# Compact Quadband Bandstop Filter Based on Concentric Split Ring Resonators with Perturbation for Multifunctional Wireless Systems

Authors: Pierre Moukala Mpele
Journal: International Journal of Antennas and Propagation
 (2022)

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## Abstract

Bandstop filters play an essential role in many radio frequency (RF) and microwave communication systems to block undesired signals or reject spurious harmonics. This paper presents the design and experiment of a compact quadband bandstop filter centered at 1.2/1.97/2.96/4.78 GHz with a passband insertion loss ranging from 1.07 to 2.9 dB. The overall volumetric size of the proposed filter is 0.197λg × 0.197λg × 0.01λg, where λg is the guided wavelength at 1.2 GHz. The desired performance is achieved by introducing two diamond-shaped concentric split ring resonators (DSCSRRs) intercoupled and defected ground structure. The metamaterial properties of the DSCSRR have been verified by extracting and analyzing its effective permittivity and permeability. This research shows that DSCSRRs can generate multiband characteristics and yield high selectivity with good band-to-band isolation by generating transmission zeros between passbands. The filter is designed, optimized, and analyzed using High-Frequency Structural Simulator (HFSS). A good agreement is observed between simulated and experimental results. The measured results demonstrate that the proposed quadband banstop filter exhibits a minimum stopband rejection of 11.22 dB and fractional bandwidth greater than 4.51%, which makes it suitable for front-end transceiver components or multifunctional wireless systems to suppress unwanted signals at four separate frequency bands.


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## Body

## 1. Introduction

The suppression of unwanted frequency ranges and noise avoidance are essential issues in microwave and wireless communication systems. Band-stop filters perform this particular role owing to their band rejection ability. Besides, with the diversity of wireless applications, the demand for multifrequency filtering elements has increased. However, unlike multiband bandpass filters [1–7], multiband bandstop filters have not been as widely explored [8]. Also, the majority of multiband banstop filter design developed in the last decade were mostly concentrated on dual band and triband filtering responses [9–11]. In the literature, Split Ring Resonators (SRRs) are widely used in metamaterial cell configurations where the concept of single- and double-negative media can be exploited to reconfigure bandstop filters to bandpass filters (and vice versa) in both technologies [12]. Moreover, metamaterials though SRRs help in achieving the miniaturization of a filter structure with low insertion loss, and high out off-band rejection [13].Unlike other microstrip passive components, quadband bandstop filter designs are relatively less in the scientific literature, to the best of the author’s knowledge. In [14], a compact quadband bandstop filter using square spiral resonators based on folded stepped impedance resonators, while dual-plane defected structures and open-loop resonators have been employed to develop a quadband bandstop filter in [15]. Another technique has been suggested for quadband filtering response based on coupled-line and shorted stub-loaded half-wavelength microstrip resonator. The quad-section stepped impedance open stub was proposed in [16], whereas the dual-mode open-loop resonators having thin-film capacitors in [17]. In addition to the aforementioned work, multiple-mode resonator have also been explored for quadband filtering characteristic [18].This paper introduces and discusses a new quadband bandstop filter with diamond-shaped concentric split ring resonators (DSCSRRs). The DSCSRRs exhibit simultaneously single negative and double-negative behaviors in some particular frequency ranges. Those properties are helpful in microwave engineering. The proposed filter is compact and generates four transmission zeros which improve the selectivity and yield a high band to band isolation. Finally, the proposed quadband bandstop filter is analyzed, fabricated, and measured to validate its performance. A good agreement is found between simulated and measured results. The proposed filter has good performance in stopbands as well as passbands. It is cost-effective and easy to manufacture, making it an outstanding candidate for use in multifunctional wireless communication systems.


## 2. Filter Design

The main focus of this research is to construct a bandstop filter to reduce interferences from received signal. The proposed quadband bandstop filter is based on diamond-shaped concentric split ring resonators (DSCSRRs), designed and fabricated using a 1.524 mm thick FR-4 substrate with a permittivity of 4.4 and a loss tangent of 0.02. The design geometry configuration is presented in Figure1 below.In addition to using the DSCSRRs, a diamond-shaped slot whose configuration is depicted in Figure1(b) is inserted in the ground plane, yielding the proposed filter configuration. In Figure 2, the width of each open ring is the same, with the distance separating two consecutive open-loops. The optimized design parameters of the proposed filter are provided in Table 1.Figure 1
Proposed filter design configuration: (a) top view, (b) bottom view.
(a)(b)Table 1
Optimized design parameters of the proposed filter.
ParameterValue (mm)L30Lf5.4755LS11.5Lp14Lu12.5Wf0.75gap0.1s0.375


### 2.1. Filter Design Procedure

This section presents the main steps that have been used to design the hybrid quadband bandstop investigated in this paper.The design starts with a simple diamond-shaped fed by using two microstrip transmission lines (Figure2(a)). The corresponding frequency response presented in Figure 3(a) shows bandstop filter characteristics with a 3 dB cutoff frequency at 1.17 GHz. The filter has poor sharpness and stopband rejection while achieving an ultrawideband operation with a 6-dB fractional bandwidth of 105.65% though. Also, two passbands are observed at 5.16 GHz and 6.92 GHz with a return loss of 14.3 dB and 13.73 dB, respectively. The passband insertion loss is 2.09 dB and 2.6 dB for the first and the second passband. No transmission zero is observed at this stage. This implies that the filter exhibits poor selectivity.Figure 2
Design procedure of the proposed filter: (a) Step 1, (b) Step 2, (c) Step 3, and (d) Step 4.
(a)(b)(c)(d)In the second step (Figure2(b)), the interior metallization of the patch is removed. The frequency response displayed in Figure 3(b) illustrates a dual-band lowpass-bandpass behavior similar to the design proposed in [19]. But, in this case, the band-to-band isolation is relatively poor, with a maximum stopband rejection of 4.1 dB. The 3 dB cutoff frequency of the lowpass filter is fount at 4.75 GHz, and the bandpass resonant frequency of the bandpass filter is 6.42 GHz with 1.23 dB insertion loss. Also, the frequency response illustrates two transmission poles (reflection zeros) located at 1.2 GHz and 4 GHz in the lowpass filter. This kind of filter can be used in some applications such as mixers and hybrid fiber-coaxial supported systems [20].Figure 3
Design process of the proposed hybrid quadband lowpass-passband filter: (a) Step 1, (b) Step 2, (c) Step 3, and (d) Step 4.
(a)(b)(c)(d)The third step of the design procedure is shown in Figure2(c). As it can be seen, a split is etched on the diamond-shaped loop created in Step 2 above. This leads to an ultrawide stopband filter with a 3 dB fractional bandwidth of 86.62%, as illustrated by the frequency response shown in Figure 3(c). Besides, a transmission zero (TZ) is observed at 2.92 GHz with 35.04 dB stopband rejection, improving filter selectivity. Two transmission poles are also displayed at 5.1 GHz and 6.5 GHz with passband insertion loss of 1.72 dB and 1.35 dB. It is important to note that up to this stage, the filter does not exhibit a multiband bandstop characteristic as from Figures 3(a)–3(c).To address this, a diamond-shaped concentric split ring resonators (DSCSRRs) unit cell is designed and inserted to the design configuration (Figure2(d)) along with the 45°-rotated square slot in the ground plane. The multiband behavior is achieved. From Figure 3(d), a quadband-bandstop behavior is observed. Four transmission zeros are obtained at 1.31 GHz, 1.92 GHz, 2.75 GHz, and 4.22 GHz with 13.82 dB, 11.02 dB, 28.82 dB, and 22.83 dB stopband rejection, respectively. The corresponding return loss at these stopbands is 2.28 dB, 3.1 dB, 0.58 dB, and 0.87 dB. This illustrates a good stopband rejection characteristic for the proposed quadband bandstop filter.Moreover, in the passbands, the insertion loss is 0.81 dB, 1.59 dB, and 2.9 dB at the respective resonant frequencies, which are 1.41 GHz, 2.01 GHz, and 3.72 GHz. The corresponding return loss is 23.86 dB, 17 dB, and 11.81 dB. These performance parameters are further validated by manufacturing the filter prototype and taking measurements.The proposed quadband bandstop filter can be modeled by an equivalent circuit made of passive lumped elements (inductor and capacitor in parallel grouping) based on the theory of the stopband filter described in [21] where the following formulas are employed to calculate the elements,(1)C=12πZfu−fl,L=14π2f02C.fu and fl are upper and lower cutoff frequencies at −10 dB, f0 is the resonant frequency, and Z denotes the input impedance of filter and can be obtained from the simulated results.Figure4 illustrates the equivalent resonant circuit model of the proposed quadband bandstop filter in which each stopband is modeled as a parallel LC resonant circuit.Figure 4
Equivalent LC circuit model of the designed filter.


### 2.2. Diamond-Shaped Concentric Split Ring Resonators (DSCSRRs)

In this research, DSCSRRs are studied, and their fundamental properties are investigated. The coupling between the resonators is controlled by the line width “s” of the line separating two consecutive diamond-shaped loops, as shown in Figure5. Increasing the line width “s” between the resonators will decrease coupling and consequently decrease the stopband bandwidth. A split-ring resonator (SRR) is commonly involved as an elementary cell for producing a magnetic response [22]. The proposed DSCSRRs unit cell shown in Figure 5 is designed on top of a 18 × 18 × 1.524 mm3 FR-4 substrate and simulated using HFSS where a 1.5 mm width microstrip line is inserted to respond electrically to electromagnetic fields. The material’s effective parameters are retrieved with a MATLAB computer code provided in [23].Figure 5
(a) DSCSSRs unit cell configuration, (b) Unit cell simulation setup in HFSS.
(a)(b)Figure5(b) presents the simulation setup for the proposed unit cell where the perfect electric and perfect magnetic conductor boundaries are employed along with wave ports to extract its main parameters. The Perfect Electric and Perfect Magnetic boundaries are applied to the pairs (1, 3) and (2, 4) as boundary conditions. The wave port excitations are employed on the faces labeled “5” and “6.”From the metamaterial parameters retrieval techniques described in [23–25], effective permittivity and permeability are related to the simulated reflection (S11) and transmission (S21) coefficients by following equations,(2)n=1k0dcos−112S211−S112+S212,z=±1+S112−S2121−S112−S212.n denotes the refractive index, k0, the free space wavenumber, z, the wave impedance of the slab, ε the effective permittivity, μ, the effective permeability of the material, and d, the cell dimension.The simulation is performed using HFSS, which is a 3D full wave simulator based on Finite Element method (FEM). The scattering parameters of the proposed unit cell are presented in Figure6 below. It can be observed that the transmission coefficient achieves its lowest values at around 0.6 GHz and 5.26 GHz, whereas the resonance and filtering characteristics are seen from 2.25 GHz and above.Figure 6
Scattering parameters of the DSCSRR.To further characterize the proposed DSCSRR unit cell, the real parts of the effective permittivity and permeability are extracted and presented in Figure7. It can be observed that the DSCSRRs exhibit either a single negative (SNG) or double-negative (DNG) behavior in the frequency bands of interest, which are the most helpful metamaterial properties.Figure 7
Retrieved real effective permittivity and permeability of the DSCSSRs.Contains Table2 all the frequency responses for the proposed metamaterial unit cell. The extracted real permittivity and permeability are provided with their respective signs in the given frequency bands.Table 2
Extracted real permittivity and permeability values.
Frequency rangeReal permittivityReal permeability0.5–0.59 GHzNegativePositive0.59–0.9 GHzPositivePositive0.9–1.85 GHzNegativePositive1.85–2 GHzNegativeNegative2–3.12 GHzPositiveNegative3.12–3.76 GHzNegativeNegative3.76–3.86 GHzNegativeNegative3.86–4.13 GHzNegativePositive4.13–4.38 GHzNegativePositive4.38–4.81 GHzPositivePositive4.81–5.10 GHzNegativePositive5.10–5.27 GHzPositivePositive5.27–5.61 GHzNegativePositive5.61–5.67 GHzPositivePositive5.67–6.08 GHzNegativeNegative6.08–7.24 GHzPositiveNegative7.24–7.5 GHzNegativeNegativeIt can be observed that in the frequency regions 0.59–0.9 GHz, 4.38–4.81 GHz, 5.61–5.67 GHz, and 6.08–7.24 GHz, the proposed DSCSRR unit cell achieves positive real permittivity and permeability. The substrate provides a normal behavior of a standard insulator. This property does not add value in perturbating the current distribution or the electric field.In the frequency ranges 1.85–2 GHz, 3.12–3.86 GHz, 5.67–6.08 GHz, and 7.24–7.5 GHz, the proposed unit cell performs a double-negative behavior, which affects allow waves to propagate in the opposite direction (backward waves). This behavior is commonly exploited for bandwidth in many applications, such as bandwidth improvement and miniaturization in microwave engineering. Lastly, the single negative behavior is observed from the regions 0.5–0.59 GHz, 0.9–1.85 GHz, 2–3.12 GHz, 3.86–4.38 GHz, 4.81–5.10 GHz, and 5.27–5.61 GHz. This filtering property slows down or blocks the wave’s propagation, leading to a filtering behavior. This feature is commonly used for mutual coupling reduction in MIMO antenna systems and bandstop filters.


### 2.3. Realization of the Proposed Filter

Figure8 displays a photograph of the filter prototype fabricated on a double-sided FR4 substrate using the high precision LPKF ProtoMat S103. The copper cladding top and bottom is 35 μm. The footprint of the proposed quadband filter is 30 × 30 mm2(0.197λg × 0.197λg).Figure 8
Photograph of the fabricated prototype: (a) top view; (b) bottom view.
(a)(b)


## 2.1. Filter Design Procedure

This section presents the main steps that have been used to design the hybrid quadband bandstop investigated in this paper.The design starts with a simple diamond-shaped fed by using two microstrip transmission lines (Figure2(a)). The corresponding frequency response presented in Figure 3(a) shows bandstop filter characteristics with a 3 dB cutoff frequency at 1.17 GHz. The filter has poor sharpness and stopband rejection while achieving an ultrawideband operation with a 6-dB fractional bandwidth of 105.65% though. Also, two passbands are observed at 5.16 GHz and 6.92 GHz with a return loss of 14.3 dB and 13.73 dB, respectively. The passband insertion loss is 2.09 dB and 2.6 dB for the first and the second passband. No transmission zero is observed at this stage. This implies that the filter exhibits poor selectivity.Figure 2
Design procedure of the proposed filter: (a) Step 1, (b) Step 2, (c) Step 3, and (d) Step 4.
(a)(b)(c)(d)In the second step (Figure2(b)), the interior metallization of the patch is removed. The frequency response displayed in Figure 3(b) illustrates a dual-band lowpass-bandpass behavior similar to the design proposed in [19]. But, in this case, the band-to-band isolation is relatively poor, with a maximum stopband rejection of 4.1 dB. The 3 dB cutoff frequency of the lowpass filter is fount at 4.75 GHz, and the bandpass resonant frequency of the bandpass filter is 6.42 GHz with 1.23 dB insertion loss. Also, the frequency response illustrates two transmission poles (reflection zeros) located at 1.2 GHz and 4 GHz in the lowpass filter. This kind of filter can be used in some applications such as mixers and hybrid fiber-coaxial supported systems [20].Figure 3
Design process of the proposed hybrid quadband lowpass-passband filter: (a) Step 1, (b) Step 2, (c) Step 3, and (d) Step 4.
(a)(b)(c)(d)The third step of the design procedure is shown in Figure2(c). As it can be seen, a split is etched on the diamond-shaped loop created in Step 2 above. This leads to an ultrawide stopband filter with a 3 dB fractional bandwidth of 86.62%, as illustrated by the frequency response shown in Figure 3(c). Besides, a transmission zero (TZ) is observed at 2.92 GHz with 35.04 dB stopband rejection, improving filter selectivity. Two transmission poles are also displayed at 5.1 GHz and 6.5 GHz with passband insertion loss of 1.72 dB and 1.35 dB. It is important to note that up to this stage, the filter does not exhibit a multiband bandstop characteristic as from Figures 3(a)–3(c).To address this, a diamond-shaped concentric split ring resonators (DSCSRRs) unit cell is designed and inserted to the design configuration (Figure2(d)) along with the 45°-rotated square slot in the ground plane. The multiband behavior is achieved. From Figure 3(d), a quadband-bandstop behavior is observed. Four transmission zeros are obtained at 1.31 GHz, 1.92 GHz, 2.75 GHz, and 4.22 GHz with 13.82 dB, 11.02 dB, 28.82 dB, and 22.83 dB stopband rejection, respectively. The corresponding return loss at these stopbands is 2.28 dB, 3.1 dB, 0.58 dB, and 0.87 dB. This illustrates a good stopband rejection characteristic for the proposed quadband bandstop filter.Moreover, in the passbands, the insertion loss is 0.81 dB, 1.59 dB, and 2.9 dB at the respective resonant frequencies, which are 1.41 GHz, 2.01 GHz, and 3.72 GHz. The corresponding return loss is 23.86 dB, 17 dB, and 11.81 dB. These performance parameters are further validated by manufacturing the filter prototype and taking measurements.The proposed quadband bandstop filter can be modeled by an equivalent circuit made of passive lumped elements (inductor and capacitor in parallel grouping) based on the theory of the stopband filter described in [21] where the following formulas are employed to calculate the elements,(1)C=12πZfu−fl,L=14π2f02C.fu and fl are upper and lower cutoff frequencies at −10 dB, f0 is the resonant frequency, and Z denotes the input impedance of filter and can be obtained from the simulated results.Figure4 illustrates the equivalent resonant circuit model of the proposed quadband bandstop filter in which each stopband is modeled as a parallel LC resonant circuit.Figure 4
Equivalent LC circuit model of the designed filter.


## 2.2. Diamond-Shaped Concentric Split Ring Resonators (DSCSRRs)

In this research, DSCSRRs are studied, and their fundamental properties are investigated. The coupling between the resonators is controlled by the line width “s” of the line separating two consecutive diamond-shaped loops, as shown in Figure5. Increasing the line width “s” between the resonators will decrease coupling and consequently decrease the stopband bandwidth. A split-ring resonator (SRR) is commonly involved as an elementary cell for producing a magnetic response [22]. The proposed DSCSRRs unit cell shown in Figure 5 is designed on top of a 18 × 18 × 1.524 mm3 FR-4 substrate and simulated using HFSS where a 1.5 mm width microstrip line is inserted to respond electrically to electromagnetic fields. The material’s effective parameters are retrieved with a MATLAB computer code provided in [23].Figure 5
(a) DSCSSRs unit cell configuration, (b) Unit cell simulation setup in HFSS.
(a)(b)Figure5(b) presents the simulation setup for the proposed unit cell where the perfect electric and perfect magnetic conductor boundaries are employed along with wave ports to extract its main parameters. The Perfect Electric and Perfect Magnetic boundaries are applied to the pairs (1, 3) and (2, 4) as boundary conditions. The wave port excitations are employed on the faces labeled “5” and “6.”From the metamaterial parameters retrieval techniques described in [23–25], effective permittivity and permeability are related to the simulated reflection (S11) and transmission (S21) coefficients by following equations,(2)n=1k0dcos−112S211−S112+S212,z=±1+S112−S2121−S112−S212.n denotes the refractive index, k0, the free space wavenumber, z, the wave impedance of the slab, ε the effective permittivity, μ, the effective permeability of the material, and d, the cell dimension.The simulation is performed using HFSS, which is a 3D full wave simulator based on Finite Element method (FEM). The scattering parameters of the proposed unit cell are presented in Figure6 below. It can be observed that the transmission coefficient achieves its lowest values at around 0.6 GHz and 5.26 GHz, whereas the resonance and filtering characteristics are seen from 2.25 GHz and above.Figure 6
Scattering parameters of the DSCSRR.To further characterize the proposed DSCSRR unit cell, the real parts of the effective permittivity and permeability are extracted and presented in Figure7. It can be observed that the DSCSRRs exhibit either a single negative (SNG) or double-negative (DNG) behavior in the frequency bands of interest, which are the most helpful metamaterial properties.Figure 7
Retrieved real effective permittivity and permeability of the DSCSSRs.Contains Table2 all the frequency responses for the proposed metamaterial unit cell. The extracted real permittivity and permeability are provided with their respective signs in the given frequency bands.Table 2
Extracted real permittivity and permeability values.
Frequency rangeReal permittivityReal permeability0.5–0.59 GHzNegativePositive0.59–0.9 GHzPositivePositive0.9–1.85 GHzNegativePositive1.85–2 GHzNegativeNegative2–3.12 GHzPositiveNegative3.12–3.76 GHzNegativeNegative3.76–3.86 GHzNegativeNegative3.86–4.13 GHzNegativePositive4.13–4.38 GHzNegativePositive4.38–4.81 GHzPositivePositive4.81–5.10 GHzNegativePositive5.10–5.27 GHzPositivePositive5.27–5.61 GHzNegativePositive5.61–5.67 GHzPositivePositive5.67–6.08 GHzNegativeNegative6.08–7.24 GHzPositiveNegative7.24–7.5 GHzNegativeNegativeIt can be observed that in the frequency regions 0.59–0.9 GHz, 4.38–4.81 GHz, 5.61–5.67 GHz, and 6.08–7.24 GHz, the proposed DSCSRR unit cell achieves positive real permittivity and permeability. The substrate provides a normal behavior of a standard insulator. This property does not add value in perturbating the current distribution or the electric field.In the frequency ranges 1.85–2 GHz, 3.12–3.86 GHz, 5.67–6.08 GHz, and 7.24–7.5 GHz, the proposed unit cell performs a double-negative behavior, which affects allow waves to propagate in the opposite direction (backward waves). This behavior is commonly exploited for bandwidth in many applications, such as bandwidth improvement and miniaturization in microwave engineering. Lastly, the single negative behavior is observed from the regions 0.5–0.59 GHz, 0.9–1.85 GHz, 2–3.12 GHz, 3.86–4.38 GHz, 4.81–5.10 GHz, and 5.27–5.61 GHz. This filtering property slows down or blocks the wave’s propagation, leading to a filtering behavior. This feature is commonly used for mutual coupling reduction in MIMO antenna systems and bandstop filters.


## 2.3. Realization of the Proposed Filter

Figure8 displays a photograph of the filter prototype fabricated on a double-sided FR4 substrate using the high precision LPKF ProtoMat S103. The copper cladding top and bottom is 35 μm. The footprint of the proposed quadband filter is 30 × 30 mm2(0.197λg × 0.197λg).Figure 8
Photograph of the fabricated prototype: (a) top view; (b) bottom view.
(a)(b)


## 3. Results and Discussion

All the measurements were performed using R&S ZVA50 VNA. The proposed quadband filter’s simulated and measured reflection coefficient is presented in Figure9(a), whereas Figure 9(b) illustrates the transmission coefficient. A good agreement is achieved between simulated and measured results, which validates the proposed design methodology and practically demonstrates the proposed configuration’s effectiveness and advantages. Some of the slight discrepancies observed between simulated and measured results may be due to the soldering, reflections from the connectors, the finite substrate, or the manufacturing machine’s precision.Figure 9
Simulated and measured reflection and transmission coefficients of the proposed quadband filter: (a) reflection coefficient; (b) transmission coefficient.
(a)(b)


### 3.1. Reflection Coefficient (S11)

The measured results presented in Figure9(a) show return loss of 24.94 dB, 18.44 dB, 15.04 dB, 13.52 dB, and 31.64 dB at 1.4 GHz, 2.11 GHz, 3.93 GHz, 5.69 GHz, and 6.67 GHz, respectively. Five transmission poles (TP) are observed in Figure 10(a) whose the corresponding passband insertion loss is 1.07 dB, 1.76 dB, and 2.5 dB, 2.92 dB, and 2.08 dB. Besides, the -6 dB bandwidth is about 490 MHz (1.33–1.82 GHz), 260 MHz (2.04–2.3 GHz), and 360 MHz (3.73–4.09 GHz). This demonstrates that the proposed quadband bandstop filter can be used in several modern wireless applications such as GPS1200 (1227–1575 MHz), WMTS (1395–1400 MHz, 1427–1432 MHz), UMTS band I (1920–2170 MHz), 5G bands n77 (3.3–4.2 GHz), n78 (3.3–3.8 GHz), and a part of UWB range (3.1–5 GHz).Figure 10
Measured reflection and transmission coefficient of the proposed quadband filter.


### 3.2. Transmission Coefficient (S21)

From both simulation and measurement transmission coefficient results displayed in Figure9(b), the proposed filter configuration achieves four bandstops. The transmission coefficient analysis reveals stopbands centered (geometric mean) at 1.2 GHz, 1.97 GHz, 2.96 GHz, and 4.78 GHz, with a -6 dB fractional rejection bandwidth of 8.7%, 4.51%, 36.69%, and 23.32%. Moreover, the filter achieves six transmission zeros (TZ), which improves the selectivity with stopband rejection of 16.30 dB, 11.22 dB, 18.97 dB, 20.6 dB, 15.51 dB, and 25.92 dB, at 1.28 GHz, 2.01 GHz, 2.63 GHz, 2.81 GHz, 4.4 GHz, and 4.68 GHz, respectively. The return loss at the aforementioned stopband frequencies is about 1.92 dB, 3.58 dB, 1.59 dB, 1.39 dB, 2.02 dB, and 1.16 dB, which illustrates good bandstop performance for the proposed compact quadband filter.It can be used for suppressing several unwanted modern wireless application signals, including LTE2300/2500, 5G band n40/n41/n77/n78, WiMAX3500, ISM/Bluetooth/Wi-Fi, GSM1800, C-band, and GPS1200 signals.The measured results are summarized in Figure10 above. It can be noticed that as the center frequency increases, the insertion loss increases for the passbands. The proposed bandstop filter achieves a −6 dB fractional bandwidth of 31.49%, 12%, and 9.22% for the first, the second, and the third passband bandpass span frequencies.Transmission zeros separate the four passbands at 1.28 GHz, 2.01 GHz, 2.81 GHz, and 4.68 GHz giving 16.30 dB, 11.22 dB, 20.92 dB, and 15.51 dB stopband rejection, respectively. This results in high band-to-band isolation. The return loss in the passband between the stopbands is better than 15 dB, and the measured passband insertion loss is less than 2.5 dB. Finally, this proposed filter design can be suitably employed for RF/microwave modern and high-speed communications systems, owing to these encouraging results.Table3 gives a performance comparison with some reported multiple-band BSFs which shows that the proposed quadband bandstop filter in this work has compact size, wide fractional bandwidths, and good selectivity, in addition to the high band-to-band isolation around the rejection bands.Table 3
Comparison between this work and other reported multiband bandstop filters.
Ref.StopbandsCenter frequencies of stopbands (GHz)Fractional bandwidth (%)Size (λg × λg)[16]41.24/3.2/6/840/30/25/260.139 × 0.171[26]41.16/1.58/1.94/2.375.2/6.9/2.9/1.30.26 × 0.25[9]31.8/2.4/320/12/220.44 × 0.44[27]33.8/6.7/9.519.2/6.7/3.30.682 × 0.325[28]21.4/2.5712.7/10.110.650 × 0.380[29]32.24/4.8/6.5279/26/130.090 × 0.310[30]23.35/5.756/1.70.270 × 0.270This work41.2/1.97/2.96/4.788.7/4.51/36.69/23.320.197 × 0.197


## 3.1. Reflection Coefficient (S11)

The measured results presented in Figure9(a) show return loss of 24.94 dB, 18.44 dB, 15.04 dB, 13.52 dB, and 31.64 dB at 1.4 GHz, 2.11 GHz, 3.93 GHz, 5.69 GHz, and 6.67 GHz, respectively. Five transmission poles (TP) are observed in Figure 10(a) whose the corresponding passband insertion loss is 1.07 dB, 1.76 dB, and 2.5 dB, 2.92 dB, and 2.08 dB. Besides, the -6 dB bandwidth is about 490 MHz (1.33–1.82 GHz), 260 MHz (2.04–2.3 GHz), and 360 MHz (3.73–4.09 GHz). This demonstrates that the proposed quadband bandstop filter can be used in several modern wireless applications such as GPS1200 (1227–1575 MHz), WMTS (1395–1400 MHz, 1427–1432 MHz), UMTS band I (1920–2170 MHz), 5G bands n77 (3.3–4.2 GHz), n78 (3.3–3.8 GHz), and a part of UWB range (3.1–5 GHz).Figure 10
Measured reflection and transmission coefficient of the proposed quadband filter.


## 3.2. Transmission Coefficient (S21)

From both simulation and measurement transmission coefficient results displayed in Figure9(b), the proposed filter configuration achieves four bandstops. The transmission coefficient analysis reveals stopbands centered (geometric mean) at 1.2 GHz, 1.97 GHz, 2.96 GHz, and 4.78 GHz, with a -6 dB fractional rejection bandwidth of 8.7%, 4.51%, 36.69%, and 23.32%. Moreover, the filter achieves six transmission zeros (TZ), which improves the selectivity with stopband rejection of 16.30 dB, 11.22 dB, 18.97 dB, 20.6 dB, 15.51 dB, and 25.92 dB, at 1.28 GHz, 2.01 GHz, 2.63 GHz, 2.81 GHz, 4.4 GHz, and 4.68 GHz, respectively. The return loss at the aforementioned stopband frequencies is about 1.92 dB, 3.58 dB, 1.59 dB, 1.39 dB, 2.02 dB, and 1.16 dB, which illustrates good bandstop performance for the proposed compact quadband filter.It can be used for suppressing several unwanted modern wireless application signals, including LTE2300/2500, 5G band n40/n41/n77/n78, WiMAX3500, ISM/Bluetooth/Wi-Fi, GSM1800, C-band, and GPS1200 signals.The measured results are summarized in Figure10 above. It can be noticed that as the center frequency increases, the insertion loss increases for the passbands. The proposed bandstop filter achieves a −6 dB fractional bandwidth of 31.49%, 12%, and 9.22% for the first, the second, and the third passband bandpass span frequencies.Transmission zeros separate the four passbands at 1.28 GHz, 2.01 GHz, 2.81 GHz, and 4.68 GHz giving 16.30 dB, 11.22 dB, 20.92 dB, and 15.51 dB stopband rejection, respectively. This results in high band-to-band isolation. The return loss in the passband between the stopbands is better than 15 dB, and the measured passband insertion loss is less than 2.5 dB. Finally, this proposed filter design can be suitably employed for RF/microwave modern and high-speed communications systems, owing to these encouraging results.Table3 gives a performance comparison with some reported multiple-band BSFs which shows that the proposed quadband bandstop filter in this work has compact size, wide fractional bandwidths, and good selectivity, in addition to the high band-to-band isolation around the rejection bands.Table 3
Comparison between this work and other reported multiband bandstop filters.
Ref.StopbandsCenter frequencies of stopbands (GHz)Fractional bandwidth (%)Size (λg × λg)[16]41.24/3.2/6/840/30/25/260.139 × 0.171[26]41.16/1.58/1.94/2.375.2/6.9/2.9/1.30.26 × 0.25[9]31.8/2.4/320/12/220.44 × 0.44[27]33.8/6.7/9.519.2/6.7/3.30.682 × 0.325[28]21.4/2.5712.7/10.110.650 × 0.380[29]32.24/4.8/6.5279/26/130.090 × 0.310[30]23.35/5.756/1.70.270 × 0.270This work41.2/1.97/2.96/4.788.7/4.51/36.69/23.320.197 × 0.197


## 4. Conclusion

In this paper, a quadband bandstop filter loaded with DSCSRRs and a slot in the ground plane has been designed, fabricated, and tested. The filter does not have any additional matching network, which is advantageous in reducing its physical size. With a physical footprint of 30 × 30 mm2, the proposed device achieves a maximum passband insertion loss of about 2.5 dB and a return loss greater than 11 dB across all the frequency band of interest. Furthermore, it performs a minimum −6 dB passband bandwidth of 260 MHz, whereas the stopband fractional bandwidth greater than 4.5%. The merits of compact size, acceptable insertion loss, good return loss, high passband selectivity and band-to-band isolation make the proposed quadband stopband filter attractive in modern communication and sensor applications.



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*Source: 7847015-2022-05-20.xml*