# Miniaturization and Bandwidth Enhancement of Fractal-Structured Two-Arm Sinuous Antenna Using Gap Loading with Meandering

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## Abstract

**:**

## 1. Introduction

## 2. Antenna Principle

_{1}, the outer radius of the outermost cell, which also determines the size of the antenna. Designing a sinuous antenna as a self-complementary structure ensures that the input impedance of the antenna has a constant characteristic that is independent of frequency. This condition is expressed as:

## 3. The Proposed Antenna Design

#### 3.1. Applying the Meander Shape to a Basic Sinuous Antenna

#### 3.2. Proposed Antenna Simulation

_{m}. From Figure 6a, it can be seen that the lowest resonant frequency decreases with increasing ${A}_{m}$ until 3.5 mm. However, starting from 4 mm, the reflection coefficient value decreases to −10 dB or less after the lowest operating frequency. Figure 6b shows that the lowest operating frequency decreases as each frequency $M$ increases, especially when $M$ changes from 10 to 30, and the change in operating frequency is small when $M$ changes from 30 to 50. Figure 6c shows that the operating frequency decreases sharply from 0.62 GHz to 0.52 GHz when gap loading is used, albeit the change in gap $d$ is insignificant. Figure 6d shows that when the linewidth of the gap-loading ring is 0.5 mm, only the 0.6–0.64 GHz band of the 0.5–0.7 GHz band satisfies the reflection coefficient value (−10 dB). In addition, when the linewidth is 1 mm or more, the reflection coefficient of −10 dB is satisfied from 0.52 GHz. Figure 7a–f show the simulated current distribution results at 0.6, 0.8, 2, 5, 8, and 10 GHz. At 0.6 GHz, the current distribution shows that there is a strong current flowing outside the antenna arm and in the gap-loading ring. The current distribution at a frequency of 0.8 GHz shows a weakening of the current distribution formed on the outside of the antenna arm and the gap-loading ring compared to the 0.6 GHz current distribution. At 2 GHz, the current distribution exhibits a diminished outward current distribution in comparison to the current distribution observed at 0.8 GHz. Looking at the current distribution at 5, 8, and 10 GHz, we can see that the current distribution becomes progressively weaker from the outer cells. The outer of the proposed antenna arm and the gap-loading ring contribute to the lowest operating frequency radiation, while the cells inside the antenna contribute to the higher frequency radiation.

## 4. Experiment and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The iterative process of progressively incorporating meandering into a basic sinuous antenna configuration.

**Figure 4.**(

**a**) Structure of the antenna combined with the balun; (

**b**) top view of the balun; and (

**c**) bottom view of the balun.

**Figure 6.**Simulation results for the reflection coefficient as a function of (

**a**) amplitude constant A

_{m}; (

**b**) angular frequency M; (

**c**) gap-loading distance d; and (

**d**) gap-loading width W

_{m}.

**Figure 7.**Simulated magnitude of the current distribution for (

**a**) 0.6 GHz; (

**b**) 0.8 GHz; (

**c**) 2 GHz; (

**d**) 5 GHz; (

**e**) 8 GHz; and (

**f**) 10 GHz.

**Figure 8.**Fabricated prototype antenna: (

**a**) top view; (

**b**) side view; and (

**c**) far-field-radiation pattern measurement setup.

Parameter | Dimension | Parameter | Dimension (mm) | Parameter | Dimension (mm) |
---|---|---|---|---|---|

${R}_{1}$ | 70.8722 mm | ${S}_{01}$ | 2.168 | ${G}_{01}$ | 4.57 |

τ | 0.707 | ${S}_{02}$ | 2.069 | ${G}_{02}$ | 3.625 |

${a}_{p}$ | 90° | ${S}_{03}$ | 1.972 | ${G}_{03}$ | 2.998 |

$\delta $ | 45° | ${S}_{04}$ | 1.874 | ${G}_{04}$ | 2.596 |

$N$ | 2 | ${S}_{05}$ | 1.776 | ${G}_{05}$ | 2.222 |

Cell | 8 | ${S}_{06}$ | 1.678 | ${G}_{06}$ | 1.939 |

${A}_{m}$ | 3.5 mm | ${S}_{07}$ | 1.581 | ${G}_{07}$ | 1.704 |

${W}_{m}$ | 1 mm | ${S}_{08}$ | 1.483 | ${G}_{08}$ | 1.467 |

$M$ | 30 | ${S}_{09}$ | 1.385 | ${G}_{09}$ | 1.287 |

$d$ | 4 mm | ${S}_{10}$ | 1.287 | ${G}_{10}$ | 1.123 |

${t}_{s}$ | 12.5218 mm | ${S}_{11}$ | 1.189 | ${G}_{11}$ | 1.004 |

${t}_{e}$ | 70.0931 mm | ${S}_{12}$ | 1.091 | ${G}_{12}$ | 0.891 |

$W$ | 7 mm | ${S}_{13}$ | 0.993 | ${G}_{13}$ | 0.81 |

${S}_{14}$ | 0.896 | ${G}_{14}$ | 0.758 | ||

${S}_{15}$ | 0.798 | ${G}_{15}$ | 0.714 | ||

${S}_{16}$ | 0.7 | ${G}_{16}$ | 0.676 |

Ref. | Antenna Type | Reflection Coefficient Bandwidth (GHz)/Fractional Bandwidth (%) | Gain (dBi) | Antenna Width × Length $\left({\mathit{\lambda}}_{\mathit{g}}\right)$ |
---|---|---|---|---|

[22] | 4-arm sinuous w/balun | 1–10/163.6 | −1~6 | 0.495 × 0.495 |

[24] | 4-arm sinuous w/balun | 0.8~10/170.4 | N/A | 0.79 × 0.79 |

[27] | 4-arm sinuous w/balun | 0.45~6/172.1 | −1~5.5 | 0.64 × 0.64 |

[28] | 4-arm sinuous w/balun | 0.4~2/133.3 | N/A | 0.955 × 0.955 |

[38] | 4-arm sinuous on dielectric lens | 0.6~2.5/115 | 3.9~12 | 0.7 × 0.7 |

[40] | 4-arm sinuous on dielectric lens | 6~24/120 | N/A | 1.2 × 1.2 |

[23] | 2-arm sinuous w/CPWG | 0.46~4.5/162.9 | 2.9~5.7 | 0.67 × 0.63 |

[37] | 2-arm sinuous w/balun | 2~18/160 | 4.3~5.1 | 0.495 × 0.495 |

[39] | 2-arm sinuous on dielectric lens w/balun | 1~10/163.6 | 6~12 | 0.554 × 0.554 |

This work | 2-arm sinuous w/balun | 0.74~10.53/173.7 (SIM.) | 2.8~5.7 (SIM.) | 0.552 × 0.552 |

This work | 2-arm fractal-structured sinuous w/balun | 0.51~10.72/181.8 | −3.5~8.2 | 0.443 × 0.443 |

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**MDPI and ACS Style**

Kim, J.; Keun, J.; Yoo, T.; Lim, S.
Miniaturization and Bandwidth Enhancement of Fractal-Structured Two-Arm Sinuous Antenna Using Gap Loading with Meandering. *Fractal Fract.* **2023**, *7*, 841.
https://doi.org/10.3390/fractalfract7120841

**AMA Style**

Kim J, Keun J, Yoo T, Lim S.
Miniaturization and Bandwidth Enhancement of Fractal-Structured Two-Arm Sinuous Antenna Using Gap Loading with Meandering. *Fractal and Fractional*. 2023; 7(12):841.
https://doi.org/10.3390/fractalfract7120841

**Chicago/Turabian Style**

Kim, Junghyeon, Jongho Keun, Taehoon Yoo, and Sungjoon Lim.
2023. "Miniaturization and Bandwidth Enhancement of Fractal-Structured Two-Arm Sinuous Antenna Using Gap Loading with Meandering" *Fractal and Fractional* 7, no. 12: 841.
https://doi.org/10.3390/fractalfract7120841