# Innovative battery-free wireless piezoresistive sensor for green-IoT applications

Mario Costanza, Abdo-Rahmane Anas Laaraibi, Antonino Pagano, Gurvan Jodin, Florence Razan, Ilenia Tinnirello, Samuel Margueron, Roberto La Rosa

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Mario Costanza, Abdo-Rahmane Anas Laaraibi, Antonino Pagano, Gurvan Jodin, Florence Razan, et al.. Innovative battery-free wireless piezoresistive sensor for green-IoT applications. Internet of Things, 2025, 30, pp.101483. 10.1016/j.iot.2024.101483. hal-04984648

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Submitted on 10 Mar 2025

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# Innovative battery-free wireless piezoresistive sensor for green-IoT applications

Mario Costanza<sup>a, ID</sup>, Abdo-Rahmane Anas Laaraibi<sup>b,c ID</sup>, Antonino Pagano<sup>d,e ID,*</sup>, Gurvan Jodin<sup>b,c</sup>, Florence Razan<sup>b,c</sup>, Ilenia Tinnirello<sup>d,e,f</sup>, Samuel Margueron<sup>a</sup>, Roberto La Rosa<sup>g ID</sup>

## ARTICLE INFO

**Keywords:**

Internet of Things (IoT)

Battery-free

Energy harvesting

Time Domain to Digital Conversion

Bluetooth Low Energy

Wireless sensor network

Wireless sensor node

Mechanical strain sensor

## ABSTRACT

This paper unveils an innovative wireless piezoresistive sensor designed to operate autonomously without batteries, addressing the critical challenge of energy sustainability in Internet of Things (IoT) applications. Traditional sensor systems often rely on batteries, which pose significant limitations in maintenance, environmental impact, and operational lifespan. Our proposed solution integrates an energy-harvesting system that efficiently converts ambient light into electrical energy, enabling continuous operation in various environments. The findings demonstrate that the developed sensor exhibits high sensitivity and accuracy in measuring mechanical strain, with a coefficient of determination ($r^2$) of 0.99 and a root mean square error (RMSE) of 1.17 N, making it suitable for real-time monitoring applications. The integration of Time Domain to Digital Conversion (TDDC) technology significantly reduces power consumption by eliminating the need for conventional analog-to-digital converters, thus enhancing the overall energy efficiency of the wireless sensor network (WSN). The contributions of this work are multifaceted: we present the first demonstration of TDDC for force and resistive measurements in battery-free sensor nodes, propose a mathematical model for resistance to time domain digital conversion, and develop two calibration methods tailored for force and resistance measurements. These innovations advance the field of green wireless sensor technologies and pave the way for scalable and sustainable IoT solutions. The implications of this research extend to various applications, including structural health monitoring, industrial condition monitoring, and environmental sensing, where long-term data collection is essential for proactive maintenance and fault detection.

<footnote><sup>a</sup> FEMTO-ST Institute, University of Franche-Comté, ENSMM, CNRS UMR6174, Besançon, 25030, France</footnote>

<footnote><sup>b</sup> OASIS, IETR UMR CNRS 6164, Université de Rennes, 35042 Rennes, France</footnote>

<footnote><sup>c</sup> Department of Mechatronics, and the SATIE Laboratory, UMR CNRS 8029, École Normale Supérieure de Rennes, 35170 Bruz, France</footnote>

<footnote><sup>d</sup> Department of Engineering, University of Palermo, Viale delle Scienze, Palermo, Italy</footnote>

<footnote><sup>e</sup> CNIT, Consorzio Nazionale Interuniversitario per le Telecomunicazioni, Parma, Italy</footnote>

<footnote><sup>f</sup> Department of Electrical, Electronics and Computer Science Engineering, University of Catania, Italy</footnote>

<footnote><sup>g</sup> STMicroelectronics, Stradale Primosole 50, Catania 95121, Italy</footnote>

<footnote>* Corresponding author at: Department of Engineering, University of Palermo, Viale delle Scienze, Palermo, Italy.</footnote>

<footnote>E-mail addresses: mario costanza@tyndall.ie (M. Costanza), abdo rahmane-anas.laraibi@ens-rennes.fr (A.-R.A. Laaraibi), antonino pagano@unipa.it (A. Pagano), gurvan jodin@ens-rennes.fr (G. Jodin), florence razan@ens-rennes.fr (F. Razan), ilenia.tinnirello@unipa.it (I. Tinnirello), samuel margueron@femto-st.fr (S. Margueron), roberto.larosa@st.com (R.L. Rosa).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Architecture of piezoresistive sensor for green-IoT.</figcaption></figure>

# 1. Introduction

Wireless Sensor Nodes (WSNs) are utilized in Internet of Things (IoT) technology to gather data such as pressure assessments, temperature variations, humidity levels, etc. [1,2]. In such IoT applications, energy efficiency and maintenance are critical issues for network reliability, as the installed wireless sensor nodes require constant and reliable power to perform IoT monitoring, interact with the rest of the network, and transmit information to the server. The deployment of a mass-scale IoT sensor requires synergy between environmental health, economic prosperity, and social progress of current and future green communication networks to promote sustainability [3,4]. As a result, energy harvesting is becoming an increasingly popular choice for powering sustainable wireless nodes, as maintenance required for periodic battery replacement can be a disabling factor for mass-scale IoT deployments. State-of-the-art wireless sensor nodes use batteries, which require periodic physical maintenance that can be tedious, environmentally harmful, and costly [5].

Indeed, battery replacement costs can exceed the value of the IoT device itself. Even with a 10-year battery lifespan, there would still be several million battery replacements per day for IoT devices [6]. Therefore, achieving energy autonomy for wireless sensor nodes is a primary goal in the deployment of mass-scale IoT, which drives engineers to adopt an energy-harvesting approach. Depending on the environment, several types of harvester are available, and making an optimal choice among the available options is crucial. For example, solar panels can be a convenient option for home automation or smart agriculture [7], and piezoelectric harvesters can be a good choice near vibrating elements, such as machines and engines [8]. However, the use of harvesters also presents other challenges in energy management, as the available energy is intrinsically variable and typically very low. A previously published work [9,10] shows a solution that combines devices ultra-low-power, which are capable of implementing proper power management [11], with the Time Domain to Digital Conversion (TDDC) techniques [9,10]. TDDC is well-known in the literature as a technique for measuring time intervals in nuclear and particle physics [12]; nevertheless, this is also proposed for various IoT applications: for measuring Time-of-Flight [13], in Light Detection or LiDAR applications [14,15], as a temperature sensor [16,17], in time-domain ADCs [18], in RFID (radio frequency identification) tag sensors [19], in ADPLL (all digital phase-locked loop) [20], and as flow meters [21]. Recently, the authors in [22] introduced innovative methods for Resistance-to-Time-to-Digital conversion. These techniques can be implemented for resistive sensors and offer rapid, accurate, and low-energy consumption readings of the sensors. The main advantage is that the sensor reading implements direct interface circuits [23,24] and the TDDC techniques. In fact, instead of using analog-to-digital converters (ADC), these solutions adopt a different approach based on converting time to digital and then to resistance.

In this process, time measurements are obtained through charging–discharging cycles of a capacitor and subsequently processed by a microprocessor that expresses the results in terms of the number of internal clock cycles. These solutions can be applied to resistive, inductive, and capacitive sensors [25,26]. Furthermore, [22] has demonstrated that energy consumption can be reduced by up to 75%, making the TDDC technique ideal for developing ultra-low power energy-autonomous wireless sensor nodes in green IoT. This reduction in power consumption within a microcontroller component may seem minimal; however, it is crucial to recognize that a decrease in power consumption, when coupled with appropriately sized energy systems, can yield significant environmental benefits for the IoT. In [27], an environmental impact assessment tool for IoT devices is introduced. One case study involves a network of IoT air quality sensors powered by solar panels in conjunction with a battery. A comparison is made between a system with oversized solar panels and batteries and a “green solution” with optimized sizing. The findings indicate that, over time, energy consumption can be reduced by a factor of three, while electronic waste can be diminished by a factor of fifteen.

In this context, the objective of the present study is to develop an Energy-Autonomous Wireless Piezoresistive Sensor Node (EAWPSN) integrated with time-to-digital conversion. The work presents a green-IoT device designed for sensing mechanical stress or strain with an energy-autonomous and battery-free system. The architecture of the green-IoT node is shown in Fig. 1; it comprises a piezoresistive sensor, a solar cell, and a storage capacitor to harvest and store ambient energy, a Bluetooth Low Energy (BLE) wireless communication interface for data transmission, and an ultra-low-power microcontroller that implements power management and the time-to-digital conversion. Furthermore, piezoresistive sensors are used in a broad range of IoT applications, including automotive,
industry, healthcare, and sports, thanks to their ability to sense mechanical stress and deformations [28]. Typical applications are force sensors such as scale. They are based on metallic strain gauges. With a careful setup and precision electronics, a strain of $10^{-6}$ is measurable. Piezoresistive elastomer composite that often consists in conductive carbon material in an elastomeric matrix allows for larger strains to be measured, making it compatible with human activity. For instance, they are embedded in cloth for breath monitoring for sports [29] or health monitoring [30]. They can also be used as flexible force sensors, such as insoles to measure the dynamic plantar pressure [31,32].

## 1.1. Motivation and scope of research

This work is motivated by the awareness that a combined implementation of EAWPSN and TDDC technique could significantly improve energy performance, reliability, and sustainability of sensing in green IoT technologies. Indeed, the use of batteries today poses a bottleneck for the widespread adoption of the Internet of Things. Moving towards a future with trillions of IoT devices, battery replacement will be prohibitively expensive and irresponsible. Energy-autonomous and battery-free sensors could reshape the Internet of Things into a wider dimension and a more sustainable societal infrastructure [33]. In this direction, the proposed system is an innovative contribution to achieving massive and sustainable monitoring in various mechanical and strain applications.

## 1.2. Paper contributions

The work introduces several innovative aspects, including:

* The first ever demonstration of a TDDC technique for force and resistive measurements, in the context of wireless, battery-free sensor nodes;

* An approach that allows for low-complexity and low-cost designs, making it compatible for truly mass-scale, battery-less IoT applications;

* The presentation of a mathematical model for the resistance to time domain digital conversion technique;

* The development of two calibration methods of the TDDC technique for either force and resistance measurements.

These innovations have the potential to significantly advance the field of green wireless, battery-free sensor nodes, and enable new applications that were previously impossible due to power constraints. In particular, the EAWPSN can be employed for infrastructure monitoring, such as assessing the structural health of buildings and bridges. Furthermore, it can be integrated into wearable devices to monitor vital parameters without relying on disposable batteries, enhancing sustainability. Lastly, it offers the possibility to be used in environmental applications, such as wireless sensors for monitoring air quality and weather conditions.

## 1.3. Statement of section distribution

The remainder of this article is organized as follows: Section 2 describes the system architecture and discusses the design procedure followed to achieve the optimum energy and cost efficiency. Section 3 describes the time-to-digital conversion technique used to measure the sensor's resistance. Section 4 shows the experimental results. Future research directions and possible applications are discussed in Section 5. Section 6 reports the conclusions.

# 2. System description and design

## 2.1. System description

The EAWPSN works in a distributed sensing green IoT architecture, where direct and easy access to the sensors' environment could be hard to reach. Under this objective, each EAWPSN performs time measurements locally using the TDDC technique and reports the acquired values to a remote Base Station (BS) through a wireless communication protocol such as BLE, LoRa, NB-IoT, and the like. In this work, the EAWPSN implements BLE connectivity.

The BS is a device equipped with a Bluetooth receiver that is powered continuously either through a main power source or a battery. As a result, the device does not encounter any power-related issues. It collects data sent by one or more nodes and can perform energy-intensive operations.

Being energy-autonomous and battery-free, the proposed EAWPSN device is a WSN that is inherently maintenance-free, sustainable, environmentally friendly [34], safe [35], low-cost, low-volume, and easy to deploy and expand [36].

Fig. 2 illustrates the architecture of the EAWPSN. Each WSN is composed of a System and Energy Control Unit (SECU), an Energy Harvester Unit (EHU), one Energy Storage Unit (ESU), and Sensor Unit (SU). The EHU can include one or more energy harvesters and is the only system power source. The SECU executes the finite state machine, monitors and manages the power generated by the EHU, the power flowing into the ESU, and biases the sensors accordingly.

The EAWPSN works by alternating an *harvesting phase* to an *active phase*. During the harvesting phase, the system is configured to work under the lowest possible power consumption to minimize the quiescent power consumption and allow the harvested energy to flow efficiently into the ESU. In the active phase, the system uses the harvested energy to perform an energy-intensive action, like sensing or communicating with external devices through the radio.
<figure><img src="image_5.png" /><figcaption>Fig. 2. Block diagram of the green IoT system.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Typical work cycle of the EAWPSN.</figcaption></figure>

This approach possesses the secondary advantage of reducing the minimum requirements of the EHU, allowing for lower costs and complexity for the node.

The ESU is a low-cost and low-volume ceramic capacitor $C_{stor}$. Fig. 3 shows the typical work cycle of the EAWPSN. Each active phase follows cyclically after the harvesting phase. During the harvesting phase, the voltage $V_{stor}$ reaches a defined voltage threshold value $V_H$, which corresponds to the highest level of energy harvested in the capacitor $C_{stor}$. In the active phase, as the power consumption of the EAWPSN (in the order of tens of milliwatt) is much greater than the power provided by the EHU (in the order of tens of microwatts), the voltage $V_{stor}$ drops steeply down to the lowest voltage threshold $V_L$. The value of the capacitor $C_{stor}$, calculated as in (1), can store enough energy so that the voltage $V_{stor}$ never drops below the lowest voltage $V_L$, while the system accomplishes the assigned tasks during the active phase. The voltage $V_L$ is set to minimize the value of $C_{stor}$ at the lowest possible voltage that keeps the Microcontroller out of its reset state.

$$C_{stor} = \frac{2 \cdot E_{harv}}{V_H^2 - V_L^2} \qquad (1)$$

In steady-state operation, the time $t_{harv}$ it takes the EAWPSN to harvest the energy depends on the energy $E_{harv}$, the power generated by the harvester $P_{geh}$, and the quiescent power of the system $P_q$ as in (2):

$$t_{harv} = \frac{E_{harv}}{P_{geh} - P_q} \qquad (2)$$

$t_{harv}$ is digitally converted to the number of clock pulses $N_{harv}$ counted by the timer LPTIM that runs at the frequency $f_{clk}$ as in (3).

$$t_{harv} = \frac{N_{harv}}{f_{clk}} \qquad (3)$$

It is worth noting that, as already described in La Rosa et al. [37], once the parameters $V_H$, $V_L$ and $C_{stor}$ are fixed, the energy value $E_{harv}$ during the harvesting phase is constant. Therefore, the knowledge of $N_{harv}$ provides the value of the power $P_{geh}$ (4).

$$P_{geh} = \frac{E_{harv} \cdot f_{clk}}{N_{harv}} + P_q \qquad (4)$$
In practical applications, for the system to be capable of harvesting energy, the minimum power generated by the harvester $P_{geh\_min}$ must be greater than the quiescent power $P_q$ so that the condition in (5) must be satisfied.

$$P_{geh\_min} \gg P_q \qquad (5)$$

## 2.2. System design

The WSN proposed in this work exploits BLE for the low-energy system requirement and the widespread compatibility of the protocol with commercially available IoT devices such as computers, smartphones, and tablets. Specifically, the device used for the radio system is the commercially available BlueNRG-2 provided by STMicroelectronics, configured to send beacons at a transmission power of +8 dBm with a peak current of ≈14 mA. It is worth noting that the Bluetooth standard requires beacon emissions to be distant in time no less than 100 ms [38]. For this purpose, the EAWPSN uses a specific ultra-low-power timer LPTIM to measure the advertising time, implement the TDDC technique and assure a Bluetooth standard-compliant elapsed timing between consecutive broadcast events.

The SECU is implemented with the off-the-shelf ultra-low-power Cortex-M0+ microcontroller from STMicroelectronics (STM32L031F4) [11]. During the harvesting phase, the microcontroller is configured in stop mode with a quiescent current $I_q$ of 1 µA that results in a quiescent power $P_q$ of 2.5 µW. The device can supply external devices, i.e., the BLE radio, the sensors, and the like, through a General Purpose Input/Output (GPIO) capable of driving a maximum current of 10 mA.

Depending on the target green IoT application of the device, several types of harvesters can be used. In this work, the harvester used was the commercially available AM-1606C amorphous silicon photovoltaic cell provided by Panasonic, with an open-circuit voltage of 3.7 V and capable of providing ≈ 10 µW at the defined optimal operating point [39]. This photovoltaic cell offers several benefits, including the biasing of the system with a minimum light intensity of 200 lux, as it provides a current of 3 µA. Moreover, its small size (1.5 cm × 1.5 cm) allows for easy integration into the developed system requiring miniaturization.

The value of the capacitor $C_{stor}$ must ensure that during the energy-intensive active phase, the voltage $V_{stor}$ does not drop below the minimum bias voltage $V_{dd\_min}$ of the used electronic devices that, which for the off-the-shelf devices used, corresponds to a minimum voltage of 1.8 V. For the proposed device, a capacitor $C_{stor}$ of 440 µF provides storage for 1.1 mJ of energy when $V_H = 3.0$ V and $V_L = 2.0$ V.

Several transducers and technologies are available that can be categorized by the physical phenomenon for sensing pressure or applied force:

* Piezoelectric transducers use the generation of an electric potential whose value is proportional to the applied mechanical stress on piezoelectric crystals [40],

* Electret-based transducers use dielectric materials possessing a permanent electric dipole exploiting the voltage variation from the deformation caused by applied stress [41],

* Piezoresistive transducers rely on the piezoresistive effect, which causes a change in the electrical resistance of a material under mechanical stress [28].

Piezoelectric and Electret-based transducers require an amplifier, adding to the cost and power consumption of the EAWPSN. Piezoresistive sensors are cheap, widely used, and their value can be sensed via an ADC and a test resistor [31]. The EAWPSN embeds the piezoresistive transducer described in Section 2.3.

## 2.3. Description of the piezoresistive sensor

Piezoresistive polymers are a type of material that exhibit changes in electrical resistance when under mechanical stress. These polymers are flexible, inexpensive, and reliable, which makes them an excellent choice for monitoring pressure distribution [42]. These polymers are used in a wide range of applications, including the design of flexible IoT sensors [43,44] and in mechatronic and biomedical devices [30].

The piezoresistive effect is responsible for the changes in electrical resistivity observed in these materials when subjected to mechanical stress. This effect is illustrated in Fig. 4, which shows that, by applying a compressive force, the distance between charged particles inside the piezoresistive film decreases, thereby increasing the number of conductive paths and resulting in lower resistivity.

Piezoresistive sensors can be fabricated utilizing different materials, such as Velostat® [45], a polymer composite of polyethylene impregnated with carbon black. Table 1 provides a summary of the physical properties of the material used in the manufacture of these sensors.

The model proposes the use of multilayer piezoresistive sensor, as shown in Fig. 5. These sensors consist of six layers of Velostat, each with a thickness of 0.1 mm. The layers are arranged in series using an Anisotropic Conductive Film (ACF) [46] adhesive to bond them together. Copper tapes, 0.065 mm thick, are positioned above and below the Velostat without any adhesive, serving as electrodes. In order to optimize the compatibility of the piezoresistive sensor with conditioning electronics, two layers of adhesive insulators (polyimide), each 0.076 mm thick, are applied above and below the electrodes for environmental protection and sensor assembly consolidation.
<figure><img src="image_7.png" /><figcaption>Fig. 4. Schematic illustration of piezoresistivity, and the effect of the applied pressure tends to change the particles distances. With $R_{pressure} < R_0$.</figcaption></figure>

<table><caption>Table 1
Selected mechanical and electrical properties.</caption><thead><tr><th colspan="2">Technical specifications</th></tr></thead><tbody><tr><td>Thickness</td><td>0.1 mm</td></tr><tr><td>Size</td><td>4.2 cm × 2.6 cm</td></tr><tr><td>Temperature limits</td><td>-45 °C to 65 °C (-50 °F to 150 °F)</td></tr><tr><td>Volume fraction of carbon particles</td><td>0.2873</td></tr><tr><td>Diameter of carbon particles</td><td>500 nm</td></tr><tr><td>Volume resistivity</td><td>≤500 Ω cm</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Multilayer sandwich structure with the ACF adhesive between the piezoresistive layers.</figcaption></figure>

This enhances the resistance value of the sensor, according to [31], research suggests that multilayer sensors utilizing ACF adhesive exhibit superior sensitivity compared to those lacking ACF.

ACF is an electrically anisotropic, conductive pressure-sensitive adhesive tape infused with silver particles that enables interconnection through the adhesive thickness (z-axis) between substrates. Contact between the adhesive and Velostat is established by applying finger pressure at 15 psi (0.10 MPa).

In this context, the use of ACF ensures continuous electrical contact, even without pressure, facilitating higher resistance, which is advantageous for electronic integration.

## 3. Resistive sensing technique

### 3.1. System setup

The sensing of the resistance *R* is performed through several methods and techniques. Most of these techniques typically require an (Analog to Digital Converter) ADC, a conditioning circuit, or a separate discrete device, which implies an extra, typically significant amount of energy to account for the sensing activity. In this work, the EAWPSN computes the resistance *R*, using the TDDC technique that measures the discharge time *t*<sub>m</sub> of the voltage *V*<sub>stor</sub> across the capacitor *C*<sub>stor</sub> through the resistor *R* between two voltage thresholds *V*<sub>H</sub> and *V*<sub>L,R</sub> with *V*<sub>H</sub>>*V*<sub>L,R</sub>.

Fig. 6 shows the block diagram of the EAWPSN. The resistor *R* to measure is connected to the microcontroller directly through the GPIO1. Similarly, two calibration resistors *R*<sub>cal1</sub> and *R*<sub>cal2</sub> are respectively connected through GPIO2 and GPIO3 to cyclically calibrate the system and ensure the reliability and accuracy of the measurements.

Referring to Fig. 7, during the measurement phase, the resistor *R* is connected to the voltage *V*<sub>stor</sub> through GPIO1 so that the voltage *V*<sub>R</sub> through the resistor *R* is equal to the voltage *V*<sub>stor</sub>.

This causes the capacitor *C*<sub>stor</sub> to discharge through the resistor *R* and the voltage *V*<sub>stor</sub> drops exponentially with the time constant *τ* = *R*·*C*<sub>stor</sub>. Therefore, the resistance *R* can be indirectly calculated from the time *t*<sub>m</sub> needed to discharge the storage capacitor *C*<sub>stor</sub> by exploiting the fact that its value is known and static. The voltage *V*<sub>stor</sub> varies between two defined voltage thresholds, the high voltage threshold *V*<sub>H</sub> and the low threshold voltage *V*<sub>L,R</sub>.

In addition to being inherently low-power, this approach translates into minimal use of hardware resources and system simplicity as it takes advantage of the internal hardware peripherals of the microcontroller, i.e., PVD (Programmable Voltage Detector) and
<figure><img src="image_9.png" /><figcaption>Fig. 6. Block diagram of the resistance measurement system.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. $V_{stor}$ and $V_R$ evolution during the resistor measurement phase.</figcaption></figure>

LPTIM (Low-Power Timer), which are already required to monitor the $V_{stor}$ voltage during the energy harvesting stage and just one additional GPIO per each measured resistor. This approach has the relevant advantage of leading to the use of simplified and low-cost microcontrollers.

Another advantage of this method is that the energy $E_{meas}$ used per each measure, given by (6), is constant. The voltage thresholds $V_H$ and $V_{L,R}$ are defined simply via the PVD with on-the-fly configurable voltage values in the range from 2.0 V to 3.2 V with programmable discrete steps of 200 mV [11].

$E_{meas}$ represents the energy required to perform the measurement, and it is lower than $E_{harv}$ since the latter is necessary to complete a BLE transmission. As a result, $V_{L,R}$ is usually higher than $V_L$.

It is worth noting the dual use of the storage capacitor $C_{stor}$ that is simultaneously used as a storage device to harvest the energy and as a measurement device in the measurement process of the resistor $R$.

$$E_{meas} = \frac{1}{2} \cdot C_{stor} \cdot (V_H^2 - V_{L,R}^2) \qquad (6)$$

The measurement of the time $t_m$ is executed as follows:

1. The system wakes up from the harvesting phase, i.e., ($V_{stor}=V_H$),

2. The LPTIM clock is configured to run at the highest frequency to maximize the measurement resolution and accuracy,

3. The signal $V_R$ is connected to $V_{stor}$ through the GPIO1,

4. The Microcontroller monitors the value of the voltage $V_{stor}$ through the PVD,

5. The value of $t_m$ is digitally converted in the number of clock pulses $N_m$ through the timer LPTIM,

6. The value of $N_m$ is recorded when the threshold $V_{L,R}$ is reached,

7. The signal $V_R$ is disconnected from $V_{stor}$ through GPIO1,

8. The MCU enters in Stop Mode, i.e., in the energy harvesting phase.

Eq. (7) evaluates the power balance of the system:

$$P_{geh} + P_{C_{stor}} = P_R + P_q \qquad (7)$$
$P_R$ and $P_{Cstor}$ are respectively the power dissipated through R and the power flowing through $C_{stor}$.

As shown already in (5) the quiescent power $P_q$ is negligible with respect to $P_{geh}$, so that (7) can be approximated as in (8).

$$P_{geh} + P_{Cstor} \approx P_R \qquad (8)$$

In practical cases, the voltage $V_{stor}$ is nearly constant as the EAWPSN is designed so that $V_{stor}$ varies between the two values $V_H$ and $V_{L,R}$ which differ for a couple of hundred millivolts. Therefore, $P_{geh}$ can be considered invariant with $V_{stor}$ leading to (9).

$$P_{geh} - C_{stor} \cdot V_{stor}(t) \cdot \frac{dV_{stor}(t)}{dt} = \frac{V_{stor}^2(t)}{R} \qquad (9)$$

Solving (9), and imposing the initial condition $V_{stor(0)}=V_H$, the voltage $V_{stor}(t)$ is given by (10):

$$V_{stor}(t) = \sqrt{(V_H^2 - R \cdot P_{geh}) \cdot e^{-2t/RC_{stor}} + R \cdot P_{geh}} \qquad (10)$$

The system is designed so that the voltage $V_{stor}$ drops from the voltage $V_H$ to the voltage $V_{L,R}$ within the time $t_m$. Therefore, by imposing the condition $V_{stor(t_m)}=V_{L,R}$ in (10), the time $t_m$ is given by (11):

$$t_m = \frac{R \cdot C_{stor}}{2} \cdot \ln \left( \frac{V_H^2 - R \cdot P_{geh}}{V_{L,R}^2 - R \cdot P_{geh}} \right) \qquad (11)$$

Eq. (11) cannot be easily inverted to calculate the value of R and must be solved numerically. Therefore, this equation cannot be used on the EAWPSN, and R can only be calculated remotely at the BS.

Eq. (11) can be simplified to the linear (12) when the applicable condition of (13) is met.

$$t_m \approx R \cdot C_{stor} \cdot \ln \left( \frac{V_H}{V_{L,R}} \right) \qquad (12)$$

$$V_{L,R}^2 \gg P_{geh} \cdot R \qquad (13)$$

Given the currently available power from the harvester, the condition from (13) defines the maximum range of validity for (12), as in (14). Therefore, the condition in (5) de facto defines the maximum measurable value of R as in (15).

$$R \ll \frac{V_{L,R}^2}{P_{geh}} \qquad (14)$$

$$R_{max} \ll \frac{V_{L,R}^2}{P_{geh\_min}} \qquad (15)$$

Eq. (15) reveals that to maximize $R_{max}$, $V_{L,R}$ must be maximized and set at the highest possible value, as in (16).

$$V_{L,R} \approx V_H \qquad (16)$$

By defining $V_{avg}$ and $V_{\Delta V}$ as in (17) and (18) respectively

$$V_{avg} = \frac{V_H + V_{L,R}}{2} \qquad (17)$$

$$V_{\Delta V} = V_H - V_{L,R} \qquad (18)$$

$V_H$ and $V_{L,R}$ can be calculated as in (19) and (20).

$$V_H = \frac{V_H + V_{L,R}}{2} + \frac{V_H - V_{L,R}}{2} = V_{avg} + \frac{V_{\Delta V}}{2} \qquad (19)$$

$$V_{L,R} = \frac{V_H + V_{L,R}}{2} - \frac{V_H - V_{L,R}}{2} = V_{avg} - \frac{V_{\Delta V}}{2} \qquad (20)$$

Combining (11), (19) and (20) leads to (21).

$$t_m \approx R \cdot C_{stor} \cdot \ln \left( \frac{1 + \frac{V_{\Delta V}}{2 \cdot V_{avg}}}{1 - \frac{V_{\Delta V}}{2 \cdot V_{avg}}} \right), \qquad (21)$$

The condition expressed in (16) implies that $V_{\Delta V}/V_{avg}<1$ that allows to further simplify (21) as in (22).

$$t_m \approx 2 \cdot R \cdot C_{stor} \cdot \frac{V_H - V_{L,R}}{V_H + V_{L,R}} \qquad (22)$$
<figure><img src="image_11.png" /><figcaption>Fig. 8. R vs. N<sub>m</sub>.</figcaption></figure>

Eq. (22) can be inverted, and the value of R can be calculated also by the EAWPSN by simply applying (23).

$$R \approx \frac{1}{2 \cdot C_{\text{stor}}} \cdot \frac{V_H + V_{L,R}}{V_H - V_{L,R}} \cdot t_m \qquad (23)$$

t<sub>m</sub> is digitally converted to the number of clock pulses N<sub>m</sub> counted by the timer LPTIM that runs at the frequency f<sub>clk</sub> as in (24).

$$t_m = \frac{N_m}{f_{\text{clk}}} \qquad (24)$$

From (23) and (24) derives the value of R in terms of the number of pulses counted by the timer LPTIM as in (25).

$$R \approx \frac{1}{2 \cdot C_{\text{stor}} \cdot f_{\text{clk}}} \cdot \frac{V_H + V_{L,R}}{V_H - V_{L,R}} \cdot N_m \qquad (25)$$

Eq. (25) shows that the minimum measurable resistance, i.e., the Limit of Detection (LoD) of the measurement system is given by (26)

$$R_{\min} \gg \frac{1}{C_{\text{stor}} \cdot f_{\text{clk}}} \cdot \frac{V_H + V_{L,R}}{V_H - V_{L,R}} \qquad (26)$$

Even if (25), in the measurement interval from R<sub>min</sub> to R<sub>max</sub>, can supply an accurate approximation in the considered measurement system, it cannot yet provide sufficiently precise results. Indeed, especially to evaluate low values of R, i.e., close to R<sub>min</sub>, it is necessary to take into account the value of the resistor of GPIO1 that connects C<sub>stor</sub> to R. Therefore, two main factors can influence the accuracy of R, i.e., the variation of the slope S<sub>R</sub>, whose nominal value is given in (28), and the intercept R<sub>0</sub> of the function R vs. N<sub>m</sub> shown in Fig. 8 and represented by (27).

$$R = R_0 + S_R \cdot N_m \qquad (27)$$

where the nominal value of S<sub>R</sub> is given by (28).

$$S_R = \frac{1}{2 \cdot C_{\text{stor}} \cdot f_{\text{clk}}} \cdot \frac{V_H + V_{L,R}}{V_H - V_{L,R}} \qquad (28)$$

R varies from its nominal value due to the manufacturing variations and tolerances from the nominal values of the parameters C<sub>stor</sub>, V<sub>H</sub>, V<sub>L,R</sub>, and f<sub>clk</sub> and (29) shows how the value of R deviates from its nominal value by dR given in (30).

$$R \pm dR = R_0 + S_R \cdot N_m \qquad (29)$$

$$dR = dS_R \cdot N_m \qquad (30)$$

where dS<sub>R</sub> is expressed in terms of the relative variations of C<sub>stor</sub>, f<sub>clk</sub>, V<sub>H</sub> and V<sub>L,R</sub> by (31).

$$dS_R = \frac{\partial S_R}{\partial C_{\text{stor}}} \cdot dC_{\text{stor}} + \frac{\partial S_R}{\partial f_{\text{clk}}} \cdot d f_{\text{clk}} + \frac{\partial S_R}{\partial V_H} \cdot dV_H + \frac{\partial S_R}{\partial V_{L,R}} \cdot dV_{L,R} \qquad (31)$$

By combining (29) and (30), R can be expressed as in (32).

$$R = R_0 + S_R \cdot \left( 1 \mp \frac{dS_R}{S_R} \right) \cdot N_m \qquad (32)$$
By defining $\alpha$ as in (33), a more accurate equation for the measurement of $R$ is given by (34).

$$ \alpha = 1 \mp \frac{dS_R}{S_R} \qquad (33) $$

$$ R = R_0 + \alpha \cdot S_R \cdot N_m \qquad (34) $$

Finally, (35) represents the sensitivity of $S_R$. Interestingly, it provides design insight for achieving the best accuracy of $R$, indicating the need to select a capacitor $C_{stor}$ with sufficient accuracy, maximize $f_{clk}$, and suggest maximizing the voltage difference between $V_H$ and $V_{L,R}$. This last condition contradicts the one previously expressed in (16) and highlights how the optimal choice of $V_{L,R}$ results from balancing the measurement range and the desired accuracy.

$$ \frac{dS_R}{S_R} = -\frac{dC_{stor}}{C_{stor}} - \frac{df_{clk}}{f_{clk}} - \frac{2 \cdot V_{L,R}}{V_H^2 - V_{L,R}^2} \cdot dV_H + \frac{2 \cdot V_H}{V_H^2 - V_{L,R}^2} \cdot dV_{L,R} \qquad (35) $$

## 3.2. System calibration

The calibration procedure to derive the parameters $R_0$ and $\alpha$ of (34) is performed as described in the following steps:

1. Through the GPIO2 the MCU connects the capacitor $C_{stor}$ to a known calibration resistor $R_{cal1}$ ($R_{min} < R_{cal1} < R_{max}$), as shown in Fig. 6,

2. The MCU counts the numbers of pulses $N_{cal1}$ related to the time $t_{cal1}$ elapsed to discharge $C_{stor}$ through $R_{cal1}$,

3. Through the GPIO3 the MCU connects the capacitor $C_{stor}$ to a known calibration resistor $R_{cal2}$ ($R_{min} < R_{cal2} < R_{max}$ and $R_{cal1} < R_{cal2}$), as shown in Fig. 6,

4. The MCU counts the numbers of pulses $N_{cal2}$ related to the time $t_{cal2}$ elapsed to discharge $C_{stor}$ through $R_{cal2}$.

Once recorded $N_{cal1}$ and $N_{cal2}$, the parameters $\alpha$ and $R_0$ are provided in (37) and (38) respectively as the unique solution of the system of Eqs. (36). Finally, the calibration parameters for the experiments performed in this work are shown in Table 3.

$$ \left\{ \begin{array}{l} R_{cal1} = R_0 + \alpha \cdot S_R \cdot N_{cal1} \\ R_{cal2} = R_0 + \alpha \cdot S_R \cdot N_{cal2} \end{array} \right. \qquad (36) $$

$$ \alpha = \frac{1}{S_R} \cdot \frac{R_{cal2} - R_{cal1}}{N_{cal2} - N_{cal1}} \qquad (37) $$

$$ R_0 = \frac{R_{cal1} \cdot N_{cal2} - R_{cal2} \cdot N_{cal1}}{N_{cal2} - N_{cal1}} \qquad (38) $$

## 3.3. Assessment metrics

The performance of the TDDC technique for resistance measurements was evaluated using different performance evaluation metrics. In particular, the goodness-of-fit indicators are: (i) the Root Mean Square Error (RMSE), with a target value of zero when there are no differences between the predicted and measured values [47]; (ii) the coefficient of determination ($r^2$), with a target value of one, indicating that the variance of the observed values is explained by the model [48]; (iii) the Mean Bias Error (MBE), with a target value of zero [49]. The relative error ($R_{error}$) on the resistance estimation was calculated using Eq. (39):

$$ R_{error}(\%) = 100 \cdot \frac{R - R_{ref}}{R} \qquad (39) $$

Lastly, the same metrics were used to validate the force measurement performed with the TDDC technique.

# 4. Measurement setup and experimental results

## 4.1. System validation

Several tests were conducted to measure the electrical resistance of the piezoresistive sensor in the EAWPSN, as explained in Section 4.2. Fig. 9 shows the experimental setup and highlights its most important parts. Additionally, the energy harvester and an LED, used as a light source, were contained within the light-box to achieve a controlled and repeatable light environment. The measurement data were simultaneously captured via Bluetooth using a computer connected to a remote BS and directly probing the signals $V_R$ and $V_{stor}$ on the EAWPSN using an oscilloscope. The TDDC resistance measurement technique was initially tested and calibrated with various resistance values using the PRS-330 Precision Programmable Resistance Box [50]. Later, the piezoresistive sensor was connected to the system and measured with different masses, as shown in Section 4.2.

Fig. 10 shows the evolutions of $V_{stor}$ and $V_R$ during two reading cycles of time $t_m$ for two sample resistance values: 0.4 kΩ, 6 kΩ. These two values were chosen because they belong to the range of resistance values obtained from piezoresistive sensor during static characterization. In this case, the measured times $t_m$ were respectively 13.5 ms for 0.4 kΩ (Fig. 10(a)) and 200 ms for 6 kΩ (Fig. 10(b)). These results were obtained when the harvester was subjected to a controlled lighting condition with a luminous power
<figure><img src="image_12.png" /><figcaption>Fig. 9. Experimental setup.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Evolution of the voltage $V_{stor}$ and $V_R$ vs. time, during the time readings $t_m$ for two different sample resistance values: (a) 0.4 kΩ, (b) 6 kΩ.</figcaption></figure>

<table><caption>**Table 2**

Setup parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>C<sub>stor</sub></td><td>440 μF</td></tr><tr><td>V<sub>H</sub></td><td>3.15 V</td></tr><tr><td>V<sub>L</sub></td><td>2.00 V</td></tr><tr><td>V<sub>L,R</sub></td><td>2.85 V</td></tr><tr><td>f<sub>clk</sub></td><td>37 kHz</td></tr><tr><td>P<sub>coh</sub></td><td>1 mW</td></tr><tr><td>Light intensity</td><td>1900 lux</td></tr></tbody></table>

<table><caption>**Table 3**

Calibration parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>R<sub>cal1</sub></td><td>400 Ω</td></tr><tr><td>R<sub>cal2</sub></td><td>10 000 Ω</td></tr><tr><td>t<sub>m,cal1</sub></td><td>13.5 ms</td></tr><tr><td>t<sub>m,cal2</sub></td><td>351 ms</td></tr><tr><td>N<sub>cal1</sub></td><td>499</td></tr><tr><td>N<sub>cal2</sub></td><td>12 980</td></tr><tr><td>α</td><td>1.25</td></tr><tr><td>R<sub>0</sub></td><td>16.36 Ω</td></tr></tbody></table>

of 1900 lux, along with the setup parameters summarized in Table 2. Under these conditions, the operating range of the EAWPSN is between 40 Ω and about 15 kΩ according to formulas (26) and (14). In particular, when substituting the parameters from Table 2
<caption>**Table 4**</caption>

Comparison between the reference resistance values and those calculated by the WSN through linear approximation as a function of digital time $t_m$, before and after calibration.

<table><thead><tr><th rowspan="2">R<sub>ref</sub> (Ω)</th><th rowspan="2">t<sub>m</sub> (ms)</th><th rowspan="2">N<sub>m</sub></th><th colspan="2">Pre-calibration</th><th colspan="2">Post-calibration</th></tr><tr><th>R (Ω)</th><th>R<sub>error</sub> (%)</th><th>R (Ω)</th><th>R<sub>error</sub> (%)</th></tr></thead><tbody><tr><td>40</td><td>1.0</td><td>37</td><td>22.7</td><td>43.2</td><td>101.6</td><td>-11.9</td></tr><tr><td>100</td><td>3.0</td><td>111</td><td>68.2</td><td>31.8</td><td>379.5</td><td>-1.6</td></tr><tr><td>363</td><td>12.8</td><td>473</td><td>290.5</td><td>19.96</td><td>399.5</td><td>-4.6</td></tr><tr><td>400</td><td>13.5</td><td>499</td><td>306.5</td><td>23.37</td><td>417.9</td><td>0.1</td></tr><tr><td>430</td><td>14.2</td><td>523</td><td>321.2</td><td>25.29</td><td>439.4</td><td>2.8</td></tr><tr><td>455</td><td>14.9</td><td>551</td><td>338.4</td><td>25.62</td><td>473.2</td><td>3.4</td></tr><tr><td>494</td><td>16.1</td><td>595</td><td>365.5</td><td>26.02</td><td>510.1</td><td>4.2</td></tr><tr><td>539</td><td>17.4</td><td>643</td><td>395.0</td><td>26.72</td><td>564.6</td><td>5.4</td></tr><tr><td>602</td><td>19.3</td><td>714</td><td>438.6</td><td>27.15</td><td>663.6</td><td>6.2</td></tr><tr><td>715</td><td>22.8</td><td>843</td><td>517.8</td><td>27.58</td><td>760.4</td><td>7.2</td></tr><tr><td>828</td><td>26.2</td><td>969</td><td>595.2</td><td>28.11</td><td>797.2</td><td>8.2</td></tr><tr><td>871</td><td>27.5</td><td>1017</td><td>624.7</td><td>28.28</td><td>910.9</td><td>8.5</td></tr><tr><td>1000</td><td>31.5</td><td>1165</td><td>715.6</td><td>28.44</td><td>1123.6</td><td>8.9</td></tr><tr><td>1250</td><td>39.0</td><td>1442</td><td>885.8</td><td>29.14</td><td>1345.4</td><td>10.1</td></tr><tr><td>1505</td><td>46.8</td><td>1731</td><td>1063.3</td><td>29.35</td><td>1558.9</td><td>10.6</td></tr><tr><td>1750</td><td>54.3</td><td>2009</td><td>1234.0</td><td>29.48</td><td>1791.5</td><td>10.9</td></tr><tr><td>2010</td><td>62.5</td><td>2312</td><td>1420.2</td><td>29.35</td><td>2765.9</td><td>10.9</td></tr><tr><td>3075</td><td>96.8</td><td>3581</td><td>2199.6</td><td>28.47</td><td>3913.8</td><td>10.1</td></tr><tr><td>4300</td><td>137.2</td><td>5076</td><td>3117.9</td><td>27.49</td><td>5755.0</td><td>8.98</td></tr><tr><td>6155</td><td>202.0</td><td>7474</td><td>4590.9</td><td>25.41</td><td>8271.9</td><td>6.5</td></tr><tr><td>8500</td><td>290.6</td><td>10752</td><td>6604.4</td><td>22.3</td><td>9988.0</td><td>2.7</td></tr><tr><td>10000</td><td>351.0</td><td>12987</td><td>7977.3</td><td>20.23</td><td>11351.6</td><td>0.12</td></tr><tr><td>11150</td><td>399.0</td><td>14763</td><td>9068.2</td><td>18.67</td><td>13681.1</td><td>-1.81</td></tr><tr><td>13000</td><td>481.0</td><td>17797</td><td>10931.8</td><td>15.91</td><td>16380.0</td><td>-5.24</td></tr><tr><td>15500</td><td>576.0</td><td>21312</td><td>13090.9</td><td>15.54</td><td>16380.0</td><td>-5.68</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Resistance values as a function of the number of clock pulses.</figcaption></figure>

in (26), an approximate value of 1.2 Ω is obtained. As a result, the value $R_{min} = 40$ Ω is selected to ensure strict compliance with the inequality (26). Furthermore, this value represents the Limit of Detection (LoD) of the EAWPSN.

The Table 4 compares the reference resistance values and those calculated by EAWPSN using the linear approximation as a function of digital time $t_m$ before and after calibration. The relative error ($R_{error}$) on the resistance estimation was calculated using (39).

Table 4 also displays the number of clock pulses $N_m$ counted by the LPTIM timer to obtain the measured digital time $t_m$. According to the findings, WSN reading accuracy is significantly improved by calibration. Before calibration, percentage errors were considerable, with values as high as 43%. After calibration, the percentage errors notably decrease, with 95% of values falling below 10%. This affirms that calibration enhances the accuracy of WSN.

The results demonstrate the importance of this calibration process in achieving more reliable and accurate TDDC conversions. This phenomenon is evident in Fig. 11, which compares the resistance values measured using the TDDC technique before and after calibration with reference values (black line). In particular, it emerges that, in the absence of calibration (red line), the TDDC technique tends to underestimate the resistance values, while when calibration is applied (blue line), the R values are very close to the reference values. Furthermore, in Fig. 11, it is possible to observe and appreciate the linearity of the sensor through its correlation with the number of pulses ($N_m$) counted by the LPTIM timer. Fig. 12 shows the percentage error of the proposed TDDC technique, representing the error in the operating range of the WSN between the estimated resistance value of the BS and the reference resistance values connected to the EAWPSN.
<figure><img src="image_15.png" /><figcaption>Fig. 12. Percentage error in resistance estimation within the operational range of the EAWPSN.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 13. Static characterization of multilayer sensors with the ACF adhesive (error bars representing min and max).</figcaption></figure>

## 4.2. Static characterization of the piezoresistive sensor

To obtain a static characterization of the relationship between resistance (R) and force (F) for the piezoresistive material, we
performed the following procedure on the sensor:

* Connected the piezoresistive sensor to the Digital Multimeter M-3650, which has an accuracy of ±0.5% of the reading + 3 digits.

* Mechanically loaded the piezoresistive sensor with a test mass.

* Let the system rest for 4 min to allow any transient effect to dissipate.

* Measured the resistance value and plotted it versus the applied force.

We repeated the procedure for various test masses ranging from 15 g to approximately 5 kg, and we calculated the dispersion and mean values, as shown in Fig. 13. The system showed lower accuracy when the weakest force was applied because, in this condition, the piezoresistive sensor is mechanically less stable, and specifically for this condition, the standard deviation was 0.70 kΩ, and the average measured resistance value was 15.5 kΩ. However, the standard deviation decreased to 10 Ω for an applied force of 1.22 N and dropped further to a few ohms when the applied force exceeded 3 N. The minimum measured resistance value was 363 Ω with a standard deviation of only 3.78 Ω when a force of 48 N was applied to the sensor.

In addition to analyzing resistance values, the data were also explored in terms of conductance (G) to provide further insight
into the static behavior of the piezoresistive sensor. In particular, this analysis revealed a limit of detection (LoD) in terms of
conductance equal to 64 µS and a linear relationship between conductance values and the applied force (F). Furthermore, two
regions with different sensitivities were identified. Specifically, for forces lower than 10 N, the sensitivity (dG/dF) was found to be
0.194 mS/N (Fig. 14(a)); while for forces greater than 10 N, dG/dF was equal to 0.02 mS/N (Fig. 14(b)).
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 14. Conductance as a function of the force applied to the piezoresistive sensor. Black line is the best linear fit.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 15. Experimental measurements of $N_m$ vs. applied force (log scale).</figcaption></figure>

### 4.3. Force-to-time-to-digital conversion results

This section presents the experimental results of the WSN readout based on force-to-time-to-digital conversion. Fig. 15 shows the relationship between the number of pulses counted ($N_m$) by the LPTIM using the TDDC technique and the different applied forces. Observations indicate that the curve has a monotonic trend, which allows for a linear approximation.

Since $N_m$ and applied forces are inversely proportional, to further explore the linearity of the force-to-time-digital conversion method and understand the WSN's sensitivity, it is interesting to observe the relationships between $1/N_m$ and the applied forces, as depicted in Fig. 16. The analysis of the results revealed three distinct sensitivities in the relationship between $1/N_m$ and $F$. As a result, the experimental measurement interval of applied forces, which spans from 0.25 N to 48.07 N, is divided into three sub-intervals characterized by the following linear relationships between force and $1/N_m$.

$$F = \frac{3.957 \cdot 10^3}{N_m} - 0.048 \quad \text{with } F \in [0.25 \text{ N} - 2.55 \text{ N}] \qquad (40)$$

$$F = \frac{8.767 \cdot 10^3}{N_m} - 4.005 \quad \text{with } F \in [2.55 \text{ N} - 13.0 \text{ N}] \qquad (41)$$

$$F = \frac{1.156 \cdot 10^5}{N_m} - 195.3 \quad \text{with } F \in [13.0 \text{ N} - 48.07 \text{ N}] \qquad (42)$$

Table 5 compares the reference forces ($F_{ref}$) with the results obtained by force-time-digital conversion before and after calibration. The data provided include the measured time ($t_m$), the number of pulses counted ($N_m$), the force calculated from the empirical relations ($F$) in Newtons and the percentage error ($F_{error}$) concerning the reference force. Some results before calibration, for example, those associated with forces around 1.37 N and 3.97 N, displayed low accuracy, with percentage errors exceeding 14%. The low accuracy observed for specific applied forces suggested the need for calibration. Consequently, the same calibration technique used for the resistance measurement was applied to the force estimation using the three linear regression equations. The empirically derived linear relationships in the three force sub-intervals can be expressed in the following form: $F = F_0 + \frac{a_F \cdot S_F}{N_m}$; where $S_F$ was equal to 3957, 8767, and $1.156 \cdot 10^5$ for (40), (41), and (42) respectively. To perform the calibration, reference force pairs
<figure><img src="image_20.png" /><figcaption>Fig. 16. Experimental results of 1/N<sub>m</sub> vs. applied force and its linear fits before (red line) and after calibration (blue line).</figcaption></figure>

<table><caption>**Table 5**

Comparison of reference forces and experimental results of the force-time-digital conversion method.</caption><thead><tr><th rowspan="2">F<sub>ref</sub> (N)</th><th rowspan="2">t<sub>m</sub> (ms)</th><th rowspan="2">N<sub>m</sub></th><th colspan="2">Pre-calibration</th><th colspan="2">Post-calibration</th></tr><tr><th>F (N)</th><th>F<sub>error</sub> (%)</th><th>F (N)</th><th>F<sub>error</sub> (%)</th></tr></thead><tbody><tr><td>0.25</td><td>399.0</td><td>14763</td><td>0.22</td><td>-13.6</td><td>0.25</td><td>0.0</td></tr><tr><td>0.30</td><td>351.0</td><td>12987</td><td>0.26</td><td>-15.4</td><td>0.28</td><td>-7.1</td></tr><tr><td>0.34</td><td>290.6</td><td>10752</td><td>0.32</td><td>-6.3</td><td>0.33</td><td>-3.0</td></tr><tr><td>0.72</td><td>131.2</td><td>4854</td><td>0.77</td><td>6.5</td><td>0.69</td><td>-4.3</td></tr><tr><td>1.03</td><td>90.8</td><td>3359</td><td>1.13</td><td>8.8</td><td>0.98</td><td>-5.1</td></tr><tr><td>1.37</td><td>63.5</td><td>2349</td><td>1.64</td><td>16.5</td><td>1.38</td><td>0.7</td></tr><tr><td><b>1.61</b></td><td><b>54.3</b></td><td><b>2009</b></td><td>1.92</td><td>16.1</td><td>1.61</td><td>0.0</td></tr><tr><td>2.01</td><td>46.8</td><td>1731</td><td>2.24</td><td>10.3</td><td>1.86</td><td>-8.1</td></tr><tr><td>2.45</td><td>38.0</td><td>1406</td><td>2.77</td><td>11.6</td><td>2.29</td><td>-7.0</td></tr><tr><td><b>2.98</b></td><td><b>31.9</b></td><td><b>1180</b></td><td>3.43</td><td>13.1</td><td>2.98</td><td>0.0</td></tr><tr><td>3.97</td><td>27.5</td><td>1017</td><td>4.62</td><td>14.1</td><td>4.28</td><td>7.2</td></tr><tr><td>4.46</td><td>26.2</td><td>969</td><td>5.04</td><td>11.5</td><td>4.75</td><td>6.1</td></tr><tr><td>5.89</td><td>22.8</td><td>843</td><td>6.40</td><td>8.0</td><td>6.22</td><td>5.3</td></tr><tr><td>7.85</td><td>19.3</td><td>714</td><td>8.28</td><td>5.2</td><td>8.28</td><td>5.2</td></tr><tr><td>9.81</td><td>17.4</td><td>643</td><td>9.63</td><td>-1.9</td><td>9.76</td><td>-0.5</td></tr><tr><td><b>10.72</b></td><td><b>16.3</b></td><td><b>604</b></td><td>10.51</td><td>-2.0</td><td>10.72</td><td>0.0</td></tr><tr><td>12.45</td><td>15.9</td><td>588</td><td>10.91</td><td>-14.1</td><td>11.15</td><td>-11.7</td></tr><tr><td><b>16.67</b></td><td><b>14.9</b></td><td><b>551</b></td><td>14.53</td><td>-14.7</td><td>16.67</td><td>0.0</td></tr><tr><td>22.54</td><td>14.4</td><td>534</td><td>21.21</td><td>-6.3</td><td>22.44</td><td>-0.4</td></tr><tr><td>28.45</td><td>14.2</td><td>525</td><td>24.93</td><td>-14.1</td><td>25.64</td><td>-10.0</td></tr><tr><td>34.33</td><td>13.5</td><td>499</td><td>36.40</td><td>5.7</td><td>35.55</td><td>3.4</td></tr><tr><td>39.29</td><td>12.9</td><td>479</td><td>46.08</td><td>14.7</td><td>43.91</td><td>10.5</td></tr><tr><td><b>46.11</b></td><td><b>12.8</b></td><td><b>474</b></td><td>48.62</td><td>5.2</td><td>46.11</td><td>0.0</td></tr><tr><td>48.10</td><td>12.7</td><td>469</td><td>51.22</td><td>6.1</td><td>48.35</td><td>0.5</td></tr></tbody></table>

were selected in the three sub-intervals. Finally, for each value of reference force (highlighted in bold in Table 5), the associated $N_m$ were measured to calculate $\alpha_F$ and $F_0$ as follows.

$$ \alpha_F = \frac{N_{cal1} \cdot N_{cal2}}{S_F} \cdot \frac{F_{cal2} - F_{cal1}}{N_{cal1} - N_{cal2}} \quad (43) $$

$$ F_0 = \frac{F_{cal1} N_{cal1} - F_{cal2} N_{cal2}}{N_{cal1} - N_{cal2}} \quad (44) $$

The results suggest that calibration is required to ensure high accuracy of the TDDC method over a wide range of forces. Indeed, after the calibration, the percentage errors decrease, with many values below 10%.

## 5. Discussion and possible application

In this section we discuss assessment metrics in terms of resistance and force measures with the proposed EAWPSN and present possible applications and future directions. The results presented in the Table 6 show a comparison of key assessment metrics for both resistance and force estimation using the TDDC technique before and after calibration. In the case of resistance estimation, the $r^2$ coefficient remained constant at 0.94 for both pre- and post-calibration, indicating that the calibration process did not
<table><caption>**Table 6**
Comparison of assessment metrics in resistance and force estimation with the TDDC technique before and after calibration.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Resistance estimation</th><th colspan="3">Force estimation</th></tr><tr><th>r<sup>2</sup></th><th>RMSE (Ω)</th><th>MBE (Ω)</th><th>r<sup>2</sup></th><th>RMSE (N)</th><th>MBE (N)</th></tr></thead><tbody><tr><td>Pre-calibration</td><td>0.94</td><td>1058</td><td>-713.9</td><td>0.98</td><td>1.93</td><td>0.39</td></tr><tr><td>Post-calibration</td><td>0.94</td><td>1107</td><td>627.7</td><td>0.99</td><td>1.17</td><td>0.11</td></tr></tbody></table>

<table><caption>**Table 7**
A comparative analysis of piezoresistive system solar energy harvesting: ADC vs. TDDC as reported in [53].</caption><thead><tr><th>Systems</th><th>Measurement technique</th><th>Harvester's power [mW]</th><th>Power consumption</th><th>Measurement accuracy [%]</th></tr></thead><tbody><tr><td>[54]</td><td>ADC with 12 bits</td><td>[81-360]</td><td>Low-power</td><td>±0.025</td></tr><tr><td>This work</td><td>TDDC</td><td>1</td><td>Ultra-low-power</td><td>±4</td></tr></tbody></table>

significantly affect the goodness of fit. However, there was a slight increase in the RMSE from 1058 Ω to 1107 Ω, while the MBE error suggests a reduction in bias after calibration. For force estimation, there was a more noticeable improvement post-calibration. The r² value increased from 0.98 (pre-calibration) to 0.99 (post-calibration), which indicates a better fit of the force estimation model to the observed data after calibration. Similarly, the RMSE for force estimation improved significantly from 1.93 N to 1.17 N, demonstrating a more accurate force estimation post-calibration. The MBE also showed a substantial reduction, dropping from 0.39 N pre-calibration to 0.11 N post-calibration, indicating that the calibration helped minimize the bias in force measurements.

**Table 7** provides a detailed comparison between two studies leveraging solar energy harvesting in piezoresistive systems. It examines various factors such as measurement techniques, system consumption, accuracy, and harvesting power. The choice between ADC and TDDC methods depends on application requirements. For example, ADC excels in real-time tracking scenarios like athlete monitoring, where precision is critical. In contrast, TDDC is more suitable for intermittent measurements, such as temperature monitoring, as it does not require continuous data acquisition. This adaptability highlights the importance of selecting the appropriate methodology for specific use cases.

The design of the EAWPSN with integrated TDDC, opens up new perspectives for IoT applications, particularly in contexts requiring long-term data collection. The choice of ambient light power offers a sustainable solution by reducing dependence on batteries, which have a negative environmental impact due to their manufacture, maintenance and disposal [51]. By exploiting natural or artificial light to generate energy, this sensor is positioned as an environmentally-friendly alternative in the IoT field.

The integration of TDDC in this sensor system, which reduces power consumption and simplifies signal processing, significantly contributes to a more energy-efficient and environmentally-conscious design. Indeed, as discussed in [27], this power reduction can lead to environmental benefit over the lifetime of the IoT device is the whole system is correctly sized. To further enhance its positive environmental impact, it would be beneficial to incorporate recyclable or biodegradable materials into the sensor's construction and to prioritize production methods that minimize carbon emissions [52]. Furthermore, while Bluetooth Low Energy (BLE) communication already improves energy efficiency, exploring the potential use of even more energy-efficient communication protocols could prove advantageous in applications with higher data transfer demands or in energy-limited contexts.

Although the EAWPSN has been tested for resistance and strength measurements, the integrated TDDC method is suitable for measuring resistance and is not limited to piezoresistive sensors. It encompasses a wide range of resistance-based sensors [55], including those that measure temperature such as thermistors [56], chemical conductivity, luminosity [37] or gas sensors [57], and etc. Moreover, the deployment of these sensors in remote or difficult-to-access locations minimizes maintenance requirements, which not only reduces operational costs but also decreases the environmental footprint associated with travel and physical interventions for installation and upkeep. This reduced need for maintenance aligns well with sustainability goals, as it lowers emissions and resource use associated with long-term sensor deployment. Overall, this technology represents a promising advance toward autonomous, sustainable IoT systems, and future design iterations could continue to integrate eco-friendly materials and low-impact practices, further supporting the transition to greener and more sustainable technologies.

Potential applications for the EAWPSN include structural health monitoring in remote infrastructures, where data monitoring is essential for early detection of potential issues [58]. Indeed, the EAWPSN can be deployed in various environments to assess the structural health of houses, buildings, skyscrapers, bridges, and overpasses, all while reducing the need for battery replacements and minimizing its environmental footprint. Furthermore, the EAWPSN can be adopted for monitoring some physical parameters in agriculture. In fact, a piezoresistive sensor combined with the TDDC method can be used to estimate soil moisture [59], soil nutrients [60], detect the presence of pathogens in crops [61], and manufacture bio-based pressure sensors [62]. Lastly, our solution can be used in the healthcare and sports sectors, integrating EAWPSN into wearable devices to monitor vital parameters such as blood pressure or muscle activity [31,44], ensuring real-time monitoring for patients or athletes without having to resort to disposable batteries. These latter applications present research challenges such as the integration of energy harvesting systems in wearable devices and a future direction could be to integrate the EAWPSN with flexible solar cells as proposed in recent works [63-65]. On the other hand, monitoring vital signs using battery-free wearable devices raises research challenges for the security of IoT connection and data, as discussed extensively in [33,66]. Due to their deeply integrated nature and their relationship with the surrounding physical environment, IoT systems are at risk of cyberattacks, and battery-free devices are no exception. Consequently, greater efforts are needed to investigate the operation of batteryless devices during cyberattacks, and new detection and mitigation techniques should be implemented to counteract these occurrences [33,67]. Future research directions to mitigate attacks should consider
integrating the EAWPSN into a blockchain-inspired Internet of Things architecture to ensure security and reduce the vulnerability of the architecture to different types of cyberattacks [68,69].

Finally, the ability to integrate the EAWPSN into smart application for health monitoring or into wireless environmental sensors to monitor air quality and weather conditions makes them an ideal solution for a wide range of sustainable IoT applications, promoting the transition to greener, more energy-efficient technologies.

## 6. Conclusion

In conclusion, this study successfully presents an energy-autonomous wireless piezoresistive sensor that integrates the capabilities of the Time Domain to Digital Conversion (TDDC), addressing the critical need for sustainable and maintenance-free monitoring solutions in the Internet of Things (IoT) landscape. Our findings demonstrate that the proposed sensor effectively harnesses ambient energy, enabling continuous operation without reliance on traditional battery power. This innovation not only enhances the sensor's energy efficiency but also simplifies the overall design by eliminating the need for power-hungry analog-to-digital converters. The high sensitivity and accuracy of the piezoresistive device make it suitable for a wide range of applications, including real-time structural health monitoring and industrial condition assessment. By aligning our research with the growing demand for environmentally friendly IoT solutions, we contribute to the advancement of green technologies that can support the deployment of large-scale sensor networks. Future work will focus on optimizing the sensor performance and exploring additional applications, further solidifying its role in the evolving landscape of sustainable IoT monitoring.

## CRediT authorship contribution statement

**Mario Costanza:** Writing – review & editing, Writing – original draft, Software, Conceptualization.
**Abdo-Rahmane Anas Laaraibi:** Visualization.
**Antonino Pagano:** Writing – review & editing, Writing – original draft, Validation, Formal analysis, Data curation.
**Gurvan Jodin:** Visualization, Investigation.
**Florence Razan:** Formal analysis.
**Ilenia Tinnirello:** Supervision.
**Samuel Margueron:** Methodology, Conceptualization.
**Roberto La Rosa:** Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work was partially supported by the following projects:

* The European Union's Horizon Europe research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101086359.

* The Agence Nationale de la Recherche (ANR) within the framework of the EUR EIPHI project (ANR-17-EURE-0002).

* The ANR within the framework of the PIA EUR DIGISPORT project (ANR-18-EURE-0022).

* The Centre National de la Recherche Scientifique (CNRS) through the INSIS project "Grappillage d'Energie".

* The European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Telecommunications of the Future" (PE00000001 - program "RESTART"), CUP F83C22001690001 and CUP E63C22002070006.

## Data availability

Data will be made available on request.

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