Dual Band-Pass Filter Based on Split Ring Resonators with Controlled Asymmetric Bandwidth Response
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript present a design methodology for dual-band bandpass filters based on split-ring resonators (SRRs), with an emphasis on controlling the bandwidth ratio through electromagnetic energy considerations. The topic is relevant to modern microwave filter design, particularly in the context of multiband wireless systems.
The paper addresses an important challenges in achieving independent control of passband characteristics while maintaining compact size. The proposed approach, combining coupling matrix synthesis with SRR-based implementation, is conceptually interesting and potentially valuable.
However, several important issues need to be addressed before the work can be considered for publication. The following comments are provided to improve the manuscript.
1-The abstract does not include quantitative results (e.g., achieved bandwidths, insertion loss, size). Could the authors include key numerical results to better highlight the effectiveness of the proposed method?
2-The manuscript uses multiple terms such as “SRR”, “BWR”, “FBW”, and “bandwidth ratio” without clear initial definitions. Could the authors ensure consistent notation and provide definitions when first introduced? (They are only mentioned at the end of the text!)
3- Several statements (e.g., claims about limitations of prior work) are not sufficiently supported by references. Could the authors use appropriate citations?
4- The contribution section is not clear and includes some repetition, making it difficult to identify the main contributions. The authors are encouraged to shorten this section and present the key contributions in a clear and concise way, while clearly distinguishing them from existting work.
5- The introduction contains repetitive statements regarding complexity and bandwith control limitations of prrior works. Could the authors streamline the discussion and avoid redundancy? While the importance of dual-band filters is discussed, the specific research gap is not clearly formulated. Could the authors explicitly define the main limitation in existing works that this paper aims to solve?
6- The authors selected Rogers RO3010 substrate (εr = 10.2, h = 0.64 mm) for the implementation. However, no clear justification is provided for this choice, why you have selected this substrate?
This point is particularly important given the main claim of the paper, where bandwidth ratio (BWR) control is achieved through the electromagnetic energy stored in the SRR. Since the stored electric and magnetic energies depend strongly on the substrate properties, such as the dielectric constant and loss tangent, the proposed method appears to be sensitive to the choice of substrate.
In particular:
The high dielectric constant (10.2) significantly alters field confinement, effective capacitance/inductance, and thus the resonance behavior of the SRRs.
The dielectric loss directly affect the quality factor, which is a key parametere in the filter performance. The very small geometrical features (e.g., narrow gaps and strip widths) combined with a high-εr substrate make the design highly sensitive to fabrication tolerances, which in turn impacts coupling coefficients, stored energy distribution, and ultimately the BWR.
Therefore, the following points require clarification:
- Is the proposed bandwidth-control mechanism, based on stored energy, valid only for the specific substrate used in this work?
- How would the bandwidth ratio (BWR) and overall filter performance be affected if a different substrate with a lower dielectric constant or different loss tangent were used?
- does the claimed independent control of the bandwidths remain valid and stable under changes in substrate
The manuscript would benefit from a discusion on the substrate dependency of the proposed method and its general applicability.
In addition, although the authors claim a good agreement between simulation and measurement, the experimental validation is not sufficiently documented. While the use of a vector network analyzer (E8364B PNA) is mentioned, no measured S-parameter plots or instrument screenshots are provided. Furthermore, the measurement setup itself is not described. important detail such as the port connections, connector types, and calibration procedure are missing.
Moreover, the presented results appear overly ideal compared to typical experimental measurements. In practice, measured S-parameters usually exhibit noise, ripple, connector mismatch effects, and slight frequency deviations. The absence of such non-idealities raises concerns regarding the completenes and authenticity of the reported measurement data.
Therefore, the following clarifications are required:
- Provide measured S11 and S21 plots directly obtained from the network analyzer, include raw measurement traces and at least screenshots of the results to support the reported data.
- Clearly explain the measurement setup, including port connections, connectors, and the calibration methods, and clarify how the measured results were extracted and processed.
Without these details, the reliability and reproducibility of the reported experimental results remain uncertain. the work appears largely simulation-based, while the experimental validation is not sufficiently supported.
It should be noted that RF measurements are inherently non-trivial and typically include effects such as noise, mismatch, and slight deviations from simulations. The absence of these characteristics, along with the lack of measurement setup details and raw data, raises concerns about the credibility of the reported results.
Optional: As a suggestion, the authors are encouraged to investigate the sensitivity of the proposed design to fabrication tolerances in HFSS, particularly variations in SRR gap and coupling dimensions, as these factors may significantly affect the reported bandwidth ratio (BWR). Such an analysis would further enhance the robustness and practical relevance of the proposed approach.
7- In Table 7, the comparison of the quality factor (Q) of different resonators is presented. Do all the reported resonators use the same substrate (dielectric constant, loss tangent, and thickness)? If yes, please explicitly state this in the text. If not, please clarify how a fair comparison between different substrate technologies has been ensured?
Comments on the Quality of English Language
The text needs revision because it contains several errors, long, and repetitive words. For example:
F ilter Network
f ilters
f ixed
Adual-band
Author Response
Response to Reviewer 1 comments:
This manuscript present a design methodology for dual-band bandpass filters based on split-ring resonators (SRRs), with an emphasis on controlling the bandwidth ratio through electromagnetic energy considerations. The topic is relevant to modern microwave filter design, particularly in the context of multiband wireless systems.
The paper addresses an important challenges in achieving independent control of passband characteristics while maintaining compact size. The proposed approach, combining coupling matrix synthesis with SRR-based implementation, is conceptually interesting and potentially valuable.
However, several important issues need to be addressed before the work can be considered for publication. The following comments are provided to improve the manuscript.
Comment1:
The abstract does not include quantitative results (e.g., achieved bandwidths, insertion loss, size). Could the authors include key numerical results to better highlight the effectiveness of the proposed method?
Response to the reviewer
We thank the reviewer for this observation. We agree that the abstract should report the main quantitative results. In the revised manuscript, we will include the measured center frequencies, 3-dB bandwidths, insertion losses, and filter footprints for both fabricated prototypes in order to better demonstrate the effectiveness of the proposed method.
Revised abstract
A synthesis method for compact dual-band bandpass filters with based on split-ring resonators (SRRs) is presented. The method combines coupling-matrix synthesis with an energy-based SRR model with a control technique of the center frequencies and the bandwidth ratio (BWR) of the two passbands. Two third-order microstrip prototypes were fabricated on Rogers RO3010 (εr=10.2, h=0.64 mm ) to validate the approach. The first prototype operates at 1.9 and 2.4 GHz with measured 3-dB bandwidths of 200 and 100 MHz, insertion losses of 1.0 and 1.95 dB, and BWR ≈ 0.5. The second prototype operates at 1.9 and 2.4 GHz with measured bandwidths of 100 and 200 MHz, insertion losses of 1.8 and 0.6 dB, and BWR ≈ 1.9. The corresponding footprints are 32×12.37 mm2 and 27.87×12.42 mm2, respectively. The measured responses agree well with electromagnetic simulations and confirm that asymmetric dual-band bandwidths can be achieved in a compact planar topology without additional reconfigurable elements.
Comment 2:
The manuscript uses multiple terms such as “SRR”, “BWR”, “FBW”, and “bandwidth ratio” without clear initial definitions. Could the authors ensure consistent notation and provide definitions when first introduced? (They are only mentioned at the end of the text!)
Response to the reviewer
We agree. In the revised manuscript, all abbreviations and symbols will be defined at first use in the Abstract and Introduction, and the notation will be made consistent throughout the paper.
In particular, we will define split-ring resonator (SRR), bandpass filter (BPF), fractional bandwidth (FBWi=Δfi/f0i), and bandwidth ratio (BWR=Δf2/Δf1)(\text{BWR} = \Delta f_2 / \Delta f_1)(BWR=Δf2​/Δf1​) at the beginning of the manuscript.
Comment 3
Several statements (e.g., claims about limitations of prior work) are not sufficiently supported by references. Could the authors use appropriate citations?
Response to the reviewer
We thank the reviewer for this comment. We agree that several comparative statements were too broad. In the revised manuscript, we will add references immediately after each statement describing the limitations of prior work, and we will soften statements that were previously overgeneralized.
Comment 4:
The contribution section is not clear and includes some repetition, making it difficult to identify the main contributions. The authors are encouraged to shorten this section and present the key contributions in a clear and concise way, while clearly distinguishing them from existting work.
Response to the reviewer
The contribution section will be shortened and reformulated in a clearer way. The revised manuscript will present the contributions in three concise points and will explicitly distinguish them from previous SRR-based and dual-band filter designs.
Added replacement text in the Introduction
This work makes four main contributions. First, it proposes a unified synthesis-to-implementation methodology for dual-band bandpass filters based on split-ring resonators (SRRs), in which the target specifications (f01, f02, FBW1, FBW2) are mapped to a realizable filter network via a coupling-matrix formulation. This enables explicit control of the asymmetric dual-band response without requiring additional resonators or reconfigurable elements. Second, the method establishes a direct design link between the desired BWR and the electromagnetic behaviour of the SRR, using stored magnetic energy and its relationship with susceptance-derivative-based bandwidth metrics to guide the selection of the resonator parameters. Third, by employing concentric SRRs as multi-resonance resonators, the proposed approach reduces the number of design variables, enhances strong internal coupling, and achieves a compact footprint, since the resonators are not arranged side by side. In this sense, the method provides a practical alternative to recent dual-band designs with fixed BWR or higher implementation complexity. Fourth, the methodology is experimentally validated using two fabricated third-order prototypes for communication applications, which demonstrate opposite asymmetric responses while preserving compact size and consistent center-frequency placement.
With respect to our previous work, the stored-energy-based SRR bandwidth-control concept builds on the controllable dual-band band-stop filter framework reported in \cite{Castillo-Aranibar2017}. However, the present manuscript extends that concept in three key ways: it targets dual-band bandpass filtering instead of band-stop filtering, it integrates SRR bandwidth-ratio control into a complete coupling-matrix synthesis procedure, and it combines that formulation with the single-to-multiband frequency transformation reported in \cite{Garcia-Lamperez2011} to provide a full synthesis-to-layout workflow. In addition, the paper contributes new experimental validation through two dual-band bandpass prototypes implemented under the same topology and substrate constraints, which constitutes original material in this manuscript.
Comment 5
The introduction contains repetitive statements regarding complexity and bandwith control limitations of prrior works. Could the authors streamline the discussion and avoid redundancy? While the importance of dual-band filters is discussed, the specific research gap is not clearly formulated. Could the authors explicitly define the main limitation in existing works that this paper aims to solve?
Response to the reviewer
We agree and have streamlined the Introduction. Repetitive statements regarding complexity and bandwidth-control limitations will be removed, and the research gap will be stated explicitly together with the comment 5.
Research-gap paragraph added
Existing planar dual-band filters generally fall into three categories: designs with fixed or nearly symmetric passband widths, designs that require additional resonators or reconfigurable elements to tune the two bands, and designs that achieve good selectivity at the cost of higher structural complexity. What remains insufficiently addressed is a compact single-layer method that treats the bandwidth ratio between passbands as an explicit synthesis parameter and links that parameter to physical resonator quantities. The present work addresses this gap by combining coupling-matrix synthesis with an energy-based SRR model, thereby enabling analytical control of the two center frequencies and the passband bandwidth ratio within a compact planar topology.
Comment 6
The authors selected Rogers RO3010 substrate (εr = 10.2, h = 0.64 mm) for the implementation. However, no clear justification is provided for this choice, why you have selected this substrate?
Response to the reviewer
We appreciate this important comment. We agree that the manuscript must better justify the choice of substrate and provide a more complete description of the measurement procedure. We will revise the paper accordingly:
Comment 6.1:
This point is particularly important given the main claim of the paper, where bandwidth ratio (BWR) control is achieved through the electromagnetic energy stored in the SRR. Since the stored electric and magnetic energies depend strongly on the substrate properties, such as the dielectric constant and loss tangent, the proposed method appears to be sensitive to the choice of substrate.
In particular:
The high dielectric constant (10.2) significantly alters field confinement, effective capacitance/inductance, and thus the resonance behavior of the SRRs.
The dielectric loss directly affects the quality factor, which is a key parameter in the filter performance. The very small geometrical features (e.g., narrow gaps and strip widths) combined with a high-εr substrate make the design highly sensitive to fabrication tolerances, which in turn impacts coupling coefficients, stored energy distribution, and ultimately the BWR.
Therefore, the following points require clarification:
Is the proposed bandwidth-control mechanism, based on stored energy, valid only for the specific substrate used in this work?
How would the bandwidth ratio (BWR) and overall filter performance be affected if a different substrate with a lower dielectric constant or different loss tangent were used?
does the claimed independent control of the bandwidths remain valid and stable under changes in substrate
The manuscript would benefit from a discusion on the substrate dependency of the proposed method and its general applicability.
Response to reviewer:
Rogers RO3010 (εr=10.2, h=0.64 mm, tanδ=0.0022 was selected because its high dielectric constant enables substantial miniaturization of the concentric SRR structure, while the 0.64 mm thickness provides a practical compromise between compactness, coupling control, and manufacturability. The relatively low loss tangent helps preserve acceptable unloaded quality factors in both passbands. The proposed method is not restricted to this specific substrate. However, the distributed parameters of the SRR, the extracted couplings, the stored electromagnetic energy, and the unloaded quality factor are substrate-dependent. Therefore, when a different substrate is used, the resonator dimensions and couplings must be re-synthesized. In this sense, the method is substrate-aware rather than substrate-specific: the design principle remains valid, but the achievable BWR range, insertion loss, and sensitivity to fabrication tolerances depend on the substrate and on the realizable internal and external couplings.
Added paragraph to add in the manuscript
Although the proposed synthesis is general, the final resonator dimensions and achievable performance are substrate-dependent because the effective permittivity, distributed inductance/capacitance, coupling strength, and loss mechanisms all depend on the substrate properties. Therefore, for a different substrate, the same design flow remains valid, but the SRR dimensions, coupling distances, unloaded quality factor, and attainable BWR range must be recalculated.
Comment 6.2:
In addition, although the authors claim a good agreement between simulation and measurement, the experimental validation is not sufficiently documented. While the use of a vector network analyzer (E8364B PNA) is mentioned, no measured S-parameter plots or instrument screenshots are provided. Furthermore, the measurement setup itself is not described. important detail such as the port connections, connector types, and calibration procedure are missing.
Moreover, the presented results appear overly ideal compared to typical experimental measurements. In practice, measured S-parameters usually exhibit noise, ripple, connector mismatch effects, and slight frequency deviations. The absence of such non-idealities raises concerns regarding the completenes and authenticity of the reported measurement data.
Therefore, the following clarifications are required:
Provide measured S11 and S21 plots directly obtained from the network analyzer, include raw measurement traces and at least screenshots of the results to support the reported data.
Clearly explain the measurement setup, including port connections, connectors, and the calibration methods, and clarify how the measured results were extracted and processed.
Without these details, the reliability and reproducibility of the reported experimental results remain uncertain. the work appears largely simulation-based, while the experimental validation is not sufficiently supported.
It should be noted that RF measurements are inherently non-trivial and typically include effects such as noise, mismatch, and slight deviations from simulations. The absence of these characteristics, along with the lack of measurement setup details and raw data, raises concerns about the credibility of the reported results.
Response to the reviewer
We also agree that the measurement section needs to be more explicit. In the revised manuscript, we will add a dedicated paragraph describing the complete measurement setup, including the connector type, port connections, calibration method, reference planes, and whether any smoothing or post-processing was applied. We will also provide raw VNA screenshots and exported measured ∣S11​∣ and ∣S21∣ traces as Supplementary Material.
At the same time, we respectfully note that the current measured results are not idealized. The manuscript already shows typical experimental non-idealities, including reduced return loss, increased insertion loss, ripple in the upper passband of Prototype 1, and shifts of the reflection zeros relative to the lossless model. We will make these deviations more explicit in the revised discussion.
Added measurement paragraph
Measurements were performed with a two-port vector network analyzer (E8364B PNA). The fabricated filters were connected through coaxial SMA connectors to the 50-Ω microstrip input and output lines. Before measurement, a full two-port calibration was carried out at the connector reference planes. The measured ∣S11∣and ∣S21∣ responses shown in Figs. 6 and 9 were exported directly from the analyzer. To improve reproducibility, raw screenshots and measured traces will be included as Supplementary Material.
Optional: As a suggestion, the authors are encouraged to investigate the sensitivity of the proposed design to fabrication tolerances in HFSS, particularly variations in SRR gap and coupling dimensions, as these factors may significantly affect the reported bandwidth ratio (BWR). Such an analysis would further enhance the robustness and practical relevance of the proposed approach.
Optional tolerance study
Manuscript action in Section 3.2
Although the proposed two-stage synthesis reduces the number of design variables and clarifies the role of the different couplings, the final response remains sensitive to fabrication tolerances in narrow gaps, feed lines, conductor widths, and substrate properties. Thus, the implemented filters are sensitive to deviations in narrow gaps and line widths. Variations in the inter-ring gap modify the internal SRR coupling and, therefore, the resonance splitting and BWR, whereas variations in the feed gaps modify the external quality factor and, hence, the passband widths and matching. Variations in conductor width or effective substrate parameters mainly shift the center frequencies and affect the unloaded quality factor.
That is consistent with broader reports showing that fabrication inaccuracies and material variations can shift the frequency response of microwave circuits, even though the exact mechanisms depend on the specific manufacturing technology. [18] showed systematic S-parameter frequency shifts in a fabricated microstrip filter due to inaccurate milling depth, and [19] described significant substrate-permittivity variation in 3D-printed microwave structures that required post-fabrication compensation.
Comment 7:
In Table 7, the comparison of the quality factor (Q) of different resonators is presented. Do all the reported resonators use the same substrate (dielectric constant, loss tangent, and thickness)? If yes, please explicitly state this in the text. If not, please clarify how a fair comparison between different substrate technologies has been ensured?
Response to the reviewer
We agree that this point must be clarified. Table 7 should not be interpreted as a substrate-normalized benchmark. The resonators compared in Table 7 do not all use the same substrate technology. For example, the design cited as [1] uses Rogers RT/Duroid 5880 with εr=2.2 and thickness 0.79 mm, the design cited as [11] is reported on a substrate with εr=2.65, tanδ=0.003, and h=1 mm; and the modified hexagonal SRR in [15] is analyzed on a substrate with εr=6.15, tanδ=0.002, and h=0.762 mm. Our prototypes use Rogers RO3010 with εr=10.2 and h=0.64 mm. Therefore, the comparison in Table 7 will be explicitly described as a qualitative comparison of reported Qu​ values at similar frequency ranges, not as a strictly normalized comparison across identical substrate conditions.
New caption for Table 7
Comparison of reported unloaded quality factors Qu for representative resonators. The values correspond to different substrates, thicknesses, and technologies; therefore, the comparison is qualitative rather than substrate-normalized.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsA design methodology for dual-band bandpass filters with controlled asymmetric response is proposed based on SRRs. This approach uses electromagnetic analysis of SRRs with coupling matrix synthesis to enable direct control over both the center frequencies and the BWR. Two prototypes targeting the 4G and WLAN bands are designed. Some minor suggestions are shown as follows.
- Please clarify how to control the coupling coefficient between the SRR.
- Why the measured loss of the higher passband is much larger than the simulated one?
Author Response
Response to Reviewer 2 comments:
A design methodology for dual-band bandpass filters with controlled asymmetric response is proposed based on SRRs. This approach uses electromagnetic analysis of SRRs with coupling matrix synthesis to enable direct control over both the center frequencies and the BWR. Two prototypes targeting the 4G and WLAN bands are designed. Some minor suggestions are shown as follows.
Comment 1:
Please clarify how to control the coupling coefficient between the SRR.
Response to the reviewer
We thank the reviewer for this comment. We agree that the manuscript should more clearly distinguish between the internal coupling within each SRR and the external/filter coupling. In the proposed method, the normalized coupling coefficient k of each dual-resonance block is first obtained from the dual-band coupling matrix through Equations (1)–(2). After the lowpass-to-bandpass transformation, it is converted into the physical bandpass coupling K, which is then implemented in the SRR geometry. In practice, the internal SRR coupling is controlled mainly by the inter-ring spacing s and the common coupled length l​c; decreasing s or increasing lc ​ strengthens the coupling and increases the resonance splitting, while increasing s weakens it. By contrast, the absolute bandwidths of the filter are mainly controlled by the external and inter-resonator couplings, which depend on the feed-to-SRR spacing and the spacing between adjacent SRRs. We will clarify this distinction in Section 2.2 and add a short paragraph explicitly relating k, K, s, and lc ​.
Text added in Section 2.2
The coupling coefficient associated with the two rings inside each SRR is obtained from the synthesized dual-band block and then implemented physically through the SRR geometry. After the lowpass-to-bandpass transformation, the physical coupling K is controlled mainly by the inter-ring spacing s and the common coupled length lc​. A smaller spacing s or a larger coupled length l​c increases the internal electromagnetic coupling and therefore the resonance splitting. In contrast, the absolute passband bandwidths are governed mainly by the external and inter-resonator couplings, which are set by the feed structure and the spacing between adjacent SRRs.
Comment 2:
Why the measured loss of the higher passband is much larger than the simulated one?
Response to the reviewer
We thank the reviewer for this observation. We agree that this point should be discussed more explicitly. The discrepancy is mainly observed in the upper passband of prototype 1, where the measured insertion loss is 1.95 dB while the simulated value is 0.4 dB; for prototype 2, the upper-band difference is much smaller (0.6 dB measured versus 0.2 dB simulated). We attribute the larger discrepancy in prototype 1 to the combined effect of: first, higher conductor and dielectric losses at the upper frequency, second the greater sensitivity of the narrower upper passband to deviations in the narrow coupling gaps and line widths, and third, launch and connector parasitics that were not fully represented in the EM model. In addition, the measured shift of the reflection zeros increases the mismatch in the upper band, which raises the apparent band-center insertion loss. We will add this discussion in Section 3.1 and clarify that this effect is most pronounced in the upper passband of prototype 1.
Text added after Table 4
The larger discrepancy between measured and simulated insertion loss is concentrated in the upper passband of prototype 1. This behavior is attributed to the combined effect of higher loss at the upper frequency, the strong sensitivity of the narrow upper passband to small deviations in the coupling gaps and strip widths, and parasitic effects associated with the connectors and transitions. These mechanisms perturb the external coupling and the reflection-zero positions, thereby increasing the measured insertion loss relative to the idealized EM model.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript "Dual Band-Pass Filter Based on Split Ring Resonators with Controlled Asymmetric Response" presents a methodology for designing dual-bandpass filters. This is a well written paper. The authors clearly show the evolution of the present proposal in relation to their previous work (reference 12). Furthermore, the experimental results provided by the two fabricated prototypes closely match the simulations. However, the following issues need to be addressed:
1. Table 8 must be expanded to include other fundamental filter figures of merit. Furthermore, a more accurate survey of the literature and comparisons with previously published papers should be provided in order to highlight the novelty.
2. The authors should include a broader set of references dealing with asymmetric dual-band filters to fairly compare the performance of the proposed SRR topology against competing methods.
3. The authors should add a brief discussion of how typical manufacturing errors affect the structure's response.
4. While the amplitude response is analyzed, modern 4G/WLAN applications require good phase linearity. Could the authors provide and discuss the measured/simulated group delay within the passbands?
Comments on the Quality of English LanguageThis is a well written article. I didn't find any serious typos or grammatical errors. I only suggest that the authors do a general review of the work.
Author Response
Response to Reviewer 3 comments:
The manuscript "Dual Band-Pass Filter Based on Split Ring Resonators with Controlled Asymmetric Response" presents a methodology for designing dual-bandpass filters. This is a well written paper. The authors clearly show the evolution of the present proposal in relation to their previous work (reference 12). Furthermore, the experimental results provided by the two fabricated prototypes closely match the simulations. However, the following issues need to be addressed:
Comment 1:
- Table 8 must be expanded to include other fundamental filter figures of merit. Furthermore, a more accurate survey of the literature and comparisons with previously published papers should be provided in order to highlight the novelty.
Response to the reviewer
We agree. Table 8 in its current form is too narrow because it emphasizes only a subset of performance parameters. In the revised manuscript, Table 8 will be expanded to include additional figures of merit such as substrate, filter order, insertion loss, return loss, inter-band rejection, normalized size, and whether the design provides explicit BWR control as part of the synthesis method. We will also revise the literature survey so that the novelty is highlighted not only in terms of measured performance, but also in terms of design methodology and degrees of freedom.
Manuscript action
Table 8 was updated
Comment 2:
- The authors should include a broader set of references dealing with asymmetric dual-band filters to fairly compare the performance of the proposed SRR topology against competing methods.
Response to the reviewer
We thank the reviewer for this suggestion and agree that the literature survey should be broadened. In the revised manuscript, we will include additional references on dual-band filters with individually controllable passbands, independently controllable passband responses and explicitly asymmetric dual-band responses. This broader survey will help position the proposed method more fairly against competing approaches and clarify the specific novelty of introducing the bandwidth ratio as an explicit synthesis parameter in an SRR-based coupling-matrix workflow.
Manuscript action in the introduction
Beyond dual-band designs that mainly control center frequencies and bandwidths, more advanced synthesis-oriented approaches have also been reported. \cite{SunTan2016} presented dual-band filters with individually controllable passband responses and orders, where each passband can be assigned a different prototype and order through the element-by-element synthesis of dual-band resonators and inverters. Therefore, although it confirms that independent passband control is possible at the synthesis level, it does not address the specific problem of linking asymmetric bandwidth control to a compact SRR-based planar implementation.
More recently, \cite{Hugar2024} proposed a multi-band band-pass filter with independently controlled asymmetric dual-band response based on an asymmetric stepped-impedance resonator and a metacell structure. However, the control mechanism is topology-specific and depends on assigning different structural roles to the two passbands, rather than on an analytical dual-band synthesis framework with an explicit bandwidth-ratio parameter. Independent passband tunability has also been demonstrated in compact microstrip dual-band filters, in} \cite{Lalbakhsh2020} \hl{presented a narrowband dual-band BPF with independently tunable passbands using a compact coupling system integrated with flag-shaped and stepped-impedance resonators. However, the independent control is implemented mainly through geometric retuning of structural parameters, whereas the present work aims to introduce the bandwidth ratio into the synthesis stage itself and relate it to the electromagnetic-energy behavior of SRR-based resonators.}
Also, the Table 8 and Table 9 were updated with the included references.
Comment 3:
- The authors should add a brief discussion of how typical manufacturing errors affect the structure's response.
Proposed response to the reviewer
We agree. A brief discussion of fabrication sensitivity will be added in the revised manuscript. In the proposed topology, the most critical dimensions are the inter-ring gap, the feed-to-resonator gap, and the narrow line widths. Variations in the inter-ring gap mainly affect the internal SRR coupling and therefore the resonance separation and BWR, while variations in the feed gaps mainly affect the external quality factor, the absolute bandwidths, and the return loss. Deviations in line width or substrate properties shift the effective electrical length and the unloaded quality factor, thereby affecting center frequency and insertion loss. We will include this discussion.
Manuscript action
The implemented filters are sensitive to deviations in narrow gaps and line widths. Variations in the inter-ring gap modify the internal SRR coupling and, therefore, the resonance splitting and BWR, whereas variations in the feed gaps modify the external quality factor and, hence, the passband widths and matching. Variations in conductor width or effective substrate parameters mainly shift the center frequencies and affect the unloaded quality factor.
That is consistent with broader reports showing that fabrication inaccuracies and material variations can shift the frequency response of microwave circuits, even though the exact mechanisms depend on the specific manufacturing technology. [18] showed systematic S-parameter frequency shifts in a fabricated microstrip filter due to inaccurate milling depth, and [19] described significant substrate-permittivity variation in 3D-printed microwave structures that required post-fabrication compensation.
Comment 4:
- While the amplitude response is analyzed, modern 4G/WLAN applications require good phase linearity. Could the authors provide and discuss the measured/simulated group delay within the passbands?
Response to the reviewer
We agree that group delay is relevant for practical 4G/WLAN applications. In the revised manuscript, we will add simulated and measured group-delay plots obtained from the phase of S21​ for both prototypes and discuss the group delay and its variation within each passband. This will complement the amplitude-response analysis and provide a more complete assessment of in-band phase linearity.
Manuscript action:
To complement the amplitude-response analysis, the group delay was extracted from the phase of S21 for both the simulated and measured responses. The obtained results show reasonably smooth in-band behavior for the two prototypes, with no abrupt excursions inside the useful passbands. From Fig. 10, for the prototype with BWR 1:2, the average group delay is approximately 3.1 ns in the lower passband and 4.9 ns (simulation) / 4.5 ns (measurement) in the upper passband. For the prototype with BWR 2:1, the corresponding average values are approximately 5.4 ns / 5.4 ns in the lower passband and 3.0 ns / 2.9 ns in the upper passband. In both filters, the narrower passband exhibits a higher delay and greater in-band variation, whereas the wider passband shows a flatter response. This trend is consistent with the expected phase behavior of narrow dual-band microstrip filters and indicates acceptable phase linearity for the intended 4G/WLAN operation, since the group delay remains bounded and moderately smooth within each passband.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsIn this contribution, the authors describe a new design for dual-band pass-band filters. The paper is clear and well organized but repetitive in some points. The results are accurate, compared to simulations but the novelty of the paper should be clarified. In detail:
The authors state: “Unlike existing designs, our method achieves independent control of the passband’s bandwidths through analytical synthesis and physical modeling, without requiring additional resonators or reconfigurable elements”. However, since there are many filter designs in the literature, the comparison must be more quantitative than qualitative to demonstrate the novelty of the contribution. Indeed, although a comparison table is included at the end of the paper, it describes only the performance, not the design method, which is a claimed novel point. Also, the fact that this design should be simpler should be demonstrated.
The text is too verbose and repetitive from page 2, line 42 to page 3, line 97.
In Section 2, the authors should clarify and explicitly list the novel elements of the design methodology compared to known methods.
Have you simulated the current and field distributions, in addition to the analytical dissertation, to show figures?
Have you performed a statistical analysis to consider possible effects of prototyping uncertainties? If not, do you consider your design reliable against manufacturing defects, as described in:
Ferro, L.; Cardillo, E. Frequency Shift in Microwave Circuits Manufactured with Circuit Board Plotters: Case Study of a Parallel Coupled Lines Filter. Electronics 2024, 13, 3100. https://doi.org/10.3390/electronics13153100.
Z. Iman, Z. Akhter, Y. Yu and A. Shamim, "Post-Fabrication Technique to Manage Material Variations in 3-D Printed Microstrip Antenna Substrates," in IEEE Open Journal of Antennas and Propagation, vol. 4, pp. 571-580, 2023, doi: 10.1109/OJAP.2023.3283994.
Author Response
Response to Reviewer 4 comments:
In this contribution, the authors describe a new design for dual-band pass-band filters.
Comment 1:
The paper is clear and well organized but repetitive in some points. The results are accurate, compared to simulations but the novelty of the paper should be clarified. In detail:
Response to the reviewer
We thank the reviewer and agree that the novelty should be defined more rigorously. In the revised manuscript, we will avoid broad qualitative statements suggesting generic superiority over all previous dual-band filters. Instead, the novelty will be stated more precisely: the proposed contribution is the introduction of the bandwidth ratio (BWR) as an explicit synthesis parameter in a coupling-matrix-to-SRR design workflow, along with its implementation in a compact, single-layer topology without additional reconfigurable elements. To support this claim quantitatively, the comparison section will be expanded to include methodological metrics such as the number of metal layers, the presence of vias or lumped tuning/reconfigurable elements, the number of distinct resonator types, and whether FBW1_11​, FBW2_22​, and BWR are explicitly specifiable by the design equations.
That is the correct response. The present wording in the manuscript is too broad. The novelty is not the mere existence of asymmetry, but the way it is synthesized and mapped onto the SRR structure.
Manuscript action in introduction:
This work makes four main contributions. First, it proposes a unified synthesis-to-implementation methodology for dual-band bandpass filters based on split-ring resonators (SRRs), in which the target specifications ($f_{01}, f_{02}, FBW_1, FBW_2$ ) are mapped to a realizable filter network through a coupling-matrix formulation that explicitly incorporates the bandwidth ratio (BWR) as a synthesis parameter. This enables analytical prescription of the asymmetric dual-band response without requiring additional resonators or reconfigurable elements. Second, the method establishes a direct design link between the desired BWR and the electromagnetic behaviour of the SRR, using stored magnetic energy and its relationship with susceptance-derivative-based bandwidth metrics to guide the selection of the resonator parameters. Third, by employing concentric SRRs as multi-resonance resonators, the proposed approach reduces the number of design variables, enhances strong internal coupling, and achieves a compact footprint in a single-layer topology. Fourth, the methodology is experimentally validated using two fabricated third-order prototypes that exhibit opposite asymmetric responses while maintaining compact size and consistent center-frequency placement.
Comment 2:
The authors state: “Unlike existing designs, our method achieves independent control of the passband’s bandwidths through analytical synthesis and physical modeling, without requiring additional resonators or reconfigurable elements”. However, since there are many filter designs in the literature, the comparison must be more quantitative than qualitative to demonstrate the novelty of the contribution. Indeed, although a comparison table is included at the end of the paper, it describes only the performance, not the design method, which is a claimed novel point. Also, the fact that this design should be simpler should be demonstrated.
The text is too verbose and repetitive from page 2, line 42 to page 3, line 97.
Response to the reviewer
We agree and will substantially shorten that segment. The current text repeats the same ideas regarding compactness, complexity, and independent control. In the revised manuscript, this part will be replaced by a concise statement of the research gap.
Suggested replacement text
The introduction has been modified and highlighted
Comment 3:
In Section 2, the authors should clarify and explicitly list the novel elements of the design methodology compared to known methods.
Response to the reviewer
We agree. At the beginning of Section 2, we will explicitly list the novel elements of the methodology to distinguish them from existing dual-band filter methods.
Manuscript action inserted at the start of Section 2
The proposed methodology differs from previous dual-band filter approaches in some aspects. First, the bandwidth ratio (BWR) is introduced as an explicit design parameter in addition to the conventional dual-band specifications of center frequencies and bandwidths. Second, the filter is synthesized through a dual-band coupling matrix whose second-order dual-resonance blocks directly define the resonator-level specifications. Third, these synthesized blocks are mapped onto split-ring resonators (SRRs) by establishing an equivalence between the coupling-matrix model and the physical SRR model. Fourth, the method provides an explicit electromagnetic interpretation of BWR by relating it to the susceptance derivative and to the stored magnetic energy at the two SRR resonances.
Comment 4:
Have you simulated the current and field distributions, in addition to the analytical dissertation, to show figures?
Response to the reviewer
We thank the reviewer for this valuable suggestion. We agree that current-density and field-distribution plots can provide useful physical insight into the modal behavior of SRR-based filters. However, in the present work, the primary objective is not to perform a full field-based modal characterization of the structure, but rather to present and validate a synthesis-to-implementation design methodology. In particular, the manuscript focuses on demonstrating how the target dual-band specifications, including the bandwidth ratio (BWR), are introduced at the synthesis stage through the coupling matrix and then mapped to the SRR physical parameters through the energy-based model. For this reason, the paper emphasizes the analytical design flow, the coupling-matrix-to-SRR transformation, and the experimental validation of the resulting prototypes, instead of a detailed electromagnetic field interpretation.
The resonator behavior is already characterized in the paper through the susceptance formulation, the coupling parameters, the distributed current reconstruction used to calculate the stored magnetic energy, and the measured agreement of the fabricated prototypes with the theoretical and EM results, which is the main purpose of the manuscript.
We consider that a deeper study of current-density and electromagnetic-field distributions is more appropriate as a follow-up investigation devoted specifically to modal analysis, local energy concentration, and coupling mechanisms in SRR-based dual-band filters. Such a study would allow a more systematic discussion of the spatial distribution of the resonant modes and of the relation between local field confinement and bandwidth control, which goes beyond the design-oriented scope of the present paper. We have clarified this point in the revised manuscript and identified it as a relevant direction for future work.
Manuscript action in conclusions
Future work will conduct a deeper modal analysis of the proposed SRR topology, including current-density and electromagnetic-field distributions, to complement the present design-oriented methodology with a more detailed physical interpretation of the resonant mechanisms.
Comment 5:
Have you performed a statistical analysis to consider possible effects of prototyping uncertainties? If not, do you consider your design reliable against manufacturing defects, as described in:
Ferro, L.; Cardillo, E. Frequency Shift in Microwave Circuits Manufactured with Circuit Board Plotters: Case Study of a Parallel Coupled Lines Filter. Electronics 2024, 13, 3100. https://doi.org/10.3390/electronics13153100.
- Iman, Z. Akhter, Y. Yu and A. Shamim, "Post-Fabrication Technique to Manage Material Variations in 3-D Printed Microstrip Antenna Substrates," in IEEE Open Journal of Antennas and Propagation, vol. 4, pp. 571-580, 2023, doi: 10.1109/OJAP.2023.3283994.
Response to the reviewer
We thank the reviewer for this important comment. A full statistical tolerance analysis was not performed in the present work. Accordingly, we have revised the manuscript to clarify that the proposed filters are sensitive to deviations in narrow gaps, feed-line spacing, conductor width, and substrate properties. In particular, variations in the inter-ring gap affect the internal SRR coupling and, in turn, the resonance splitting and BWR, whereas variations in the feed gaps affect the external quality factor, passband widths, and matching. Variations in conductor width or effective substrate parameters mainly shift the center frequencies and modify the unloaded quality factor. We have also added a brief discussion, supported by the references the reviewer suggested, to indicate that this behavior is consistent with broader reports of fabrication- and material-induced frequency shifts in microwave circuits. Therefore, rather than claiming intrinsic robustness, we now state more carefully that the method is practically implementable, but its final response remains sensitive to manufacturing tolerances and material variations.
Manuscript action in Section 3.2
Although the proposed two-stage synthesis reduces the number of design variables and clarifies the role of the different couplings, the final response remains sensitive to fabrication tolerances in narrow gaps, feed lines, conductor widths, and substrate properties. Thus, the implemented filters are sensitive to deviations in narrow gaps and line widths. Variations in the inter-ring gap modify the internal SRR coupling and, therefore, the resonance splitting and BWR, whereas variations in the feed gaps modify the external quality factor and, hence, the passband widths and matching. Variations in conductor width or effective substrate parameters mainly shift the center frequencies and affect the unloaded quality factor.
That is consistent with broader reports showing that fabrication inaccuracies and material variations can shift the frequency response of microwave circuits, even though the exact mechanisms depend on the specific manufacturing technology. [18] showed systematic S-parameter frequency shifts in a fabricated microstrip filter due to inaccurate milling depth, and [19] described significant substrate-permittivity variation in 3D-printed microwave structures that required post-fabrication compensation.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
I appreciate the authors’ efforts in revising the manuscript and addressing several of the previously raised concerns. The clarifications regarding substrate selection, and the overall design procedure are helpful and acknowledged. However, a few important issues still need further improvement to strengthen the technical validity and completeness of the work.
First, with respect to the dependence on the substrate, although this aspect has been partially addressed in the response, the manuscript still includes wording that may suggest a more general applicability of the proposed method. This should be revised more carefully. Since the resonator dimensions, coupling behavior, and bandwidth are inherently influenced by substrate properties, the claims of generality should be moderated. It would be more accurate for the manuscript to explicitly state that the presented results are validated specifically for the chosen Rogers RO3010 substrate, and that any change of substrate would require re-optimization of the design.
Second, about my optional comment, a purely qualitative discussion is not sufficient for this type of study. Fabrication tolerances are particularly critical in narrow-gap SRR-based structures. Therefore, the authors should either provide quantitative evidence, such as HFSS simulation results, showing how variations in gap and coupling dimensions affect bandwidth, resonance frequency, and S-parameters, Either explain it properly or ignore the optional comment! Without numerical or graphical support, qualitative explanations alone do not adequately demonstrate the robustness of the proposed claim.
Third, concerning the simulation and measurement results, the revision still does not include new figures. At present, the manuscript relies mainly on descriptive statements, which is not sufficient. In particular, experimental validation in the form of measured S-parameter plots is still missing. Additionally, the close agreement shown in Figures 6 and 9 appears somewhat idealized compared to typical microwave measurements, which usually include noise, small frequency shifts, ripple effects, and connector or calibration imperfections. To improve credibility, it is important to include actual VNA measurement screenshots along with a clear explanation of the measurement setup, calibration method, and data processing procedure. Providing only a photograph of the fabricated component is not sufficient!
Thanks
Author Response
Response to Reviewer 1 comments (2nd round):
I appreciate the authors’ efforts in revising the manuscript and addressing several of the previously raised concerns. The clarifications regarding substrate selection, and the overall design procedure are helpful and acknowledged. However, a few important issues still need further improvement to strengthen the technical validity and completeness of the work.
Response to the reviewer
We sincerely thank the reviewer for carefully reviewing the revised manuscript and for the constructive follow-up comments. We appreciate the acknowledgment of the clarifications already introduced regarding the substrate choice and the overall design procedure. We also agree that several aspects still require more rigorous treatment to strengthen the paper's technical validity and completeness. In the new revision, we have addressed these points by further moderating the claims of generality, by strengthening the discussion of fabrication sensitivity, and by improving the presentation of the experimental validation.
First, with respect to the dependence on the substrate, although this aspect has been partially addressed in the response, the manuscript still includes wording that may suggest a more general applicability of the proposed method. This should be revised more carefully. Since the resonator dimensions, coupling behavior, and bandwidth are inherently influenced by substrate properties, the claims of generality should be moderated. It would be more accurate for the manuscript to explicitly state that the presented results are validated specifically for the chosen Rogers RO3010 substrate, and that any change of substrate would require re-optimization of the design.
Response to the reviewer
We agree with the reviewer that the previous statement may still suggest broader applicability than is directly validated in the manuscript. Although the synthesis framework is general in formulation, the reported experimental results are validated specifically for prototypes implemented on Rogers RO3010. Since the effective permittivity, distributed inductance/capacitance, coupling behavior, unloaded quality factor, and attainable bandwidth ratio are all influenced by substrate properties, any change of substrate requires a new optimization of the resonator dimensions and coupling distances. In the revised manuscript, we have therefore moderated the corresponding statements and now explicitly indicate that the reported performance is substrate-specific and that a change of substrate requires re-optimization of the design. This clarification has been incorporated in the substrate discussion and reinforced in the conclusions.
Added sentence in abstract
The proposed methodology is experimentally validated for prototypes implemented on Rogers RO3010. Although the synthesis procedure is general in formulation, any change of substrate requires re-optimization of the SRR dimensions, couplings, and achievable bandwidth ratio.
Added sentence in Section 3.1
The experimental validation presented in this work is specific to the Rogers RO3010 substrate. Since the effective permittivity, distributed inductance/capacitance, coupling strength, and loss mechanisms depend on the substrate properties, any change of substrate requires re-optimization of the SRR dimensions, coupling distances, unloaded quality factor, and attainable BWR range. Therefore, the results reported here should be interpreted as substrate-specific validations of the proposed design methodology.
Added sentence in Conclusions
All numerical and experimental demonstrations reported in this work correspond to implementations on Rogers RO3010; therefore, extension to a different substrate should be understood as requiring a new design optimization rather than a direct transfer of dimensions.
Second, about my optional comment, a purely qualitative discussion is not sufficient for this type of study. Fabrication tolerances are particularly critical in narrow-gap SRR-based structures. Therefore, the authors should either provide quantitative evidence, such as HFSS simulation results, showing how variations in gap and coupling dimensions affect bandwidth, resonance frequency, and S-parameters, Either explain it properly or ignore the optional comment! Without numerical or graphical support, qualitative explanations alone do not adequately demonstrate the robustness of the proposed claim.
Response to the reviewer
We thank the reviewer for this important observation. We agree that a qualitative discussion alone is insufficient for narrow-gap SRR-based structures. Accordingly, the manuscript has been revised to include quantitative HFSS-based tolerance evidence for both prototypes. A combined geometrical sensitivity analysis was performed by simultaneously perturbing the inter-ring gap, the feed-coupling gap, and the strip width by +/-0.02 mm around their nominal values. The resulting S-parameter curves and extracted response quantities show measurable changes in center frequency, bandwidth, and BWR for both filters. For the BWR 1:2 prototype, the nominal BWR of 0.514 varies between 0.581 and 0.414 under the imposed perturbations, while for the BWR 2:1 prototype the nominal BWR of 1.973 varies between 2.108 and 1.812. These results confirm that the proposed narrow-gap SRR-based structures are sensitive to realistic fabrication deviations, particularly in the dimensions governing the asymmetric response. The corresponding discussion in the manuscript has therefore been revised and is now presented as a quantitative sensitivity assessment in a new section.
Added Section
3.3. Sensitivity to fabrication tolerances
To quantify the effect of fabrication tolerances on the proposed SRR-based filters, a combined geometric sensitivity analysis was carried out for both prototypes by simultaneously perturbing the most critical dimensions of the structure by ±0.02 mm around their nominal values. In particular, the inter-ring gap, the feed-coupling gap, and the strip width were varied together in order to emulate a realistic fabrication deviation affecting the narrow coupling regions of the filters. For each perturbed case, the corresponding S parameters were recomputed, and the main response quantities were extracted, namely the center frequencies of the two passbands, the 3-dB bandwidths, the return loss, and the BWR.
Fig.11 and Fig.12, together with Table 10 and Table 11, summarize the effect of the combined geometrical perturbation on the prototypes with BWR 1:2 and BWR 2:1, respectively. For the BWR 1:2 prototype, the nominal response exhibits center frequencies of 1.908 GHz and 2.384 GHz, with bandwidths of 284 MHz and 146 MHz, giving BWR = 0.514. Under the $-0.02$ mm perturbation, the response shifts to 1.986 GHz and 2.342 GHz and the BWR increases to 0.581, whereas for the +/-0.02 mm perturbation the upper passband shifts upward to 2.452 GHz, its bandwidth decreases to 118 MHz, and the BWR is reduced to 0.414. For the BWR 2:1 prototype, the nominal case yields center frequencies of 1.920 GHz and 2.384 GHz, with bandwidths of 146 MHz and 288 MHz, giving BWR = 1.973. When the dimensions are simultaneously reduced by 0.02 mm, the BWR increases to 2.108, whereas for the $+0.02$ mm perturbation it decreases to 1.812. In both prototypes, the results show that simultaneous dimensional deviations produce measurable shifts in center frequency and bandwidth, and that the passband maintaining the asymmetric response is the most sensitive to the perturbation: the upper passband in the BWR 1:2 case and, again, the wider upper passband in the BWR 2:1 case.
Overall, the combined tolerance analysis confirms that the final response of the proposed narrow-gap SRR-based structures remains sensitive to realistic manufacturing deviations. Since the three critical dimensions were perturbed simultaneously, the obtained results should be interpreted as the cumulative effect of fabrication tolerances rather than as the isolated contribution of a single geometrical parameter. These results therefore provide quantitative support for the tolerance discussion and reinforce the practical limitations associated with tightly coupled SRR implementations, particularly in the dimensions that control the asymmetric bandwidth response.
That is consistent with broader reports showing that fabrication inaccuracies and material variations can shift the frequency response of microwave circuits, even though the exact mechanisms depend on the specific manufacturing technology.
\cite{Ferro2024} showed systematic S-parameter frequency shifts in a fabricated microstrip filter due to inaccurate milling depth, and \cite{Iman2023} described significant substrate-permittivity variation in 3D-printed microwave structures that required post-fabrication compensation.
The proposed synthesis methodology remains valid, since the target dual-band response can still be prescribed through the coupling-matrix-to-SRR design flow. However, the numerical tolerance analysis indicates that the final response is sensitive to geometric deviations in the structure's strongly coupled regions. Consistent with the design formulation, the inter-ring spacing s is expected to be especially critical, since it governs the internal SRR coupling and directly affects the resonance splitting and the bandwidth ratio. The feed-coupling gap mainly influences the external coupling and, consequently, the passband matching and the realized bandwidths. The combined results obtained for the two prototypes confirm that even small simultaneous variations of +/- 0.02 mm already produce measurable shifts in center frequency and noticeable changes in the BWR. Therefore, the method should be regarded as analytically well-defined but is sensitive to fabrication tolerances in narrow-gap regions.
Third, concerning the simulation and measurement results, the revision still does not include new figures. At present, the manuscript relies mainly on descriptive statements, which is not sufficient. In particular, experimental validation in the form of measured S-parameter plots is still missing. Additionally, the close agreement shown in Figures 6 and 9 appears somewhat idealized compared to typical microwave measurements, which usually include noise, small frequency shifts, ripple effects, and connector or calibration imperfections. To improve credibility, it is important to include actual VNA measurement screenshots along with a clear explanation of the measurement setup, calibration method, and data processing procedure. Providing only a photograph of the fabricated component is not sufficient!
Response to the reviewer
We also agree with the reviewer that the previous revision relied too heavily on descriptive statements. Following the reviewer’s suggestion, the measurement setup description has been expanded. The revised manuscript now specifies the analyzer settings available from the exported instrument file, including the measurement frequency range, calibration type, calibration method, reference planes, and reference impedance. This additional information improves the transparency and reproducibility of the experimental validation.
Second, the measured S-parameter plots are now presented more explicitly as experimental results, and the discussion has been expanded to emphasize the non-ideal features observed in practice, including insertion-loss degradation, ripple, reflection-zero shifts, and small frequency deviations. Third, raw VNA screenshots and exported measured |S_11| and |S_21| traces for both manufactured prototypes are now provided as Supplementary Material.
We believe that these additions improve the credibility and transparency of the experimental validation and make clear that the agreement between simulation and experiment is not idealized, but rather includes the expected imperfections associated with practical microwave measurements.
Once again, we thank the reviewer for these observations. We believe that the additional revisions substantially improve the manuscript by making the scope of the validation more precise, clarifying its sensitivity to fabrication tolerances, and strengthening the presentation of the experimental results.
Added sentence in Section 3.1
Measurements were obtained with an Anritsu VNA Master MS2027C/10. The measured traces were acquired over the 1.5-2.8 GHz range. A full two-port SOLT calibration was applied using a coaxial calibration line, with the reference planes set at 0 mm at both ports and a reference impedance of 50 $\Omega$. No smoothing or aperture post-processing were used in the measurement. The device under test was measured through coaxial connections identified in the instrument file as N-type connectors. The exported traces were then used to compare the measured response with the lossy HFSS simulations and the circuit model, as shown in Figs. 6 and 9. A comparison of the specifications obtained from simulation and measurements is shown in Table 4. Raw VNA screenshots and exported measured |S11| and |S21| traces for both prototypes are provided as Supplementary Material. The measured responses exhibit the non-ideal features typically expected in practical microwave measurements and therefore should not be interpreted as perfectly smooth or idealized traces. In particular, the measured results show small ripple effects, frequency shifts with respect to the simulated passbands, a reduction and displacement of the reflection zeros, and an increase in insertion loss relative to the lossy HFSS model. These discrepancies are consistent with the cumulative effect of connector transitions, calibration residuals, fabrication tolerances in narrow-gap regions, and small deviations in the realized coupling dimensions. In the present prototypes, such effects are more evident in the narrowest passband, where the response is intrinsically more sensitive to local perturbations. Therefore, the measured-to-simulated mismatch should be interpreted as a realistic manifestation of practical non-idealities rather than as an inconsistency of the proposed design methodology. Before making the final prototype, a choice on the manufacturing technology was required. Although laser drilling provides more accurate gap and strip widths, it was found to cause deeper substrate removal around the microstrip lines, which is inconsistent with the assumptions of the proposed design method. For this reason, a photolithographic process was selected. In the prototype with BWR 1:2, the main measurement-to-simulation discrepancy is concentrated in the upper passband, where the narrower bandwidth makes the response more sensitive to small deviations in coupling gaps and strip widths. This explains the larger measured insertion loss in that band and the visible ripple at the upper-frequency side of the response. A good overall agreement between the circuit model, the lossy HFSS simulation, and the measured response can still be observed in Fig. 6b). Nevertheless, the measured response shows a reduction and small displacement of the reflection zeros, as well as a local increase in S_11 around 1.97 GHz. These effects are attributed to the combined influence of fabrication tolerances in the narrow feed-coupling regions and the sensitivity of the external coupling to small geometrical deviations. As a consequence, the observed resonant behavior differs slightly from the nominal symmetric assumption used in the initial synthesis stage.
Added sentence in Section 3.2
As in the previous prototype, the measured response exhibits practical non-idealities associated with losses, coupling tolerances, and connector/coupling imperfections, although in this case the deviations are less pronounced.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors addressed all my concerns.
Author Response
Thanks
Round 3
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have adequately addressed most of the previously raised concerns and significantly improved the clarity of the manuscript. In particular, the additional explanations regarding the substrate dependency, measurement procedure, and practical implementation limitations have strengthened the technical presentation of the work.
Although actual VNA screenshots during measurement were not provided, the revised manuscript now contains sufficient methodological details and discussion to allow readers to better understand the experimental procedure and interpret the reported results. The clarifications regarding fabrication tolerances, calibration, and substrate effects are appreciated.
Overall, the manuscript is technically improved and suitable for publication in its revised form.
Thanks!
