The notion of microstrip patch antenna appeared in the 1950s [2] . A microstrip patch antenna is an antenna with printed radiating elements. These antennas are compact (not bulky) and can be placed on any flat or non-flat surfaces. Their geometries are relatively simple. They are inexpensive and mechanically robust. Microstrip patch antennas ( Figure 2 ) are made up of three elements: the radiating element, the dielectric substrate and the ground plane. The power line and the patch forming a unit rest on the dielectric substrate. The patch is the conductive or radiating part of the antenna. The dielectric substrate is the insulating part of the antenna. It generally has a rectangular shape. It is characterized mainly by its thickness, its relative permittivity and its loss tangent. Its dimensions must be greater than those of the patch and power line assembly. The dimensions of the substrate influence the performance and resonance frequency of the antenna. The ground plane taken as a potential reference (0 Volt potential) is located below the substrate. However, it can cover the entire surface of the substrate or only part of it. The modification of the ground plane also influences the performance of the antenna [3] - [5] .

The design phase of an antenna, using suitable software, is a mandatory step in the interest of saving time and optimizing the structure to the desired parameters. For this, we chose an HFSS version 15.0 electromagnetic simulation tool. It is dedicated to the high frequency simulation of microwave circuits. This is powerful software that allows you to simulate complex structures in three dimensions. It is used in particular to calculate the S parameters, the resonance frequencies as well as the electric and magnetic fields and also the visualization of the 3D radiation diagram.

The design of the antenna in HFSS follows the flowchart in Figure 3 .

The practical design procedure of a rectangular patch antenna assumes knowledge of the substrate dielectric constant (εr), resonant frequency (fr), and substrate height (h). The design therefore follows the following steps [14] :

Specification of fr, εr and h.

Determination of the width (W) and length (L) of the patch.

To ensure effective radiation, the practical patch width is calculated according to Equation (1).

$W=\frac{C}{2f_r}\sqrt{\frac{2}{{\epsilon }_r+1}}$ (1)

where c is the speed of light.

The length of the antenna L can be described as (Equation (2)):

$L=\frac{C}{2f_0\sqrt{{\epsilon }_{reff}}}-2\Delta L$ (2)

where ${\epsilon }_{reff}$ is the effective permittivity of the substrate define by (Equation (3)):

${\epsilon }_{reff}=\frac{{\epsilon }_r+1}{2}+\frac{{\epsilon }_r-1}{2}{\left(1+12\frac{h}{W}\right)}^{-\frac{1}{2}}$ (3)

And ΔL is the extension of the patch length defined as follows (Equation (4)):

$\Delta L=0.412h\frac{\left({\epsilon }_{reff}+0.3\right)\left(\frac{W}{h}+0.264\right)}{\left({\epsilon }_{reff}-0.258\right)\left(\frac{W}{h}+0.8\right)}$ (4)

To determine the width Ws and the length Ls of the substrate, we generally use Equations (5) and (6) [17] .

$w_s=W+6h$ (5)

$L_s=L+6h$ (6)

FR-4 (Flame Retardant-4) substrate with relative permittivity 4.4, loss tangent 0.02 and thickness 1.6 mm are chosen to design the antenna structure because this type of substrate is less expensive. The ground and the radiating element are each 0.03 mm thick.

An RF/DC conversion circuit and the associated impedance matching stage can be made from localized components and/or partly using distributed elements. Among existing commercial software, the Advanced Design System (ADS) software developed by Keysight Technologies is chosen for the work carried out in this thesis. Indeed, ADS [1] is a reference in the field; it is 2.5D simulation software allowing the design of all types of electrical circuits operating in the RF domain. It has the advantage of integrating specific analysis tools particularly suited to circuits composed of non-linear elements as we will present later. The steps of the rectifier design methodology are shown in Figure 4 .

The diode is chosen to realize the rectifier is Sckottky type. This choice is justified by the fact that with the diode-based rectifier we will not need an external power source, therefore, less bulky, easy to make and at low cost. Thus, the sensitivity of our rectifier will be linked to that of the diode. Thus, the Schottky diode HSMS2850 (AVAGO) was selected for use in the circuit recovery because it has high efficiency in high frequencies ( Figure 5 ). This is a diode widely used in detection and measurement circuits, with very precise sensitivity.

As shown in Figure 6 , this diode has a series resistance (RS) of 25 Ω, a threshold voltage of 0.25 V, and a junction capacitance of (Cj) 0.18 pF. It is one of the Schottky diodes with a much lower threshold voltage.

RF/DC conversion efficiency is the ratio of the load power to the RF input power collected by the antenna. This efficiency η is given by:

$\eta \left(\%\right)=\frac{P_{out}}{P_{in}}\times 100=\frac{V_{out}^2}{P_{in}\times Z_{load}}\times 100$ (7)

where P_in and P_out are respectively the antenna input power and the power at the load terminals;

V_out is the charging voltage;

Z_load is the module of the load impedance.

The designed antennas must comply with the following characteristics:

Table 1 shows the geometric dimensions of the different parts of the antennas designed and radiating at the frequency 1800 MHz, 2100 MHz and 2500 MHz respectively. The substrate used for the three antennas is Rogers RT/duroid 5880 and relative permittivity εr = 2.2 whose thickness is 1.6 mm. The power line has a width of Wf and a length of Lf.

Figure 7(a) , Figure 7(b) and Figure 7(c) illustrate the evolution of the reflection coefficient S11 (respectively in (1800 MHz), (2100 MHz) and (2500 MHz). It shows an S11 of −22.12 dB at the frequency 1800 MHz of −17.70 dB at the frequency 2100 MHz and −28.50 dB at the frequency 2500 MHz. This indicates that the three (3) antennas are well matched and operate effectively in the chosen frequency bands.

Figure 8(a) , Figure 8(b) and Figure 8(c) illustrate the evolution of the radiation gain (respectively in (1800 MHz), (2100 MHz) and (2500 MHz). It presents a gain of 3.26 dB, a gain of 7.1 dB and a gain of 5.1 dB respectively at the frequency 1800 MHz, 2100 MHz and 2500 MHz.

The 2D radiation pattern is a graphical representation of how an antenna emits or receives electromagnetic waves in space depending on the viewing angle relative to the antenna axis, in a given plane. The following figure illustrates the curve which shows the representation of the angle φ is equal to 0 degrees and 360 degrees in a directional radiation diagram ( Figure 9 ). The evolution of this radiation pattern of the designed rectangular patch antennas shows directional radiation, indicating directional radiation in the H (horizontal) plane. This directivity makes it possible to concentrate the energy emitted in specific directions, thus optimizing the transmission and reception of signals in these directions. In the elevation plane (E), the radiation presents a vertical main lobe, confirming the effectiveness of the antenna for point-to-point communications.

These three (3) patch antennas have conversion efficiencies of 96.7%, 98% and 97% respectively.

Designing the rectifier circuit to optimize energy conversion in a rectenna is essential to ensure maximum efficiency in energy harvesting from RF signals. Our circuit, consisting of an AC source at PORT1 and a matching circuit including a capacitor, an inductor and an HSMS2850 Schottky diode, represents a typical approach for the rectification of RF signals.

Adding the filter capacitor in parallel to the load helps smooth out the rectified voltage and provides a more stable DC output to the load. This ensures better use of the energy captured by the rectenna.

The simulations were carried out using Advanced Design System (ADS) software. To adapt the input impedance of the rectifier and the other part of the circuit we used the ADS Smith chart tool. So, for the bandwidth 1800 MHz, we find the values of L and C ( Figure 10 ) [15] [16] , which are respectively 25.62 nH and 1.56 pF. While at the bandwidth 1800 MHz, and 2500 MHz we find 18.81 nH and 1.21 pF, and 13.36 nH and 1.55 pF, respectively.

We found for the three (3) frequency bands reflection coefficients close to those found with the antennas. These results demonstrate a good adaptation of the energy source and the rest of the circuit.

Figure 11 illustrates the RF generator input voltage (1800 MHz) and output voltage across the load. The evolution of this voltage is also of the same form for the 2100 MHz and 2500 MHz RF generators. Thus, the output voltage of the matched rectifier is 670 mV at the frequency of 1.8 GHz, 870 mV at the frequency of 2.1 GHz and 760 mV at the frequency of 2.5 GHz.

Evaluating and optimizing conversion efficiency is essential for designing efficient and economical energy systems. Figure 12 shows the efficiency as a function of the input and output power at the load terminals for frequency 1.8 GHz. We have a similar evolution for the 2.1 GHz and 2.5 GHz frequencies. Thus, we obtained satisfactory conversion efficiency, reaching 60% for the 1.8 GHz frequency, 55% for the 2.1 GHz frequency and 62% for the 2.5 GHz frequency.