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In this article, a Fibonacci circle fractal is inscribed into a circular radiator in order to provide ultra-wideband behavior as well as a 50% size reduction compared to a conventional circular monopole. The third iteration of the Fibonacci series allows the antenna to obtain a steady S11 parameter over the operation bandwidth, going from 2.7 GHz to 14 GHz, an average gain around 1 dB, with a quasi-omnidirectional radiation pattern and a group delay no bigger than 1 ns, suitable for short-pulsed communications.

According to FCC regulations, communications based of short pulses need ultra-wideband devices in order to fulfill the required bandwidth without introducing dispersion, which is why UWB antennas must introduce small levels of group delay over a bandwidth from 3.1 to 10.6 GHz [

Fractals are also used to enhance other characteristics of antennas, including bettering the bandwidth [

In order to compare the performance of a conventional circular monopole and a circular monopole interacting with a fractal, the first one is designed by following the instructions given in [

Conventional circular monopole with dimensions.

The frequency response of the conventional monopole is presented in Figure

Simulated S11 parameter of the conventional circular monopole.

To make the port matching deeper [

(a) Fibonacci spiral and (b) Fibonacci circles.

Since the radiator radius was already calculated by (

Fibonacci series related to fractal Fibonacci circles.

Sequence value | Radius value (mm) |
---|---|

13 | 1.12125 |

21 | 1.81125 |

34 | 2.9325 |

55 | 4.74375 |

89 | 7.67625 |

144 | 12.42 |

From Table

Moreover, to enhance the port matching over the entire UWB bandwidth, two other techniques were also introduced into the prototype: a bevel technique on the ground plane underneath the feeding line and the Kraus technique, where the shape of the ground plane is modified in order to avoid abrupt changes and discontinuities over the surface electric path. Figure

Simulated S11 parameter by employing the fractal and fractal-Kraus combination.

Proposed configuration with inscribed fractal Fibonacci circles, beveling, and Kraus technique: (a) front view and (b) back view.

As observed from Figure

In order to improve this behavior, the beveling technique is introduced. It has been demonstrated that this technique can be applied at lower or higher frequencies to satisfy the matching requirements by modifying the current distribution on the ground plane, making the impedance stable over certain narrow bandwidth. The shape and size of the etching below the feeding line will determine the operation frequency of the beveling [

The proposed beveling is implemented by etching another fractal geometry composed by stepped squares. The goal of using this configuration, which has been selected after a parametric analysis was made in HFSS, is to increase the port matching at a required frequency or narrow bandwidth. In this case, it was optimized to match the port impedance at the higher cutoff frequency in order to recover the 1 GHz bandwidth lost when the Kraus technique was introduced.

Figure

The simulated S11 parameter of the proposed configuration of Figure

Simulated S11 parameter of the proposed antenna.

Figure

Simulated radiation gain patterns in the XY plane: (a) 3, 5, and 7 GHz and (b) 9, 12, and 15 GHz.

As observed from Figure

On the other hand, to show that the antenna behaves with a small dispersion, the simulated group delay is presented in Figure

Simulated group delay.

Once the final configuration is met, the prototype is built and characterized and results are shown below.

The antenna prototype is presented in Figure

Antenna prototype: (a) front view and (b) back view.

Measured S11 parameter of the proposed antenna.

According to the measured results in Figure

The measured radiation pattern is presented in Figure

Measured radiation pattern on the XY plane at 3, 4, 5, and 6 GHz.

As observed, the radiation pattern shows a quasi-omnidirectional characteristic at frequencies below 5 GHz; however, at 6 GHz, the out-of-roundness increases significantly, losing omnidirectionality at certain angles, where minimums are observed.

On the other hand, the measured group delay is presented in Figure

Measured group delay.

Finally, the comparison of the simulated and measured gain is presented in Figure

Comparison of simulated and measured peak gain and radiation efficiency.

At lower frequencies, where measurements could be achieved, the gain shows a convergence to the results in the simulation process, and as observed, the radiation efficiency lowers its value as the gain is decreased, going from 96 to 90%. It is also observed that there is a divergence of results for the measured and simulated gains around 5 GHz. These results were closer if a bigger mesh and a lower convergence point in the electromagnetic simulator were chosen. However, doing so requires a longer calculation time and computing resources. Authors consider that this difference can be misprized.

Finally, a comparison of different UWB antennas is made in Table

Comparison of different UWB antennas.

Reference | Bandwidth (GHz) | Antenna footprint (mm^{2}) |
Peak gain variation (dB) |
---|---|---|---|

This work | 3.0–14.1 | 50 × 50 ( |
-1.3 to 1 |

[ |
3–11.2 | 24 × 22 ( |
-2 to 5.2 |

[ |
2.85–15.12 | 85 × 85 ( |
4.5 to 6.5 |

[ |
2.21–11.5 | 42 × 48 ( |
3.6 to 7.6 |

[ |
2–3.12 and 4.5–5.77 | 50 × 50 ( |
6.74 to 7.1 |

[ |
3.2–10.8 | 90 × 107 ( |
0.5 to 4 |

[ |
2.43–3.26 and 6.05–15.03 | 20 × 20 ( |
Not defined |

From Table

The use of fractals in conventional radiators improves the electric characteristics of the antenna. However, not all fractals are easy to implement, since many of them are inscribed into the radiator by an empirical way and optimized by simulations or measurements. In this paper, the fractal inscribed into the conventional circular monopole is based in a well-known theory: the Fibonacci series, making the fractal easy to implement. Moreover, since the fractal has no abrupt transitions like those shown in [

On the other hand, as observed in Figure

Circular monopole radiators behave inherently as wideband antennas; however, there is a possibility to achieve some mismatches in the required bandwidth as observed in this previous design. To overcome this drawback, in this article, a novel Fibonacci fractal configuration was selected in order to make the antenna to perform over a wider bandwidth and to get a deeper port matching, accomplishing an UWB operation from 3 GHz to 14 GHz, approximately, but more importantly, achieving a size reduction. Moreover, to increase the port matching, other techniques were also employed: a fractal beveling technique beneath the feeding line and the Kraus technique over the ground plane. With all these combinations, the antenna presents a good behavior, obtaining a 50% size-reduced UWB antenna but paying the price of reducing the gain. In spite of this latter disadvantage, the antenna shows a very small dispersion which lets the radiator to be employed in short-pulse communications.

The data used to support the findings of this study are included in the article.

The authors declare that they have no conflicts of interest.

This work was supported by the Instituto Politécnico Nacional (project SIP-IPN 20180161).