3dB fractional bandwidth of 43.5% at center frequency f0 of 2.04 GHz. The return loss in the passband is better than − 12 dB. Furthermore, because of the multiple transmission zeros generated in upper-stop-band, the designed BPF has an extremely strong out-of-band rejection of -40dB from 1.5 f0 to 4 f0 (f0 is the center frequency). The designed SSPPs-DGS-based BPF is fabricated by conventional printed circuit board (PCB) technology with a compact size of only 0.68λg*0.34λg (λg is the wavelength at the center frequency). The measured results have a good agreement with the simulation ones, which verifies the rationality and feasibility of the design. The miniaturized wideband BPF with broad out-of-band rejection may make it has good application prospect in the new generation microwave communication field.
As one of the most important components in the RF front-end of the communication systems, band pass filter (BPF) can effectively receive signals within a specific frequency while suppressing other signals outside of that range. Recently, various works about advanced BPF design have been proposed for different applications1,2,3. For example, Wu et al. presented a BPF based on substrate-integrated waveguide (SIW) structure, which achieved high-performance band pass characteristics from 2.94 GHz to 4.44 GHz1. Xu et al., introduced a slow-wave aperture structure to obtain narrowband band-pass characteristics at 5.8 GHz2. Wu et al., designed an electrically tunable BPF based on graphene integrated micostrip resonators3, which allows for a slightly dynamic tunability of the amplitude within the passband. Although those BPFs demonstrate impressive filtering performances including capability of achieving passband regulation, the relatively intricate structures and larger dimensions restrict their utilization in progressively integrated communication system.
In this work, we present a miniaturized broadband BPF by combining hollow bow-tie structure SSPPs and complementary H-type defected grounded structures (DGSs). First, a compact hollow bow-tie SSPP unit cell with excellent low-pass filtering performance is designed, which indicate an excellent slow wave characteristic. Next, to obtain high inhibition characteristic in upper stop-band, transition structure of folded slant antenna is proposed in two ports. The influence of the folded angles of the folded slant antenna on the filtering and out-of-band inhibition performance is also analyzed. And then, a hybrid composite structure of the combined complementary H-DGS with hollow bow-tie SSPPs is introduced by using aperture coupling. Dispersion properties of the hybrid structure and the electric field distribution of the surface are analyzed to illustrate the band pass characteristics and filtering mechanism of the proposed SSPPs-DGS-based BPF. Besides, equivalent circuit models (ECMs) for unit cells of SSPPs-based loss-pass filter and SSPPs-DGS-based BPF are established to further illustrate the filtering characteristic, revealing that the results of ECM and EM simulation have a good agreement with each other. Finally, the novel SSPPs-DGS-based BPF was fabricated by the traditional printed circuit board (PCB) technology, and the corresponding measured results have a high consistency with the simulation ones. The proposed BPF has the advantages of compact size, easy fabrication, excellent passband performance, and wide out-of-band rejection can be friendly integrated with microwave RF system.
The novel SSPP unit cell proposed here is like a hollow bow-tie shape, as shown in Fig. 1b. Compared with the traditional rectangular SSPP unit cell in Fig. 1a, the hollow bow-tie one is much adjustable because of the more parameters on both sides, meaning that the degree of freedom is higher. The substrate used in Fig. 1 is the Rogers company (Ro4350B), with thickness of ts = 0.508 mm and relative dielectric constant of (3.66 + i0.0037). The yellow part is covered with copper film with electrical conductivity of 5.8 × 107 S / m and thickness of tp=0.035 mm.
(a, b) Schematic diagram of the unit cells of a normal rectangular structure and hollow bow-tie structure SSPPs, (c) comparison of the dispersion curves of two SSPP unit cells.
The initial parameters of the hollow bow-tie SSPP unit cell is: l1 = 5 mm, l2 = 30 mm, l3 = 12 mm, a = 0.25 mm, b = 6 mm, c1 = 3 mm, c2 = 0.5 mm, w1 = 0.2 mm, w2 = 0.125 mm, ts = 0.508 mm, tp = 0.037 mm, where l1 represents the period of the structure, w1 indicates the width of the center line, a is the transverse width of the microband transmission line of the central axis, b is the length of the connecting line between the bowties, c1 and c2 indicate the length and width of the outer end, respectively. To investigate the EM wave propagation mechanism of the designed hollow bow-tie SSPPs, the dispersion characteristics of the unit cell are analyzed firstly. The dispersion curve relationship of the designed hollow bow-tie structure SSPP can be expressed as25,26:
where β0 is the phase constant of the EM wave in vacuum, l1 is the period of the unit cell structure, and a and tp are the transverse width and thickness of the mid-axial microband transmission line, respectively.
The surface dispersion curves of conventional rectangular and hollow bow-tie structure SSPP unit cells with the same height of l3 are simulated using CST Microwave Studio Suite 2020 based on finite element method (FEM). In Fig. 1a and b, the EM wave propagation direction (z-axis direction) is set as periodic boundary, x and y are set as electric boundary. The dispersion curves of parameter sweep results are illustrated in Fig. 1c. As shown in Fig. 1c, the light line separates the fast-wave region and slow-wave region. The hollow bow-tie and traditional rectangular SSPP unit cells are both in the slow-wave region which limits the EM wave to the metal surface. Compared with traditional SSPP unit cell, the hollow bow-tie structure exhibits more obvious deviation, lower cut-off frequency, and larger wave vector. This means that the hollow bow-tie structure SSPP has more excellent slow wave effect and stronger surface wave constraint ability. In addition, the smaller the line length between the hollow bow-tie b, the higher the cut-off frequency, and the length c1 of the upper ends of the bow-tie closure loop is directly proportional to its cut-off frequency. This means that the dispersion characteristics of the proposed dispersion SSPP can be adjusted by changing the size of the structure parameters. Thus, such results show that the proposed hollow bow-tie structure SSPP has excellent performance in slow-wave characteristics and bandwidth regulation, and has a higher degree of freedom, which provides a new possibility for miniaturized and strongly constrained filter design.
(a) Schematic front and back views of the hollow bowtie-type SSPPs-based low-pass filter, (b) front and back views of the folded slant antenna structure, (c) side view of the SSPP unit cell structure.
As shown in Fig. 2a, a hollow bow-tie SSPPs-based low-pass filter with the folded slant antenna is constructed. Due to the fact that microstrip lines primarily support quasi-TEM wave propagation, whereas the hollow bow-tie SSPPs structure sustains SPPs wave propagation, directly connecting a microstrip port to the hollow bow-tie SSPPs structure would prevent a smooth transition from the quasi-TEM wave to the SPPs wave27,28. This disparity would lead to momentum mismatch and subsequently cause significant return loss. In order to achieve low return loss and strong out-of-band rejection, a folded slant antenna structure is designed at both ends of the hollow bow-tie structure SSPPs in Fig. 2b. Figure 2c presents the side view of the SSPP unit cell structure. The initial parameters of the folded slant antenna structure are p3 = 3.8 mm, θ = 45°, where p3 and θ are the length and offset folded angle of the folded slant antenna, respectively.
The low-pass characteristics of the hollow bow-tie SSPPs-based filter with the folded slant antenna coupling are different with the various folded angles. Generally, S-parameters (S21 and S11) are defined as the ratio of the voltage waves reflected from and transmitted through a linear two-port network to the incident voltage waves at each port of the network, where S21 and S11 are transmission and reflection coefficients, respectively. Figure 3a-f show the S-parameters (S21 and S11) when θ equal 0°, 45°, 90°, 135°, 180°, respectively. In Fig. 3a, without folded slant antenna, the hollow bow-tie SSPPs-based low-pass filter exhibits a large return loss in 0–2.45 GHz from coefficient of reflection (S11) due to the momentum mismatch, and the performance of out-of-band suppression of transmission coefficient (S21) is poor from 6 to 10 GHz. When θ = 0°, as shown in Fig. 3b, the return loss has undergone a significant enhancement, falling below − 8 dB, while the out-of-band rejection is larger than 30 dB up to 10 GHz. After optimizing folded angle (θ) of the folded slant antenna, the superior filtering characteristics can be achieved when θ = 45°, as illustrated in Fig. 3c. The hollow bow-tie SSPPs-based low-pass filter exhibits a return loss below − 10dB, and its out-of-band rejection surpasses − 40dB within the range of 2.6 GHz to 9.5 GHz, featuring at least three transmission zeros. Upon comparing Fig. 3b with Fig. 3c, it is evident that the return loss (S11) is below − 10dB when θ = 45°, demonstrating a superior performance compared to that observed when θ = 45°. As shown in Fig. 3d-f, when the folded angle θ is increased to 90°, 135° and 180°, the performance of out-of-band suppression from 6 to 10 GHz is gradually deteriorated. Thus, the port coupling of the folded slant antenna with θ = 45° greatly optimizes the low-pass transmission capability and out-of-band rejection characteristic of the hollow bow tie SSPPs-based low-pass filter.
(a-f) Simulation S-parameter curves of the hollow bow-tie SSPPs-based low-pass filter without/with folded slant antenna and the folded angle θ set as 0°, 45°, 90°, 135° and 180°.
Hollow bow-tie SSPPs combined with folded slant antenna port coupling can achieve excellent low-pass characteristics with extreme wide out-of-band rejection. In order to achieve band pass feature as shown in Fig. 4a, b, complementary H-type DGS structure is added by metal via hole to connect hollow bow-tie SSPPs. The initial parameters are set as: d = 0.5 mm, h1 = 3 mm, h2 = 3 mm, m = 0.5 mm, where d is diameter of the metal via hole, h1 and h2 indicate the center length and two side length of complementary H-DGS, respectively, and m is the line width of complementary H-DGS.
(a, b) Front, back, and side views of hollow bowtie-type SSPP loaded with H-type DGS using aperture coupling format (SSPP-DGS), (c) the comparison of dispersion curves of SSPP-DGS unit cells with different size parameters of the hollowed H-type DGS.
As shown in Fig. 4c, the dispersion curves of the SSPPs-DGS unit cells under the initial parameters are in the fast light region at 0–1.6 GHz. It means that the SPPs wave transformed in the SSPPs-DGS unit cell decays exponentially. The low cut-off frequency of SSPPs-DGS is 1.6 GHz. With the frequency increasing, the dispersion curve is converged at 2.48 GHz, which is the upper cut-off frequency of SSPPs-DGS unit cell. As also seen from Fig. 4c, the upper cut-off frequency of SSPPs-DGS unit cell will be significantly decreased with the increase of the length h1 of the H-DGS, and the lower cut-off frequency also has small variation. Therefore, it is improved that the bandwidth can be adjusted by changing the structure parameters of SSPPs-DGS unit cell.
(a) The schematic configurations of the proposed BPF (top is blue, bottom is yellow), (b) the corresponding S-parameters.
After parameters optimization, the final proposed SSPPs-DGS based BPF is designed in Fig. 5a. The z- and x-axis are set as electric boundary, while y-axis direction is set to be the open boundary for 3D EM simulation. The simulation results illustrated in Fig. 5b shows that the pass band range of the designed BPF with − 3 dB is 1.61–2.48 GHz, which is consistent with its performance in optical dispersion characteristics. In addition, due to the resonance interaction between the folded slant antenna and the SSPP cell29, four transmission zeros appear at 3.2 GHz, 4.9 GHz, 5.6 GHz, and 6.1 GHz. The out-of-band rejection capability reaches − 40 dB in the 2.6–8.2 GHz band, which significantly improves the EM immunity of the BPF based on SSPPs-DGS.
In order to further analyze the transmission characteristics of the proposed SSPPs-DGS based BPF, the equivalent circuit models (ECMs) of the unit cells for the hollow bow-tie SSPPs-based low-pass filter and SSPP-DGS-based BPF are constructed based on transmission line theory. As shown in Fig. 6a, the equivalent inductance of the transmission line on the both sides of the hollow bow-tie SSPP unit cell is simplified as L1. L2 is the middle central axis equivalent inductance of the hollow bow-tie SSPP. The equivalent capacitors and inductance of metal hollow bowtie ring are simplified to C1, C2 and L3, respectively. Based on the above analysis, the ECM of the unit cell for the hollow bowtie SSPPs-DGS-based BPF is depicted in Fig. 6c. The equivalent capacitor of the hole which coupling hollow bow-tie SSPPs and complementary H-DGS is C3. L4 is the equivalent inductance of the hollow H-DGS.
(a, c) Equivalent circuit models (ECMs) of the unit cells for the hollow bow-tie SSPPs-based low-pass filter and SSPP-DGS-based BPF, (b, d) the corresponding comparison of S-parameters between ECM and FEM simulation.
The final optimized LC parameters of the ECMs by ADS are L1 = 3.306 nH, L2 = 1174.102 pH, L3 = 1.234 nH, L4 = 18.3 nH, C1 = 2120.6 fF, C2 = 1.476 pF and C3 = 6.532 pF. The S-parameters of corresponding ECM and FEM simulations are illustrated in Fig. 6b, d, respectively. The results show that there is a good agreement with the ECM and the FEM simulations, which verify the effectiveness of the design. The slight deviation in return loss is primarily attributed to the neglection of parasitic coupling in the ECM and the actual loss incurred by the dielectric substrate. To more intuitively observe the transmission characteristics of the SSPPs-DGS based BPF, Fig. 7 presents the electric field distributions at 0.5 GHz, 2 GHz and 4 GHz, respectively. The bright blue color indicates the lowest amplitude of the electric field, whereas the highest amplitude is represented by the bright red color.
(a-c) The simulated distributions of z-component of the electric field on the front and back layer of SSPP-DGS-based BPF at 0.5 GHz, 2.0 GHz, and 4.0 GHz.
As seen from Fig. 7a, most of the EM energy propagating along + z axis is concentrated at the slant antenna with the first two complementary H-shaped DGS at 0.5 GHz. This means that most energy is significantly dissipated and resulting in the EM wave unable to pass the SSPP-DGS-based BPF smoothly. At 2.0 GHz, as shown in Fig. 7b, electric field is uniformly distributed across the entire BPF structure due to the ability of the quasi-TEM wave, which is supported by the folded slant antenna structure, to transition smoothly into SPPs waves that facilitate surface wave transmission. So, the SPPs wave in this frequency can smoothly pass through the SSPP-DGS-based BPF structure without being dissipated. It is also observed that the z-component of the electric field predominantly concentrates on the lower region of the hollow bowtie-shaped SSPP structure within the propagating passband centered at 2.0 GHz, as the electric field in the upper section is redirected towards the backside DGS via the metal vias. This means that when the EM signal in the passband passes through the BPF, part of the signal passes through the lower part of the hollow bowtie-shaped SSPP structure, and rest part of the signal passes through the metal-coupled space and arrives at the back-DGS. At the high frequency of 4 GHz, as shown in Fig. 7c, because the frequency is greater than the upper cut-off frequency, the EM energy is reflected back by SSPPs-DGS structure.
To further substantiate the broadband filtering capabilities of the designed SSPPs-DGS-based BPF, microwave experiment is imperative. As an initial step, a prototype of the SSPPs-DGS-based BPF is fabricated using traditional PCB technology, adhering closely to the optimized simulation outcomes. The final geometric parameters of the proposed BPF are tabulated in Table 1, with default length unit of millimeters.
The final fabricated BPF with actual size of 0.68λg × 0.34λg (λg is the guided wavelength at central frequency) is depicted in Fig. 8a. The measurement is performed using the vector network analyzer (Ceyear 3656D). Figure 8b presents that the measurement results and simulation results have good agreement with each other. The small discrepancies can be attributed to the non-ideal factors such as the fabrication accuracy error and the quality of the SMA connectors. As expected, the central frequency f0 of the fabricated filter is 2.04 GHz, with a -3 dB fractional bandwidth (FBW) up to 43.5%. And the return loss in passband is better than − 12 dB. The spurious suppression level of the SSPPs-DGS-based BPF is over 40 dB in the 1.5f0-4.0f0 range outside the high frequency because of the existing of transmission zeros at 3.95 GHz, 5.2 GHz and 5.8 GHz.
(a) The test sample of the fabricated SSPP-DGS-based BPF, (b) the comparison of S-parameters obtained from measurement and simulation.
The performance comparison results of the previous BPFs based on different SSPPs structures are listed in Table 2. It is worth noting that our SSPPs-DGS-based BPF stands out not only for its excellent broadband pass capability but also for its superior performance in rejection level, transmission zeros, insertion loss, and return loss. Moreover, the compactness of our proposed SSPPs-DGS-based BPF underscores the advantages of our design in this work.
In conclusion, we have proposed and demonstrated a novel miniaturized broadband BPF based on hollow bow-tie SSPPs and complementary H-DGS. The designed BPF structure is composed of hollow bow-tie SSPPs with low-pass filtering function combined with the complementary H-type DGS through the hole coupling, with folded angle antenna structure connecting port and SSPPs. The dispersion characteristics of SSPP and SSPP-DGS unit cells are analyzed numerically. Furthermore, the transmission characteristics of the designed hollow bow-tie SSPPs-based low-pass filter and SSPP-DGS-based BPF are respectively illustrated and analyzed by FEM and ECM simulations. Simulation results indicate that the proposed SSPPs-DGS-based BPF has more compact size, better return loss characteristic and higher rejection level in upper out-of-band. Meanwhile, the upper and lower cut-off frequencies of can be adjusted by changing the related geometry parameters independently. The designed SSPPs-DGS-based BPF with compact size of 0.68λg × 0.34λg is fabricated by traditional PCB technology. The experimental results are highly agreement with the simulation ones, demonstrating that the designed BPF has wide − 3 dB bandwidth covering from 1.61 GHz to 2.48 GHz with lower than − 12 dB return loss. The measured upper out-of-band rejection level is lower than − 40 dB within 1.5f0-4.0f0. The proposed miniaturized broadband high out-of-band suppression BPF has widely applications in increasingly integrated communication systems due to its superior electrical performance, high integration and low cost.
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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This work was supported in part by the Natural Science Foundation for Exploration Program of Wuhan (Grant No. 2024040801020342).
School of Electronic Engineering, Hubei Engineering Research Center for Intelligent Detection and Identification of Complex Parts, Wuhan Vocational College of Software and Engineering (Wuhan Open University), Wuhan, 430205, P. R. China
School of Information Science and Engineering, Engineering Research Center for Metallurgical Automation and Detecting Technology Ministry of Education, Wuhan University of Science and Technology, Wuhan, 430081, P. R. China
Haihong Liu, Bin Cai & Yongzhi Cheng
School of Physics and Electronic Information Engineering, Hubei Engineering University, Xiaogan, 432000, P. R. China
Key Laboratory of High Temperature Electromagnetic Materials and Structure of MOE, Wuhan, 430081, P. R. China
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Author contributions. L.Y., B.C., H. L., and Y.C., jointly conceived the idea and set up the model; B.C., and L.Y. performed the calculations and composed the first draft of the manuscript; H.L., L.Y., and B. C. refined the model, L.W., provided helpful discussions; L.Y., Y.C., C.B., and L.W. coordinated the work. All authors have contributed to writing the manuscript. All authors have read and agreed to the published version of the manuscript.
The authors declare no competing interests.
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Lingling Yang, Haihong Liu, and Bin Cai are the co-first authors.
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Yang, L., Liu, H., Cai, B. et al. Miniaturized broadband high out-of-band rejection bandpass filter based on spoof surface plasmon polaritons with defected ground structure. Sci Rep 14, 26722 (2024). https://doi.org/10.1038/s41598-024-77705-y
DOI: https://doi.org/10.1038/s41598-024-77705-y
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