Most of the radio modules used in sensor nodes operate at a frequency of
[
10]. In the case where the same antenna is used for transmitting data and retrieving the ambient energy, this section discusses the design of a rectenna with optimal operation in the ISM band centralized at
. Given the random input RF power, it is important to optimize the harvesting circuit to have a minimum of usable energy. In this work, optimization will be to design a highly efficient rectifier circuit. The proposed circuit is based on a judicious choice of rectifier diode, which besides having good conversion efficiency, must be highly sensitive to detect low levels of available power. The output characteristics of the designed rectenna will then be used to evaluate the performance of the slave node.
4.1. Rectifier Diode Selection
The RF/DC converter in a rectenna allows for the conversion of RF power captured by the antenna into electrical DC power. Given the very low received power density [
38], it is important to design a high-sensitivity rectifier circuit to have an acceptable amount of usable DC power. The sensitivity of the rectifier is directly related to the sensitivity of the used diode. The influencing factor on rectenna efficiency is the diode efficiency, and a significant portion of the losses on rectenna circuit is provided by the diode’s electrical parameters. Considering the high frequency of the signals, fast-switching Schottky diodes are the most frequently used in the design of rectifier circuits. To evaluate the conversion efficiency of a Schottky diode, the equivalent circuit of the diode with a resistive load
proposed in [
40], and shown in
Figure 9 is used.
In
Figure 9,
is the series resistance;
is the junction capacitance,
the voltage across the semiconductor–metal junction, and
the junction resistance. The most commonly used diodes are manufactured by Avago [
41]. A non-exhaustive list of recently used rectifying diodes is given in
Table 3. The electrical characteristics provided by the diode datasheets [
42,
43,
44,
45] are also reported.
The diode RF/DC efficiency is expressed as a function of the load resistance
, internal elements of the diode (
,
,
,
) and the signal frequency
; it is defined as
where
is the measured output DC power on the load resistance, and
the measured RF power delivered to the diode. In [
40], the RF/DC conversion efficiency has been expressed regarding the internal parameters of the diode as
with
where
is the output self-bias DC voltage across the resistive load.
is the forward-bias turn-angle; it is a dynamic variable that depends on the input power of the diode (and thus of the output DC voltage) as follows [
40]
The junction capacitance
is a function of
as
Considering the diode’s characteristics given in
Table 3, Equation (36) to Equation (39) are used to compare the efficiencies of the different diodes at
. The result is shown in
Figure 10, and it is observed that diodes HSMS 2850 and HSMS 2860 show the best efficiencies compared to the other considered diodes. However, at low output DC voltage, it is the HSMS 2850 diode that offers the best conversion efficiency. In this work, an output voltage of
is required to supply the sensor, so diode HSMS 2850 will be used to design the rectifier circuit. Moreover, considering the previous work, it is difficult to reach output DC voltage levels of more than
with a rectenna without exceeding the permissible levels of exposure.
A simulation of the detection threshold of the two diodes HSMS 2850 and HSMS 2860 is shown in
Figure 11. The analysis is conducted using Advanced Design System (ADS) software, and the simulated circuit is that of
Figure 12. For each diode, the value of the load resistance is set to that determined in
Figure 10 when
(supply voltage to sensor).
Figure 11 validates the result in
Figure 10 because it is shown that diode HSMS 2850 is the most efficient at low power levels (below
).
4.2. Designed Rectifier and Measurements
Four rectifier topologies are commonly used in rectenna design; namely, a single series diode, single parallel diode, the full bridge, and the Voltage Doubler (VD). A comparison of the performance of these different topologies has been proposed in [
46], and for average power levels, it is the VD topology that has proven to be the most efficient. Several VD topologies exist, the Latour VD shown in
Figure 13 is used in this work. If an alternating voltage
is applied to the input of the circuit, diode
is turned on during the positive half-wave while diode
is cut-off. During this time, the capacitance
is loaded to the value
. At the negative half-cycle, diode
is turned on and diode
remains cut-off, the capacitance
is loaded to the value
, which gives a difference potential across the load of
.
The first step in our design is to determine of the optimum load resistance of the circuit. The capacitors are set at
, and the optimum load resistance of the circuit is determined from the ADS software simulations. The output DC power is simulated with respect to the rectenna load resistance at different levels of input power (
Figure 14). It is observed that the maximum power is obtained around
when the input RF power is set at
.
By setting load resistance of
on the rectifier circuit, an experimental validation of the designed rectifier circuit is implemented. The simulated schematic and corresponding fabricated circuit are shown in
Figure 15. To achieve the circuit, an RO350B substrate (
,
,
,
) from the Rogers Corporation, was chosen. A SubMiniature version A (SMA) connector is used to connect the rectifier to the microwave source.
The experimental set-up shown in
Figure 16 is used. It includes an Aritsu microwave source, MG3700A, with an internal impedance of
that is able to transmit signals up to
. The delivered output power reaches a maximum of
and a minimum of
.
The experimental results shown in
Figure 17 are easily comparable to the simulated results. A slight distortion is observed on the experimental curve, due to the parasitic elements of the housing, which are not taken into account in the simulation. At
of input RF power, a maximum conversion efficiency of
is achieved. An output voltage of
can only be reached when the resulting circuit receives an input RF power of
, which would be difficult to provide to the rectifier given the various attenuations (reflection, diffraction, and refraction) that the signal undergoes in a real environment [
29].
Note that the performance shown in
Figure 17 are achieved without the use of a matching filter between the microwave source and the rectifier circuit. In
Table 4, a comparison of these performances with related design at 2.45 GHz is shown.
4.3. Rectifier Performance Improvement
A matching circuit must be placed between the microwave source and the rectifier to ensure optimum power transfer (
Figure 1). In this work, the ADS impedance matching tool is used to size the filter. This tool allows us to place a component in our scheme, and according to certain parameters that are manually defined, generate a matching circuit that can then be optimized according to our goals. A bandpass filter is considered as in [
49]. The schematic of the generated filter and rectifier circuit are shown in
Figure 18. The optimization included in ADS software is used to find the best matching circuit and achieve better performance both in terms of efficiency and output voltage. The optimization used in this work refers to the gradient method search. This approach adjusts a set of variables according to an error function and its gradient. In the first iteration, the simulator evaluates the error function and its gradient. Subsequently, all variables are moved in the direction of the gradient of the error, thereby minimizing the error function [
50]. The error function is the Least-Squares error function. After designing a matching circuit, all components are optimized by setting two goals at the same time
The results obtained after 45 iterations are shown in
Figure 19. For an input power of
, a
output voltage is reached. A maximum conversion efficiency of
is reached at around
. The component values to achieve these performances are reported in
Table 5.
To evaluate the contribution of the design methodology proposed here,
Table 6 shows a comparison of the achieved performance with those obtained in recent designs at 2.45 GHz. It can be seen that our design offers high performance; this for an input power level lower than those obtained in the other circuits. This is an advantage for ambient energy harvesting applications because the RF energy naturally available in the environment is generally small [
38].
It is also shown in
Figure 19 that the optimal load changes with the RF input power. A Maximum Power Point Tracking (MPPT) block is necessary to keep track of the maximum efficiency operating condition. This issue is not discussed here, as MPPT is now a classical function. At
of input power, a maximum of
is reached for optimum load resistance of
. Assuming that all this recovered power is dedicated to operation of the sensor node, the available energy
during time
is defined by
where
is the maximum recoverable power. The sensor node can operate only if (
).
Figure 20 shows the minimum distance at which the WSN should be deployed to the BS to enslave the sensor node to the recovered energy; it is observed that the range of the WSN is better when the controlled physical phenomenon varies slowly. More precisely:
Figure 20a represents a WSN in which each round is performed every second; it appears that the node cannot operate because the recovered energy is insufficient.
Figure 20b is the result of the case of the measures to be taken every minute; the energy harvested remains lower than the energy demand of the node.
Figure 20c shows that the wireless should be deployed at only
from the BS if each round lasts
.
If each round is performed every
, then the BS should be located at
from the wireless nodes (
Figure 20c).