https://orcid.org/0009-0001-6106-6797
Figures
Abstract
To address the growing demand for compact and high-performance microwave filters in modern communication systems, a mixed-mode bandpass filter is proposed in the article. A dual-layer substrate integrated waveguide resonator loaded with a capacitive patch (CP-DSIWR) is proposed and theoretically analyzed, with both patch modes and cavity modes existing. To construct the bandpass filter, two rows of metallic vias are designed in the CP-SIWR to enable coupling between the two types of the modes, with the structure being fed by microstrip line. A slot is embedded in the center of the capacitive patch to tune the resonant frequencies. The simulated results of the filter show that TM01, TM10 and TE101 modes are excited, achieving a dual-band filtering response with tunable frequency characteristics. The filter is centered at 6.2 GHz and 12.9 GHz with a compact size of 0.57×0.57
. A prototype is fabricated and measured for validation, showing good agreement between the simulation and measured results.
Citation: Zeng R, Chen J, Luo X, Shen D, Xing C (2025) Dual-band mixed-mode bandpass filter based on dual-layer substrate integrated waveguide resonator loaded with A capacitive patch. PLoS One 20(9): e0330712. https://doi.org/10.1371/journal.pone.0330712
Editor: Azim Uddin, Zhejiang University, CHINA
Received: June 3, 2025; Accepted: August 5, 2025; Published: September 8, 2025
Copyright: © 2025 Zeng et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data can be found on GitHub at: https://github.com/zengrihui/Dual-band-Mixed-mode-BandpassFilter.git.
Funding: This work was supported by Yunnan Fundamental Research Projects (grant NO. 202401AT070042). The funders provided financial support for device fabrication and testing.
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
With the rapid advancement of wireless communication systems, the demand for compact and high-performance multi-band filters is increasing. A technology of planar microwave circuits, substrate integrated waveguide (SIW), is characterized by its low cost, low transmission loss, compact size, and excellent compatibility with other planar microwave circuits, has become prevalent in the design of highly reliable planer filters [1–2]. Traditional SIW bandpass filters, designed based on the fundamental TE101 mode [3–4], posed challenges in achieving compact multi-band filtering characteristics.
To address these limitations, researchers have explored various methods to enable multi-mode and multi-band operation. Typically, there are three primary methods for implementing multi-band bandpass filters. The straightforward approach involves forming multiple coupling paths between the source and load by combining independent single-band filters, which has been extensively implemented on SIW and microstrip platforms [5–9]. However, the strategy for multi-band filter results in relatively larger circuit size. An alternative method entails dividing a wide passband into several sub-passbands by introducing multiple transmission zeros. This technique has been explored for achieving dual- and tri-band filters [10–13], although it is limited to specific frequency ratios.
To solve the problem, an advanced approach leveraging dual- or tri-mode resonators has emerged, offering advantages such as compact size and enhanced design flexibility [14–17]. A dual-band dual-mode bandpass SIW filter with wide bandwidth and controllable transmission zeros was presented, which used two modes without adjustable center frequency [14]. Another work introduced two dual-band filters within a single cavity through overlapping mode control, achieving excellent frequency ratios [15]. A dual-band quad-mode SIW filter with multi-mode characteristics was reported in [16], and a quad-mode quad-band filter was reported in [17]. Despite their high selectivity and excellent out-of-band rejection, these designs exhibit large insertion loss at lower frequency, such as 2.21 dB in [16] and 2.39 dB in [17].
In the paper, a dual-layer substrate integrated waveguide resonator loaded with a capacitive patch (CP-DSIWR) is proposed to introduce both patch modes and cavity modes, thereby significantly increasing the number of available resonant modes. Based on the technology of CP-DSIWR, a dual-band mixed-mode bandpass filter is constructed. The capacitive patch is designed to generate additional patch modes when fed appropriately, ensuring the simultaneous presence of both patch modes and cavity modes within the resonator. By embedding a slot on the capacitive patch, the frequencies of these resonant mixed-modes can be controlled, and a transmission zero is introduced to the right of second passband.
2 Mixed-mode bandpass filter theory and analysis
2.1 Analysis and design of dual-layer substrate integrated waveguide resonator loaded capacitive patch
Generally, the resonant modes existing in a SIW cavity are limited to cavity modes. In this section, an improved SIW cavity is constructed by introducing a capacitive patch between two vertically stacked SIW cavities, forming what is referred to as a dual-layer substrate integrated waveguide resonator loaded with a capacitive patch (CP-DSIWR). In the CP-DSIWR, both patch modes and cavity modes exist.
The configuration of the proposed CP-DSIWR, illustrated in Fig 1, consists of two dielectric layers and three conductive layers. The dielectric substrates, layer 2 and the layer 4, are Rogers RT5880, with a relative permittivity , a loss tangent
, dimensions of
and a thickness of 0.508 mm. Layer 1 and the layer 5 form the top and bottom conducting surfaces of the resonant cavity, respectively. Layer 3 is the loaded capacitive patch with dimensions of
. For all examples presented in this paper, the diameter of the metallic vias is selected as
mm, and the pitch between adjacent vias is set to
mm.
To investigate the effects of the capacitive patch on resonant modes in the CP-DSIWR, a comparison is conducted between the proposed CP-DSIWR and a traditional SIW resonator with the same physical dimensions. Both structures are simulated and analyzed in the software ANSYS with the eigenmode solver.
To explore the frequency characteristics of the patch modes and cavity modes in the proposed CP-DSIWR, the electric field distributions of the resonant modes for the CP-DSIWR within frequency range of 0 ~ 20 GHz are simulated, as shown in Fig 2. The simulated electric field distributions reveal that eight eigenmodes exist in the CP-DSIWR: (a)TM01, (b)TM10, (c)TE101, (d)TM11, (e)TM02, (f)TE201, (g)TE102 and (h)TM20, which including both cavity modes corresponding to TE modes and patch modes corresponding to TM modes.
(a)TM01; (b)TM10; (c)TE101; (d)TM11; (e)TM02; (f)TE201; (g)TE102; and (h)TM20.
To highlight the advantages of the proposed CP-DSIWR, its performance is compared with that of a traditional SIW resonator. Also, within the frequency range of 0 ~ 20 GHz, and with identical physical dimensions of and a thickness of 1.016 mm, the traditional SIW resonator is modeled and simulated. The electric field distributions of the resonant modes for the traditional SIW resonator are shown in Fig 3, and only three TE modes (TE101, TE102 and TE201) exist which are shown in Fig 4. Compared with the traditional SIW resonator, there are five additional resonant modes in the CP-DSIWR, which demonstrating its mixed-mode resonant characteristics. The loaded capacitive patch in the CP-DSIWR not only generates additional patch modes but also influences the eigenfrequencies of the resonator.
(a) TE101; (b) TE102; and (c) TE201.
To study the effects of dimension of the loaded capacitive patch and the relative permittivity of the dielectric substrates on resonant modes in the CP-DSIWR, the simulations of the resonator with different values of the patch dimensions and
when
and various
are performed. The simulated results of eight modes in Fig 2 are categorized into three cavity modes (TE101, TE102, TE201) in Fig 5(a) and five patch modes (TM01, TM10, TM11, TM02, TM20) in Fig 5(b). In these figures, the impact of the patch dimensions on the resonant modes is analyzed. Furthermore, Fig 5(c) illustrates the effect of the relative permittivity on these eight modes, providing insights into how variations in material property affect their resonant behavior.
(a) The cavity modes with varying and
when
; (b) The patch modes with varying
and
when
; and (c) The cavity modes and the patch modes with varying
.
As indicated in Fig 5(a), when and
vary from 5 mm (0.23
) to 10 mm (0.47
), the eigenfrequencies of the cavity modes decrease. The guided wavelength
in the CP-DSIWR at the fundamental cavity mode frequency 12.8 GHz can be calculated by (1), where
is the vacuum wavelength,
is the relative permittivity of the dielectric substrate,
and
are the distances between the centers of the outermost vias along the width and length directions, respectively, and
and
are the equivalent width and length of the proposed CP-DSIWR, can be calculated by (2) [18].
As shown in the simulated results of Fig 5(b), the eigenfrequencies of the patch modes also decrease with increasing sizes of the loaded capacitive patch, which can be explained with the stripline resonant theory. The resonant frequency of the TM10 mode can be expressed as [19].
where and
are the vacuum permittivity and vacuum permeability, respectively.
To utilize the TE101 mode to design a bandpass filter, its eigenfrequency characteristic are studied in detail and significant conclusion can be found from Fig 5(a). As the patch size reach up to 7.5 mm × 7.5 mm (0.35
×0.35
), the eigenfrequency of the TE101 mode decreases linearly, due to the change of electric field distribution for the cavity mode TE101 by the increasing size of the capacitive patch. However, once the capacitive patch size exceeds 0.35
×0.35
, the eigenfrequency of the TE101 mode remains almost constant, same with the case of the traditional SIW resonator. This behavior can be attributed to capacitive loading saturation, which occurs when the capacitive loading effect reaches a limit, while additional coverage of the capacitive patch almost does not introduce changes of electromagnetic field distribution. In the state of capacitive loading saturation, further increases in patch size have minimal effect. Therefore, the field distribution of the TE101 mode becomes predominantly determined by the traditional SIW structure. Consequently, the eigenfrequency characteristics of the TE101 mode in the CP-DSIWR stabilizes and behaves similar to those of the TE101 mode in a traditional SIW resonator.
Based on the above analysis, the resonant frequency of the TE101 mode can be revised based on that of the traditional SIW resonator. When the capacitive patch size (CPS) is smaller than 0.35 ×0.35
, its eigenfrequency can be approximated in (4), which was derived through multiple fitting calculations. Conversely, when the capacitive patch size exceeds 0.35
×0.35
, the eigenfrequency of the TE101 mode is approximated in (4) [1].
where is the speed of light in vacuum, and
is relative permeability of the dielectric substrate.
As observed from Fig 5(a), the eigenfrequency characteristics of the TE102 and TE201 modes exhibit a complementary downward trend that depends on the dimensions of the capacitive patch. The TE102 mode maintains a nearly constant frequency with increasing CPS until 7 mm × 7 mm (0.330.33
). Beyond the size, the eigenfrequency of TE102 decreases as the loaded capacitive patch perturbs the dual-peak electric field distribution for the TE10 mode. With a complementary downward trend, the TE201 mode presents frequency reduction with increasing patch size smaller than 7 mm × 7 mm, due to orthogonal field pattern with TE102. This delayed decreasing behavior of TE102 versus TE201 originate from their differences of electric field distribution. When the loaded capacitive patch sufficiently covers their respective mode electric field more than 85%, the eigenfrequencies characteristics of TE102 and TE201 maintain constant. Fig 5(c) illustrates that both patch modes and cavity modes exhibit decreasing eigenfrequencies with increasing relative permittivity
, consistent with the theoretical predictions from (3) and (4). Notably, TM modes show smaller frequency shifts (TM10: 1.12 GHz) compared to TE modes (TE101: 1.62 GHz), and high-order modes such as TM20 (2.24 GHz) and TM02 (2.53 GHz) exhibit even larger frequency shifts, with
varying from 2.0 to 2.6. So, high-order mode indices require more stricter control over substrate permittivity to obtain stable frequency performance in multi-mode SIWR designs. The above analysis provides predictable physical parameters and material property of the CP-DSIWR to design multi-band filter.
For the capacitive patch size of mm and the relative permittivity of
, the unload quality factors (
) of the first three resonant modes with the resonant frequency around 15 GHz in the CP-DSIWR are simulated using HFSS, as shown in Table 1. Due to the nearly enclosed cavity structure, these modes possess relatively high
.
2.2 Design of dual-band bandpass filter
2.2.1 Mixed-mode bandpass filter.
According to the analysis in Section 2, a direct-fed CP-DSIWR filter is designed, as shown in Fig 6(a). The filter consists of a CP-DSIWR with a pair of input and output direct feeding structures connected to the capacitive patch. Each feeding structure consists of a 50 Ω microstrip line and a transition structure. Fig 6(b) show the structure of layer 3, which features a central patch connects to a 50 Ω microstrip feedline of width and length
through a tapered section of length
and transitions to a stripline with width
and length
. This integrated feeding design ensures good impedance matching from patch to feedline. Fig 7 shows the simulated S-parameters for this feeding configuration, demonstrating the excitation of the TM10 mode.
(a) Filter configuration; and (b) The configuration of the layer 3.
To excite both patch modes and cavity modes, the direct-fed CP-DSIWR filter is revised by incorporating two rows of periodic metallic vias with diameter =0.8 mm and pitch
=1 mm positioned centrally in the layer 4. The coupling between the patch modes and cavity modes is achieved by electrically connecting the capacitive patch to the ground plane through these metallic vias. Specifically, the metallic vias serve as conductive paths that connect the capacitive patch to the ground plane, through which the electric fields of the patch modes and cavity modes is redistributed and propagated to the ground plane, forming new coupling paths. The propose structure enables the realization of a mixed-mode bandpass filter utilizing both the cavity and patch modes of the proposed CP-DSIWR.
Fig 8 shows the structure of the layer 4 of the proposed mixed-mode bandpass filter with its coupling topology. In the layer 4, two rows of metallic vias with diameter are arranged in the center of the bottom cavity, which facilitates the coupling between the patch modes and the cavity modes, enabling effective mixed-mode operation. The coupling topology, shown in bottom of Fig 8, where nodes 1 and 2 represent the TM01 and TM10 patch modes, and nodes 3 represent the TE101 cavity mode. The input and output are defined by nodes S and L, respectively.
Fig 9 presents the simulated S-parameters and the electric field distributions of the first three resonant modes. Compared to the configuration without metallic vias, the addition of two rows of metallic vias successfully excites additional modes: the TM01 patch mode and the TE101 cavity mode. This confirms that the proposed filter design with mixed-mode excitation is capable of simultaneously exciting both patch and cavity modes. The TM01, TM10 and TE101 modes corresponding to (a), (b), and (c) in Fig 2, are operating in the mixed-mode bandpass filter.
Fig 10 shows the simulated S-parameter versus the length of the capacitive patch. It can be seen that the resonant frequency of TE101 increases as
increases. However, the bandwidth of the second passband decreases, indicating that the size of the capacitive patch affects the cavity modes.
The final dimensions of the mixed-mode bandpass filter are as follows: mm,
mm,
mm,
mm,
mm,
mm,
mm,
mm,
mm.
2.2.2 Dual-band mixed-mode Bandpass Filter.
Based on the mixed-mode filter in subsection 2.2.1, a dual-band mixed-mode bandpass filter is proposed by introducing a slot in the center of the layer 3 of the capacitive patch. As shown in Fig 11(a) and 11(b), the design features a slotted capacitive patch to strategically tune resonant frequencies by altering current distribution, enabling precise control over the coupling strength between the TM01 and TM10 patch modes and altering the coupling path to achieve dual-band performance.
(a) Filter configuration; and (b) The configuration of layer 3 and the coupling topology.
Fig 12 presents the variations of the S-parameters versus the parameter . The slot controls both TM10 and TE101 resonant frequencies tuning and the transmission zero positioning. As shown in Fig 12(a), the transmission zero, marked by circular markers, shifts to lower frequency and stabilizes in the upper stopband of the second passband as
increases. Meanwhile, Fig 12(b) demonstrates that with increasing
, the slot is introduced to optimize passband formation by shifting the resonant frequency of TM10 mode toward TM01 mode, marked by circular markers and triangle markers respectively, to form a passband.
(a) |S21|; and (b) |S11|.
To further analyze the operational principles of the dual-band mixed-mode bandpass filter, an equivalent-circuit model is designed which is shown in Fig 13. The first passband is generated by the effect of the slot on the coupling of TM01 and TM10, which can be equivalent as a resonant circuit represented by the capacitor and the inductor
. The second passband is generated by the resonance of the cavity mode TE101, which is equivalent to the parallel connection of inductor
and capacitor
.
and
represent the coupling between the capacitive patch and the CP-DSIWR, and the parallel connection of
and
represents the external coupling of the CP-DSIWR.
As shown in Fig 14, for the dual-band mixed-mode bandpass filter, the electromagnetic (EM) simulation results for the S-parameters are as follows: the insertion losses of the two passbands is 0.16 dB and 1.12 dB respectively and the return losses of the simulations is better than 17 dB. The 3-dB bandwidths of the two passbands are 2.13 GHz and 0.17 GHz. The transmission zero is located at 13.87 GHz with −53.7 dB insertion loss. The S-parameters obtained from the equivalent circuit model match well with the electromagnetic simulation results, validating the accuracy of the equivalent circuit model.
The results confirm that the proposed dual-band mixed-mode bandpass filter achieves precise control over both center frequencies and bandwidths, demonstrating improved performance through effective resonant frequencies tuning. The final dimensions of the dual-band mixed-mode bandpass filter are identical to those of the mixed-mode bandpass filter, with the exception of the slot, characterized by the following parameters: mm,
mm.
3 Fabrication and measurement
Fig 15(a) shows the photograph of the measurement setup, which includes a KEYSIGHT PNA-L Network Analyzer (Model: N5234A) with a frequency range of 10 MHz to 43.5 GHz, connected to the two 2.92 mm RF connectors of the filter prototype. Fig 15(b) shows the fabricated filter prototype, including its front view and top view. The dual-band mixed-mode bandpass filter is assembled by extending the PCB in the L-direction, with alignment holes and nylon screws to ensure precise layer stacking and stability during testing. The final fabricated filter has a compact size of 0.57 × 0.57. Fig 16 presents the simulation and measured results for the dual-band mixed-mode bandpass filter. The measured results indicate that the two passbands are centered at 6.2 GHz and 12.9 GHz with return losses exceeding 26 dB and 12 dB, respectively. The measured minimum in-band insertion losses of the two passbands are around 1.1 dB and 2.7dB. Machining accuracy and measurement tolerances can cause some slight deviations between the measured and simulated results.
(a) The measurement setup; and (b) The filter prototype.
4 Comparison and discussion
As shown in Table 2, compared to the dual-band filters reported in [12,16], the proposed dual-band mixed-mode bandpass filter can achieve bandwidth control. Compared to the dual-band filters in [8,10,12,17], the proposed filter coexists two types of modes, the patch mode and the cavity mode, with a higher richness of mode’s types and a larger number of modes to choose. The dimensions of the proposed filter are greatly reduced, occupying less than one-fourth of the size compared to those in [8,10,12,16,17]. Therefore, the size of the dual-band mixed-mode bandpass filter is significantly reduced compared to traditional SIW filters, demonstrating a substantial improvement in compactness. This is achieved by the use of a dual-layer structure and the loading of the capacitive patch without destroying the structure of the original resonator.
The proposed bandpass filter exhibits dual-band filtering characteristic. However, the stopband between the two passbands is not good, which will be improved in future work. Moreover, multiple modes will be exploited in multi-mode filters to enable the design of multi-band or wideband filters in the future.
5 Conclusion
Based on the SIW structure, this paper presents a dual-band mixed-mode bandpass filter utilizing a novel dual-layer substrate integrated waveguide resonator loaded with a capacitive patch, fed by a microstrip line. A detailed eigenmode analysis is conducted, and an experimental formula is derived. With metallic vias and slot embedded in the CP-DSIWR, a dual-band filter with tunable resonant frequencies is obtained, utilizing the TM01, TM10 and TE101 modes. This work breaks through the inherent idea of traditional cavity filters with only one type of resonant mode. Compared to traditional solutions, the proposed mixed-mode bandpass filter offers the advantage of mode controllability, providing a novel approach for designing dual-band or multi-band filter.
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