# A Super-Efficient GSM Triplexer for 5G-Enabled IoT in Sustainable Smart Grid Edge Computing and the Metaverse

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## Abstract

**:**

_{g}

^{2}, which is the smallest compared to the previous works. The proposed triplexer has very low insertion losses of 0.12 dB, 0.09 dB, and 0.42 dB at the first, second, and third channels, respectively. We achieved the minimum insertion losses compared to previous triplexers. Additionally, the common port return losses (RLs) were better than 26 dB at all channels.

## 1. Introduction

_{g}

^{2}which is the best compared to the previously reported triplexers. Moreover, having a wide fractional bandwidth (FBW) is an advantage in the design of triplexers. Our triplexer achieves an FBW of 15%, which is the best compared to the previous works. Additionally, the proposed triplexer is a low-loss microstrip device which makes it suitable for energy harvesting applications, while the majority of the previous triplexers had higher insertion losses at all channels than ours.

- (1)
- First, we propose an approach that combines the concepts of sustainable smart grid edge computing and Metaverse technology to achieve a sustainable concept;
- (2)
- Second, we describe how 5G-enabled IoT completes the digitalization process for sustainable smart grids and Metaverses, emphasizing that it is crucial for creating a sustainable infrastructure;
- (3)
- Third, we analyze the requirements for nodes in the edge layer and the edge node and highlight the need for highly efficient IoT operations with 5G. We suggest that achieving this efficiency is essential for the success of the framework;
- (4)
- Finally, we design, manufacture, and measure a new GSM triplexer that is specifically designed for 5G-enabled IoT. A GSM triplexer is a device that separates signals in the radio frequency range, and our device is particularly efficient for 5G-enabled IoT. Despite its compact size, the performance of the proposed triplexer is good as it has very low insertion losses.

_{g}

^{2}, compared to previous works. Additionally, the proposed triplexer exhibits very low insertion losses of 0.12 dB, 0.09 dB, and 0.42 dB at the first, second, and third channels, respectively, and outperforms previous triplexers. Furthermore, the common port return losses (RLs) are better than 26 dB at all channels, indicating the effectiveness of the proposed approach.

## 2. A Framework for 5G-Enabled IoT

## 3. Structure Analysis of the Proposed GSM Triplexer for 5G-Enabled IoT

_{a}, l

_{b}, l

_{c,}and l

_{d}were replaced by the inductors L

_{a}, L

_{b}, L

_{c,}and L

_{d}, respectively. The equivalent of coupled lines was approximated, while in the more accurate model we have to increase the number of inductors and capacitors.

_{1}, as follows:

_{2}can be calculated as follows:

_{3}can be obtained easily using the following equation:

_{2}in Equation (3), Z

_{3}is changed as follows:

_{4}) is:

_{0}is the impedance of terminals. According to the above equation, the scattering matrix (S) is defined by:

_{11}|

^{2}+ |S

_{21}|

^{2}= 1, the condition for decreasing the loss can be found as follows:

_{c}inductor is less important in setting the resonant frequency and achieving low losses. However, without approximation the value of this inductor would appear in Equation (11). In total, by using the last equation it is possible to simultaneously adjust the resonance frequency and apply the necessary conditions to reduce losses. Using the analyzed resonator, three BPFs were designed. Figure 4 illustrates the BPFs with their frequency responses, where all dimensions are in mm. The widths of all thin lines were 0.1 mm. The frequency responses were obtained by Advanced Design Systems using an EM simulator with 0.005 GHz linear steps. A Rogers_RT_Duroid5880 substrate with a dielectric constant of 2.22, h = 0.7874 mm and tan(δ) = 0.0009 was used to design our filters and triplexer.

_{g}× 0.045 λ

_{g}= 0.007 λ

_{g}

^{2}, where λ

_{g}is the guided wavelength calculated at 0.815 GHz.

_{1}, l

_{4}, l

_{5}, w

_{1,}and w

_{3}, while the lower channel is only impacted by changing l

_{2}. By increasing the physical length l

_{2}and width w

_{3}, some harmonics will appear. Increasing the length l

_{3}leads to the appearance of harmonics created by BPF3. Also, decreasing l

_{6}results in the appearance of the harmonics. However, the width of w

_{2}should be neither large nor small, to suppress the harmonics.

## 4. Results and Comparison

- 10 MHz to 20 GHz measurement range;
- 76 dB dynamic range;
- Accurate swept power measurements;
- 40 dB directivity bridges;
- Four independent display channels;
- Limit testing built in;
- Save/recall setup and data;
- Direct plotter or printer output.

_{O1}= 0.815 GHz, F

_{O2}= 1.58 GHz, and F

_{O3}= 2.65 GHz, with three low insertion losses of 0.12 dB, 0.09 dB, and 0.42 dB, respectively. The first and second channels were wide, with 20% and 27.2% fractional bandwidths (FBW

_{1}and FBW

_{2}), respectively. The common port return losses in the first, second, and third channels was better than 26.6 dB, 38.4 dB, and 27.1 dB, respectively. The measured losses were a little more than simulations due to copper and SMA losses. As shown in Figure 9, the isolations between channels (S

_{23}, S

_{24}, and S

_{34}) were better than −20 dB. The RLs from ports 2, 3, and 4 (S

_{22}, S

_{33,}and S

_{44}) were better than 27.7 dB, 45.1 dB, and 21.7 dB, respectively.

_{1}, IL

_{2,}and IL

_{3}were the insertion losses at the first, second, and third channels, respectively. The RLs at the first, second, and third channels were presented by RL

_{1}, RL

_{2,}and RL

_{3}, respectively. Since the design of a microstrip triplexer is more complicated and difficult than microstrip filters and diplexers, there are not many recent triplexers to compare with our design. The actual performance gain in the triplexer design depends on various factors including novel structure, designing process, compact size, low losses, high isolation, wide FBW, and agreement between the mathematical analysis, simulation, and experimental results. Therefore, it is fair to compare the performance of triplexers with the parameters presented in our comparison table. These are the same parameters that the previous works mentioned to compare and show their superiority.

_{g}

^{2}, while no triplexers with a size smaller than 0.01 λ

_{g}

^{2}have been reported yet. We obtained this achievement without any negative effects on the frequency responses. As shown in Table 2, we could minimize the losses while keeping our triplexer bandwidth reasonable. The proposed structure is novel and it is presented for the first time in this work. Its physical structure is not similar to the other previous structures. In addition, the obtained return losses are good. As can be seen, the measurement (experimental) results confirm the mathematical analysis and simulation results. Therefore, our triplexer is a novel design and has high performance compared to the previous works. Table 3 presents the parameters and components used to design the proposed triplexer.

## 5. Discussion

_{g}

^{2}, making it significantly smaller than reported microstrip triplexers, which typically could not achieve a size less than 0.01 λ

_{g}

^{2}. Despite its compact size, our triplexer has good performance, with very low insertion losses at the first, second, and third channels, which are 0.12/0.09/0.42 dB, respectively. The common port return loss (RL) at the first, second, and third channels is good, and better than 26/38/27 dB, respectively. To achieve this good performance, we designed a resonator consisting of three pairs of coupled lines that were mathematically analyzed to tune the resonance frequency and reduce losses. We also optimized the physical dimensions of the triplexer to further improve its performance.

## 6. Conclusions

_{g}

^{2}= 555 mm

^{2}.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Proposed framework for enabling immersive interactions among diverse consumers. The framework incorporates cloud servers, edge computing layers, 5G-enabled IoT technology, and a triplexer to facilitate seamless communication between various types of consumers. The integration of the metaverse and the smart grid network enables the efficient management of complex systems.

**Table 1.**The features of the previous triplexers (WLANs: Wireless Local Area Networks, WiMAX: Worldwide Interoperability for Microwave Access).

Refs. | Basic Resonator | Applications | Advantages | Disadvantages |
---|---|---|---|---|

[13] | Coupled meandrous lines | GSM, WLANs | Wide channels | Large size, high losses |

[14] | Star-junction topology | WiMAX | Attenuated harmonics | Large size, high losses |

[15] | Asymmetric split-ring | WiMAX | --- | Large size, high insertion loss |

[16] | Parallel coupled line | GSM | High isolation | Large size, high insertion loss, narrow channels |

[17] | Common triple mode | GSM | --- | Large size, high insertion loss, narrow channels |

[18] | Multimode net type | Wireless | High selectivity | Large size, high losses |

[19] | Coupled step impedance | 4G, WiMAX | Low losses | Large size |

[20] | Zigzag coupled lines | GSM, WLANs | --- | Large size |

[21] | Open loop | GSM, WiMAX | Good return loss | Large size, high insertion loss |

[22] | Coupled lines | GSM, WiMAX | Good return loss | Large size, high insertion loss |

[23] | Quarter-wave | GSM, WiMAX | Good return loss | Large size, high insertion loss |

Refs. | F_{O1}/F_{O2}/F_{O3}(GHz) | IL1/IL2/IL3(dB) | RL1/RL2/RL3(dB) | FBW1, FBW2, FBW3 | Size (λ _{g}^{2}) |
---|---|---|---|---|---|

This Triplexer | 0.81/1.58/2.65 | 0.12/0.09/0.42 | 26.6/38.4/27.1 | 20%, 27.2%, 5% | 0.007 |

[3] | 3.2/3.7/4.4 | 2.7, 2.5, 1.8 | 16/16/16 | 6.5%, 7%, 8% | 0.048 |

[15] | 1.2/1.8/2.4 | 1.3/1.3/1.2 | 11.6/14/10 | 14.4%, 14%, 13.6% | 0.055 |

[16] | 3.3/3.89/4.56 | 2.2/2.3/2.3 | Better than 14 | --- | 0.275 |

[17] | 2.15/2.95/3.8 | 2.2/1.9/1.7 | Better than 20 | --- | 0.0164 |

[18] | 1.5/1.7/1.9 | 4.9/5.8/5.95 | --- | 3.3%, 2.9%, 3.6% | 0.132 |

[19] | 1.88/2.1/2.6 | 1.3/2.3/3.2 | 22/25/21 | 0.86%, 1.4%, 0.96% | 0.1 * |

[20] | 1/1.25/1.5 | 2.7/1.8/3.2 | Better than 16 | 9.5%, 4.2%, 4.5% | 0.064 |

[21] | 2.67/3.1/3.43 | 0.72/0.63/0.71 | 24.5/24/24.7 | --- | 0.137 |

[22] | 0.9/2.4/5.5 | 0.7/1.7/1.5 | --- | --- | --- |

[23] | 1.8/3.2/4.4 | 1.97/1.99/2.3 | 24/22/25 | 7.44%, 7.45%, 6.2% | 0.177 |

[24] | 1.4/1.8/3.2 | 0.1/2/1 | 25/20/20 | 5.2%, 2.8%, 9.4% | 0.014 |

[25] | 1.75/2.35/3.68 | 1.3/1.4/1.7 | 20/25/30 | 5.7%, 8.5%, 6.8% | 0.027 |

[26] | 1.45/2.15/2.75 | 3.6/4.3/4.8 | 15/20/15 | 6%, 6%, 4% | 0.020 |

[27] | 2.4/3.5/5.2 | 2.42/1.62/1.95 | Better than 15 | 3%, 7%, 3% | 0.164 |

[28] | 2.3/3.2/3.6 | 0.78/1.1/0.62 | 19.8/10/28 | 5.2%, 5.5%, 1.6% | 0.095 |

[29] | 2.05/2.45/3.5 | 1.5/1.8/1.5 | Better than 13 | 4.8%, 4%, 5.7% | 0.346 |

[35] | 2.1/2.5/3 | 1.4/1.8/1.6 | --- | --- | 0.052 |

Substrate | Rogers RT/Duroid 5880 |
---|---|

ε_{r} | 2.22 |

h | 0.7874 mm |

tan(δ) | 0.0009 |

The software used to obtain the simulation results | Advanced Design Systems (ADS) |

The device used to measure the experimental results | HP8757A network analyzer |

Dimensions | Exactly like the proposed BPFs |

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## Share and Cite

**MDPI and ACS Style**

Jamshidi, M.; Yahya, S.I.; Nouri, L.; Hashemi-Dezaki, H.; Rezaei, A.; Chaudhary, M.A.
A Super-Efficient GSM Triplexer for 5G-Enabled IoT in Sustainable Smart Grid Edge Computing and the Metaverse. *Sensors* **2023**, *23*, 3775.
https://doi.org/10.3390/s23073775

**AMA Style**

Jamshidi M, Yahya SI, Nouri L, Hashemi-Dezaki H, Rezaei A, Chaudhary MA.
A Super-Efficient GSM Triplexer for 5G-Enabled IoT in Sustainable Smart Grid Edge Computing and the Metaverse. *Sensors*. 2023; 23(7):3775.
https://doi.org/10.3390/s23073775

**Chicago/Turabian Style**

Jamshidi, Mohammad (Behdad), Salah I. Yahya, Leila Nouri, Hamed Hashemi-Dezaki, Abbas Rezaei, and Muhammad Akmal Chaudhary.
2023. "A Super-Efficient GSM Triplexer for 5G-Enabled IoT in Sustainable Smart Grid Edge Computing and the Metaverse" *Sensors* 23, no. 7: 3775.
https://doi.org/10.3390/s23073775