Introduction

The rapid evolution of modern wireless communication systems demands increasingly complex RF front-end solutions capable of supporting multi-band operations. Dual-band bandpass filters (BPFs) are essential components in these systems, enabling efficient integration of distinct frequency bands within compact modules. Such filters enhance spectral efficiency, reduce hardware complexity, and ensure seamless operation across multiple frequency bands1,2,3,4. However, conventional dual-band BPFs face persistent challenges, particularly in managing insertion loss (IL) and unwanted signal reflections. High IL degrades signal quality and reduces overall system performance, while poor reflection control leads to interference, instability, and potential signal degradation. These limitations severely impact the reliability of high-performance communication systems.

Reflectionless or absorptive filters provode an effective solution to these issues by absorbing out-of-band signals rather than reflecting them, thereby enhancing system stability and reducing interference5,6,7,8. Despite their potential, most existing designs focus on single-band operation and fail to address dual-band functionality effectively9,10,11,12,13,14. To the best of the authors’ knowledge, limited research has been conducted on dual-band absorptive bandpass filters (ABPFs)15,16,17,18,19,20,21, primarily due to the complex requirement of achieving reflection-free out-of-band power absorption across two distinct stopband regions. In15, the transversal filtering sections (TFSs) are proposed to design lossy filters with quasi-reflectionless stopbands and high selectivity. Prototypes demonstrate excellent attenuation and passband flatness. However, the reflectionless property is quasi and not fully realized across all stopbands, which limits its applicability in sensitive RF systems. An N-shaped microstrip coupler combined with T-shaped absorption branches to achieve compact, all-frequency absorption in dual-band BPFs19. However, this design is constrained by the relatively narrow absorption bandwidth in the high-frequency stopband region. In21, a complementary duplexer-based dual-band ABPF was developed, integrating auxiliary lossy bandstop sections to achieve all-frequency absorption. The design demonstrates low IL and flexible absorption control. However, despite its dual-band functionality, the approach is hindered by its large physical size and restricted absorption bandwidth. Furthermore, the suppression of spurious harmonics in the upper band, which is critical for maintaining signal integrity, remains a considerable challenge, particularly in achieving compact and low-complexity dual-band reflectionless filters.

This work presents a novel dual-band ABPF that simultaneously achieves all-frequency reflectionless operation, dual-band filtering, and enhanced upper-band suppression. The proposed design integrates a square-ring resonator (SRR) with advanced coupled lines (CLs) and employs two types of absorptive branches to ensure broadband reflectionless performance. Additionally, radial-stub-loaded resonators (RSLSs) with high-impedance transmission lines (HITLs) are introduced to extend upper-band suppression up to 10f0 without significantly increasing the circuit footprint. The key advantages of the proposed ABPF include: (1) dual-band filtering with sharp frequency selectivity, (2) excellent inter-band isolation, (3) full-frequency absorption, (4) compact and integrable structure, (5) low IL, and (6) effective suppression of spurious harmonics. In summary, while some individual techniques have been previously reported, the proposed filter uniquely integrates dual-band operation, full-spectrum reflectionless performance, and harmonic suppression within a compact two-port design. To the best of our knowledge, this is the first demonstration of such absorptive filter architecture, representing an advancement in dual-band filter design.

Design and analyses

Dual-band bandpass filter

The proposed dual-band bandpass filter (BPF) is designed by combining coupled-line (CL) filtering theory with resonator-loading techniques to achieve compact dual-band operation with high selectivity. As illustrated in Fig. 1, the topology is derived from a conventional CL filter, where a pair of symmetrical CL sections (CL1), characterized by even- and odd-mode impedances Ze1 and Zo1, respectively, generates a wideband bandpass response. To realize dual-band behavior, a SRR is embedded between the CL sections. The SRR comprises two distinct paths: Path I is a TL with impedance Z1 and electrical length 3θ, while Path II is a CL resonator (CL2) with even- and odd-mode impedances Ze2, Zo2 and electrical length θ. Due to a 180° phase difference between the two paths, additional resonant modes and transmission zeros (TZs) are introduced between the passbands, resulting in the desired dual-band response. The electrical length θ is set to 90° at the center frequency f0, and both input and output ports are matched to a standard 50 Ω impedance. This configuration enables precise control over passband allocation and spectral selectivity while ensuring a compact footprint.

Fig. 1
figure 1

The topology of the proposed dual-band BPF.

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The circuit’s inherent symmetry enables rigorous analysis using the odd–even mode decomposition technique. The equivalent circuits for the odd mode (differential mode, DM) and even mode (common mode, CM) are depicted in Fig. 2a,b, respectively. Under DM excitation, a virtual short-circuit boundary is introduced along the symmetry axis, as illustrated in Fig. 2a, resulting in an input impedance denoted as Zb1. Conversely, for CM operation, a virtual open-circuit boundary is established along the symmetry axis, as depicted in Fig. 2b, yielding an input impedance represented by Zb2.

Fig. 2
figure 2

The equivalent circuit of the dual-band BPF. (a) Odd-mode. (b) Even-mode.

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The coupled-line section CL1, shown in Fig. 2, is derived from a four-port network under defined terminal currents I2 = I4 = 0. Based on the circuit theory ([V] = [Z][I])22, the input and output signals of CL1 can be related as

$$\left[ \begin{gathered} V_{1} \hfill \\ V_{3} \hfill \\ \end{gathered} \right] = \left[ \begin{gathered} Z_{11} \;\;Z_{13} \hfill \\ Z_{31} \;\;Z_{33} \hfill \\ \end{gathered} \right]\left[ \begin{gathered} I_{1} \hfill \\ I_{3} \hfill \\ \end{gathered} \right] = - j\left[ \begin{gathered} Z_{a} \cot \theta \;\;\;\;Z_{b} \csc \theta \hfill \\ Z_{b} \csc \theta \;\;\;\;Z_{a} \cot \theta \hfill \\ \end{gathered} \right]\left[ \begin{gathered} I_{1} \hfill \\ I_{3} \hfill \\ \end{gathered} \right]$$
(1)

when V1 = I1Zb1, V3 = − I3Zbo, Za = (Ze1 + Zo1)/2, Zb = (Ze1 − Zo1)/2.

The odd- and even-mode input impedances Zbj (j = e (even-mode) or o (odd-mode)) are given by

$$Z_{bj} = Z_{11} - \frac{{Z_{13}^{2} }}{{Z_{11} + Z_{bj1} }}{\kern 1pt} = - jZ_{a} \cot \theta - \frac{{4Z_{b}^{2} \csc^{2} \theta }}{{4jZ_{a} \cot \theta + Z_{bj1} }}$$
(2)

where

$$Z_{bj1} = Z_{bj2} Z_{cj1} /(Z_{bj2} + Z_{cj1} )$$
(3-1)
$$Z_{bo2} = \frac{{ - 2Z_{e2} Z_{o2} \tan \left( {{\theta \mathord{\left/ {\vphantom {\theta 2}} \right. \kern-0pt} 2}} \right)}}{{j\left( {Z_{e2} + Z_{o2} } \right)}}$$
(3-2)
$$Z_{be2} = \frac{{ - 2jZ_{e2} Z_{o2} \cot \left( {{\theta \mathord{\left/ {\vphantom {\theta 2}} \right. \kern-0pt} 2}} \right)}}{{(Z_{e2} + Z_{o2} )}}$$
(3-3)

The reflection parameter (Sb11) and transmission coefficient (Sb21) of the two-port dual-band BPF are expressed as

$$S_{b11} = \frac{{Z_{bo} Z_{be} - Z_{0}^{2} }}{{(Z_{bo} + Z_{0} )(Z_{be} + Z_{0} )}}$$
(4)
$$S_{b21} = \frac{{(Z_{bo} - Z_{be} )Z_{0} }}{{(Z_{bo} + Z_{0} )(Z_{be} + Z_{0} )}}$$
(5)

When |Sb21|= 0, combining Eqs. (2) and (5) allows direct extraction of the TZs using the following formulas:

$$f_{TZ1} = \frac{{2\theta_{{f_{TZ1} }} }}{\pi }f_{0}$$
(6-1)
$$f_{TZ2} = \frac{{2(\pi - \theta_{{f_{TZ1} }} )}}{\pi }f_{0}$$
(6-2)

where

$$\theta_{{f_{TZ1} }} = \arcsin \sqrt {\frac{3}{4} + \frac{{(Z_{o2} Z_{e2} )}}{{2Z_{1} (Z_{o2} + Z_{e2} )}}} {\kern 1pt} = \arcsin \sqrt {0.75 + 0.5IR}$$
(7)

This result demonstrates that the TZs of the proposed dual-band BPF are governed by the impedance ratio IR = 1/(Z1/Ze2 + Z1/Zo2), which is determined by the CL2 and TL.

Figure 3a depicts the variation in the locations of the TZs as a function of the IR. As IR increases, the two TZs gradually converge toward the center frequency f0, eventually merging into a single TZ when IR > 0.5. Figure 3b shows the corresponding magnitudes |S21| under various IR values, with CL1 fixed at Ze1 = 121.6 Ω, Zo1 = 54.5 Ω. The results indicate that the IR exclusively affects the spacing between the TZs near the f0, while the roll-off characteristics on either side of the passbands remain unaffected. An increased IR decreases the frequency selectivity by reducing TZ separation, thereby broadening the passband bandwidth. Therefore, the bandwidth and frequency selectivity can be independently tuned through IR adjustment, while transmission matching at f0 is preserved. Moreover, the parameters Z1, Zo2, and Ze2 offer additional degrees of freedom for bandwidth optimization, confirming the scalability and tunability of the proposed design.

Fig. 3
figure 3

Theoretical calculations. (a) TZs variation with IR. (b) |Sb21| variation with IR. (c) EM simulated and theoretical calculations results.

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Based on the above analysis, the ideal circuit parameters in Fig. 1 are derived analytically using Eqs. (1)–(7). A comparison between the theoretical calculations and the 3D full-wave electromagnetic (EM) simulation results are provided in Fig. 3c, confirms that the two passbands are centered at 1.4 GHz and 2.6 GHz, with transmission zeros (TZs) at 1.87 GHz and 2.2 GHz, ensuring excellent frequency selectivity and band-to-band isolation exceeding 35 dB. The circuit exhibits three distinct reflection regions: Reflection Region I at f0/4 and 3f0/2, and Reflection Region II centered at f0. Figure 4 presents the surface current distributions at f0/4 and f0, which reveal critical insights into the reflection absorption mechanism of the proposed design. At f0/4 (Fig. 4a), the surface current is highly concentrated along the lower conductor of CL1, particularly at terminals 2, indicating strong signal reflection due to impedance mismatch. At f0 (Fig. 4b), obvious current localization is observed around the SRR and terminals 1 and 4. This phenomenon establishes parasitic coupling paths for out-of-band signals to ingress into the input/output ports, resulting in undesirable out-of-band reflections that compromise the filter’s spectral purity. In addition, significant current distribution is also observed at terminals 2 and 3, indicating localized energy accumulation that contributes to undesired port reflections. Therefore, to further mitigate reflections, additional absorber circuits can be introduced at terminals 2 and 3 of CL1. By strategically incorporating lossy resistor within these absorber circuits, the reflected signals can be effectively dissipated, thereby minimizing impedance mismatches and suppressing undesired port reflections. This modification ensures a more robust reflection suppression mechanism, ultimately achieving reflectionless operation across all three identified reflection regions.

Fig. 4
figure 4

Surface current distributions. (a) at f0/4. (b) at f0.

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Design and analysis of dual-band ABPF

To enable broadband reflectionless behavior, two complementary bandstop-type absorptive branches (Branches I and II) are incorporated into the BPF structure, as shown in Fig. 5. Branch I consists of TL2 (Z2, θ), R1, and a short-circuited TL3 (Z3, θ), with TL4 (Z4, θ) and TL5 (Z5, θ) in parallel at both ends of R1 to enhance absorption. This branch is connected to the open ends of CL1 and is designed to absorb strong reflections at f0/4 and 3f0/2. Branch II employs a single-port coupled-line (CL3) with even- and odd-mode impedances (Ze3, Zo3), an electrical length θ, and a short-circuited TL cascaded with R2 to improve absorption. Branch II is positioned near the SRR and is designed to absorb reflections at f0.

Fig. 5
figure 5

The circuit schematic of the two-port dual-band ABPF.

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The odd-mode (DM) and even-mode (CM) equivalent circuits of the overall topology are depicted in Fig. 6. The input impedances of Absorptive Branches I and II are given by:

$$Z_{s2} = R_{2} + j\frac{{2Z_{e3} Z_{o3} \tan \theta }}{{Z_{e3} - Z_{o3} \tan^{2} \theta }}$$
(8)
$$Z_{s1} = Z_{2} \frac{{Z_{{\text{c}}} + jZ_{2} \tan \theta }}{{Z_{2} + jZ_{{\text{c}}} \tan \theta }}$$
(9)

where

$$Z_{c} = \frac{{Z_{3} Z_{4} Z_{5} \cot \theta + jR_{1} (Z_{3} Z_{5} - Z_{4} Z_{5} \cot^{2} \theta )}}{{j(Z_{3} Z_{4} + Z_{3} Z_{5} - Z_{4} Z_{5} \cot^{2} \theta ) + R_{1} (Z_{4} \cot \theta - Z_{3} \tan \theta )}}$$
(10)
Fig. 6
figure 6

The equivalent circuits of the dual-band ABPF. (a) Odd-mode and at f = 2nf0 (n = 0, 1, 2…). (b) Even-mode and at f = 2nf0 (n = 0, 1, 2…).

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The CL1 section shown in Fig. 6 can be obtained from the four-port network with defined terminal currents I2 = 0, V4 = I4Zs4. In this case, the Z-matrix of the two-port network in Eq. (1) for CL1 can be reformulated as23,24:

$$\left[ {\begin{array}{*{20}c} {Z_{11} } & {Z_{13} } \\ {Z_{31} } & {Z_{33} } \\ \end{array} } \right]_{{CL_{1} }} = \left[ {\begin{array}{*{20}c} {\frac{{Z_{a}^{2} \tan \theta - jZ_{a} Z_{s2} }}{{Z_{s2} \tan \theta - jZ_{a} }}} & {\frac{{ - jZ_{b} Z_{s2} }}{{Z_{s2} {\text{sin}}\theta - jZ_{a} \cos \theta }}} \\ {\frac{{ - jZ_{b} Z_{S2} }}{{Z_{s2} {\text{sin}}\theta - jZ_{a} \cos \theta }}} & {\frac{{(Z_{b}^{2} - Z_{a}^{2} )\cot \theta - jZ_{a} Z_{s2} }}{{Z_{s2} \tan \theta - jZ_{a} }}} \\ \end{array} } \right]$$
(11)

Accordingly, the odd- and even-mode input impedances Zinj (j = e (even-mode) or o (odd-mode)) in Fig. 7 are expressed as:

$$Z_{inj} = \frac{{Z_{inj1} Z_{s1} }}{{Z_{inj1} + Z_{s1} }}$$
(12)

where

$$Z_{inj1} = Z_{11} - \frac{{Z_{13} Z_{31} }}{{Z_{bj1} + Z_{33} }}$$
(13)
Fig. 7
figure 7

Theoretically calculated Zin, Zs1 and Zs2.

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Finally, the overall input impedance Zin, transmission parameters S11(dB) and reflection parameters S21(dB) of the complete circuit are derived from the Eqs. (4), (5), (11), (12) and (13) as follows:

$$Z_{in} = \frac{{Z_{0} \left( {1 + \left| {\frac{{Z_{ine} Z_{ino} - Z_{0}^{2} }}{{(Z_{ine} + Z_{0} )(Z_{ino} + Z_{0} )}}} \right|} \right)}}{{{\kern 1pt} {\kern 1pt} \left( {1 - \left| {\frac{{Z_{ine} Z_{ino} - Z_{0}^{2} }}{{(Z_{ine} + Z_{0} )(Z_{ino} + Z_{0} )}}} \right|} \right)}}$$
(14-1)
$$S_{11} (dB) = 20\lg \left| {\frac{{Z_{ino} Z_{ine} - Z_{0}^{2} }}{{(Z_{ino} + Z_{0} )(Z_{ine} + Z_{0} )}}} \right|$$
(14-2)
$$S_{21} (dB) = 20\lg \left| {\frac{{(Z_{ine} - Z_{ino} )Z_{0} }}{{(Z_{ine} + Z_{0} )(Z_{ino} + Z_{0} )}}} \right|$$
(14-3)

Given that the operational frequencies of the two passbands are f1 and f2 (f1 < f2), with corresponding electrical lengths θ1 and θ2 derived in the previous section, the parameters of the Absorptive Branches I and II can be optimized using Eqs. (8)–(10). To elucidate the absorptive circuit’s working mechanism, the input impedance Zin of the complete circuit, along with the input impedances Zs1 and Zs2 of Absorptive Branches I and II, obtained through numerical calculations, are illustrated in Fig. 7. The shaded regions indicate the two passband frequencies. Based on this analysis, several key observations and conditions are derived:

  1. 1.

    Absorptive Branch I: The input impedance Zs1 approaches infinity at f0 while exhibiting low impedance near DC and 2f0. As a result, the Absorptive Branch I effectively matches the stopband region II, enabling reflected signals within this region to be absorbed by R1.

  2. 2.

    Absorptive Branch II: the input impedance Zs2 approaches infinity at f1 and f2 while showing low impedance at DC, f0, and 2f0. This allows absorptive branch II to match the stopband regions I and II, thereby directing reflected signals to R1 for absorption. Here \(Z_{s2} (\theta_{1} ) = Z_{s2} (\theta_{2} ) = \infty\), based on Eq. (8), the impedance of CL3 is constrained as:

    $$\frac{{Z_{e3} }}{{Z_{o3} }} = \tan^{2} \theta_{1} = \tan^{2} \theta_{2}$$
    (15)
  3. 3.

    Impedance matching and absorption: The input impedance Zin exhibits minimal variation across the spectral range [0, 2f0], ensuring broadband impedance matching and efficient signal absorption.

  4. 4.

    Equivalent circuit at harmonics: At f = 2nf0 (n = 0, 1, 2, …), the equivalent circuit reduces to a parallel combination of R1 and R2, as depicted in the lower-right inset of Fig. 6. The corresponding condition is given by:

    $$\frac{1}{{R_{1} }} + \frac{1}{{R_{2} }} = \frac{1}{{Z_{0} }}$$
    (16)

Based on the preceding analysis, Absorptive Branch I effectively addresses stopband redions I and II, while Absorptive Branch II specifically targets the stopband region II. Once the operating frequencies f1 and f2 are defined, the initial values of CL3 (Ze3 and Zo3) are determined using Eq. (15). Subsequently, R2 is fine-tuned to eliminate reflection in stopband region I. With R2 specified, the value of R1 is computed using Eq. (16). Finally, the impedances Z2, Z3, Z4, and Z5 are meticulously optimized to ensure a reflectionless characteristic across the stopband region II.

Figure 8 presents the S-parameters of the dual-band ABPF under varying absorptive branch configurations, illustrating their impact on performance. The results indicate that the absorptive branches exert minimal influence on the transmission coefficient |S21|, while significantly affecting the reflection coefficient |S11|. Specifically, Fig. 8a illustrates that as R1 increases, |S11| initially improves and subsequently deteriorates near DC and 2f0, while demonstrating an opposite trend in regions outside these frequencies near the passband. Notably, the stopband region I remains largely unaffected. Figure 8b demonstrates that increasing R2 initially enhances |S11| in both stopband regions I and II but results in degradation at the upper edge of the passbands. Figure 8c reveals that increasing Z2 reduces absorption efficiency in stopband region II with minimal impact on stopband region I, while improving impedance matching within the passband, thereby enhancing overall performance. Figure 8d shows that variations in Ze3/Zo3 do not affect the absorption in the stopband but affect matching in the passband. Furthermore, Fig. 8e, f, and g indicate that as Z3, Z4, and Z5 increase, |S11| initially worsens and subsequently improves in stopband region II, while exerting a comparatively smaller effect in stopband region I.

Fig. 8
figure 8

The S-parameters of the dual-band ABPF for various absorptive branches parameters and determined performance. (a) R1, (b) R2, (c) Z2, (d) Ze3/Zo3, (e) Z3, (f) Z4, (g) Z5, (h) Determined performance.

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Based on the above analysis, the following parameters are selected for optimal performance: Z1 = 80.6 Ω, Ze1 = 121.6 Ω, Zo1 = 54.5 Ω, Ze2 = 164.8 Ω, Zo2 = 51.2 Ω, Ze3 = 139.8 Ω, Zo3 = 41.4 Ω, Z2 = 139.8 Ω, Z3 = 45.5 Ω, Z4 = 129.2 Ω, Z5 = 86.5 Ω, R1 = 110 Ω, R2 = 86 Ω. Figure 8h presents the S-parameters obtained from ADS simulation and theoretical calculation based on these parameters, showing excellent agreement. The two passbands are centered at 1.395 GHz and 2.595 GHz, with 10-dB bandwidths of 32.26% (1.17–1.62 GHz) and 17.34% (2.37–2.82 GHz), respectively. The reflection coefficient |S11| remains below -11 dB across all stopband regions, demonstrating excellent full-frequency absorption performance.

The low-pass scheme for upper-band suppression

Suppressing spurious harmonics in the upper-frequency band is essential for maintaining signal integrity and minimizing interference in high-performance dual-band filters. This is achieved through a low-pass response using radial-stub-loaded resonators (RSLSs) integrated with high-impedance transmission lines (HITLs), forming a compact filtering section embedded within the 50-Ω input/output TLs without increasing circuit footprint. To broaden the passband and enhance stopband selectivity, three pairs of RSLSs (Parts 1 and 2) are used, with a radial stub (Part 3) added to the second resonator pair (Part 2). Figure 9a,b illustrate the layout and lumped-element equivalent circuit of the RSLSs, where Parts 1 and 2 exhibit parasitic capacitors along with their inductor, while Part 3 approximates an ideal inductor. It is worth noting that some elements in the equivalent model exhibit relatively high impedance values, which reflect the narrow-line and high-impedance behavior of the distributed resonators. These characteristics are essential for generating strong rejection in the upper stopband and are accurately represented by the lumped-element approximation. Such an equivalent modeling approach for RSLSs has also been validated in previous literature25. The improvement in upper-band suppression stems from the resonant rejection of the RSLSs, which present high impedance above their resonant frequency, thereby attenuating higher-order harmonics. The cascaded multi-stage topology sharpens the stopband roll-off by introducing multiple transmission zeros. In addition, the HITLs between the resonators act as impedance inverters, reinforcing low-pass behavior and further reducing signal transmission in the upper stopband. Figure 9c compares the equivalent circuit model and EM simulations, showing strong agreement in both magnitude and trend. The addition of Part 3 significantly enhances stopband performance without degrading in-band characteristics.

Fig. 9
figure 9

(a) The layout of the RSLSs. (b) Its lumped-element equivalent circuit. (c) The results of the equivalent circuit and EM simulation.

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Full-wave simulated and measured results

For practical demonstration, the proposed two-port all-frequency dual-band ABPF (Prototype I) and the dual-band ABPF with wide upper-band suppression (Prototype II) were fabricated on a Rogers RO4003C substrate (εr = 3.55, tanδ = 0.0027) with a thickness of 1.524 mm. Simulations were performed using the commercial 3D electromagnetic simulation software CST Microwave Studio (CST MWS), while measurements were conducted using a Keysight N5230C vector network analyzer.

Prototype I: Two-port all-frequency dual-band ABPF

A two-port all-frequency reflectionless dual-band bandpass BPF with a compact size of 120.92 mm × 86.5 mm (1.52 λg × 1.09 λg, where λg is the effective wavelength at ƒ0 = 2 GHz) has been designed and fabricated. Figure 10 presents the photograph and detailed dimensions of the fabricated prototype. The final dimensions of the filter are as follows (unit: mm): W1 = 1.46, L1 = 73, W2 = 0.68, S2 = 0.19, L2 = 21, W3 = 0.93, Wg = 0.26, S3 = 0.13, L3 = 22.6, WCL1 = 1.1, S1 = 0.4, LCL1 = 23, W5 = 0.3, L5 = 24.92, W6 = 1.1, L6 = 23.7, W7 = 4, L7 = 21, W4 = 0.2, L4 = 25.8, W0 = 3.38, Lport = 25, Rvia = 0.2. The Lossy resistor R1 = 110 Ω, R2 = 86 Ω.

Fig. 10
figure 10

The proposed fabricated dual-band ABPF. (a) Layout, (b) Photographs.

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Figure 11 illustrates the simulated and measured S-parameters and group delay of Prototype I. As shown in Fig. 11a, there is excellent agreement between the 3D full-wave simulation and measurement results, confirming the validity of the proposed circuit design and theoretical analysis. The two passbands are centered at 1.38 GHz and 2.63 GHz, with 3-dB fractional bandwidths (FBWs) of 19.5% and 9.7%, respectively. The minimum measured ILs (|S21|) are 0.95 dB and 1.47 dB for the first and second passbands, respectively, with measured in-band return loss (RL) exceeding 20 dB. In addition, the isolation between the two passbands is measured to be better than 45 dB. In the stopbands, the measured RL (|S11|) is consistently better than 10.48 dB across the entire spectral range of [0, 2.5f0]. Additionally, an RL greater than 20 dB is achieved within specific stopbands from DC to 1.1 GHz and from 3.2 GHz to 4 GHz, indicating strong absorption characteristics. The RL parameters |S11| and |S22| exhibit good consistency, further validating the dual-port all-frequency reflectionless properties of the proposed design. The simulated and measured group delay results are presented in Fig. 11b. In the two passbands, the group delay varies from 2.74 to 3.77 ns in the first passband and from 2.4 to 3.83 ns in the second passband, demonstrating stable and low delay characteristics within the passbands.

Fig. 11
figure 11

Simulated and measured results of Prototype I, (a) S-parameters and (b) Group Delay.

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ABPF prototype II: enchanced upper-band suppressions

In this case, only the sector-structured components are utilized, ensuring that the structural parameters of the individual elements remain consistent with those defined in sections 2.4 and 3.1. The fabricated Prototype II is shown in Fig. 12a, with a circuit size of 130.92 mm × 86.5 mm (1.64 λg × 1.09 λg). Figure 12b provides a comparison of the simulated and measured results over the frequency range from DC to 5 GHz. The two passbands are centered at 1.38 GHz and 2.63 GHz, with minimum measured ILs of 1.02 dB and 1.72 dB, respectively. A measured RL of 11.34 dB is achieved consistently across the spectral range [0, 2ƒ0]. Figure 12c presents the measured |S21| of both Prototype I and Prototype II over the extended frequency range of DC to 20 GHz. The results indicate a significant improvement in harmonic suppression in the high-frequency band for Prototype II compared to Prototype I, while maintaining nearly identical transmission characteristics in the low-frequency region. Prototype II achieves extensive upper-band suppression, with measured attenuation levels of 22.8 dB across the frequency range of 2.9–20 GHz and 28.5 dB within the 3.0–12 GHz range. This demonstrates the effectiveness of the proposed modifications in enhancing high-frequency harmonic suppression without compromising the performance in the low-frequency band, further validating the design’s practical utility. The difference between simulation and measurement above 4 GHz are mainly due to fabrication tolerances and limited EM mesh resolution at high frequencies. These factors may slightly shift the resonances and reduce the predicted attenuation in simulation.

Fig. 12
figure 12

The proposed fabricated Prototype II. (a) Layout. (b) S-parameters. (c) Measured |S21| of the proposed prototype I &II from DC to 20 GHz.

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Table 1 summarizes the key performance metrics of the proposed dual-band ABPFs and compares them with both existing dual-band absorptive filters15,16,17,18,19,20,21 and recent dual-band BPFs featuring enhanced stopband suppression26,27,28,29,30. This broader comparison offers insights into the advantages of the proposed filters in terms of reflectionless performance, harmonic suppression, and structural compactness. As shown, the proposed prototypes exhibit competitive fractional bandwidths, low relative coefficients (RC, where a lower RC indicates higher selectivity), minimal IL, and outstanding upper-band suppression. Notably, Prototype II achieves up to 22.8 dB attenuation over a wide range, extending up to 10f0. In addition, both prototypes demonstrate full-band, dual-port reflectionless properties, excellent passband power matching, and a simplified structural design, making them highly practical and efficient for advanced applications. The combination of superior performance metrics and a streamlined design highlights the practicality and applicability of the proposed designs in modern microwave systems.

Table 1 Comparison between the proposed dual-band ABPFs and other works.
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Conclusion

This paper introduced two dual-band absorptive bandpass filters (ABPFs) with full-band reflectionless properties and enhanced upper-band suppression. Prototype I achieved excellent in-band performance with 3-dB FBWs of 19.5% and 9.7% at 1.38 GHz and 2.63 GHz, respectively, low insertion losses of 0.95 dB and 1.47 dB, and inter-band isolation exceeding 45 dB. Prototype II further enhanced upper-band suppression, achieving 22.8 dB attenuation from 2.9 to 20 GHz while maintaining compact size and low complexity. The key contributions of this work include: (1) the realization of a dual-band, full-spectrum reflectionless filter; (2) a tunable and compact structure offering independently controlled bandwidth and TZs; and (3) integrated harmonic suppression up to 10f0 without additional circuit area. Compared to existing absorptive filter designs, the proposed design uniquely combines dual-band filtering, full-spectrum reflectionless behavior, and extended harmonic suppression in a compact and integrable topology. These features make them highly suitable for modern RF front-end systems, including 5G/6G communications, multi-standard receivers, and radar applications, where dual-band operation, broadband absorption, and harmonic suppression are critical.