⚡ electrical engineering

A Triple-Band Bandpass Filter Using Square Open-Loop Resonators

This paper presents the design, simulation, and characterization of a compact triple-band bandpass filter operating at 2.1 GHz, 2.2 GHz, and 2.3 GHz using nine square open-loop resonators on a Rogers RT/Duroid 6010LM substrate, demonstrating high performance with low insertion losses and validating the effectiveness of this resonator transformation technique for modern multi-band wireless systems.

Original authors: Rashmi Ravi, Bhaskarareddy N C, Augustine O. Nwajana

Published 2026-07-07

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CC BY 4.0

Original authors: Rashmi Ravi, Bhaskarareddy N C, 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 at a busy train station where three different trains (signals) need to arrive and depart at the exact same time, but they are all traveling on tracks that are dangerously close to each other. If the tracks aren't perfectly separated, the trains might crash into each other, or the wrong passengers might get on the wrong train.

In the world of wireless technology (like your phone or Wi-Fi), these "trains" are radio signals, and the "tracks" are frequency bands. Engineers need a special gatekeeper to make sure only the right signals get through while blocking the rest. This gatekeeper is called a Bandpass Filter.

Here is a simple breakdown of what Rashmi Ravi and her team at the University of Greenwich achieved in this paper:

1. The Problem: Too Many Trains, Too Little Space

Traditionally, if you wanted to handle three different signals, engineers would build three separate, bulky gates and chain them together. This is like building three separate ticket booths for three different trains. It takes up a lot of space and slows everything down (causing signal loss).

The authors wanted to build one single, compact gate that could handle three specific trains simultaneously without them crashing.

2. The Solution: A "Magic" Nine-Track Gate

The team designed a Triple-Band Bandpass Filter. Think of this as a single, highly intelligent checkpoint that can sort three different groups of passengers at once.

The Target: They wanted to sort signals at three very specific frequencies: 2.1 GHz, 2.2 GHz, and 2.3 GHz. These are like three trains arriving just 100 million seconds apart—very close together, which makes the job very hard.
The Tool: They used a special shape called a Square Open-Loop Resonator. Imagine a square race track with a small gap in it. When a signal hits this track, it "rings" like a bell at a specific pitch. By arranging these tracks just right, they can catch specific pitches.
The Design: They didn't just build three separate tracks. They took the design for one track (the 2.2 GHz one) and mathematically "stretched" and "shrunk" it to create two extra tracks for the other frequencies. They then combined them into one device using nine of these square tracks (three for each frequency).

3. How They Built It

They didn't build a physical prototype yet; they built a perfect digital model using powerful computer software (Keysight ADS).

The Material: They designed it to be printed on a special high-tech board called Rogers RT/Duroid 6010LM. Think of this as a very smooth, high-quality road that lets the signals travel fast without getting tired (losing energy).
The Tuning: They had to adjust the distance between the square tracks very precisely. If the tracks were too close, the signals would mix up. If they were too far, the signals wouldn't get through. They found the "Goldilocks" distance (about 0.75 mm to 1.25 mm) to make the magic work.

4. The Results: A Perfect Performance

When they ran the simulation, the results were impressive:

Low Loss (High Efficiency): The signals got through with very little energy lost. It's like the trains passing through the gate with almost no friction. The "loss" was less than 1.4 dB for all three bands (a very good score).
High Precision (Great Sorting): The filter was incredibly good at rejecting the wrong signals.
- For the middle train (2.2 GHz), the filter was so precise that it achieved a 33.6 dB return loss. In everyday terms, this means it was almost perfect at saying "No" to any signal that wasn't supposed to be there. It outperformed many other designs found in scientific literature.
- The other two bands (2.1 and 2.3 GHz) also performed very well, though slightly less perfectly than the center one, simply because the whole design was optimized around the middle track.

5. Why This Matters

The paper claims this design is unique because:

It's Compact: It does the job of three separate filters in one small package.
It's Smart: It uses a clever mathematical trick to turn one design into three, rather than building three from scratch.
It's Ready for the Future: It handles frequencies used by modern 4G, UMTS, and early 5G networks.

In Summary:
The authors created a digital blueprint for a tiny, super-efficient traffic cop for radio waves. This "cop" can stand at a busy intersection and perfectly sort three very similar signals without letting them crash, all while taking up very little space. While the paper focuses on the computer simulation (the blueprint), the authors plan to build the physical version next to prove it works in the real world.

Technical Summary: A Triple-Band Bandpass Filter Using Square Open-Loop Resonators

Problem Statement
The rapid evolution of wireless communication systems (4G LTE, UMTS, 5G, Wi-Fi) necessitates compact, high-performance components capable of operating across multiple frequency bands simultaneously. Conventional approaches to achieving multi-band operation typically involve cascading multiple single-band filters. However, this method increases the physical footprint of the RF front-end, introduces higher insertion losses, and adds system complexity. There is a distinct need for integrated multi-band bandpass filters (BPFs) that can isolate specific frequency bands within a wider spectrum while maintaining a compact form factor and high performance.

Methodology
The authors propose a design methodology based on the transformation of a single-band BPF into a triple-band BPF using microstrip square open-loop resonators. The process involves the following steps:

Theoretical Circuit Design: The design begins with a standard normalised Chebyshev lowpass prototype ( $g_0=1, g_1=g_3=0.8516, g_2=1.1032, g_4=1$ ). This is transformed into a single-band BPF centered at 2.2 GHz with a 6% fractional bandwidth (FBW) and 50 Ω characteristic impedance. The circuit is initially modeled using a capacitor-only network to determine component values (series inductance $L_1$ , capacitance $C_1$ , and coupling capacitances).
Multi-Band Transformation: To achieve triple-band operation, two additional filter branches are derived from the single-band design, targeting center frequencies of 2.1 GHz and 2.3 GHz. The three branches are coupled together to form a nine-pole filter (three resonators per passband).
Parameter Extraction: Theoretical mutual coupling coefficients ( $M$ ) and external quality factors ( $Q_e$ ) are calculated based on the Chebyshev prototype and the 6% FBW. These theoretical values ( $K=0.0619$ and $Q_e=14.1933$ ) serve as targets for the physical layout.
Physical Implementation: The filter is implemented on a Rogers RT/Duroid 6010LM substrate ( $\epsilon_r = 10.7$ , $\tan \delta = 0.0023$ , thickness = 1.27 mm). The design utilizes nine square open-loop resonators.
Simulation and Optimization: The layout is constructed and simulated using Keysight Advanced Design System (ADS) electromagnetic (EM) software. Practical coupling distances ( $s$ ) and tapping lengths ( $t$ ) are iteratively adjusted in the EM simulation to match the theoretical coupling coefficients and external quality factors. Three specific resonator orientations were analyzed to extract the required coupling spacing.

Key Contributions

Transformation Technique: The paper demonstrates a reproducible technique for extending a single-band BPF design into a triple-band BPF by retaining the mutual coupling network structure while adding resonator branches.
Compact Integration: The use of square open-loop resonators allows for a compact footprint suitable for integration into modern communication devices.
Narrow-Span Operation: The design successfully achieves three simultaneous passbands within a narrow 200 MHz span (2.1, 2.2, and 2.3 GHz), addressing the challenge of closely spaced channels in 4G and sub-3 GHz 5G networks.
Nine-Pole Architecture: The implementation employs nine resonators (three per band), contributing to sharper selectivity and improved inter-band rejection compared to typical dual-band designs.

Results
The EM simulation results validate the design across all three passbands:

Center Frequencies: The filter operates at 2.1 GHz, 2.2 GHz, and 2.3 GHz.
Insertion Loss (IL): The measured IL values are 0.674 dB (2.1 GHz), 0.976 dB (2.2 GHz), and 1.314 dB (2.3 GHz). The authors note a progressive increase in loss attributed to substrate dielectric loss, coupling junction discontinuities, and frequency-pulling effects at higher frequencies.
Return Loss (RL): The return losses are 16.785 dB (2.1 GHz), 33.609 dB (2.2 GHz), and 17.162 dB (2.3 GHz). The 2.2 GHz band exhibits exceptional impedance matching, significantly exceeding the standard 20 dB benchmark, as the entire design was optimized around this frequency.
Selectivity: Two transmission zeros are observed at 2.139 GHz and 2.275 GHz, providing sharp attenuation between the passbands.
Comparison: When compared to state-of-the-art dual-band and multi-band filters in the literature, this design is unique in achieving triple-band operation from a single-band transformation technique within such a narrow frequency span, while achieving the highest return loss (33.609 dB) among the compared works.

Significance and Claims
The paper claims that the proposed filter offers a straightforward and effective solution for modern multi-band wireless systems, specifically targeting 4G LTE, UMTS, and sub-3 GHz 5G applications. The significance lies in the ability to integrate three distinct passbands into a single microstrip component without the size penalty of cascaded filters. The authors highlight that the 2.2 GHz center frequency is achieved with high precision, and the design methodology is fully reproducible and extensible to other bands or higher-order filters.

Future Work
The authors identify the immediate next step as the physical fabrication and measurement of the prototype to validate simulation results against real-world factors such as substrate thickness variation, metal surface roughness, and connector effects. They also suggest potential extensions, including:

Scaling the design for quad-band or higher-order filters.
Further miniaturization using folded-arms square open-loop resonators (FASOLR).
Integration with filtering power-divider technology.
Reconfiguring the operating frequencies for other bands (e.g., 3.5 GHz 5G NR, 2.4 GHz Wi-Fi) by scaling resonator dimensions.

1. The Problem: Too Many Trains, Too Little Space

2. The Solution: A "Magic" Nine-Track Gate

3. How They Built It

4. The Results: A Perfect Performance

5. Why This Matters

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