Six-Pole Dual-band Bandpass Filter for WiMAX Applications

Augustine O. Nwajana; Halimat Olamide Yusuf

REVIEW

Six-Pole Dual-band Bandpass Filter for WiMAX Applications

Halimat Olamide Yusuf, Augustine O. Nwajana

Signal Processing · Submitted 8 Jul 2026 · 23 references

Pith's verdict: Competent but incremental dual-band filter design; the synthesis claim is underspecified.

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arXiv ID2607.07661 (version 1)

Pith IDGYIHA6AR, Pith's permanent record of this paper and its review

CitationAugustine O. Nwajana, Halimat Olamide Yusuf. "Six-Pole Dual-band Bandpass Filter for WiMAX Applications." arXiv:2607.07661 (2026). https://pith.science/paper/GYIHA6AR

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Editor's note

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Short version: this is a workmanlike conference paper that builds a six-pole dual-band microstrip filter using FASOLR resonators for WiMAX at 2.3 GHz. The simulations show the intended dual-band response, but the paper's claim of a 'structured synthesis route' from single-band to dual-band is not actually backed by a derivation. It's a topology description, not a synthesis method. For a conference venue it's acceptable; for a journal it would need work. I lean toward a serious referee if the authors are willing to address the synthesis gap. What's new and done well: the specific configuration of three poles per band using FASOLR at 2.3/2.4 GHz is a legitimate new data point. The circuit-level and EM simulations agree reasonably, and the filter achieves return loss better than 10/19 dB and insertion loss under 1.5 dB in both bands. The footprint (0.62 λg × 0.42 λg) is competitive for a six-resonator structure, and the comparison table places the work in context. The FASOLR structure is properly cited to [23], and the Chebyshev prototype synthesis follows Hong's textbook [3] correctly. The soft spots are real but proportionate. The main one: the paper claims a 'structured higher-order synthesis route in which the poles of each band are directly derived from the single-band prototype,' but never shows the math. Adding three resonators (A1, B1, C1) coupled to the main line with the same coupling coefficient k = 0.0722 is described, but there's no frequency transformation, no coupling matrix, and no explanation of why this topology yields two passbands rather than one six-pole passband. The stress-test concern lands here. The bandwidth deviation reinforces this: the designed 7% FBW becomes 5.13%/6.17% at circuit level — a ~27% error before EM effects even enter. If the synthesis were predictive, the circuit-level response should match the target. The authors attribute this to inverter approximation, which is plausible but underscores that the method doesn't fully predict outcomes without empirical tuning. No measured results, which limits validation to simulation. This is a conference paper (GICITE 2026), and for that venue it's fine. If the authors are targeting a journal, they need to either provide the dual-band transformation derivation or drop the 'structured synthesis' framing and present this as an empirical design with simulation validation. The reader's CONDITIONAL verdict and moderate confidence are about right. I'd add a serious referee is warranted if the authors can strengthen the synthesis argument or reframe the contribution honestly.

Referee report

Major objections (3)

§I and §II: The central methodological claim is that a three-pole single-band BPF is 'transformed' into a six-pole dual-band BPF through a 'structured higher-order synthesis route in which the poles of each band are directly derived from the single-band prototype' (§I). However, the paper does not provide the mathematical mechanism for this transformation. Standard dual-band filter synthesis requires either an explicit frequency transformation (e.g., lowpass-to-dual-band mapping) or a coupling-matrix synthesis that allocates poles to each band. The paper instead describes the transformation at the circuit-topology level as adding three resonators with the same coupling coefficient k = 0.0722 (Eq. 1) used for the original inter-resonator couplings. No justification is given for why this particular topology and uniform coupling value produces two distinct passbands rather than a single six
§IV, Figure 5 and associated text: The realized fractional bandwidths (5.13%/6.17% for circuit, 5.09%/5.48% for EM) deviate substantially from the 7% design target—a 20–27% shortfall. The authors attribute this to admittance-inverter approximation and physical coupling adjustments, but these are expected effects that should be quantified or bounded during design, not only observed post-simulation. If the synthesis route is to be presented as structured and generalizable, the authors should either (a) provide sensitivity analysis showing how inverter approximation maps to bandwidth error, or (b) revise the claim to reflect that empirical post-layout tuning is required to achieve the target response. As stated, the gap between the 7% claim and the realized values undermines the design methodology's reproducibility.
§IV: No fabricated prototype or measured results are presented. The abstract states the filter 'is implemented' on Rogers RT/Duroid 6010LM, but only simulation results are shown. For a conference paper this may be acceptable, but the language should be corrected to accurately reflect that this is a simulation-only study. The performance comparison in Table I places this work alongside designs with measured results, which could mislead readers about the validation level achieved.

Minor objections (6)

Reference [3]: The author name is listed as 'Jia-Sheng Hong and Jia-Sheng Hong,' which is a duplication. This should be corrected to 'Jia-Sheng Hong.'
§II: The capacitor-only network values (C = 16.8368 pF, L = 0.2844 nH, C01 = 1.3840 pF, C12 = 1.2159 pF) are given without showing the intermediate equations or the inverter-to-capacitor conversion formulas. Including these or citing the specific equations from [3] would help reproducibility.
Table I: The 'TL' column header is unclear. Based on the footnote, it appears to indicate the transmission-line technology (MS = microstrip, SIW = substrate-integrated waveguide). A clearer header (e.g., 'Technology') would improve readability.
§III, Eq. (1)–(2): The coupling coefficient is denoted 'K' in Eq. (1) but 'k' in the surrounding text. Consistent notation (lowercase k is standard for coupling coefficient) should be used.
Abstract: The abstract states the filter has 'a fractional bandwidth of 7%,' but the realized bandwidths are 5.09–6.17%. The abstract should clarify that 7% is the design target, not the realized value.
Figure 4: Dimensions are stated to be in mm, but the figure quality and labeling should be verified to ensure all critical dimensions (coupling gaps, resonator widths) are labeled legibly.

Simulated authors' rebuttal

read the rebuttal and 3 point-by-point responses

We thank the referee for a careful and constructive review. The referee raises three major points: (1) the absence of a mathematical derivation for the single-to-dual-band transformation, (2) the bandwidth shortfall relative to the 7% design target and the lack of sensitivity analysis, and (3) the absence of measured results and potentially misleading language about the validation level. We agree that all three points identify genuine weaknesses in the manuscript as currently presented. We will revise the manuscript to add a coupling-matrix-based explanation of the transformation, provide quantitative discussion of the bandwidth deviation, and correct the language to accurately reflect the simulation-only nature of the study. We cannot fully resolve the referee's concern about generalizability of the synthesis route within the scope of a conference paper, as a complete mathematical framework would require a full journal-length treatment.

Referee: §I and §II: The central methodological claim is that a three-pole single-band BPF is 'transformed' into a six-pole dual-band BPF through a 'structured higher-order synthesis route in which the poles of each band are directly derived from the single-band prototype.' However, the paper does not provide the mathematical mechanism for this transformation. Standard dual-band filter synthesis requires either an explicit frequency transformation or a coupling-matrix synthesis that allocates poles to each band. The paper instead describes the transformation at the circuit-topology level as adding three resonators with the same coupling coefficient k = 0.0722. No justification is given for why this particular topology and uniform coupling value produces two distinct passbands rather than a single six-pole response.

Authors: The referee is correct that the manuscript does not currently provide the mathematical mechanism underlying the single-to-dual-band transformation. We acknowledge this as a genuine gap. In the revised manuscript, we will add a subsection in §II that explains the transformation in coupling-matrix terms. Specifically, the three auxiliary resonators (A1, B1, C1) are coupled to their corresponding main-line resonators (A, B, C) with the same inter-resonator coupling coefficient k derived from the Chebyshev prototype. This auxiliary coupling splits each original pole into a pole pair: the main-line resonator and its auxiliary partner form a two-resonator coupled system whose even and odd resonant modes straddle the original resonance frequency. Because all three main-line resonators undergo this splitting simultaneously, the original three-pole passband becomes two three-pole passbands—one associated with the lower (even-mode) branch and one with the upper (odd-mode) branch of each pair. The uniform coupling value k = 0.0722 determines the inter-band separation, while the main-line couplings (A–B, B–C) preserve the Chebyshev pole allocation within each band. We will make this mechanism explicit in the revised text and include the corresponding coupling-matrix structure. We will also soften the claim of 'generalizable synthesis route' to reflect that the transformation is demonstrated for the Chebyshev third-order case and that extension to other prototypes would require further derivation. revision: yes
Referee: §IV, Figure 5 and associated text: The realized fractional bandwidths (5.13%/6.17% for circuit, 5.09%/5.48% for EM) deviate substantially from the 7% design target—a 20–27% shortfall. The authors attribute this to admittance-inverter approximation and physical coupling adjustments, but these are expected effects that should be quantified or bounded during design, not only observed post-simulation. If the synthesis route is to be presented as structured and generalizable, the authors should either (a) provide sensitivity analysis showing how inverter approximation maps to bandwidth error, or (b) revise the claim to reflect that empirical post-layout tuning is required to achieve the target response.

Authors: The referee's observation is accurate: the realized bandwidths fall 20–27% short of the 7% target, and the current manuscript only explains this deviation qualitatively after the fact. We agree that this is insufficient for a methodology presented as structured and reproducible. In the revision, we will adopt option (b): we will revise the language to state clearly that the 7% value is the initial design specification derived from the Chebyshev prototype, and that empirical post-layout adjustment of the physical coupling spacings is required to approach the target bandwidth. We will also add a brief quantitative discussion of the inverter approximation error: the capacitor-only network approximates an ideal admittance inverter over a finite bandwidth, and the effective inverter parameter J(f) varies with frequency, leading to a realized coupling coefficient that is approximately 5–7% lower than the target k = 0.0722 at the band edges. This maps to a bandwidth reduction consistent with the observed 5.09–6.17% range. We will include this sensitivity discussion in §IV and adjust the abstract to state the realized bandwidths rather than only the 7% design target. revision: yes
Referee: §IV: No fabricated prototype or measured results are presented. The abstract states the filter 'is implemented' on Rogers RT/Duroid 6010LM, but only simulation results are shown. For a conference paper this may be acceptable, but the language should be corrected to accurately reflect that this is a simulation-only study. The performance comparison in Table I places this work alongside designs with measured results, which could mislead readers about the validation level achieved.

Authors: The referee is correct. The manuscript uses the phrase 'is implemented' in the abstract and 'has been designed and realized' in the conclusion, which overstates the validation level achieved. No physical prototype was fabricated, and no measured S-parameters were obtained. We will revise the language throughout the manuscript—abstract, §IV, and conclusion—to state that the filter was 'designed and simulated' on the specified substrate, and that results are from circuit-level and full-wave electromagnetic simulations only. Regarding Table I, we will add a column or a footnote explicitly indicating the validation type (simulation vs. measurement) for each entry, including our own work, so that readers can correctly assess the comparison. We note that fabrication and measurement are planned as future work but cannot be included in this revision. revision: yes

Objections the simulated rebuttal did not resolve

The referee's underlying concern about generalizability of the synthesis route cannot be fully resolved within the scope of a conference paper. A complete mathematical framework—deriving the transformation for arbitrary filter order, arbitrary prototype, and arbitrary band spacing—would constitute a journal-length contribution. We will provide the coupling-matrix explanation for the specific third-order Chebyshev case demonstrated and will scope the claims accordingly, but we cannot claim a fully general derivation.

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The paper

The paper claims

Three-Pole Filter Doubled to Six-Pole Dual-Band at 2.3 GHz

The reading

This paper presents a method for converting a standard three-pole single-band bandpass filter into a six-pole dual-band bandpass filter by adding three additional resonators coupled to the main signal path. The authors use a Folded-Arms Square Open-Loop Resonator (FASOLR) microstrip structure—a compact variant of the conventional half-wavelength resonator—to implement the design on a Rogers RT/Duroid 6010LM substrate. The resulting filter produces two passbands centered at approximately 2.2 GHz and 2.4 GHz, with three transmission poles allocated to each band, yielding sharper selectivity than typical second-order dual-band designs. The approach is validated through circuit-level and electromagnetic simulations that show good agreement, with return loss better than 10 dB in the first band and 19 dB in the second, and insertion loss below 1.5 dB across both bands.

What carries the argument

FASOLR (Folded-Arms Square Open-Loop Resonator): a microstrip resonator formed by folding the arms of a square open-loop resonator inward, reducing side length to ~λg/10; admittance inverter (J-inverter) replaced by capacitor-only coupling network; Chebyshev low-pass prototype with element values g0=g4=1.0, g1=g3=0.8516, g2=1.1032; frequency-splitting technique for extracting practical coupling coefficients from EM simulation.

Extended reading notes

Core claim

The central claim is that a dual-band bandpass response can be structurally derived from a single-band prototype by duplicating the three-resonator chain and coupling the duplicate set to the main line, raising the filter order from three to six and splitting the single passband into two symmetric bands. The FASOLR geometry serves as the enabling physical structure: by folding the arms of a square open-loop resonator inward, the side length shrinks to roughly one-tenth of a guided wavelength, achieving approximately 20% size reduction over the unfolded version. The paper reports that this synthesis route produces two passbands symmetric about the 2.3 GHz design frequency, each carrying three

Load-bearing premise

The paper assumes that coupling three additional resonators to the main signal path will naturally produce the intended dual-band behavior with three poles per band, without requiring independent tuning of the inter-pair coupling. The realized bandwidths deviate from the 7% design target, which the authors attribute to the approximation of ideal admittance inverters and physical coupling adjustments—indicating the synthesis route does not yield target specifications without

Editorial extensions

If this is right

The single-to-dual-band conversion principle could extend to tri-band or multi-band filters by adding further resonator sets coupled to the main chain, each set contributing additional poles.
The FASOLR geometry's compactness (~λg/10 side length) on high-permittivity substrates makes it a candidate for filter miniaturization in space-constrained RF front-ends beyond WiMAX.
The discrepancy between designed (7%) and realized (5.09–6.17%) fractional bandwidths suggests that the capacitor-only admittance inverter approximation introduces systematic bandwidth compression that could be characterized and compensated in future designs.
Higher-order dual-band filters (e.g., four poles per band) could be explored using the same duplication-and-coupling approach, potentially improving selectivity further at the cost of larger footprint.

Original abstract

Recent advances in multi-band wireless communication systems have driven the increasing need for dual-band bandpass filters. These types of filters are capable of isolating a small section of the frequency spectrum within a broader spectrum. Over the years, coplanar waveguide, microstrip, slotline, stripline, and other planar transmission line technologies have been widely employed in the design of microwave circuits and systems. This work employs a Folded-Arms Square Open-Loop Resonator (FASOLR) microstrip planar structure, designed and simulated using PathWave Advanced Design System (ADS). A third order (three-pole) single bandpass filter is transformed into a sixth order (six-pole) dual-band bandpass filter. The proposed six-pole dual-band bandpass filter is centred at 2.3 GHz, with a fractional bandwidth of 7% and produces two passbands centred at approximately 2.2 GHz and 2.4 GHz. The design is implemented on a commercially available Rogers RT/Duroid 6010LM substrate with a dielectric constant of 10.7, a loss tangent of 0.0023, a substrate thickness of 1.27 mm, and 35 micro meter copper cladding on both sides. The overall filter component has a compact footprint of 30.56 mm by 20.56 mm. The design is validated through comparison of circuit-level and electromagnetic (EM) simulation results, which show good agreement. The EM simulation responses indicate a return loss better than 10 dB on the first band and better than 19 dB on the second, and an insertion loss better than 1.5 dB, demonstrating its suitability for WiMAX applications.

Figures

**Figure 2.** a, in which the shunt resonators are formed by equal capacitance C and inductance L, and the inter-resonator coupling is provided by the capacitor networks C01 and C12. The single-band network is then converted into the corresponding six-pole dual-band configuration shown in Figure 2b. The conversion is achieved by extending the circuit, with an additional set of three resonators coupled to the main-line resonators through a similar capacitor-only mutual-coupling network, thereby raising the filter order from three to six and producing the dual-band response. The resulting capacitor…

**Figure 3.** Filter coupling arrangements: (a) three-pole single-band; (b) sixpole dual-band. K = FBW √g1g2 = 0.0722 (1) Qext = g0g1 FBW = 12.17 (2) With the coupling arrangements of

**Figure 4.** Microstrip layout of the proposed six-pole dual-band bandpass filter (dimensions in mm). IV. RESULTS AND DISCUSSION This section presents and discusses the simulation results for the proposed six-pole dual-band bandpass filter. The circuit-level (theoretical) response is examined first, followed by the electromagnetic (EM) (practical) response. A comparison between the theoretical and practical responses is then presented to validate the microstrip realisation. The theoretical S-parameter response is shown in Figure 5a. The filter exhibits two passbands positioned symmetrically…

**Figure 5.** b. As in the theoretical case, the filter exhibits two passbands positioned symmetrically about the 2.3 GHz design frequency, separated by a deep inter-band rejection at the centre, with the first passband centred near 2.2 GHz and the second near 2.4 GHz. The return loss remains better than 10 dB across the first passband and better than 19 dB across the second, with an insertion loss better than 1.5 dB in both bands, confirming that the practical microstrip implementation preserves the dual-band response established at the circuit level. The theoretical and practical responses are…

Showing 4 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2607.07661 by the authors.

References

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Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [23]

A. O. Nwajana and E. R. Obi, “Application of Compact Folded - Arms Square Open -Loop Resonator to Bandpass Filter Design,” Micromachines (Basel). , vol. 14, no. 2, Feb. 2023, doi: 10.3390/mi14020320

View on Pith doi:10.3390/mi14020320 2023

[2] [3]

Jia-Sheng Hong and Jia -Sheng Hong, Microstrip Filters for RF / Microwave Applications, 2nd ed., vol. 235. John Wiley & Sons, Incorporated, 2011. Accessed: Feb. 14, 2026. [Online]. Available: https://ebookcentral.proquest.com/lib/gre/detail.action?docID=64 4868&accountid=15997

View on Pith 2011

[3] [1]

G. Karimi, Y. Pourasad, A. Lalbakhsh, H. Siahkamari, and B. Mohamadzade, “Design of a compact ultra-narrow band dual band filter for WiMAX application,” AEU - International Journal of Electronics and Communications, vol. 110, no. 9, p. 152827, Oct. 2019, doi: 10.1016/j.aeue.2019.152827

View on Pith doi:10.1016/j.aeue.2019.152827 2019

[4] [2]

M. Pal, J. Chatterjee, and R. Ghatak, “A compact dual band bandpass filter for WLAN/WiMAX application,” 2011 IEEE Applied Electromagnetics Conference, AEMC 2011 , 2011, doi: 10.1109/AEMC.2011.6256879

View on Pith doi:10.1109/aemc.2011.6256879 2011

[5] [4]

E. Shankar, K. V. Phani Kumar, and V. K. Velidi, “Design of High Selectivity Compact Dual -Band Bandpass Filter with Seven Transmission-Zeros for GPS and WiMAX Applications,” IEEE Transactions on Circuits and Systems II: Express Briefs , vol. 70, no. 7, pp. 2395 –2399, Jul. 2023, doi: 10.1109/TCSII.2023.3238792

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