A low-loss dual-band bandpass filter using open-loop stepped-impedance resonators and spur-lines for sub-6 GHz 5G mobile communications

: This article presents the design of a low-loss microstrip dual-band bandpass filter with improved inter-band isolation and selectivity for 5G sub-6 GHz mobile communications. The proposed filter utilizes the two first resonance mode frequencies provided by the stepped-impedance resonator to generate its two passbands at 3.6 GHz and 3.5 GHz, and spur-lines located before the input / output ports to improve the isolation and selectivity between passbands. The filter is designed using an RT / Duroid 5870 substrate with a relative permittivity of 2.33 and a thickness of 0.79 mm, manufactured and tested to validate the proposed design. The experimental results show that the filter operates at 3.61 GHz and 5.51 GHz with a 3-dB fractional bandwidth of 12.74% and 16.7%, respectively. Insertion losses at the two passbands center frequencies are 0.6 dB and 0.9 dB. In addition, the proposed filter has the advantage of covering the licensed and unlicensed 5G bands and provides a simple structure without using vias or DGS structures.


Introduction
The sub-6 GHz spectrum is getting more congested with several applications.Given that the licensed 5G bands may not have sufficient bandwidth to fulfill 5G requirements in this spectrum, the unlicensed band 5150-5925 MHz has recently been included in the 5G spectrum to satisfy high data rate requirements.Therefore, low-loss, compact dual-band bandpass filters (BPFs) with good passband selectivity and high inter-band isolation are highly demanded for 5G mobile communications.
In recent years, a large variety of different methods have been developed and utilized to design dualband BPFs, such as combining two single-band BPFs with different passbands.For instance, by using open-circuited stubs [1] and sub-loaded open complementary split-ring resonator (SL-OCSRR) [2].Or using the first two resonance frequency modes of loaded resonators [3] and stepped-impedance resonators (SIRs) [4].Furthermore, substrate-integrated waveguides have also been used to design widely separated passbands [5,6].Besides, several works and techniques have been reported in the literature to reduce the size of the filter.Among them, folding the two open-ended arms of SIR coupled with each other [7], bending microstrip lines, rectangular and SIR resonators [8], using λ/4 and multimode resonators [9][10][11].
For 5G mobile communications, various single-and dual-band BPFs have been reported in recent years [12][13][14][15][16][17][18].In [12], a single-band CPW BPF is formed by using spiral-shaped DGSs and m-shaped DGSs.It resonates at 3.45 GHz with a fractional bandwidth of 10.1% ranging from 3.35 to 3.71 GHz.A wideband BPF with broad stopband and ultra-wide reflectionless range is reported in [13], where the measured operating frequency is from 3.1 to 5.3 GHz.A high selectivity narrowband SIW cavity BPF with perturbing vias and CSRR operating at 4.947 GHz with a fractional bandwidth of 1.16% is presented in [14].Furthermore, a quasi-elliptic dual-band planar BPF centered at 4.6 GHz and 5.4 GHz is presented in [15], where the fractional bandwidth of the two passbands are 13.5/11.5%.A miniaturized dual-band filter using dual-mode dielectric waveguide resonator is studied in [16], it resonates at 2.91/3.53GHz with a fractional bandwidth of 2.27/1.67%.A compact dual-band BPF based on the substrate integrated suspended line (SISL) platform that operates at 3.46/4.87GHz with a fractional bandwidth of 16.2/7.7%is presented in [17].A self-packaged dual-band BPF centered at 3.45/4.9GHz with a fractional bandwidth of 11.0/6.9% is designed in [18].However, all these reported filters work only in the licensed 5G bands.
This article presents several complementary improvements related to our previous work in [18], which aimed to design a compact dual-band BPF for the licensed 3400-3800 MHz and unlicensed 5150-5850 MHz 5G bands and discuss the results obtained from simulations and measurements.In addition to that, a comparison between the proposed dual-band BPF and other recent 5G BPFs is provided.
The organization of the rest of this article is as follows: Section 2 presents the details of the analysis and design procedure of the dual-band BPF.Then, simulated and experimental results are given in Section 3. Finally, conclusions are presented in Section 4.

Design and analysis of the proposed dual-band BPF
The design of the proposed dual-band BPF is accomplished by using two open-loop SIRs and two spur-lines fed by 50 Ω input/output tapped lines.In this work, all simulations have been carried out using CST Microwave Studio software.high impedance lines are 2θ 2 and θ 1 , respectively.In our design, we chose θ 1 = θ 2 = θ for simplicity.In this case, the input impedance of the conventional SIR can be expressed as [20]:

Design of dual-band BPF using two open-loop SIRs
where R z = Z 1 /Z 2 is the ratio of the two characteristic impedances.The resonance conditions, i.e., Y in = 1/Z in = 0, can be described by the two equations: Thus, the first four resonant mode frequencies f 1 , f 2 , f 3 and f 4 can be deduced from Eq. 2.2, which can be expressed as Therefore, the normalized frequencies f 2 / f 1 , f 3 / f 1 and f 4 / f 1 can be written as To design the dual-band BPF, the first and second resonant frequencies of the SIR f 1 and f 2 are used as the center frequencies of the upper and lower passband of the filter.In our study, we set f 1 = 3.6 GHz and f 2 = 5.5 GHz.According to equation (2.7), the calculated impedance ratio R Z is 2.75.By choosing Z 1 = 50 Ω, the initial lengths and widths of the low and high impedance lines of the SIR can be calculated using the following formulas: ) ) .13)where Z 0 is the characteristic impedance of the microstrip line, h is the thickness of the substrate, ϵ r and ϵ e are the relative and effective dielectric constants of the substrate and λ g and λ 0 are the guided and free-space wavelengths, respectively.These initial parameters are: L 1 = 9.76 mm, L 2 = 19.52 mm, w 1 = w 2 = 2.37 mm, w 3 = 0.24 mm, g 1 = 0.5 mm and g 2 = 0.6 mm.For miniaturization, two open-loop SIRs are used rather than conventional SIRs fed by 50 Ω input/output tapped lines, as shown in Figure 2.
The reason behind choosing the tapped lines to excite the filter is to produce two transmission zeros in the lower and upper stopband of the first passband [19].The response of the filter is depicted in Figure 3, which illustrates that f 1 constructs the first passband at 3.78 GHz, whereas f 2 constructs the second passband at 5.87 GHz.Some slight discrepancies between analysis and simulation are observed due to the coupling between resonators and the coupling between the edges of the high-impedance lines, since in the analysis one SRR is considered.This deviation can be fixed by varying the length of the SIR.From Figure 4, it can be seen that the bandwidth of the first passband is affected by the position of the tapped line.As the tapping position becomes closer to the center position of the resonator, the external quality factor value becomes larger since the bandwidth becomes narrower.Plus, the bandwidth of both passbands can also be simultaneously adjusted by properly changing the separation between resonators g 1 as illustrated in Figure 5.The smaller is the separation, the larger is the bandwidth.
As the tapped lines produce two transmission zeros in the lower stopband of the first passband and between two passbands, another transmission zero can be observed in the upper stopband of the filter.This transmission zero can be adjusted by controlling the coupling between high-impedance lines, as shown in Figure 6.By selecting the appropriate value of the gap, g 2 , the out-of band rejection and the skirt characteristic of the upper band-edge of the second passband can be improved.Based on this analysis, the filter above is optimized, and its final physical dimensions are as follows: L 1 = 10.31 mm, L 2 = 20.65 mm, w 1 = w 2 = 2.37 mm, w 3 = 0.24 mm, g 1 = 0.58 mm and g 2 = 0.57 mm. Figure 7 depicts its simulated frequency responses.As can be seen, the filter operates at 3.6 GHz and 5.55 GHz, covering 3381-3871 MHz and 8150-5840 MHz bands.Insertion losses of 0.37 dB at 3.6 GHz and 0.42 dB at 5.5 GHz with more than 26 dB and 30 dB return losses, respectively, were
achieved.Two transmission zeros in the lower and upper stopbands are clearly observed at 2.93 GHz and 6.29 GHz, and one transmission zero located at 4.4 GHz provides 43.6 dB isolation between passbands.Moreover, the roll-off rate of the lower transition of the upper passband is 49.4 dB/GHz.The size of the filter without feed lines is 0.25λ g ×0.30λ g , where λ g is the guided wavelength at 3.6 GHz.

Inter-Band isolation and selectivity improvement
It is true that the passband frequencies of the filter can be controlled by the impedance ratio of the SIR.However, the inter-band isolation and selectivity of the filter must be improved, especially if the passband frequencies are widely separated.In our design, the two passbands are relatively close to each other.Adding a transmission zero between passbands should not affect the filter response.For that, to achieve the best performance with fabrication simplicity and low-cost methodology, a simple method based on adding a pair of spur-lines before the input/output ports of the filter is employed.In general, the spur-line can be created by etching an L-slot in the main transmission line, as depicted in Figure 8, where W 0 and L are the width of the main transmission line and the length of the spur-line, which is equal to the quarter-wavelength at the fundamental frequency.g is the gap between the coupled lines.Figure 9 depicts the structure of the improved filter.Here, the spur-lines are meandered to reduce the size of the filter.Based on the results shown in Figure 7, the variation of the introduced transmission zero is investigated when the length of the spur-line is varied (Figure 10).As can be seen, the frequency of the transmission zero increases with increasing length L. Also, it can be anticipated from Figure 11 that the two transmissions zero between passbands become insensitive to the gap g when its value becomes larger.In this case, the two transmission zeros can be overlapped.Figure 12 shows the simulated frequency responses for the filter with and without spur-line, it is found that the transmission zero, which is caused by adding the spur-line, has improved the isolation between the two passbands (48.2 dB) and also the selectivity of the second passband (the roll-of rate of the lower transition of the upper passband is 69.2 dB/GHz) without perturbing the response of the previous filter.
The current distributions of the proposed dual-band BPF filter at the center frequencies 3.6 GHz and 5.5 GHz and at the transmission zero frequencies 2.95 GHz, 4.4 GHz, 4.5 GHz and 6.3 GHz are shown in Figure 13.From this figure, we can observe that high current is concentrated on the high impedance lines at 3.6 GHz and 5.5 GHz.However, there is no current flowing from the input port to the output port at 2.95 GHz, 4.4 GHz, 4.5 GHz and 6.3 GHz, which indicates the BPF behavior of the structure.

Experimental results and discussion
In order to examine the validity of the proposed design, the proposed dual-band BPF is designed and manufactured on an RT/duroid 5870 substrate with a relative permittivity of 2.33 and a thickness of 0.79 mm.Its physical dimensions are as follows: L 1 = 20.65 mm, L 2 = 10.31 mm, w 1 = w 2 = 2.37 mm, w 3 = 0.24 mm, g = 0.1 mm, g 1 = 0.58 mm, g 2 = 0.57 mm, w = 0.2 mm and L = 13 mm.
The photograph of the fabricated dual-band BPF with its measurement equipment are depicted in Figure 14, and its size without feed lines is 0.25 λ g × 0.47λ g , where λ g is the guided wavelength at 3.6 GHz. Figure 15    To highlight the performances of the proposed dual-band BPF, a comparison with other works are listed in Table 1.The benefits of our proposed filter can be summarized as follows: first, the proposed filter covers the licensed and unlicensed 5G bands.Second, the inter-band isolation and selectivity of the filter are improved due to the use of spur-lines before the input/output ports, which generate a transmission zero between passbands without degrading the passband performance.Finally, there is good performance in terms of low insertion loss, good return losses and simplicity of the design since no vias or DGS structures are used in this filter.

Conclusions
This article presents a low-cost dual-band BPF using open-loop SIRs with improved inter-band isolation and selectivity centered at 3.61/5.51GHz for 5G sub-6 GHz licensed and unlicensed bands mobile communications.Both simulation and measured results have been provided to validate the proposed design, and good agreement between them has been found.The transmission zero generated by the spur-line improves the isolation and selectivity between the closely spaced passbands without degrading the passband performance, making the filter easy to design and implement since no vias or DGS structures are used.The proposed dual-band BPF has insertion losses of 0.6 dB and 0.9 dB and return losses of 32.9 dB and 17.24 dB at 3.61 GHz and 5.51 GHz, respectively.The roll-off rate of the lower transition of the second passband is 101.6 dB/GHz, and the upper stopband ranges from 6.14 GHz to 8 GHz with a rejection level of 18 dB.Compared with other reported works, the proposed dual-band BPF exhibits the advantages of low insertion loss, good return loss and a simple structure, indicating that it would be a good candidate for 5G sub-6 GHz mobile communications.

Figure 1 .
Figure 1.The conventional structure of the λ g /2 SIR.

Figure 2 .
Figure 2. Structure of the dual-band BPF.

Figure 3 .
Figure 3. Simulated response of the initial-designed bandpass filter.

Figure 4 .
Figure 4. Variation of |S 21 | versus the tapped feeding lines t.

Figure 6 .
Figure 6.Variation of |S 21 | versus the gap between edges of the high-impedance lines g 2 .

Figure 7 .
Figure 7. Simulated S-parameters of the filter shown in Fig. 2.

Figure 8 .
Figure 8. Structure of the spur-line section.

Figure 9 .
Figure 9. Structure of the improved dual-band BPF.

Figure 10 .
Figure 10.Variation of |S 21 | versus the length of the spur-line L.

Figure 11 .
Figure 11.Variation of |S 21 | versus the gap of the spur-line g.

Figure 12 .
Figure 12.Comparison between the filter with and without spur-line.
Figure 14, and its size without feed lines is 0.25 λ g × 0.47λ g , where λ g is the guided wavelength at 3.6 GHz.Figure15depicts the simulated and measured S-parameters of the experimental filter designed at 3.6/5.5GHz, and good agreement between them is observed.The measured center frequencies of the proposed dual-band BPF are 3.61 GHz and 5.51 GHz, with 3-dB bandwidth ranging from 3390 to 3850 MHz and 4970 to 5860 MHz, respectively.The measured in-band return losses are 32 dB and 17.2 dB, with insertion losses of 0.6 dB and 0.9 dB at 3.61 GHz and GHz, respectively.Four measured transmission zeros are found at 2.94 GHz, 4.37 GHz, 4.58 GHz and 6.27 GHz with a peak attenuation of 40.4 dB, 48.6 dB, 45.8 dB and 39.3 dB, among them two between passbands.In addition to that, the out-of-band rejection in the lower stopband is better than 20 dB in the frequency range of 1 to 3.1 GHz, while in the upper stopband is better than 18 dB.The measured roll-off rate of the lower transition of the second passband is 101.6 dB/GHz.

Figure 14 .
Figure 14.Photograph of the fabricated dual-band BPF with its measurement equipment.

Figure 15 .
Figure 15.Simulated and measured S-parameters of the proposed dual-band BPF.

Table 1 .
Comparison between this work and other previous 5G BPFs.