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The Microwave Power Transmission (MPT) is the possibility of feeding a system without contact by using microwave energy. The challenge of such system is to increase the efficiency of transmitted energy from the emitter to the load. This can be achieved by rectifying the microwave energy using a rectenna system composed of an antenna of a significant gain associated with a rectifier with a good input impedance matching. In this paper, a new multiband antenna using the microstrip technology and fractal geometry is developed. The fractal antenna is validated into simulation and measurement in the ISM (industrial, scientific, and medical) band at 2.45 GHz and 5.8 GHz and it presents a wide aperture angle with an acceptable gain for both bands. The final antenna is printed over an FR4 substrate with a dimension of 60 × 30 mm^{2}. These characteristics make the antenna suitable for a multiband rectenna circuit use.

The wireless power transmission concept was introduced in the last decade of the 19th century by Nicola Tesla’s experiment in which he tried to light bulbs wirelessly by transmitting energy from distant oscillators operated to 100 MV at 150 KHz, but he could not implement his system for commercial use due to its very low efficiency [

1950 has known the true start of wireless power transmission thanks to the development of high power microwave tubes by Raytheon company [

The rectenna’s greatest conversion efficiency ever recorded was in 1977 by Brown in Raytheon company [

Other frequencies were used to design rectenna circuit like 35 GHz frequency [

Figure

Block diagram of a rectenna circuit [

In order to have an efficient rectenna circuit, the antenna must present good performance. A good return loss to avoid reflected energy, a big gain, and wide aperture angles to maximize RF harvested energy. The rectenna conversion efficiency

When only conduction losses of the diode are considered and all the other losses are neglected, the conversion efficiency can be determined by [

Since its invention, the rectenna was used for various applications like RFID [

Fractal antenna is an antenna based on fractal geometry. This term was first used by the French mathematician Mandelbrot in 1975 to describe a fractal shape that can be subdivided in many parts; each one of them is a reduced-size copy of the whole. Fractal term is derived from Latin word “Fractus” meaning “broken” [

The fractal dimension

The “Number of self similar pieces” represents the number of copies identical to the original shape when applying a fractal aspect from one step (or iteration) to another. The “magnification factor” signifies the scaling value between an iteration and the next one when applying a fractal technique.

The fractal antenna developed in this paper is based on Sierpiński triangle fractal geometry introduced by the Polish mathematician Sierpiński in 1916 [

Sierpiński triangle at iterations from 0 to 4.

To reach the second iteration, the same process is applied to the 3 equilateral triangles obtained in the first iteration; the result is 9 triangles and so on.

The number of copies from an iteration to the next one is multiplied by 3 and the size of the triangles is divided by 2. In consequence, the Sierpiński triangle fractal dimension is

The Sierpiński triangle is widely used in antenna design due to its multiband behavior. The resonant frequency of an antenna is related to its length. When applying Sierpiński fractal concept to an equilateral triangle, different equilateral triangles with diverse sizes are created that lead to the multiband aspect of Sierpiński triangle antenna as explained in Figure

Sierpiński triangle multiband behavior.

As explained above, Sierpiński triangle antenna is known for its multiband behavior. Some researches present accurate equations that predict the resonance frequencies of a standard Sierpiński antenna [

As illustrated in Figure

The patch (left) and the ground (right) of the designed antennas: (a) iteration 1, (b) iteration 2, and (c) iteration 3.

Table

Antennas’ dimensions in mm.

Parameter | Length |
---|---|

| 65 |

| 30 |

| 26 |

| 25.8 |

| 1.3 |

| 15 |

| 4.7 |

| 3 |

| 3 |

Figure

The designed antennas return loss at iterations 1, 2, and 3.

The three iterations present almost the same behavior in the simulated frequency range. The −10 dB simulated return loss bandwidths cover ISM 2.4 GHz and 5.8 GHz bands. From iteration 1 to iteration 3 the resonance frequencies decrease slightly, while the input impedance matching decreases at the lower band and increases at the higher band. It is deduced that applying a fractal aspect over the new Sierpiński triangle designed structure has a very low effect on the return loss results. For more detailed study the

Figure

Antenna radiation pattern comparison of the three iterations at 2.4 GHz (

We notice that at 2.4 GHz the three iterations present exactly the same behavior: an omnidirectional propagation in the

At 5.8 GHz, the radiation pattern difference between the three iterations is very small. In the

The simulation shows that the antenna radiation pattern characteristics stay almost stable at both resonance frequencies for the three iterations.

Figure

Figure

Designed antennas current distribution at 2.45 GHz (left) and 5.8 GHz (right) in iterations 1 (a), 2 (b), and 3 (c).

The current distribution is the same at the three iterations. At 2.4 GHz the current is distributed over all the structure while at 5.8 GHz it is more distributed in the half of the structure near to the feeding line.

After a study of the designed Sierpiński triangle antennas at the three first iterations, we deduced that the antennas characteristics do not change too much. We then chose to realize the structure at the second iteration as illustrated in Figure

Realized antenna picture.

Figure

Comparison between simulated and measured antenna return loss.

The simulated and measured return losses show good agreement. The slight difference is generally related to connector use which is not considered during simulation. Table

Comparison between simulated and measured antenna return losses.

Bands | Simulation | Measurement |
---|---|---|

Band 1 | [2.25–2.8] GHz | [2.35–2.86] GHz |

Band 2 | [5.5–6] GHz | [5.48–6.16] GHz |

The −10 dB measured return loss bandwidths (19.5% and 11.7% at the low and high resonance frequencies, resp.) cover ISM 2.4 GHz (2.4–2.5 GHz) and 5.8 GHz (5.725–5.875 GHz) bands.

Figure

Measured radiation pattern of the realized antenna at 2.5 GHz (

The measured radiation at 2.5 GHz is distributed over all directions but presents a maximum through the

We notice that there is considerable radiation attenuation around 180° relative to the antenna back in the

The achieved antenna presents good characteristics that are suitable for wireless power transmission (WPT) applications. The size is small (60 × 30 mm^{2}). The dual ISM bands covered by the antenna in this work are commonly used for WPT. The radiation pattern is almost omnidirectional in both bands, which permits harvesting a maximum of energy. The antenna gain could be improved by several techniques.

In [

Table

Performance comparison between the proposed antenna and other compact antennas.

Published literature versus proposed antenna | Antenna size (mm^{2}) | Bands (GHz) | Gain (dBi) |
---|---|---|---|

| | 2.4 | 2.2 |

5.8 | 5.8 | ||

| | 5.2 | 4.4 |

5.8 | 6.6 | ||

| | 1.8 | 3.9 |

| | 2.4 | 10 |

A new planar multiband fractal antenna based on Sierpiński triangle is presented. In the first Sierpiński triangle, three iterations are designed and studied. The second iteration structure was printed over an FR4 substrate of 60 × 30 mm^{2} as dimension, a relative permittivity equal to 4.4, 1.6 mm of thickness, and 0.025 of loss tangent. The measurements present good performance at ISM 2.4 GHz and 5.8 GHz. The structure is simple to fabricate, low cost, and easy to associate with integrated circuits. These characteristics are suitable for wireless power transmission applications.

The authors declare that they have no conflicts of interest.

The authors have to thank Mr. Mohamed Latrach, Professor in ESEO, Engineering Institute in Angers, France, for allowing them to use all the equipment and electromagnetic solvers available in his laboratory.