Reconfigurable Wideband Bandpass Filter Using Stepped Impedance Resonator Based on Liquid Crystals

Abstract

In this paper, a capacitively coupled-fed reconfigurable wideband bandpass filter (BPF) is proposed based on liquid crystal (LC) technology, which achieved three transmission poles across varying bias voltages (V_B). An open-ended stepped impedance resonator configuration enables multi-mode resonance, offering significantly wider bandwidth compared to uniform-impedance resonators. The fractional bandwidth (FBW) and transmission pole positions are determined by the impedance ratio of the two resonators, allowing the filter to meet specific design requirements. An analytical methodology employing multilayer transmission line formulations and resonant frequency ratios was used to predict the modal stability of transmission poles under dielectric constant variation, which was subsequently validated through simulation. Experimental results show that the center frequency can be adjusted from 10.76 to 9.47 GHz with a maximum V_B of 30 V, achieving a tuning range of 12.71%. The normalized 3 dB FBW exceeds 64.66%, and the return loss remains above 10 dB from 0 to 30 V, offering the widest FBW among the reported LC BPFs without pole merging or mode collapse. The frequency response of the fabricated filter shows good agreement with the simulation results.

1. Introduction

Reconfigurable filters have become essential components in modern wireless communication systems as the demand for multifunctional and multi-band devices has increased. Among these, wideband bandpass filter (BPF) technology plays a critical role in wireless applications requiring high-speed data transfer, such as vehicular radar, through-wall imaging, surveillance imaging, medical imaging, and communication and measurement systems [1]. Reconfigurable BPFs can be broadly categorized into two types: those that adjust the center frequency [2,3,4] and those with bandwidth tunability at a fixed center frequency [5,6,7]. By applying reconfigurable BPFs, the system can achieve miniaturization, multifunctionality, and cost reduction.

A variety of technologies have been used to realize reconfigurability, such as pin diodes [8], varactors [9], and microelectromechanical systems (MEMs) [10] in the microwave frequency. In particular, liquid crystals (LCs) have distinctive characteristics, including amenability to continuous control of effective permittivity, responsiveness to external biases, and decreasing dielectric loss in the microwave region as tunable materials. Because of these characteristics, LCs are widely used in various applications, including filters [11,12,13], phase shifters [14,15,16], antennas [17,18,19], and reconfigurable frequency selective surfaces [20,21,22]. In LC-based reconfigurable filters, the center frequency is mainly adjusted by changing the effective permittivity of the transmission line in response to external biases.

In recent years, numerous reconfigurable broadband BPFs using LCs have been suggested. For example, one study combined a periodic open spiral stub loading structure with LCs, achieving a fractional bandwidth (FBW) of 19.80% and a tuning range of 3.99% [23]. Another study reported a ring resonator structure with two tuning stubs using orthogonal feed based on LCs, achieving an FBW of 48.17% and a tuning range of 11.85% [24]. However, a review of the literature reveals that most reported methods have limited capability to achieve both an FBW above 60% and a return loss (RL) above 10 dB across the range of bias voltage V_B. Therefore, an effective design approach that delivers both high FBW and RL across the V_B range is required for reconfigurable wideband applications.

In this context, stepped impedance resonators (SIRs) can contribute to the realization of wideband BPFs. Unlike uniform stepped impedances (UIRs), SIRs consist of segments with different impedances [25]. By selecting an appropriate impedance ratio, SIRs can suppress undesired spurious resonant modes or achieve a wideband filter response by enabling multiple-mode resonance (MMR) [26,27,28]. Some studies have combined SIRs with LCs. For instance, one study introduced electrically coupled open-loop resonators into the SIR technology to improve FBW by enhancing the electrical coupling strength [29]. Another employed the SIR structure to obtain a dual-band frequency response [30]. While LC-based filters achieve tunability through dielectric constant variation in LCs, few studies have investigated the integration of LCs into SIR-based filters. However, no analytical approach has been proposed to predict how the frequency response of multi-pole SIR configurations changes with variations in LC permittivity.

In this paper, we present a reconfigurable wideband BPF that integrates SIR technology with LC technology and employs capacitively coupled-line feeding. To design the structure, we adopted the formulas for multilayer microstrip lines. Additionally, using multilayer transmission line formulations and resonant frequency ratios, we explain why the proposed structure maintains the transmission poles under the permittivity variation of LCs and functions as a tunable frequency filter. Simulation and measurement validation confirm that the proposed structure can exhibit center frequency reconfigurability without significantly changing the FBW.

2. Materials

To realize an LC-injected reconfigurable filter, three layers were utilized: a top dielectric layer patterned with signal lines to function as a wideband filter, a bottom dielectric layer laminated with a conductor serving as a ground plane, and a middle LC layer to enable tunability by adjusting voltage bias.

For the conductor-laminated dielectric materials, FR-4 (ε_r = 4.146, tan δ = 0.020 at 10 GHz) with a thickness 0.4 mm was used, laminated with 35 μm-thick copper foil (σ = 5.8 × 10⁵ S cm⁻¹). To achieve a high tuning range, LC ZOC-A017XX (JNC Corp., Tokyo, Japan) was introduced into the structure. With a nematic-isotropic phase transition temperature (T_NI) of 125 °C and a melting point (T_m) below −20 °C, the LCs can be utilized as tunable materials in the nematic phase. In this work, we focused on the frequency response at room temperature. Before designing the filter, the dielectric properties of these materials were characterized in advance using a stub resonator at 10 GHz at room temperature. For the LC, anisotropic dielectric properties were extracted under V_B = 0 V and 30 V, assuming a gap thickness of 200 μm. The extracted dielectric constants were ε_r,LC,o = 2.530 and ε_r,LC,e = 3.880, with corresponding loss tangents of tan δ_LC,o = 0.026 and tan δ_LC,e = 0.007 at 10 GHz. To maintain the gap thickness, a 0.2 mm-thick adhesive layer was inserted between the copper-clad laminate dielectric materials.

3. Methods

3.1. Fundamentals of Electric Field-Induced Nematic Liquid Crystals

Most commercial LCs used in microwave applications are thermotropic, calamite-shaped mixtures that exhibit a nematic phase at room temperature. LCs for microwave applications are typically provided as mixtures to achieve desirable characteristics, such as high anisotropy, low dielectric loss, low viscosity, and high T_NI, tailored for specific purposes [31,32,33].

The orientation of LC directors can be influenced by various external stimuli, including electric fields, magnetic fields, tensile stress, or light. LCs in microwave applications are generally operated using external bias voltage. Furthermore, the initial alignment states of LCs can be determined by applying a desired alignment solution and rubbing direction. For simplicity, we assume an anti-parallel rubbed homogeneous alignment in this section.

In the unbiased state, the LC director is uniformly aligned along the x axis (Figure 1a). When the applied field is below the threshold electric field Eth in the z direction, the LCs maintain their initial state. However, when the applied field exceeds Eth and the LCs have positive dielectric anisotropy at the operating frequency of the bias voltage, the LC directors rotate toward the direction of the electric field (Figure 1b); this reorientation phenomenon is known as the Fréedericksz transition [34]. Additionally, when the applied field is removed, the rotated LC directors relax back to their initial state due to elastic forces of LCs. Because of this behavior, the LC can be tuned reversibly and reconfigured.

3.2. Multilayer Microstrip Line Filled with Liquid Crystals (Isotropic Assumed)

The proposed filter adopts a multilayer microstrip line topology. A microstrip line consists of a signal line and a ground plane separated by a dielectric, allowing an external voltage bias to reorient the LC directors. The multilayer microstrip line filled with the LCs comprises three dielectric layers: air, a substrate patterned with the signal line, and an LC layer, as illustrated in Figure 2. To enable reconfigurable operation, the LC layer is placed between the substrate and the ground plane.

To determine the effective permittivity ε_r,eff and the characteristic impedance Z₀ of the transmission line, Svacina’s conformal mapping method for multilayer microstrip lines was used [35]. For simplicity, the thickness of the signal line was assumed to be zero, and the LC layer was treated as an isotropic medium. Additionally, the thickness of air layer was set to infinity, and the equivalent dielectric layer h_eq was defined as the thickness of the LC layer h_LC in this paper. With the help of the Wheeler’s transformation, the filling factors q₁ and q₂ and the capacitance per unit length with the dielectric substrate replaced by air C₀ can be characterized as

$$q_1=1-0.5\cdot \left[\mathit{ln}\left({\displaystyle \frac{\pi w_{ef}}{h_{eq}}}-1\right)\right]{\left[{\displaystyle \frac{w_{ef}}{h_{eq}}}\right]}^{-1}$$

(1)

$$q_2=1-q_1-0.5\cdot \left[{\displaystyle \frac{h_{eq}-v_e}{w_{ef}}}\right]\cdot ln\left[{\displaystyle \frac{\pi w_{ef}}{h_{eq}}}\cdot {\displaystyle \frac{\mathit{cos}\left(\frac{\pi v_e}{2h_{eq}}\right)}{\pi \left(\frac{h_2}{h_{eq}}-0.5\right)}}+\mathit{sin}\left({\displaystyle \frac{\pi v_e}{2h_{eq}}}\right)\right],$$

(2)

$$C_0={\displaystyle \frac{1}{120\pi c_0}}\cdot \left({\displaystyle \frac{w_{ef}}{h_{eq}}}\right),$$

(3)

for a wide strip ($w_{line}/h_{eq}\ge 1$), and

$$q_1=0.5+0.9\cdot {\left[\pi \mathit{ln}\left({\displaystyle \frac{8h_{eq}}{w_{line}}}\right)\right]}^{-1},$$

(4)

$$q_2=-\left[0.9+{\displaystyle \frac{\pi }{4}}\mathit{ln}\left(B_2\right) \cdot {\mathit{cos}}^{-1}\left[\left(1-{\displaystyle \frac{1-\frac{w_{line}}{8h_{eq}}}{h_2/h_{eq}}}\right)\sqrt{B_2}\right]\right]\cdot {\left[\mathit{\pi ln}\left({\displaystyle \frac{8h_{eq}}{w_{line}}}\right)\right]}^{-1}+0.5,$$

(5)

$$C_0={\left[60c_0\ln \left({\displaystyle \frac{8h_{eq}}{w_{line}}}\right)\right]}^{-1},$$

(6)

for a narrow strip ($w_{line}/h_{eq}\le 1$) where

$$w_{ef}=w_{line}+{\displaystyle \frac{2}{\pi }}{h}_{eq}\cdot \mathit{ln}\left[17.08\left({\displaystyle \frac{w_{line}}{2h_{eq}}}+0.92\right)\right],$$

(7)

$$v_e={\displaystyle \frac{2}{\pi }}{h}_{eq}\cdot {\mathit{tan}}^{-1}\left[\pi \left({\displaystyle \frac{h_2}{h_{eq}}}-1\right)\cdot {\left({\displaystyle \frac{\pi w_{ef}}{2h_{eq}}}-2\right)}^{-1}\right], \mathrm{and}$$

(8)

$$B_2=\left({\displaystyle \frac{h_2}{h_{eq}}}+1\right)\cdot {\left({\displaystyle \frac{h_2}{h_{eq}}}+{\displaystyle \frac{w_{line}}{4h_{eq}}}-1\right)}^{-1},$$

(9)

where h_sub is the thickness of the substrate and c₀ is the velocity of electromagnetic waves in free space (c₀ ≈ 3.0 × 10⁸ m/s) [36]. The parameters h₁ and h₂ are defined as the height from the ground plane to 1st and 2nd dielectric layers, respectively; so h₁ = h_LC and h₂ = h_LC + h_sub.

Calculating (1)–(9) yields the corresponding value of the effective permittivity ε_r,eff and the characteristic impedance Z₀ as

$${\epsilon }_{r,eff}={\epsilon }_{r1}{q}_1+{\displaystyle \frac{{\epsilon }_{r2}{\left(1-q_1\right)}^2}{q_2+{\epsilon }_{r2}(1-q_1-q_2)}}, \mathrm{and}$$

(10)

$$Z_0={\left[c_0{C}_0\sqrt{{\epsilon }_{r,eff}}\right]}^{-1},$$

(11)

where ε_r1 and ε_r2 are relative permittivities defined from the ground plane to 1st and 2nd dielectric layers, respectively; so ε_r1 = ε_r,LC and ε_r2 = ε_r,hub.

In summary, the effective permittivity is calculated by multiplying the permittivity of each dielectric region by the respective filling factors q₁ and q₂, which represent conformally mapped area ratios. These filling factors are calculated using different mathematical functions depending on the strip width. In wide-strip configurations, using the effective line width instead of the physical signal width and applying a factor v_e, which is related to h₂, is known to provide results that better match practical behavior.

The physical length of this transmission line, l_phy, can be extracted from the electrical length θ as

$$l_{phy}=\theta \cdot {\left[{\displaystyle \frac{2\pi }{{\lambda }_0}} \cdot \sqrt{{\epsilon }_{r,eff}}\right]}^{-1},$$

(12)

where λ₀ is the free-space wavelength. According to (12), when the multilayer microstrip line resonator is designed based on a fixed permittivity, the resonant frequency is expected to shift with the bias level, since the rotation of LCs leads to changes in the effective permittivity.

3.3. Stepped Impedance Resonator with Capacitive-Ended Coupled Lines

To achieve wideband BPF and operate LCs by voltage bias, we adopted the open-circuited SIR technology. The open-circuited SIR consists of two transmission lines having different characteristic admittances, Y₁ = 1/Z₁ and Y₂ = 1/Z₂ (Figure 3a). Also, the electrical length of each section is defined as θ₁ and θ₂, and the structure is terminated by open circuits at both ends. To analyze the resonant characteristics, the structure is examined using an equivalent transmission line model (Figure 3b). Assuming that θ₁ = θ₂ = θ > 0, the input admittance Y_in can be expressed as

$$Y_{in}=j{Y}_2\cdot {\displaystyle \frac{2tan\theta \left({1+R}_z\right)\left(R_z-{\mathit{tan}}^2\theta \right)}{R_z{\left(1-{\mathit{tan}}^2\theta \right)}^2-2{\mathit{tan}}^2\theta \left(1+R_z^2\right)}},$$

(13)

where R_Z = Z₂/Z₁ = Y₁/Y₂ is the impedance ratio. Since the structure exhibits symmetry, even-mode and odd-mode analysis can be applied (Figure 4). For the even-mode case, the input admittance Y_in,e is given by

$$Y_{in,e}=j{Y}_2\cdot {\displaystyle \frac{R_{z}tan{\theta }_1+tan{\theta }_2}{{1-R}_{z}tan{\theta }_{1}tan{\theta }_2}},$$

(14)

Similarly, for the odd-mode case, the input admittance Y_in,o is given by

$$Y_{in,o}=j{Y}_2\cdot {\displaystyle \frac{tan{\theta }_{1}tan{\theta }_2-R_z}{{tan{\theta }_1+R}_{z}tan{\theta }_2}}.$$

(15)

From the resonance condition Y_in,e = 0 and Y_in,o = 0, the fundamental resonances can be obtained from (14) and (15) as

$$R_{z}tan{\theta }_1+tan{\theta }_2=0 \left(\mathrm{at\; even-mode\; frequencies}\right),$$

(16a)

$$tan{\theta }_{1}tan{\theta }_2-R_z=0 \left(\mathrm{at\; odd-mode\; frequencies}\right).$$

(16b)

Applying the assumption θ₁ = θ₂ = θ > 0, these conditions can be simplified as

$$tan\theta (1+R_z)=0 \left(\mathrm{at\; even-mode\; frequencies}\right),$$

(17a)

$${\tan }^2\theta -R_z=0 \left(\mathrm{at\; odd-mode\; frequencies}\right).$$

(17b)

When R_z > 0, tanθ = ∞ at f = f₀, the even- and odd-mode resonant frequencies can be obtained as

$$f_{e1}=f_0,$$

$$f_{o1}={{\displaystyle \frac{2}{\pi }}f}_0{\tan }^{-1}\sqrt{R_z},$$

$$f_{o2}={{\displaystyle \frac{2}{\pi }}f}_0\left(\pi -{\tan }^{-1}\sqrt{R_z}\right).$$

(18)

Since the resonance condition leads to Y_in = 0, the electrical length θ(f_n) (n = 1, 2, 3, …) at resonant frequency f_n (n = 1, 2, 3, …) can be induced as

$$\theta \left(f_1\right)={\tan }^{-1}\sqrt{R_z},$$

$$\theta \left(f_2\right)={\displaystyle \frac{\pi }{2}},$$

$$\theta \left(f_3\right)={\pi -\tan }^{-1}\sqrt{R_z}.$$

(19)

Additionally, since f_o1 < f_e1 < f_o2, we define f₁ = f_o1, f₂ = f_e1, and f₃ = f_o2. By using (19), the normalized resonant frequencies relation can be obtained as

$${\displaystyle \frac{f_2}{f_1}}={\displaystyle \frac{\theta \left(f_2\right)}{\theta \left(f_1\right)}}={\displaystyle \frac{\pi }{2{tan}^{-1}\sqrt{R_z}}},$$

$${\displaystyle \frac{f_3}{f_1}}={\displaystyle \frac{\theta \left(f_3\right)}{\theta \left(f_1\right)}}={\displaystyle \frac{\pi -{tan}^{-1}\sqrt{R_z}}{{tan}^{-1}\sqrt{R_z}}}.$$

(20)

Figure 5 shows the calculated normalized frequencies as a function of the impedance ratio R_Z based on the equations above. For the dashed line (R_Z = 1), the normalized frequency ratio exhibits an integer relationship. When R_Z < 1, the distance between resonant frequencies increases as R_Z decreases. This approach can contribute to the suppression of undesired spurious resonant modes. Conversely, when R_Z > 1, the resonant frequencies become closer as R_Z increases. By grouping the resonant frequencies, this method can be used to realize a multi-band or wideband BPF based on MMR [37].

To examine the relationship between R_Z and spacing between resonant frequencies, the filter response was simulated using ANSYS HFSS 2021 R1. Since both ends of the SIR are open-circuited, parallel-coupled lines were connected to couple the resonator and feed lines (Figure 6). The parallel-coupled line length l_c was set to 1 mm to observe the weak coupling response. The physical length l_Z1 of the low-impedance section of the SIR was set to half of the guided wavelength λ_g at a center frequency f₀ of 10 GHz. As shown in Figure 7a, the adjacent frequencies moved closely together as R_Z increased, consistent with the trend in Figure 5. Although the analytical equations predict the frequency shift well, an additional approach is required to achieve a flat wideband filter response using the SIR structure.

Next, simulations were conducted under various l_c conditions to observe the effect of coupling degree at a fixed R_Z = 5. As shown in Figure 7b, increasing the l_c enhanced the coupling strength of the coupled lines, significantly reducing the insertion loss (IL) difference between the adjacent frequencies. By further increasing l_c, similar to l_Z2, a wideband and flat filter can be achieved. In the final design structure, capacitive-ended interdigital coupled lines were employed to enhance the overall coupling capacitance, as they provide a significantly wider coupling area compared to the normal coupled lines [38].

To verify the structural suitability of the proposed resonator for LC-based tunable applications, the frequency response under varying permittivity was examined. Since the transmission pole spacing of an SIR is governed by the R_Z, its variation can be used to evaluate the structural sensitivity to ε_r,LC. Using multilayer microstrip line equations from (1)–(11), R_Z was calculated for different values of w_z1 as ε_r,LC varied from 2.5 to 3.9. As shown in Figure 8a, R_Z remained nearly unchanged despite changes in ε_r,LC, indicating that the impedance ratio is robust against permittivity tuning. This implies that the LC-injected SIR resonator is structurally capable of maintaining stable pole spacing without pole merging or isolation, which is highly desirable for tunable filter applications.

Full-wave simulation further confirmed this behavior. Figure 8b shows that an SIR with fixed R_Z = 5 maintains three distinct poles across all permittivity conditions, with the relative pole positions remaining stable. Moreover, while the resonant frequencies shifted toward lower values with increasing permittivity—as expected from the inverse relationship between frequency and effective dielectric constant—the spacing between adjacent poles remained effectively unchanged. This frequency downshift behavior aligns with the theoretical expectation described by (12). These results confirm that the proposed SIR is structurally capable of preserving transmission pole behavior under LC tuning, making it well-suited for implementing reconfigurable wideband bandpass filters. By integrating these techniques, a reconfigurable wideband BPF injected LC can be designed, fabricated, and measured.

4. Results

4.1. Proposed Structure

The overall structure used for sample measurement is as follows. Two substrates were employed: the upper substrate includes a grounded coplanar waveguide (GCPW) for connector feeding, an IMSL pattern for realizing the tunable wideband filter within the LC region, and vias for connecting the top and bottom electrodes. The lower substrate serves as the ground plane for both the IMSL and the biasing signal. An adhesive tape was used between the two substrates to maintain a consistent cell gap, and the liquid crystal was filled via capillary action (Figure 9a).

The LC-injected region consists of the SIR with capacitive-ended interdigital coupled lines filled with LCs (Figure 9b). Based on (15), the impedance ratio R_Z was initially selected to be below 3.9 in order to attain the FBW above 60% at a center frequency of 10 GHz. In addition, to accomplish a wideband filter response with the RL above 10 dB across the range of V_B, the LCs were assumed to be isotropic materials with an average dielectric constant of 3.17, and the parameters were optimized. Although the SIR with capacitive-ended interdigital coupled lines can be operated as a wideband filter, it cannot be successfully tuned since DC bias is hard to transmit between unconnected electrodes. Therefore, high-impedance signal lines were connected to the SIR and the interdigital coupled lines to effectively rotate the LCs in response to V_B. Radial stubs were inserted to isolate the bias path from the high-frequency path and ensure propagation into the SIR section properly, preventing the additional signal leakage to the high transmission line. Considering performance degradation due to additional components, the final structure having the high impedance lines and radial stubs was finally optimized to have R_Z = 3.9 to operate a reconfigurable wideband filter response with the RL above 10 dB across the range of V_B (

Table 1. Geometrical parameters of the proposed structure.

Parameter	Unit [mm]
wc	0.10
lc	3.66
sc	0.10
wz1	1.32
lz1	8.60
wz2	0.10
lz2	3.76
r	3.00

).

The fabrication procedure for the LC filter is as follows. First, the FR-4 boards were cleaned using isopropyl alcohol and then dried with a nitrogen spray gun. Second, to form a homogeneous alignment, a polyimide solution (DL-2193; Dalton, Shenzhen, China) was applied to the FR-4 boards by using a spin coater (ACE-200; DongAh Trade Corp., Seoul, Republic of Korea). After being spin-coated, the coated boards were heated on a multi-hotplate stirrer (SMHS-3; Daihan Scientific, Wonju, Republic of Korea) to induce imidization. Third, the sample was mechanically rubbed twice along the x axis using a rubbing machine (SRMS-50-M; Sciencetown, Incheon, Republic of Korea) to ensure uniform alignment. Fourth, the two FR-4 boards were assembled to form an anti-parallel rubbed homogeneous alignment for the LCs. For the assembly process, adhesive PET tape was used to maintain the cell gap. Finally, the LCs were filled into the assembled cell by capillary action. To avoid air bubbles in the cell, via holes were designed outside the injection area. The semi-transparent property of FR-4 allowed visual inspection for air bubbles within the cell. After the LC injection, copper tape was attached to enable easy connection with the power supply (Figure 10a).

To measure the frequency response, the fabricated sample was connected to end-launch connectors (Withwave, Yongin, Republic of Korea). The measurements were conducted using a vector network analyzer (PNA-X N5247B; Keysight Technologies, Santa Rosa, CA, USA), and the LCs were controlled by a power supply (SDP 30–3DT; SM Techno, Seoul, Republic of Korea). The applied V_B changed from 0 to 30 V in 5 V increments. The sample was connected between the bias-tees (BT65R-HV100; SHF, Berlin, Germany) to prevent the voltage bias from damaging the measurement equipment (Figure 10b). Additionally, since the output power of the VNA is insufficient to drive the LC, it is unlikely that measurements in the microwave band would have any influence on its operation.

4.2. Simulation and Experimental Results

Prior to fabrication, simulations were conducted to evaluate the expected filter response, including tunability, FBW, or minimum RL. To explicitly describe the tunable characteristics of the LC with respect to the applied voltage, the LC was assumed to be an isotropic medium, and the dielectric constant was swept from 2.5 to 3.9 during the parameter sweep.

As shown in Figure 11, the simulated filter response S₁₁ and S₂₁ shifted downward as ε_r,LC rose, which accords with the theoretical expectation described by (12). However, unlike the ideal conditions assumed in the simulation of Section 3.3, the actual design was modified in two key aspects: (1) an additional path was introduced for LC biasing, and (2) additional transmission line structures were required for practical sample measurement. Since the ideal SIR structure is electrically disconnected from the feed line, it can function as a fixed wideband filter but not as a tunable filter by itself. Therefore, a connection method that minimizes degradation at the target frequency is essential for enabling LC operation. Moreover, because LCs are fluidic materials, the ideal structure alone cannot be measured; it is necessary to incorporate additional structures to allow connection with the VNA. In simulations that considered the external feeding structures without any optimization, the target FBW could still be achieved; however, it was difficult to maintain an RL above 10 dB across the dielectric constant sweep. Therefore, to ensure an RL above 10 dB throughout the ε_r,LC sweep, the line widths and electrical lengths of the SIR structure were re-optimized. As a result, the electrical lengths deviated from the ideal conditions, leading to non-uniform spacing between adjacent poles. Even though ε_r,LC varied from 2.5 to 3.9, the simulated sample remained an RL above 10 dB in the passband and attained the normalized 3 dB FBW from 65.27% to 62.96% according to ε_r,LC without pole merging or mode collapse. Across this range of ε_r,LC, the FBW showed a slight variation of less than 3%, and the minimum IL exhibited a difference of only 0.14 dB. These simulation results suggest that the designed filter can accomplish a reconfigurable wideband filter response within the given sweep range.

To verify the expected filter response, measurements were performed over a frequency range of 5 to 15 GHz at room temperature, with an applied V_B from 0 to 30 V in 5 V increments to reorient the LC directors. As shown in Figure 12, the frequency of the filter decreased as V_B was increased, consistent with the simulation results. This behavior is expected, since the LC directors realign along the electric field as the voltage increases, so the dielectric constant changes from ε_r,LC,o to ε_r,LC,e in terms of the propagating RF field. During the measurements, the RL remained above 10 dB, and the IL demonstrated the wideband response across the range of V_B.

To quantitatively compare the simulation and measurement data, the variations in f₀ and the 3 dB FBW were plotted (Figure 13). In the simulation, f₀ was tuned from 10.80 to 9.43 GHz, the FBW ranged from 61.51% to 64.65%, and the tuning range was expected to be 13.60%. In the measurements, f₀ was adjusted from 10.76 to 9.47 GHz, the FBW varied from 67.97% to 64.66%, and the tuning range was observed to be 12.71%. The maximum difference in f₀ between simulation and measurement was within 0.11 GHz at each voltage, and the FBW exceeded 60% in both cases. The tuning range discrepancy of less than 1% indicates that the dielectric properties of the LCs were reliably characterized. Moreover, this comparison confirms that the measurement data closely aligned with the simulation results.

Figure 14 presents the frequency responses at V_B = 0 and 30 V, respectively. The measured S₁₁ and S₂₁ show good agreement with the simulation results, where the LC was treated as an anisotropic material.

Table 2. Experimental results of the proposed structure.

VB (V)	Dielectric Constant	f0 (GHz)	3 dB BW (GHz)	3 dB FBW (%)	Min. IL (dB)
0	εr,LC,o	10.76	7.31	67.97	2.41
30	εr,LC,e	9.46	6.18	65.26	1.81

Note: f₀ = Center frequency; BW = Bandwidth; FBW = Fractional bandwidth; IL = Insertion loss.

summarizes the experimental results of the proposed structure at 0 and 30 V. Through the additional measurement using separately fabricated samples, it was confirmed that all deviations remained within 0.1 dB (insertion loss), 1% (FBW), and 0.1 GHz (f₀) regardless of the applied voltage, thereby supporting the high reliability of the measurement results presented in this work.

5. Discussion

The operating characteristics of the proposed filter were compared with the reported reconfigurable LC BPFs and summarized in

Table 3. Performance comparisons with reconfigurable LC bandpass filters.

Work	Year	Technology	f0 (GHz)	Min. FBW (%)	Tuning Range (%)	RL (dB)
[39]	2015	Dual-mode IMSL filter	4.87	16.57	13.36	>5
[41]	2018	3-pole Chebyshev SIW filter	29.75	11.20	2.35	>19
[24]	2020	Ring resonator with tuning stubs	26.15	48.17	11.85	>6
[42]	2022	Metasurface with metal patch	10.56	11.27	8.14	0
[43]	2023	3rd order groove gap resonator	30.12	1.21	3.19	>19
[40]	2024	LC Double-layer FSS	13.40	57.12	9.55	-
[44]	2024	Open-loop resonator	10.28	6.70	11.34	>15
This		SIR with capacitive coupled-line	10.11	64.66	12.71	>10

Note: f₀ = Center frequency; FBW = Fractional bandwidth; RL = Return loss; IMSL = Inverted microstrip line; SIW = Substrate integrated waveguide; FSS = Frequency-selective surface; SIR = Stepped impedance resonator.

. Among these, the widest tuning ratio was 13.36% [39], which exceeds the 12.71% obtained here. However, the proposed structure significantly outperforms prior works in terms of normalized 3 dB FBW and return loss. For instance, while a recent work reported a 3 dB FBW of 57.12% [40], our filter achieves an FBW exceeding 64.66% while consistently maintaining an RL above 10 dB across the tuning range. Notably, this performance is achieved with a single LC injection layer, whereas some high-FBW structures require double-sided LC loading or arrayed LC cells that are difficult to fabricate. The proposed structure, therefore, offers high electrical performance with fabrication simplicity, making it highly suitable for reconfigurable wideband BPF applications.

For sensitivity analysis, we conducted simulations by applying a ±10% variation in the LC cell thickness based on the target value of 200 μm used in the proposed structure. As shown in Figure 15 and Figure 16, despite a ±10% variation in the cell thickness of around 200 μm, the filter maintains similar frequency response characteristics in terms of S₂₁. In the case of S₁₁, as the LC cell thickness decreases, the transmission pole frequency exhibits a downward shift in frequency. This tendency can be reasonably explained.

According to (1), when the dielectric constant of the liquid crystal is lower than that of the substrate (ε_r,LC < ε_r,sub), a reduction in cell thickness without altering the line width decreases the filling factor q₁ of the LC while increasing the substrate filling factor q₂. As indicated in (10), this results in an increase in the effective permittivity. Furthermore, as shown in (12), for a resonator of fixed physical length, an increase in effective permittivity causes a downward shift in the resonance frequency. Therefore, the proposed structure maintains consistent frequency response behavior even under a ±10% variation in LC cell thickness around the 200 μm baseline. Moreover, when compared with the measured results, the simulated response with a 200 μm cell thickness shows the closest match to the actual resonance frequencies, indicating that the device was fabricated as intended.

As shown in Figure 14, the proposed design successfully implements a voltage-controlled frequency-reconfigurable wideband bandpass filter. However, an undesired narrow passband in the out-of-band range (5 to 5.4 GHz) was persistently observed regardless of the V_B. This spurious response originates from a parasitic low-frequency leakage path formed by the direct connection between the SIR and the coupled line for operating LCs. At 10 GHz, although the transmission line physically connects the resonator, the radial stub effectively blocks the signal path as intended, and most of the signal is observed to propagate through the resonators (Figure 17a). At 5 GHz, however, as previously noted, the SIR resonator does not satisfy the resonance condition, and thus a stopband response was expected. Nevertheless, the radial stub fails to sufficiently suppress the signal, resulting in unintended signal transmission through the direct connection rather than through the resonator (Figure 17b). Although radial stubs are commonly employed as wideband bandstop elements, they inherently exhibit limited rejection uniformity across all frequencies. As the operating frequency deviates from the target rejection frequency, the rejection performance diminishes, leading to residual signal transmission through the connecting line.

Since the undesired narrow passband appeared consistently over the V_B conditions, it can be mitigated in future designs through the inclusion of notch or stopband elements, which can eliminate the unwanted mode without compromising the main tunable passband. To suppress the parasitic passband near 5 GHz without modifying the proposed filter structure, a spurline notch filter can be implemented near the connector interface (Figure 18a). As shown in the E-field distribution at 5 GHz, most of the signal energy is concentrated around the spurline region, effectively blocking the transmission before the signal reaches the SIR structure (Figure 18b). The simulated frequency response with the spurline notch filter confirms that, since the notch element is implemented outside the LC region, it maintains stable rejection characteristics near f₀ = 5.10~5.13 GHz regardless of the applied bias voltage (Figure 19). These results demonstrate the feasibility of a reconfigurable wideband bandpass filter with successful suppression of the undesired parasitic passband.

Additionally, given that the maximum deviation in the center frequency f₀ is within 0.11 GHz and the location of the transmission poles remains consistent regardless of the applied bias voltage, it is unlikely that the discrepancy originates from inaccurate characterization of the dielectric constant. Furthermore, even with a 10% variation in LC cell thickness (from 180 μm to 220 μm), the FBW remains relatively stable without dramatic change. We consider that variations in connector engagement depth due to sample dicing tolerances may have contributed to the observed discrepancies between simulation and measurement. For instance, an increase in the cutting margin may shift the effective connector position, which can lead to an increase in FBW and minimum insertion loss. In addition, other contributing factors may include cable bending, minor deviations in LC cell fabrication, and process-induced variations during sample manufacturing. While each factor alone may appear negligible, their cumulative effect could result in increased loss and bandwidth.

In summary, the proposed design highlights several contributions toward advancing LC-based reconfigurable RF filter applications. First, unlike conventional direct-fed topologies, the adoption of the capacitive coupled-line-fed resonator structure enables design flexibility, broadening the applicability of LC integration to resonator-based filters. Especially, the combination with the coupled-line feeding and the open-ended SIR structure allowed the wideband filter response by allocating transmission poles in the passband. Second, theoretical analysis confirmed that the proposed SIR configuration maintains three transmission poles’ behavior despite variations in LC permittivity, supporting stable filter operation under tuning conditions. For this analysis, we utilized the formulas of multilayer microstrip line and analyzed why the proposed SIR structure maintained the transmission poles in spite of the dielectric constant sweep. Third, the inclusion of a high-impedance line and radial stubs successfully operated the LCs while preserving the intended passband characteristics of the coupled-line-fed resonator. Lastly, the filter demonstrated a wideband performance with a 3 dB FBW exceeding 64.66% and RL > 10 dB, confirming its practical advantage in reconfigurable wideband filter applications. We believe that the feeding techniques presented here can be extended to other resonator types, including open-loop and dual-mode structures, and will contribute to the further development of reconfigurable LC-injected filter technologies.

We briefly discuss potential approaches for future works. In this study, we demonstrated an unprecedented result—an LC-based tunable filter, achieving FBW > 64.66% regardless of the applied bias voltage. However, in addition to achieving wide FBW, compactness is also an important design consideration. It is anticipated that the use of a folded SIR structure instead of the symmetrical SIR employed in this work could facilitate size reduction [45]. Furthermore, applying a configuration based on two asymmetric SIRs with a single-step discontinuity while eliminating the coupled line may also contribute to the miniaturization of wideband BPFs [46]. In addition, integrating liquid crystals into a meandered transversal resonator with asymmetrical interdigital coupled lines could be a promising approach for realizing a reconfigurable and compact wideband BPF [47]. Furthermore, by combining the dielectric anisotropy of liquid crystals with desired beam shaping strategies, this technology may also contribute to the development of reconfigurable beam-shaped antennas [48].

In this study, we demonstrated a voltage-controlled tunable filter operating at room temperature. However, we believe that temperature-driven LC filter designs remain an open area of exploration, given that the liquid crystals used in this work are thermotropic. If tunability can be achieved without external biasing voltage, it may enable the development of alternative classes of reconfigurable filters with greater design flexibility. Additionally, while this study focused on the steady-state performance of the filter, response time or long-term reliability metrics, such as lifetime and repeatability over multiple voltage cycles, are also meaningful indicators for reconfigurable filter applications. Although such investigations remain limited in the context of microwave tunable LC filters, further research in this direction would be beneficial to the broader development of reconfigurable LC-based filter technologies.

6. Conclusions

This paper has presented a reconfigurable wideband bandpass filter (BPF) that achieves a broadband response and continuous center frequency tunability by integrating an open-ended stepped impedance resonator, capacitive-ended coupled line feeding, and liquid crystal (LC) technology. To the best of our knowledge, the proposed structure demonstrates the widest fractional bandwidth (>64.66%) among reported reconfigurable LC-based BPFs, while maintaining a substantial tuning range (12.71%) and return loss (>10 dB), despite employing only a single LC injection layer. Through an analytical approach combining multilayer transmission line formulas and resonant frequency ratios, the modal stability of transmission poles under dielectric constant variation was theoretically predicted and verified via filter response validation. The authors believe that the proposed design and multilayer microstrip line technique will contribute to the advancement of high-frequency reconfigurable LC-injected filter technology.