A Wideband Controllable Bandpass Filter Based on Spoof Surface Plasmon Polaritons

Introduction

Due to the congestion in the lower frequency ranges, more occupancy of these regimes may cause interference, crosstalk and mutual coupling problem [1]. Meanwhile, compact integrated circuits with efficient energy, low loss and low crosstalk need to be investigated to satisfy the continuous development of wireless communication. Band pass filters (BPF) are one of the essential components of the wireless transceiver, thus designing a broadband BPF is important for RF circuit designers. Several structures have been reported in this regard [2, 3]. In literature [2], the BPF structures generated dual passband notches with the help of multiple stubs attached to patch. In literature [3], the BPF structures with multiple transmission zeros enable frequency response. However, most of the reported structures were of large circuit area and complex construction due to the use of vias or fabrication limitation. Therefore, a band pass filter based on the spoof surface plasmon polariton (SSPP) may be a good candidate for future microwave communications.

Surface plasmon polariton (SPP) is a class of special surface electromagnetic wave mode, which was used only in the optical region for a long time [4]. Pendry et al. [5]and Hibbins et al. [6]proposed that the metal embedding with periodic sub wavelength structures could also support SPP-like mode in lower frequencies, which is known as spoof SPP(SSPP). The SSPP has several advantages over conventional microwave devices, including limiting the microwave field in a sub-wavelength scale, rejecting electromagnetic (EM) interference, and having a wide bandwidth. In 2013, Shen and Cui [7] proposed a planar structure that could realize SSPP. After that, many planar SSPP structures employing printed circuit board (PCB) technology were presented in microwave region from C to K bands [8, 9]. Since then, some SSPP structures have been realized by modulating periodic holes or grooves on the metal surface in [10–16]. Meanwhile, some works on GaAs–based BPFs have been reported in recent years [17–19]. In [18], a bandpass filter with a notched band has good transmission performance was constructed. In [19], a new GaAs-based wideband SSPP waveguide with super compact size was presented.

Recently, several SSPP-based bandpass filters have been proposed [20–26]. Substrate integrated waveguides (SIWs) were used to achieve high-efficiency SSPP propagation with controlled lower cut-off frequencies, allowing for more tuning freedom [20–23]. The SIW waveguide was directly coupled to the SSPP structure in literature [20], resulting in an extremely long physical length. In SIW, embedded SSPP units [21–23] were used to minimize the physical size. HMSIW was used to minimize the overall size of the filter in [24–26]. Using slotted HMSIW, a unit cell capable of supporting SSPP was proposed. The dispersion diagram, which is distinct from that of standard SSPP, may forecast both higher and lower cut-off frequencies in the passband. However, these designs were electronically adjustable, and changing the bandwidth is challenging. As a result, it is theoretically challenging to develop a planar mechanically controlled bandpass filter with separate controllability of low and high cut-off frequencies and low cost. Therefore, SSPP-based structures were a good choice for managing high cut-off frequency because of their advantages of having a high cut-off frequency that can be readily controlled by optimizing geometrical parameters [27–31]. Furthermore, some CPW- or microstrip-based coupling structures [32, 33]could be a promising candidate for controlling the low cut-off frequency following modification.

In this work, a wideband controllable bandpass filter is proposed, which is based on the SRR high-pass filter cascaded SSPP transmission line. The transmission characteristics own both the features of SRR and SSPP. The low-pass cut-off frequency can be controlled by SSPP structure, while the high-pass cut-off frequency can be controlled by SRR structure. The bandwidth can be tuned by diode reconfigurable technology. The filter has an operating passband over 5–9 GHz, an out-band rejection of −20 dB for the lower sideband, and an out-band rejection of −50 dB for the upper sideband. The physical processing is performed and verified, and the measured results agree well with the simulated results.

Configuration and Analysis

The bandpass filter is illustrated in Figures 1A–C. It can be considered as a combination of the SRR and SSPP units. The SSPP shown in Figure 1A controls the high cut-off frequency by changing the unit cell depth, while the SRR shown in Figure 1C based coupling structure controls the low cut-off frequency by changing the width of grooves. In addition, the RF diodes in Figure 1B controlled by a DC power are added in the SSPP to regulate the bandwidth of passband.

FIGURE 1

FIGURE 1. (A) the front view of the spoof surface plasmon filter, (B) the front view of the spoof surface plasmon filter using diode reconfigurable technology, and (C) the back view of the spoof surface plasmon filter.

The structure is printed on the 1 mm thick Taconic RF-35 substrate (relative permittivity ε_r = 3.5, loss tangent tanδ = 0.001). The SSPP is composed of a 50-Ω CPW transmission line using matched conversion. The width and length of SSPP uints are denoted by d_s and p, and the depth and width of grooves are denoted by w_s and k, respectively. The total width and length of the SSPP filter are marked as a and l, the access part is marked as l₁, CPW feeding part is marked as l₂, and the SRR part is marked as l₃. The gap width is marked as w₁, and the width of ground of CPW is marked as w₂. The length and width of the slotted slit are marked as s₁ and w₃, respectively. The slotted spacing is denoted by gap₁. Likewise, the distances between two SRR stages are denoted by trans, and the distances between two SRRs are denoted by d.

Configuration of Slip Ring Resonators

For the sake of clarity, the design of the bandpass filter starts with the basic bandpass filter, which consists of a CPW coupled with slip ring resonators (SRR). The structure of SRR is shown in Figure 2A. The coloring part is covered with a metal part, and its shape is the common center of two open rings spliced together. The currents will be induced in SRR when an external electromagnetic action received. The ring currents act as magnetic pole moments, which leads to the negative magnetic permeability. The coloring part of the figure is the copper-clad part, where r_out is the outer ring radius, e is the ring distance, f is the ring width, and r₀ is the average radius of the ring. These parameters are related to the main performance of the SRR. In a certain frequency range, this structure can be equivalent to the assembled element circuit diagram as shown in Figure 2B. C₀ is the equivalent capacitance between the whole ring and C_s is the series capacitance composed of the upper half and the lower half capacitances, which can be obtained from the series capacitance formula: C_s = C₀/4. L_s is the equivalent inductance of the SRR. The resonant frequency of the whole resonant circuit is given by

$\mathrm{f}=\frac{1}{2\mathrm{\pi }\sqrt{{\mathrm{L}}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{s}}}}(1)$

FIGURE 2

FIGURE 2. (A) The structure of SRR, (B) the equivalent circuit diagram of the SRR structure.

By structuring the SRR on the top of the dielectric substrate, the distributions of the electric field and the magnetic field are shown in Figures 3A,B, respectively. It can be observed that the electric- and magnetic-field distributions on the SRR symmetry surface are consistent.

FIGURE 3

FIGURE 3. (A) Simulation of electric field distribution of SRR at f = 4.75 GHz. (B) Simulation of magnetic field distribution of SRR at f = 4.75 GHz.

From Eq. 1, the resonant frequency of the SRR is related to the ring radius. Because the inductance and the length are proportional, the length of the ring equivalent and the equivalent inductance L_s both increase with the raise of the ring radius. The dielectric substrate is Rogers RO4003C with the dielectric constant ε_r = 3.38, tanδ = 0.001, and thickness h = 1 mm. The Parameter values of the SRR is shown in Table 1.

TABLE 1

TABLE 1. Parameter values of the SRR (unit: mm).

The results simulated by the model via changing only the radius r_out of the outer ring of the SRR are shown in the Figure 4.

FIGURE 4

FIGURE 4. (A) Analysis of the radius parameter r_out of the SRR outer ring. (B) Parameter analysis of the SRR ring opening spacing g. (C) Parameter analysis of the SRR ring opening spacing e.

The resonant frequency is 4.23, 4.75, and 5.75 GHz for the SRR outer ring radius r_out = 7.5, 6.5, and 5.5 mm, respectively. It can be seen that the resonant frequency of the SRR decreases with the increase of the outer ring radius. When the SRR ring opening spacing g increases, the equivalent length increases and L_s decreases, thus the resonant frequency increases. Keeping the outer radius of the SRR ring as a constant of r_out = 7.5 mm, the simulation results are obtained for different SRR ring opening spacing g. From the above simulation curve sshown in Figure 4B, the resonant frequencies of SRR are 4.2, 4.25, and 4.3 GHz for the opening pitch gap of 3, 4, and 5 mm, respectively. The resonant frequency of SRR is shifted to the high frequency direction with the increase of the ring opening pitch. If only the ring spacing e is changed without changing other parameters (g and r_out), the performance curves are obtained from the simulation shown in Figure 4C. From the analysis above, the effect of ring spacing e on the SRR is relatively small.

To complete the transition and achieve tight coupling, the coplanar waveguide (CPW) structure is placed on the front, the SRR resonant ring is symmetrically placed on the back, as shown in Figures 5A,B. This structure could produce a negative permeability effect near the resonant frequency to prevent the transmission of electromagnetic waves. The dimensions of the above structure are listed in Table 2. The equivalent circuit is shown in Figure 5C, where L₀ and C are the equivalent inductance and capacitance generated after the action of the SRR with CPW structure, respectively. L_s and C_s are the equivalent inductance and capacitance of the SRR after resonance generated in the structure, respectively. L_gnd represents the equivalent value of the grounding inductance. The series branch will change from inductive impedance to capacitive impedance. The port impedance is 50 Ω, which could matched to the SRR with CPW structure.

FIGURE 5

FIGURE 5. Schematic diagram of bandpass filter based on SRR CPW structure. (A) The front side view (B) The back side view (C) Equivalent circuit of the SRR CPW structure.

TABLE 2

TABLE 2. Parameter values of the bandpass filter with CPW structure based on SRR (unit: mm).

Keep the other parameters unchanged to perform simulations on parameters S₁ and d, the results in Figure 6 could be obtained.

FIGURE 6

FIGURE 6. (A) Performing sweep analysis on filter parameter S₁ (B) Performing sweep analysis on filter parameter d.

As shown in Figure 6, the passband bandwidth of the filter decreases when S₁ increases. This is mainly due to the increase of the ground inductance, which leads to the increase of the local resonant frequency. Simulations of parameter d show that the transmission characteristics in the passband gradually become better as d increases (the transmission coefficient S₂₁ can be inferred from S₁₁). However, its transmission bandwidth remains basically unchanged, so we conclude that the passband bandwidth can be controlled by adjusting parameters S₁ and d to regulate the impedance matching in the passband. Finally, the dimensions of the above structure are derived by optimization, as shown in Table 3.

TABLE 3

TABLE 3. Parameters of bandpass filter with CPW structure based on SRR (unit: mm) (optimized).

The scattering parameter (S-parameter) of the bandpass filter based on the SRR with CPW structure is shown in Figure 7. The S-parameter is obtained by simulating the model created by CST, and it produces good passband characteristics from 5 to 9 GHz as shown in Figure 7.

FIGURE 7

FIGURE 7. Bandpass filter simulation results of SRR-based coplanar waveguide structure.

Configuration of Spoof Surface Plasmon Polaritons

The high frequency characteristics of the filter is based on the SSPP transmission line (TL). The SSPP unit dispersion curves are displayed in Figure 8A. These curves remain in the slow wave region, which are similar to the natural SPP material. The cutoff frequency decreases when the length of the slot increases. The wave number of the SSPP-TL unit is larger than that of the microstrip line, which suggests that the SSPP-TL unit has better electromagnetic constrain, lower coupling, and lower signal crosstalk than the microstrip line. In order to investigate the transmission loss performance of the SSPP-TL, the numerical simulation is performed, as shown in Figure 8B. The depth d_s of the trench determines the cutoff frequency of the SSPP-TL. As the cutoff frequency decreases, the transmission loss decreases due to the stronger electromagnetic field binding.

FIGURE 8

FIGURE 8. (A) Dispersion performance of the SSPP-TL with different d_s. (B) S₂₁ of the SSPP-TL with different d_s. (C) S₂₁ of the SSPP-TL with different g.

As shown in Figure 8C, the slot width g has almost no effect on the transmission properties. Therefore, the deeper the slot, the lower the cutoff frequency and the stronger its binding.

Implementation and Measurement

Based on the theoretical analysis above, a bandpass filter with SSPP is designed. As shown in Figure 9, the SSPP based filter is cascaded by the SSPP transmission line and the SRR with CPW section. In the SRR with CPW section, the two-section SRR structure is used, which can effectively increase the low frequency rejection effect. The cutoff frequency of the SSPP TL is at 9.5 GHz. By adding a first-order ground inductor and SRR series structure, low-frequency stopband rejection can be achieved, and the optimized dimensions are listed in Table 4.

FIGURE 9

FIGURE 9. The SSPP filter (A) front side (B) reverse side.

TABLE 4

TABLE 4. Parameter values of SSPP filter.

As shown in Figure 10A, the proposed SSPP filter has a good window characteristics. The passband range is 5∼9.5GHz, the out-of-band rejection at 4 GHz is −20dB, and the out-of-band rejection at 10 GHz is −50dB for the bandpass filter. The measurement results and simulation results are basically consistent. Using reconfigurable technology, the passband range can be changed from 9.5 to 7.5 GHz by diode switching based on Figure 10B. A comparative study of the SSPP bandpass structures reported in recent literatures is presented in Table 5. The proposed filter features out-of-band rejection and passband range control.

FIGURE 10

FIGURE 10. (A) The S-parameters simulated and measured results of SSPP filter. (B) The transmission coefficient results of SSPP diode reconfigurable filter in Figure 1B.

TABLE 5

TABLE 5. Comparative study of the SSPP bandpass structure.

Conclusion

In this paper, a wideband pandpass SSPP filter is proposed, which structured based on a SRR CPW section and a SSPP transmission line. The passband can be controlled by the RF diodes. The passband of proposed filter is range from 5 to 9.5 GHz, out-of-band rejection of -20 dB at 4 GHz, and out-of-band rejection of −50 dB at 10 GHz. The measurement results and simulation results are in agreement. Finally, a passband controllable filter using diode reconfigurable technology is proposed, and the simulation analysis is given to provide a new scheme for future filter design.

Data Availability Statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author Contributions

XC and LL contributed to this work equally. All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Funding

This work was supported by the Natural Science Foundation of China under Grant 62001250.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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