# Filtering Power Divider Design Using Resonant LC Branches for 5G Low-Band Applications

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of the Typical WPD

_{r}= 2.2 and 0.508 mm thickness.

## 3. Proposed WPD Structure

## 4. Proposed LC Branch Analysis

_{MB}. The proposed branch line has two microstrip lines with an electrical length of θ

_{1}and a series of lumped components. The ABCD matrix for the first part is noted with M

_{1}, and the ABCD matrix for the series lumped elements is noted with M

_{LMP}.

_{1}, M

_{LMP}, and M

_{MB}are written in Equations (2)–(4):

_{0}and L

_{m}. The L

_{m}with two adjacent transmission lines creates a composite line, which provides a miniaturization of the power divider. The L

_{0}C

_{0}is tuned at the central frequency (f

_{0}), as illustrated in Figure 5. Therefore, the M

_{LMP}matrix can be written in the analysis at the central frequency as (5).

_{1}can be calculated as written in (10):

## 5. Proposed WPD with LC Branch Analysis

_{1}+ length of lumped components + θ

_{1}) should be 30°, which is equal to 0.08 λ. Thus, the θ

_{1}should be approximately 15° (0.04 λ). The lengths of the lumped components (L and C) are neglected. Until now, the value of the θ

_{1}has been calculated, and to calculate the unknown parameter of Z

_{1}, from (10) and considering Z

_{0}= 50 Ω, the Z

_{1}can be determined as follows:

_{1}= 18.9 Ω. The dimensions of the proposed branches with the applied substrate of Duroid5880 substrate with ε

_{r}= 2.2 and 0.508 mm thickness are depicted in Figure 7.

_{0}and L

_{m}. The value of L

_{m}can be easily obtained from Equation (6), considering the 900 MHz operating frequency as follows:

_{1}= 18.9 Ω and w = 2π × (900 MHz), the value of L

_{m}is 11.58 nH. L

_{0}and C

_{0}can be obtained from (13), which have several answers. If we select 0.5 PF for the applied capacitor according to (13), the L

_{0}value is 62 nH:

_{0}+ L

_{m}

## 6. The Proposed Power Divider Design

#### 6.1. Typical WPD Design

#### 6.2. First Design of the Proposed WPD without Optimization

#### 6.3. Second Design of the Proposed WPD with Improvement

_{21}parameter at the operating frequency is −3.3 dB, which offers about 0.3 dB insertion loss. The S

_{11}, S

_{22}, and S

_{23}parameters are about −20 dB, which shows good divider performance at the operating frequency. The proposed WPD has noticeable performance at higher frequencies. A wide stopband has been obtained for the proposed divider from 1.8 GHz up to 40 GHz, which shows excellent harmonics suppression. The simulated results of the proposed WPD are depicted in Figure 13b.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 11.**The scattering parameters at (

**a**) operating band and (

**b**) wide frequency range for the first design of the proposed WPD with 82% size reduction.

**Figure 13.**The scattering parameters at (

**a**) operating band and (

**b**) wide frequency range of the proposed WPD with 92% size reduction.

**Figure 16.**The simulation and measurement frequency response of the proposed WPD (

**a**) at operating frequency (

**b**) in the wide frequency range.

Values | Analysis | 1st Design | 2nd Design | Fabrication |
---|---|---|---|---|

W (mm) | 5.6 | 5.3 | 3.2 | 3.2 |

L_{1} (mm) | 9.8 | 9.4 | 6.5 | 6.5 |

L (nH) | 73.5 | 66 | 68.3 | 68 |

C (pF) | 0.5 | 0.43 | 0.43 | 0.43 |

f (MHz) | 900 | 900 | 900 | 900 |

Size Reduction | 90% | 82% | 92% | 92% |

Harmonics Suppression | ∞ | 2nd–45th | 2nd–45th | 2nd–45th |

Ref | Freq (GHz) | Size Reduction | Number of Harmonics Suppression | Methods |
---|---|---|---|---|

[41] | 1 | 0% | 2nd–4th | Open stubs |

[42] | 2.4 | 70% | 2nd–5th | EBG Cells |

[43] | 1.5 | 0% | 2nd–3rd | DGS Cells |

[44] | 2.4 | 39% | 2nd-3rd | EBG Cells |

[45] | 0.9 | 66% | 2nd–3rd | Coupled Line |

[46] | 1.5 | 0% | 2nd–3rd | Lumped Capacitor |

[47] | 2.4 | 44% | 2nd–3rd | Resonator Cell |

[48] | 0.9 | 47% | 3rd | Resonator Cell |

[49] | 1 | 55% | 2nd–5th | Open Stubs |

[50] | 2.65 | 63% | 3rd and 5th | Open Stubs |

[51] | 1 | 54% | 2nd–7th | Open Stubs |

[52] | 1 | 71% | 2nd–12th | Resonator Cell & Open Stubs |

[53] | 1 | 0% | 2nd–3rd | Open Stubs |

[54] | 1 | 0% | 2nd | Open And Short Stubs |

[55] | 2 | 0% | 2nd | Resonator Cell & Open Stubs |

[56] | 1.9 | 55 % | 2nd–4th | Resonator Cell |

[57] | 1.5 | 52% | 3rd–6th | Lumped Element & Resonator Cell |

[58] | 2.4 | 0% | 2nd–3rd | Resonator Cell |

[59] | 1.5 | 16% | 3rd–4th | Lumped Capacitor |

[60] | 1 | 60% | 2nd–4th | Lumped Inductor |

[61] | 1.65 | 35% | 3rd and 5th | Open Stubs |

[62] | 0.9 | 0% | 2nd–4th | Open And Short Stubs |

[63] | 2 | 50% | 2nd–14th | Resonator Cell |

[64] | 0.7 | 73% | 2nd–15th | Aperiodic Open Stubs |

[65] | 0.8 | 82.8% | 2nd–25th | LC Branches |

This Work | 0.9 | 92% | 2nd–45th | LC Branches |

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**MDPI and ACS Style**

Roshani, S.; Yahya, S.I.; Alameri, B.M.; Mezaal, Y.S.; Liu, L.W.Y.; Roshani, S. Filtering Power Divider Design Using Resonant LC Branches for 5G Low-Band Applications. *Sustainability* **2022**, *14*, 12291.
https://doi.org/10.3390/su141912291

**AMA Style**

Roshani S, Yahya SI, Alameri BM, Mezaal YS, Liu LWY, Roshani S. Filtering Power Divider Design Using Resonant LC Branches for 5G Low-Band Applications. *Sustainability*. 2022; 14(19):12291.
https://doi.org/10.3390/su141912291

**Chicago/Turabian Style**

Roshani, Saeed, Salah I. Yahya, Ban M. Alameri, Yaqeen Sabah Mezaal, Louis W. Y. Liu, and Sobhan Roshani. 2022. "Filtering Power Divider Design Using Resonant LC Branches for 5G Low-Band Applications" *Sustainability* 14, no. 19: 12291.
https://doi.org/10.3390/su141912291