Most RF energy harvesting systems have the synoptic diagram shown in Figure 1 . 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 purpose, the electromagnetic simulation tool HFSS version 13.0 was chosen. 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.

In this paper, two dipole antennas will be designed. One operates in the GSM 900 band (890 MHz - 960 MHz) and the other in the GSM1800 band (1710 MHz - 1880 MHz). The length (l) in meters (m) of an antenna is given by Equation (1) [7] :

$l=\frac{c}{2\sqrt{E_r}f}*0.9$ (1)

With E_r = 1 being the relative permittivity of dielectric of the ambient medium assimilated to air. The factor 0.9 reflects the fact that the RF energy will propagate across the antenna at approximately 90% of its normal speed. The frequency (f) is either 900 MHz or 1800 MHz. The dipole has a geometric shape similar to a cylindrical one of length (l) and radius R given by Equation (2).

$R=\frac{l}{60}$ (2)

Thus, the length and radius of the dipole are respectively 15 cm and 0.25 for the frequency 900 MHz and 7.5 cm and 0.125 cm for a frequency of 1800 MHz.

High Frequency Structure Simulator (HFSS) is simulation software that calculates the electromagnetic behavior of a structure.

To do this, HFSS uses partial differential equations. There are three main methods: the finite element method, the finite difference method and the method of moments. The principle of these methods is to discretize the space using a mesh specific to the method and to solve the equations. The software presented here uses the finite element method to solve the Maxwell equations.

The geometry of the model studied under HFSS ( Figure 2 ) is automatically divided into a large number of tetrahedre on which the mathematical calculation

will be more feasible. The value of a field vector (E or H) at a point inside a tetrahedron is calculated by interpolating the values of the fields in the vertices of the tetrahedron. Thus, by representing the field values in this way, HFSS calculates the fields separately in each element by setting convergence criteria, which corresponds to the maximum uncertainty between at least two successive iterations to be validated as representative of reality. This uncertainty is calculated as the percentage between two successive solutions, and if the ratio between these two solutions is greater than the convergence criterion, the iterations must continue, otherwise the solution is said to be stable and the calculation stops.

A rectifier is a system for converting alternating electrical energy into direct electrical energy. At low frequencies, this DC AC converter is made up of two blocks: the input stage corresponds to the rectification part provided by the diodes, the filtering part is provided by a low pass filter (bypass capacitor). At high frequency, it is necessary to add an input circuit ( Figure 3 ), in order to ensure the adaptation of the impedance presented by the rectifier to the RF source, therefore minimizing reflection losses, and thus block the passage of harmonics likely to be generated by the diodes at high powers.

The diode chosen to realize the rectifier is Schottky type. This choice is justified by the fact that with the diode rectifier, an external power source will be used, which is therefore less bulky, easy to manufacture and inexpensive. 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 circuit recovery because it has high efficiency in high frequencies ( Figure 4 ). This is a diode widely used in detection and measurement circuits, with very precise sensitivity.

As shown in the Figure 5 , Rj junction resistor can be express by following relation [7] [8] :

$R_j=\frac{nkT}{q\left(I_s+I_b\right)}$ (3)

with:

n: Ideality factor;

k = 1.38 10 - 23 J/˚K, Boltzmann constant;

T: Junction temperature in ˚K;

q = 1.6 10 - 19, electron electrical load;

I_s: Saturation current;

I_b: Polarization current.

The conversion efficiency is related to the load, the signal frequency and the internals of the diode Schottky [7] [8] . In general, the saturation current Is is very low and if the bias current Ib is zero, according to Equation (3), the junction resistance R_j becomes high. Which thus causes a drop in the rectified voltage expressed according to Equation (4) [7] - [12] .

$V_{out}=V_{DC}\frac{R_L}{R_L+R_j}$ (4)

with:

$V_{out}$: Rectified voltage across the load;

$V_{DC}$: Voltage across the Schottky barrier;

$R_L$: Load resistor.

The conversion efficiency RF/DC is given by Equation (5) [6] :

$\eta =\frac{P_{DC}}{P_{RF}}=\frac{1}{1+A+B+C}$ (5)

with:

$A=\frac{R_L}{\pi R_s}{\left(1+\frac{V_j}{V_{out}}\right)}^2\left[\phi \left(1+\frac{1}{2\phi }\right)-1.5\tan \tan (\phi )\right]$

$B=\frac{R_s{R}_j{C}_j^2{\omega }^2}{2\pi }\left(1+\frac{V_j}{V_{out}}\right)\left[\frac{\pi -\phi }{\left(\phi \right)}+\tan \tan \left(\phi \right)\right]$

$C=\frac{R_L}{\pi R_s}\left(1+\frac{V_j}{V_{out}}\right)\frac{V_j}{V_{out}}\left[\tan \tan \left(\phi \right)-\phi \right]$

$\tan \tan \left(\phi \right)-\phi =\frac{\pi R_s}{R_L\left(1+\frac{V_j}{V_{out}}\right)}$

$C_j=C_{j0}\cdot \sqrt{\frac{V_j}{V_j+V_{out}}}$

$\omega$: Pulsation égal to 2πf (f is the frequency);

$C_{j0}$: Junction capacity in 0 Volt;

$\phi$: Phase shift during which the diode is conducting.

The conversion efficiency $\eta$, at the rectifier terminals is obtained also by Equation (6):

$\eta =\frac{V_{out}{}^2}{P_{in}x{R}_L}$ (4)

where V_out (in Volt) is the voltage on the resistor, and Pin the input power (in Watt) of the receiving antenna.

Figure 6(a)-(b) shows the variations of the reflection coefficient as a function of frequency for each antenna design step. The reflection coefficients are −16.76 dB and −15.70 dB respectively at the frequency 899.3 MHz and 1744.8 MHz.

These 2 coefficients are satisfactory because they are less than the value 10 dB which is the reference reflection coefficient [9] - [15] .

These two figures allow us to see a bandwidth of 100 MHz around the frequency 900 MHz and a bandwidth of 250 MHz around the frequency 1800 MHz. This band corresponds to the frequency range where the best performance of the antenna is observed in terms of impedance matching, radiated power, gain, or radiation efficiency. The higher the bandwidth of a receiving antenna, the more electromagnetic radiation it is capable of capturing. So, with the 1800 MHz dipole will allow the capture of many more frequencies.

Figure 7 and Figure 8 show the dipole radiation pattern respectively at the frequency 900 MHz and 1800 MHz. They allow us to notice that a diagram pattern is directional in the E-plan and omnidirectional in the H-plan.

Figure 9(a)-(b) shows the antenna gain at both frequency bands. It is 1.72 dB and 1.69 dB at 900 MHz and 1800 GHz respectively.

The simulations were carried out using Advanced Design System (ADS) software. To adapt the input impedance of the rectifier and other parts of the circuit, the ADS smith chart design tool will be used. At 900 MHz bandwidth, the values for L and C [15] - [17] are 50.78 nH and 0.29 pF respectively ( Figure 10 , Figure 11 ). At 1800 MHz bandwidth, these values become 25.42 nH and 2.49 pF respectively ( Figure 12 , Figure 13 ).

The results show that the rectifier used is well adapted to the 900 MHz frequency, producing an output voltage of 806 mV for an input voltage of 330 mV ( Figure 14(a) ). At the frequency of 1800 MHz the system is also good and it provides an output voltage of 616 mV for an input voltage of 268 mV ( Figure 14(b) ).

After calculating the efficiency of the overall circuit, i.e. the rectenna, a value of 64% with 0 dB input power and 806 mV output voltage at 900 MHz bandwidth were found. On the other hand, at the 1800 MHz bandwidth an efficiency of 34% was obtained.

In summary, as shown in Table 1 , the dipole radiating on frequency 900 has better technical characteristics than that radiating on frequency 1800 MHz. On the other hand, the latter is less bulky and is more suitable for IoT applications.