Ultracompact Self-Shielded Rectangular Patch Bandpass Filter Based on CRLH and Meander-Line Resonators

Chunfeng Fan; Yuexiao Hao; Ke Gong; Yan Liu; Jintu Sun; Qing Liu; Yufang Liu

doi:10.26866/jees.2026.2.r.357

J. Electromagn. Eng. Sci > Volume 26(2); 2026 > Article

Fan, Hao, Gong, Liu, Sun, Liu, and Liu: Ultracompact Self-Shielded Rectangular Patch Bandpass Filter Based on CRLH and Meander-Line Resonators

Regular Paper

Journal of Electromagnetic Engineering and Science 2026;26(2):208-220.

Published online: March 31, 2026

DOI: https://doi.org/10.26866/jees.2026.2.r.357

Ultracompact Self-Shielded Rectangular Patch Bandpass Filter Based on CRLH and Meander-Line Resonators

Chunfeng Fan¹

, Yuexiao Hao¹

, Ke Gong^1,^*

, Yan Liu¹

, Jintu Sun¹

, Qing Liu²

, Yufang Liu³

¹School of Physics and Electronic Engineering, Xinyang Normal University, Xinyang, China

²Department of Electromagnetic Wave and Antenna Propagation, Information Engineering University, Zhengzhou, China

³School of Physics, Henan Key Laboratory of Infrared Materials Spectrum Measures and Applications, Henan Normal University, Xinxiang, China

^*Corresponding Author: Ke Gong (e-mail: gongkexynu@163.com)

Received July 23, 2025 Revised September 1, 2025 Accepted September 29, 2025

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a hybrid rectangular patch filter composed of two half-mode rectangular patch resonators, one composite right/lefthanded resonator (CRLHR), and one meander-line resonator (MLR). By introducing an array of metallized vias with a coupling window on the symmetry plane of the rectangular patch resonators, the symmetric fundamental mode of the rectangular patch is split to exhibit dual-mode behavior. Meanwhile, the CRLHR and MLR offer the merits of small size, adjustable frequency, and opposite phase shift characteristics, and can be embedded separately or jointly into the dual-mode rectangular patch structure to realize third- or fourth-order bandpass filters. In addition, a periodic metallic via array is introduced around the hybrid patch structure to reduce insertion loss. Effectively, two third-order and fourth-order hybrid bandpass filters are fabricated and verified. Compared with similar filters featuring a hybrid substrate integrated waveguide structure, the size of the proposed filters is reduced by approximately 50%. Overall, this self-shielded hybrid patch filter offers low insertion loss, small size, and high selectivity.

Keywords: Composite Right/Left-Handed Resonator (CRLHR), Hybrid Bandpass Filters, Meander-Line Resonator (MLR), Self-shielded, Ultracompact

I. Introduction

Driven by the rapid development of wireless communication systems, the demand for miniaturization and high selectivity of radio frequency (RF) filters has increased steadily. Notably, increasing the order of a filter and adding more transmission zeros (TZs) are common ways to enhance filter selectivity. However, an increase in the filter order means that the number of resonators must also be increased, which can pose challenges to miniaturization.

Scholars have conducted extensive research to enhance filter selectivity while maintaining a compact structure, primarily using four methods. The first method involves the introduction of perturbation structures, such as metallized vias, and etching different types of slots and corner cuts to design dual-mode or multimode resonator structures [1–11]. Second, without affecting the original resonant performance, symmetrical cutting was implemented to design fractional-mode resonators [12, 13]. Third, the order of the system was increased and its size reduced by cascading identical or different types of multi-mode resonators [9, 14– 20]. Finally, researchers created a hybrid structure by integrating various types of resonators into the original symmetric resonator cavity, effectively increasing the filter order [12, 21–29].

While all four aforementioned methods are capable of effectively reducing the overall filter size and can be applied in combination, the last method has seen widespread application, since its hybrid structure design does not add extra volume to the original resonator. Moreover, embedded resonators offer greater flexibility in both design and selection. For instance, in [12], a coplanar waveguide (CPW) resonator or a complementary split-ring resonator is individually embedded into an eighth-mode substrate integrated waveguide (SIW), thereby achieving compact dualband filters. However, the filters offer limited passband controllability and selectivity. In [23] and [24], hybrid fractional-mode SIW structures with a highly compact structure and good selectivity are reported, but the multi-layer structures employed are rather complex. Researchers have also proposed an innovative category of miniaturized hybrid filters based on SIW with full-wavelength, half-wavelength, and quarter-wavelength stripline resonators, achieving both miniaturization and high selectivity [22, 28], but their double-layer configuration incurs high fabrication costs. Meanwhile, [27] proposed fourth-order parallel and series filters based on the hybrid integration of SIW with composite right/left-handed resonators (CRLHRs) and meander-line resonators (MLRs), which exhibit quasi-elliptic characteristics and a compact structure. However, the SIW resonator occupies a larger footprint than that of the microstrip patch resonator.

In this context, microstrip patch RF filters have gained popularity owing to their many advantages, including high power-handling capability, cost-effectiveness, ease of fabrication, and compact structure. Consequently, hybrid microstrip patch filters have recently attracted the attention of a number of scholars [21, 25, 26]. For instance, Wang et al. [21] proposed a fifth-order bandpass filter based on a hybrid microstrip and CPW structure that successfully achieved a compact structural design. However, its performance in the lower stopband region is poor. Furthermore, in [25], a low-loss microstrip patch filter based on a substrate-integrated suspended line (SISL) platform is proposed, but the multi-layer structure of the filer leads to increased costs.

In this paper, for the first time, a CRLHR and an MLR are jointly embedded in a microstrip rectangular patch dual-mode structure. The key merits and innovations of this design can be outlined in terms of four key aspects. First, by introducing an array of metallized vias with a coupling window on the symmetry plane of the rectangular patch resonators, the structure is divided into left and right half-mode patch structures, thereby splitting the symmetric fundamental mode to exhibit dual-mode behavior. The dual-mode design of the rectangular patch structure, in turn, enables miniaturization. Second, without altering the original dimensions of the patch structure, compact and frequency-tunable MLRs and CRLHRs are jointly applied. This novel hybrid configuration introduces two additional poles, thereby achieving a fourth-order bandpass filtering response. Third, extensive analysis of CRLHR and MLR in [27] has highlighted their opposite phase transmission characteristics, which is expected to result in opposite TZ characteristics. Therefore, both these structures are integrated into the proposed filter to introduce two TZs at each side of the passbands. Moreover, the positions of these TZs are highly controllable, enabling the filter to exhibit a quasi-elliptic function response. Finally, the fourth aspect is the introduction of a periodic metallic via array around the hybrid patch structure, which helps reduce insertion loss.

The remainder of this paper is structured as follows. In Section II, the resonant characteristics of half-mode rectangular patch resonators (HMRPRs), CRLHRs, and MLRs are analyzed. In Section III, a third-order hybrid filter incorporating either a CRLHR or MLR structure is developed, manufactured, and tested. Next, in Section IV, a fourth-order hybrid patch filter comprising both CRLHR and MLR is thoroughly studied. Furthermore, two fourth-order filters—one with a shielded structure and the other without it—are analyzed and compared. Finally, Section V presents the conclusion.

II. Analysis of the Proposed Dual-Mode Patch Resonator

1. Rectangular Patch Resonator

The symmetrical structure of a rectangular patch resonator (RPR) significantly facilitates the design of compact filters. As illustrated in Fig. 1, electric field distributions of the first four resonant modes of a rectangular patch resonator all exhibit symmetrical axes, as indicated by the dotted lines. Due to the symmetry characteristics of the RPR, its fundamental mode TM₀₁₀ displays symmetry around the axis of symmetry, as observed in Fig. 1(a). This property can be leveraged to achieve a dual-mode rectangular patch resonator that supports both odd and even TM₀₁₀ modes by incorporating periodically arranged metallic vias into the symmetric plane. The resonant frequencies of the TM_mn0 modes can be approximately calculated using Eq. (1) [25]:

(1)

fTMmn0=c2μrɛr(mW)2+(nL)2

Here, L and W represent the equivalent length and width of the RPR, respectively; ɛ_r and μ_r denote the substrate’s relative permittivity and relative permeability, respectively; and c refers to the speed of light in a vacuum.

2. CRLHR and MLR

CRLHR and MLR are widely employed in filter design due to their suitability for miniaturization. Structural schematic diagrams of a CRLHR and an MLR are illustrated in Fig. 2(a) and 2(d), respectively. The CRLHR is realized by etching an interdigital structure on the upper metal layer above the substrate, while the MLR is achieved by etching a meandering line on the upper metal layer above the substrate. The electric field distributions of their fundamental modes are illustrated in Fig. 2(b) and 2(e).

Determining the size of the CRLHR and MLR at specific frequencies is the focus of the current study. Under ideal conditions, where parasitic capacitance is neglected, the initial dimensions of a CRLHR can be calculated using Eq. (2), where n indicates the number of fingers, l denotes the finger length, and ɛ_r stands for the substrate material’s relative permittivity [30], expressed as follows:

(2)

C(pF)=3.937×10-5l(ɛr+1)[0.11(n-3)+0.252]

Similarly, upon disregarding parasitic inductance under ideal assumptions, the initial dimensions of the MLR can be calculated using Eqs. (3)–(5) [30]. In these equations, W, t, and l correspond to the width, thickness, and length of the conductor, respectively. Furthermore, R represents the corresponding resistance, and R_s refers to the surface resistance of the conductor, measured in ohms per square. Meanwhile, K_g is a correction factor that accounts for the influence of the ground plane.

(3)

L(nH)=2×10-4 [ln (lW+t)+1.193+0.2235W+tl]·Kg

(4)

R=Rsl2(W+t)·[1.4+0.217ln (W5t)]

(5)

Kg=0.57-0.145lnWh

However, during application, all parasitics and other effects must be comprehensively considered, implying that it is extremely important to construct a reasonable equivalent circuit and perform full-wave electromagnetic simulations. The equivalent circuits for CRLHR and MLR are demonstrated in Fig. 2(c) and 2(f), respectively. The resonant frequencies of the CRLHR and MLR were calculated using Eqs. (6) and (7). Through an Advanced Design System (ADS) simulation, the following parameter values were obtained: C₁ = 2.865 pF, L₁ = 0.196 nH, C₂ = 4.04 pF, and L₂ = 0.254 nH.

(6)

ω1=12L1C1

(7)

ω2=1L2C2

It is well known that the size of a CRLHR and an MLR should ideally be a fraction of the wavelength. According to the analysis in this section, the dimensions of the CRLHR and MLR should be estimated first, followed by determining their precise specifications through electromagnetic simulation based on the equivalent circuit model. In this context, it is important to note that both the quantity of fingers n and the length of finger l of a CRLHR can be flexibly adjusted according to design requirements. Similarly, the numbers of bends in an MLR structure can also be customized as needed. Notably, the detailed analysis of the transmission characteristics of CRLHR and MLR performed in [25] provided inspiration for the design of the hybrid filter proposed in this study. In particular, the combined use of CRLHR and MLR in the proposed filter design provides two different TZs for different sidebands.

III. Third-Order Hybrid Filters

1. Third-Order Hybrid Filter with CRLHR (Filter I)

A 3D view of the proposed third-order hybrid filter equipped with a CRLHR is illustrated in Fig. 3, where Layers 1 and 3 are composed of copper and Layer 2 consists of a dielectric substrate. A schematic diagram of the filter’s planar structure is presented in Fig. 4. In this design, metallized vias with inductive windows are incorporated into the symmetrical plane of the rectangular patch, effectively dividing a single rectangular patch resonator into two HMRPRs. Consequently, a simple dual-mode rectangular patch resonator was successfully realized. To further enhance the frequency selectivity while maintaining the miniaturization of the structure, a CRLHR was introduced into the modified rectangular patch resonator without altering the original size of the rectangular patch. This third-order hybrid filter incorporating CRLHR is referred to as Filter I.

Electric field distributions of the first three resonant modes of Filter I under eigenmode analysis are illustrated in Fig. 5(a) and 5(c), indicating the odd and even TM₀₁₀ modes associated with the RPR, respectively, while the corresponding electric field vector distributions are depicted in Fig. 5(d) and 5(f). In Fig. 5(f), all electric field vectors point in the same direction, implying the even TM₀₁₀ mode. Conversely, in Fig. 5(d), the electric field vectors are oriented in opposite directions, signifying odd TM₀₁₀ mode. Fig. 5(b) and 5(e) depict the electric field intensity distribution for the fundamental mode of the CRLHR. Consequently, two transmission poles (TPs) within the passband were provided by the two HMRPRs, and one additional TP was provided by the CRLHR. Effectively, a three-pole filter was achieved by inserting the CRLHR into the two HMRPRs.

Drawing on the analysis above, the equivalent topology of Filter I is illustrated in Fig. 6, where Nodes 1 and 3 represent the left and right HMRPRs, respectively, while Node 2 signifies the CRLHR. Fig. 6 also shows that Filter I features two coupling paths. The primary coupling path is designated 1-2-3, where the odd and even TM₀₁₀ modes of the dual-mode rectangular patch couple through the fundamental mode of the CRLHR. The secondary coupling path, labeled 1–3, serves as the cross-coupling path, which is achieved by implementing a coupling window using metallized vias on the symmetrical plane of the rectangular patch. Since this coupling window is positioned at a location where the electric field in the HMRPRs is weakest and magnetic field strength is highest, it was predominated by magnetic coupling. Consequently, a −90° phase difference was observed along the cross-coupling path (1–3). Notably, in the presented design, the four metallic vias were deliberately arranged around the CRLHR to regulate the coupling between the rectangular patch and the CRLHR.

Fig. 7(a) illustrates the variations in coupling coefficients K₁₂ and K₁₃ with regard to the filter’s parameters. K₁₂ represents the coupling coefficient between HMRPR and CRLHR, which decreases as the distance (D_P) between the metal vias increases. Meanwhile, K₁₃ signifies the coupling coefficient between the HMRPRs, which increases with the size of the coupling window (W_P). These results confirm that coupling coefficients K₁₂ and K₁₃ exhibit good flexibility. Furthermore, Fig. 7(b) depicts the changes in the external quality factor (Q_e) of the TM₁₀₀ mode with regard to the parameters. It was found that Q_e is primarily determined by the lengths of CPW feedlines L₁ and L₂. Therefore, by reducing L₁ and L₂, Q_e could be increased, enabling more electromagnetic energy to couple into the HMRPR.

When f > f₀, the CRLHR introduced a +90° phase shift. Conversely, when f < f₀, it produced a −90° phase shift. Here, f refers to the working frequency, and f₀ denotes the center frequency. Based on Table 1, it can be concluded that Filter I can produce a single TZ within its lower stopband. Moreover, since the intensity of magnetic coupling can be flexibly regulated by modifying the size of the coupling window (W_P), adaptive positioning of TZs is possible. The response of the TZ with respect to parameter variations is depicted in Fig. 8, demonstrating that a reduction in the coupling window size shifts the lower band’s TZ toward higher frequencies, resulting in improved edge steepness of the filter.

To validate the proposed filter, the dielectric substrate employed was Rogers 5880 (ɛ_r = 2.2, tanδ = 0.0009) of height h = 0.508 mm, along with a 0.035-mm-thick copper layer. The structure was simulated using High Frequency Structure Simulator (HFSS). A bandpass filter with a center frequency (f₀) of 5.27 GHz and a relative bandwidth of 16.87% was designed by implementing the method outlined in [31] to synthesize the coupling matrix (CM) for the filter, which is presented in Eq. (8). Fig. 9(a) confirms that the synthesis results align well with the simulation outcomes. The final design parameters for Filter I are as follows: L = 19.02, W = 11.5, W_F = 1.5, L_F1 = 3.4, L_F2 = 1.85, W_S1 = 0.2, D = 0.4, P = 0.6, D_P = 0.6, L₁ = 6.4, W₁ = 0.6, W_S = 0.2, W_D = 0.2, and W_P = 1.8 (all units: mm).

(8)

[ S123LS01.1500011.15-0.0851.09950.26520201.09950.2199-1.09950300.2652-1.0995-0.0851.15L0001.150]

Finally, the fabrication and measurement of Filter I were conducted. A comparison of the filter’s simulated, synthesized, and measured frequency responses within the 2–10 GHz frequency range is demonstrated in Fig. 9(a), which shows highly satisfactory agreement between the measured and simulated results. The measured values for the center frequency (f₀), 3-dB fractional bandwidth (3-dB FBW), and insertion loss (IL) were 5.4 GHz, 23.12%, and 1.57 dB, respectively. Notably, the measured IL (1.57 dB) was found to be higher than the simulated IL (0.75 dB), which can be attributed to manufacturing tolerances and losses introduced by the test fixtures used during the measurement process.

2. Third-Order Hybrid Filter with MLR (Filter II)

Filter II, as depicted in Fig. 10, was achieved by incorporating an MLR into the two HMRPRs. Fig. 11 illustrates the electric field distributions of the first three resonant modes of Filter II. Similar to Filter I, Fig. 11(a) and 11(c) depict the even and odd TM₀₁₀ modes of the RPR, respectively, while Fig. 11(b) shows the fundamental mode of the MLR. The equivalent topology of Filter II is presented in Fig. 12, where Nodes 1 and 3 correspond to the left and right HMRPRs, respectively, and Node 2 corresponds to the fundamental mode of the MLR.

As depicted in Fig. 12, the coupling path 1-2-3 represents the main coupling path, where the odd and even TM₀₁₀ modes of the dual-mode rectangular patch are coupled through the fundamental mode of the MLR. The alternative coupling path, labeled 1–3, serves as the cross-coupling path, which is achieved via magnetic coupling through the coupling window on the symmetry plane of the rectangular patch. A schematic diagram of Filter II is illustrated in Fig. 10. In contrast to Filter I, when f < f₀, the MLR generated a +90° phase shift; conversely, when f > f₀, it produced a −90° phase shift. As indicated in Table 2, Filter II was able to create an upper stopband TZ. Moreover, the intensity of magnetic coupling could be conveniently regulated by altering the dimensions of the coupling window (W_P). As a result, the position of the TZ could also be manipulated accordingly. The response of TZ to varying parameters is depicted in Fig. 13.

To verify the proposed filter, a bandpass filter featuring a center frequency of 5.27 GHz and a relative bandwidth of 16.87% was developed. The CM of the filter is presented in Eq. (9). As demonstrated in Fig. 14(a), the synthesis and simulation results show a high degree of consistency. The final configuration parameters for Filter II are as follows: L = 20, W = 11.5, W_F = 1.5, L_F1 = 4.66, L_F2 = 1.8, W_S1 = 0.82, D = 0.4, P = 0.6, D_P = 0.6, W_M = 0.2, L_M = 2.84, L_D = 0.6, L₁ = 3.44, W₁ = 0.38, W_D = 0.78, and W_P = 1.5 (all units: mm).

(9)

[ S123LS01.2100011.210.12241.0780.57550201.078-0.52041.0780300.57551.0780.12241.21L0001.210]

Finally, the fabrication and measurement of Filter II were conducted. A comparison of the filter’s simulated, synthesized, and measured frequency responses is presented in Fig. 14(a), demonstrating good consistency between the measurement and simulation results. Moreover, the measured values for f₀, 3-dB FBW, and IL were 5.03 GHz, 12.33%, and 1.66 dB, respectively. It is noteworthy that the measured IL of 1.57 dB exceeded the simulated IL of 0.75 dB, which can be attributed to fabrication errors and losses incurred by the testing fixtures used during measurement.

Taken together, the above experiments demonstrate that third-order hybrid filters—Filters I and II—can generate controllable TZs either in the upper or lower band. Moreover, by designing the third-order filters, it was verified that the CRLHR and MLR possess opposite TZ characteristics. Consequently, we expected the collaborative application of the two to facilitate higher frequency selectivity in filter design.

IV. Fourth-order Hybrid Filters

1. Fourth-Order Hybrid Filter with CRLHR and MLR (Filter III)

To further improve the selectivity of Filters I and II, we created a fourth-order hybrid filter combining CRLHR and MLR. As illustrated in Fig. 15, Filter III was realized by jointly incorporating CRLHR and MLR into the two HMRPRs, Fig. 16 depicts the electric field distributions corresponding to the first three resonant modes, obtained through eigenmode analysis of Filter II. Fig. 16(a) and 16(b) depict the even and odd TM₀₁₀ modes of the RPR, respectively, while Fig. 16(c) and 16(d) illustrate the fundamental modes of the MLR and CRLHR, respectively.

Fig. 17 shows that Filter III features an equivalent box-like topology, where Nodes 1 and 4 represent the left and right HMRPRs, respectively, while Nodes 2 and 3 correspond to the MLR and CRLHR. The proposed filter is characterized by two primary coupling paths and one cross-coupling path, with the main coupling paths being 1-2-4 and 1-3-4. As analyzed above, when f < f₀, the CRLHR generates a +90° phase shift, whereas for f > f₀, it produces a −90° phase shift. As a result, the CRLHR is capable of offering an equivalent negative coupling pathway (M₃₄ =−M₁₃). Meanwhile, the cross-coupling path is realized through the inductive coupling window situated between the two HMRPRs, where magnetic coupling predominates. As a result, the sign of the coupling coefficient M₁₄ is positive. Therefore, owing to the bypass negative coupling paths and cross-coupling paths, Filter III achieved one lower stopband TZ and one upper stopband TZ, as noted in Table 3. Moreover, both TZ positions could be effectively controlled by modifying the dimensions of the coupling window (D_M) and the positioning of the CRLHR (W_P). Response curves illustrating the variations in these two TZs with regard to parameter changes are depicted in Fig. 18.

A bandpass filter with a center frequency of 5.15 GHz and a relative bandwidth of 15.5% was fabricated. The CM of the filter was derived, as presented in Eq. (10). The synthesized results were observed to align well with the simulation outcomes, as evident from Fig. 19(a). The final parameters for Filter III are as follows: L = 20.26, W = 13.3, W_F = 1.5, D = 0.4, D_P = 0.37, D_M = 1.97, D_C = 2.5, W_M = 0.2, L_M = 2.64, L_D1 = 0.6, L₁ = 3.24, W₁ = 0.76, W_D1 = 0.36, L_D1 = 0.6, L₂ = 6.8, W₂ = 0.5, W_S = 0.2, W_D2 = 0.2, D₁ = 1.15, and D₂ = 1.95 (all units: mm).

Finally, Filter III was fabricated and measured. A comparison of the simulated, synthesized, and experimentally measured frequency responses of this filter within the frequency range of 2–10 GHz is illustrated in Fig. 19(a), indicating satisfactory consistency between the testing and simulation results. Furthermore, the measured values for f₀, 3-dB FBW, and IL were 5.14 GHz, 18.46%, and 1.59 dB, respectively.

Overall, Filter III achieved two TZs—one in the upper stopband and the other in the lower stopband. Moreover, compared to Filters I and II, its higher-order design contributed to enhanced frequency selectivity. Nonetheless, although the adoption of the HWRPR enabled size reduction, the surrounding open structure may result in elevated insertion loss.

2. Fourth-Order Hybrid Filter with a Self-shielded Structure (Filter IV)

Filter IV involved integrating the MLR and CRLHR into the two HMRPRs and then enclosing the structure using a periodic array of metallized vias, as shown in Fig. 20. This configuration contributed to enhanced unloaded quality factor (Q_U) of the patch resonator, decreased insertion loss, and improved shielding effectiveness.

To clarify the operational principle of the shielded RPR, a comparative investigation was conducted through eigenmode analysis by considering various structures. In contrast to conventional RPRs, the open boundary of the proposed RPR renders it prone to radiation losses and electromagnetic energy leakage. To mitigate these extraneous radiation losses, a periodic array of metallized vias was introduced along the open edge of the RPR. The etched square slot served as a magnetic wall, simulating the open edge of conventional RPR cavities. The addition of this shielding wall partially obstructed wave propagation along the surface, thereby reducing radiation losses. Fig. 21(a) and 21(b) present the simulated unloaded quality factors (Q_U) for the investigated structures at a center frequency of 10 GHz. The results indicate that RPR equipped with shielding structures exhibits superior performance compared to traditional RPR designs.

The simulation response of Filter IV is illustrated in Fig. 22(a). The simulated IL was measured to be 0.69 dB, indicating a reduction of 0.11 dB compared to that of Filter III.

Notably, the excellent performance of the shielded RPR primarily stems from its lower radiation loss. The final parameters for Filter IV are as follows: L = 20.26, W = 13.3, W_F = 1.5, D = 0.4, P = 0.6, D_P = 0.37, D_M = 1.97, D_C = 2.5, W_M = 0.2, L_M = 2.64, L_D1 = 0.6, L₁ = 3.24, W₁ = 0.76, W_D1 = 0.36, L_D1 = 0.6, L₂ = 6.8, W₂ = 0.6, W_S = 0.2, W_D2 = 0.2, D₁ = 1.15, D₂ = 1.95, L₂ = 22.2, W₂ = 14.79, and W_S1 = 0.62 (all units: mm).

Subsequently, Filter IV was fabricated and measured. A comparison of the simulated and measured frequency responses is presented in Fig. 22(a), demonstrating strong agreement. The measured values of f₀, 3-dB FBW, and IL were 5.09 GHz, 17.29%, and 1.31 dB, respectively. As shown in Fig. 21(c), the measured IL of Filter IV achieved a reduction of 0.28 dB compared to that of the unshielded structure of Filter III, establishing that the former is characterized by a higher Q factor and offers enhanced performance.

3. Discussion and Comparison

To verify the practical value of the proposed design, Table 4 summarizes the properties of a few planar bandpass filter design schemes based on different technologies and structures that have been reported over the past three years. In this context, it should be noted that there is a contradiction between a reduction in filter size and an improvement in frequency selectivity. In practical engineering applications, design complexity, manufacturing cost, and performance requirements should all be comprehensively considered to identify the overall optimal design scheme.

As evident from the comparative analysis in Table 4, the filter proposed in this study, owing to its single-layer structure, offers the advantages of simplified fabrication and reduced manufacturing costs. Additionally, it is characterized by excellent frequency selectivity and low insertion loss, thereby outperforming conventional patch filters in overall performance. Compared to other compact filter designs, the proposed structure exhibits a notable advantage in terms of miniaturization. Furthermore, it is worth noting that although the design presented in [25] has a more compact size than the one discussed in this study, this reduction in size was accomplished by incorporating additional layers, which resulted in elevated manufacturing costs and greater design complexity.

V. Conclusion

In this study, a hybrid structured bandpass filter composed of two HMRPRs is introduced. First, two third-order hybrid filters incorporating either a CRLHR or an MLR were designed and experimentally validated, each generating a controllable TZ in the lower or upper stopband. Subsequently, the combined implementation of CRLHR and MLR introduced a TZ in each of the upper and lower stopbands, enabling the realization of a fourth-order quasi-elliptic function filter with two distinct TZs. This filter was designed, fabricated, and measured.

The proposed configuration comprises multiple arrays of metallic vias strategically positioned around the CRLH or MLR to control the coupling between the rectangular patch and microstrip resonators. Moreover, the design maintains the original patch dimensions while increasing the filter order and number of TZs, thereby achieving a compact physical footprint and enhanced frequency selectivity. Furthermore, insertion loss is minimized by integrating a periodic metallic via array around the hybrid patch structure. Overall, it is established that the compact self-shielded rectangular structure proposed in this study can be applied to 5G networks and Wi-Fi technologies.

Notes

This work was supported in part by the Scientific and Technological Innovation Leading Talents of Central China (264200510054), Scientific and Technological Innovation Team Program of Universities in Henan Province (26IRTSTHN027), Technology Research and Development Joint Funding (Industry category) Project of Henan Province (20240001), Key Technologies R&D Program of Henan Province (262102211112), National Natural Science Foundation of Henan Province (252300421515), and Postgraduate Education Reform and Quality Improvement Project of Henan Province (YJS2026XSKC54).

Fig. 1

Electric field distributions of the first four modes in the rectangular patch resonator: (a) TM₀₁₀, (b) TM₁₀₀, (c) TM₁₁₀, and (d) TM₀₂₀.

Fig. 2

Comparison of filter design for CRLHR and MLR: (a) structural diagram, (c) electric field distribution, and (e) equivalent circuit of CRLHR; (b) structural diagram, (d) electric field distribution, and (f) equivalent circuit of MLR.

Fig. 3

A 3D view of the proposed filter with CRLHR.

Fig. 4

Planar view of the third-order hybrid filter with CRLHR.

Fig. 5

Electric field intensity of the first three resonant under eigenmode analysis: (a) electric field distribution and (d) vector of the odd TM₁₀₀ mode; (b) electric field distribution and (e) vector of the CRLHR fundamental mode; (c) electric field distribution and (f) vector of the even TM₁₀₀ mode.

Fig. 6

Equivalent topology of Filter I.

Fig. 7

(a) Extracted internal coupling coefficients K₁₂ and K₁₃. (b) Extracted external quality factors of the TM₁₀₀ mode.

Fig. 8

Position of the TZ with respect to the parameters.

Fig. 9

(a) Comparison of the simulation, synthesis, and measurement results for Filter I; (b) photograph of Filter I.

Fig. 10

Planar view of the third-order hybrid filter with MLR.

Fig. 11

Electric field intensity of the first three modes under eigenmode analysis: (a) electric field distribution and (d) vector of the even TM₁₀₀ mode; (b) electric field distribution and (e) vector of the MLR foundational mode; (c) electric field distribution and (f) vector of the odd TM₁₀₀ mode.

Fig. 12

Equivalent topology of Filter II.

Fig. 13

Positions of the TZ with respect to the parameters.

Fig. 14

(a) Comparison of the simulation, synthesis, and measurement results of Filter II and (b) photograph of Filter II.

Fig. 15

Planar view of the proposed hybrid filter with MLR and CRLHR.

Fig. 16

Electric field intensity of the first four modes under eigenmode analysis: (a) even TM₀₁₀ mode, (b) odd TM₀₁₀ mode, (c) fundamental mode of MLR, and (d) fundamental mode of CRLHR.

Fig. 17

Equivalent topology of Filter III.

Fig. 18

Position of TZ in response to changes in the parameters. (a) TZs varies with D_M, (b) TZs varies with W_P.

Fig. 19

(a) Comparison of the simulation, synthesis, and measurement response of Filter III, and (b) photograph of Filter III.

Fig. 20

Planar representation of the fourth-order hybrid filter featuring a shielding structure.

Fig. 21

(a) Q_U of the unloaded four-order filter with no shielding structure, (b) Q_U factor of the unloaded four-order filter with a shielding structure, and (c) comparison between the measurement responses of the filter with a shielding structure and the filter without a shielding structure.

Fig. 22

(a) Comparison of the simulation, synthesis, and measurement responses of Filter IV, and (b) photograph of Filter IV.

Table 1

Multi-coupling-path phase relationship and the generation of TZs of Filter I

	f < f₀	f > f₀
Path 1-2-3	−90°−90°−90° = −270°	−90°+90°−90° = −90°
Path 1–3	−90°	−90°
Phase difference	180°	0°
Result	A TZ	No TZs

Table 2

Multi-coupling-path phase relationship and the generation of TZs of Filter II

	f < f₀	f > f₀
Path 1-2-3	−90°+90°−90° = −90°	−90°−90°−90° = −270°
Path 1–3	−90°	−90°
Phase difference	0°	180°
Result No	TZs	A TZ

Table 3

Multi-coupling-path phase relationship and the generation of TZs of Filter III

	f < f₀	f > f₀
Path 1-2-4	−90°+90°−90° = −90°	−90°−90°−90° = −270°
Path 1-3-4	−90°−90°−90° = −270°	−90°+90°−90° = −90°
Path 1–4	−90°	−90°
Phase difference	180° (1-3-4 and 1–4)	180° (1-2-4 and 1–4)
Result	A TZ	A TZ

Table 4

Comparison table of performance with similar filters

Study	Filter	Technology	f₀	IL	Order	TZ	TZ control	Circuit size	Layer
Liu et al. [4]	Filter II	Capacitive-loaded patch	1.81	2.61	4	4	Yes	0.32λ_g × 0.61λ_g	2
Zhu et al. [10]	Four-pole	FSIW	10	1.26	4	2	Yes	0.99 λ_g × 0.99λ_g	2
Fan et al. [15]	Filter III	Dual-mode patch	3.3	1.18	4	5	Yes	0.49λ_g × 1.09λ_g	1
Qian et al. [19]	VII	Dual-mode slow-wave patch	2.4	1.16	4	4	Yes	0.75λ_g × 1.66λ_g	2
Jiao et al. [22]	FBPF-III	SIW + Stripline	9.96	1.52	4	2	Yes	1.38λ_g × 0.69λ_g	2
Wu et al. [25]	Filter III	Patch + SISL	5.43	1.16	3	6	Yes	0.284λ_g × 0.324λ_g	5
Zhu et al. [27]	Parallel Triplet	SIW + MLR+CRLH	10.05	0.82	4	2	Yes	0.60λ_g × 0.88λ_g	1
Fan et al. [28]	II	SIW + Stripline	10.1	1.8	4	4	Yes	0.92λ_g × 0.92λ_g	2
This work	Filter I	Patch + CRLH	5.4	1.57	3	1	Yes	0.24λ_g × 0.34λ_g	1
	Filter II	Patch + MLR	5.03	1.66	3	1	Yes	0.24λ_g × 0.34λ_g	1
	Filter III	Patch + CRLH + MLR	5.14	1.59	4	2	Yes	0.24λ_g × 0.35λ_g	1
	Filter IV	Patch + CRLH + MLR	5.09	1.31	4	2	Yes	0.24λ_g × 0.36λ_g	1

λ_g denotes guided wavelength at the center frequency.

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Biography

Chunfeng Fan, https://orcid.org/0009-0004-0665-3528 received her B.S. degree in electronic information engineering from Xinyang Normal University, Xinyang, China, in 2003, and her M.S. degree in mechanical and electronic engineering from the China University of Petroleum-Beijing, Beijing, China, in 2010. She is currently pursuing her Ph.D. degree in electromagnetic field and microwave technology from Henan Normal University, Xinxiang, China. Since 2014, she has been an associate professor at Xinyang Normal University, Xinyang, China. Her research interests include microwave and millimeter-wave antennas, filters, and RF technology for satellite and mobile communication.

Biography

Yuexiao Hao, https://orcid.org/0009-0009-9336-4041 received his B.S. degree in electronic science and technology from Xinyang Normal University, Xinyang, China, in 2022. He is currently pursuing his M.S. degree in electronic science and technology at Xinyang Normal University, Xinyang, China. His research interests include microwave technology and the design of SIW filters.

Biography

Ke Gong, https://orcid.org/0000-0002-4576-1095 received his B.S. degree in physics from Xinyang Normal University, Xinyang, China, in 2000, and his M.S. and Ph.D. degrees in electromagnetic field and microwave technology from Southeast University, Nanjing, China, in 2005 and 2013, respectively. Since 2000, he has been with the School of Physics, Xinyang Normal University, Xinyang, China. He is currently a professor and Associate Dean of the College of Physics and Electronic Engineering, Xinyang Normal University. He worked at the Institute for Infocom Research (I2R), Agency for Science, Technology and Research (A*STAR), Singapore, as a research engineer from May to November 2010, and as a research fellow from April to September 2011. He has authored and coauthored more than 30 technical publications. He has also coauthored the book “Substrate-Integrated Millimeter-Wave Antennas for Next-Generation Communication and Radar Systems” (Wiley-IEEE Press, 2021). His research interests include microwave and millimeter-wave antennas, filters, and RF technology for satellite and mobile communications. Dr. Gong has served as reviewer for IEEE Transactions on Microwave Theory and Techniques and IEEE Transactions on Antennas and Propagation. He was awarded the second-class Natural Science Award by the government of Henan Province.

Biography

Yan Liu, https://orcid.org/0000-0002-9229-0724 was born in Xinyang, Henan Province, China, in 1982. He received his B.S. and M.S. degrees from Xinyang Normal University, Henan, China, in 2006 and 2015, respectively. In 2021, he received his Ph.D. degree from the University of Electronic Science and Technology of China, Chengdu, China. Since 2022, he has been with the College of Physics and Electronic Engineering at Xinyang Normal University. His recent research interests include filters, reflect arrays, transmit arrays, and plate antennas.

Biography

Jintu Sun, https://orcid.org/0000-0002-2749-9863 was born in Shandong Province, China, in 1984. He received his Ph.D. degree in theoretical physics from Lanzhou University, China, in 2010. From 2010 to 2013, he worked as a postdoctoral researcher at the Institute of Modern Physics, Chinese Academy of Sciences. Since 2014, he has been a lecturer at Xinyang Normal University, Xinyang, China. His research interests include microwave and millimeter-wave antennas, filters, RF technology for satellite and mobile communications, and computational physics.

Biography

Qing Liu, https://orcid.org/0000-0002-1833-2949 received his B.S. degree in communications engineering from Hunan University, Changsha, China, in 2014, and his Ph.D. degree from Information Engineering University, Zhengzhou, China, in 2020. Since 2023, he has been an associate professor at the Information Engineering University. He is currently a postdoctoral fellow at the Center for Microwave and RF Technologies (CMRFT), Shanghai Jiao Tong University, Shanghai, China. He has authored and coauthored more than 60 technical articles in refereed journals and conferences, and he holds six patents. His current research interests include antennas, microwave filters, frequency-selective surfaces, and other passive components.

Biography

Yufang Liu, https://orcid.org/0000-0003-1896-8864 was born in Henan Province in 1963. He holds a Doctor of Science degree and serves as a Level-Two Professor and doctoral supervisor. A recipient of the State Council Special Allowance, he has been honored with the title of Zhongyuan Scholar. His current research focuses on infrared physics and technology, spectral emissivity modulation, and the fabrication and applications of micro- and nano-photonic devices. He has served as an expert reviewer for the National Natural Science Foundation of China’s Outstanding Young Scientists Program, National Major Scientific Instrument Development Project, Excellent Young Scientists Program, Major Research Program, Key Program, General Program, and Youth Program.