⚡ electrical engineering

Six-Pole Dual-band Bandpass Filter for WiMAX Applications

This paper presents the design and simulation of a compact six-pole dual-band bandpass filter using a Folded-Arms Square Open-Loop Resonator (FASOLR) microstrip structure on a Rogers RT/Duroid 6010LM substrate, which successfully achieves two passbands centered at approximately 2.2 GHz and 2.4 GHz with low insertion and return losses suitable for WiMAX applications.

Original authors: Halimat Olamide Yusuf, Augustine O. Nwajana

Published 2026-07-09

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CC BY 4.0

Original authors: Halimat Olamide Yusuf, Augustine O. Nwajana

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are standing in a very crowded room where everyone is shouting different messages at once. Some people are talking about WiMAX (a type of wireless internet), and their voices are coming from two specific groups: one group is shouting at a pitch of 2.2 GHz, and another is shouting at 2.4 GHz. Everywhere else, there is just noise.

Your job is to build a "smart ear" that can hear only those two groups clearly while ignoring everyone else. This is exactly what the engineers in this paper, Halimat Olamide Yusuf and Augustine O. Nwajana, have built. They created a tiny electronic device called a Dual-Band Bandpass Filter.

Here is a simple breakdown of how they did it, using everyday analogies:

1. The Problem: Too Much Noise

In the world of wireless signals, the "airwaves" are like a busy highway. If you want to listen to two specific radio stations (2.2 GHz and 2.4 GHz) without hearing the traffic noise in between, you need a filter. Most old filters could only pick up one station at a time, or they were too big and clunky to fit inside modern devices.

2. The Solution: The "Folded" Ear

The team needed a filter that could hear two distinct "voices" (frequencies) simultaneously. To do this, they used a special shape called a Folded-Arms Square Open-Loop Resonator (FASOLR).

The Analogy: Imagine a long, straight piece of string (a standard antenna). It's too long to fit in your pocket.
The Trick: First, they bent that string into a square loop (like a picture frame). This made it smaller.
The Fold: Then, they took the two ends of the string and folded them inward, like closing a book. This is the "Folded-Arms" part.
The Result: This folding trick shrank the device by about 20% compared to the square version, making it very compact. It's like folding a long map so it fits in your back pocket.

3. The Magic Trick: Turning One into Two

The most clever part of their design is how they created two listening zones from a design meant for just one.

The Starting Point: They began with a blueprint for a filter that could pick up a single frequency (a "three-pole" filter). Think of this as a single tuning fork.
The Transformation: They took that single tuning fork and "doubled" the system. They added a second set of three tuning forks that were linked to the first set.
The Result: Instead of one clear voice, the device now has six tuning forks working together. Three of them vibrate for the 2.2 GHz signal, and the other three vibrate for the 2.4 GHz signal. This creates two clear "passbands" (listening zones) with a deep silence (rejection) right in the middle, so the two signals don't mix up.

4. The Construction: A High-Tech Sandwich

To build this, they didn't use just any material. They used a special board called Rogers RT/Duroid 6010LM.

The Analogy: Think of this board as a very high-quality, dense piece of wood. Because it is so dense (high "dielectric constant"), the sound waves travel slower through it, which allows the engineers to make the "folding" even tighter.
The Size: The final device is tiny—about the size of a small postage stamp (30.56 mm by 20.56 mm). It is so small that it takes up less than half the space of a single wavelength of the signal it is designed to catch.

5. The Results: Clear Voices

When they tested their creation using computer simulations (which act like a perfect, noise-free laboratory):

Clarity: The device successfully blocked out the noise. It let the 2.2 GHz and 2.4 GHz signals pass through with very little loss (like a clear phone call).
Rejection: It completely ignored the frequencies in between the two bands.
Accuracy: The computer model matched the physical design almost perfectly, proving that their "folding" math worked.

Summary

In short, these researchers took a complex mathematical idea and turned it into a tiny, folded electronic component. It acts like a smart bouncer at a club: it checks the ID of incoming signals, lets in the two specific groups (2.2 and 2.4 GHz) that belong in the WiMAX club, and kicks everyone else out, all while fitting into a space smaller than a credit card. This makes it perfect for modern devices that need to handle multiple wireless signals without getting confused.

Technical Summary: Six-Pole Dual-Band Bandpass Filter for WiMAX Applications

Problem Statement
The rapid expansion of multi-band wireless communication systems has intensified pressure on the radio-frequency spectrum, creating a critical demand for compact components capable of operating across multiple frequency bands simultaneously. While dual-band bandpass filters (BPFs) offer a solution by selecting two distinct frequency bands within a single component—thereby reducing system size and loss—many existing designs rely on lower-order structures (typically second-order per passband). These conventional approaches often depend on geometrical or modal tuning that provides limited explicit control over transmission-pole allocation, restricting their ability to achieve sharp selectivity in crowded spectral environments.

Methodology
This work proposes a structured synthesis approach that transforms a third-order (three-pole) single-band bandpass filter into a sixth-order (six-pole) dual-band configuration. The methodology proceeds through three distinct stages:

Circuit-Level Synthesis: Starting with a normalized Chebyshev low-pass prototype, a three-pole single-band BPF is derived for a center frequency of 2.3 GHz and a fractional bandwidth of 7%. Admittance inverters (J-inverters) are introduced to realize the coupled-resonator structure and subsequently replaced by an equivalent capacitor-only network to facilitate implementation in PathWave Advanced Design System (ADS). This single-band network is then expanded by coupling an additional set of three resonators to the main-line resonators, effectively doubling the filter order to six and generating the dual-band response.
Resonator Selection: The design employs a Folded-Arms Square Open-Loop Resonator (FASOLR) microstrip planar structure. This resonator is chosen for its compact geometry, which is achieved by folding the arms of a conventional square open-loop resonator (SOLR) inwards. This evolution reduces the resonator side length to approximately one-tenth of a guided wavelength, offering a size reduction of roughly 20% compared to the SOLR.
Implementation and Simulation: The filter is implemented on a Rogers RT/Duroid 6010LM substrate (dielectric constant $\epsilon_r = 10.7$ , thickness 1.27 mm, loss tangent 0.0023). The layout is constructed using ADS, where theoretical coupling coefficients and external quality factors are calculated and then realized through physical adjustments of the coupling spacing between resonators. The design is validated through a comparison of circuit-level simulations and full-wave electromagnetic (EM) simulations.

Key Contributions

Higher-Order Synthesis: The paper introduces a conversion principle that assigns three transmission poles to each of the two passbands, providing a structured higher-order synthesis route where poles are directly derived from a single-band prototype.
Compact FASOLR Implementation: The successful integration of the FASOLR structure allows for a compact footprint of $0.62 \lambda_g \times 0.42 \lambda_g$ (30.56 mm $\times$ 20.56 mm), suitable for high-permittivity substrates.
Dual-Band Realization: The design successfully generates two passbands centered at approximately 2.2 GHz and 2.4 GHz, separated by a deep inter-band rejection notch, specifically targeting WiMAX applications.

Results
The simulation results demonstrate strong agreement between the theoretical circuit-level model and the practical EM simulation:

Frequency Response: The filter exhibits two passbands centered near 2.2 GHz and 2.4 GHz.
Performance Metrics:
- Return Loss: Better than 10 dB in the first passband and better than 19 dB in the second.
- Insertion Loss: Better than 1.5 dB across both passbands.
Bandwidth: While the design target was a 7% fractional bandwidth, the realized bandwidths were approximately 5.1% and 5.5% for the practical response. The authors attribute this deviation to the frequency-dependent nature of the capacitor-only network used to approximate ideal admittance inverters and minor discrepancies in realized coupling coefficients.
Loss Factors: The practical response shows slightly higher insertion loss and shallower rejection compared to the theoretical model, which the authors attribute to conductor and dielectric losses included in the full-wave EM simulation but absent in the idealized circuit model.

Significance and Claims
The paper claims that the proposed filter offers a higher-order dual-band response with three poles per band, resulting in sharper selectivity than most reported designs which typically utilize second-order structures. While the physical footprint is larger than some ultra-compact designs (e.g., those using substrate-integrated waveguides), the authors assert that the size remains competitive for a six-resonator structure. The work is positioned as a viable solution for modern multifunctional WiMAX communication systems where two closely spaced sub-bands must be selected within a broader spectrum, demonstrating that the conversion of single-band prototypes to higher-order dual-band filters is a feasible and effective design strategy.