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Open AccessFeature PaperArticle

Low-Frequency RFID Signal and Power Transfer Circuitry for Capacitive and Resistive Mixed Sensor Array

1
Department of Information Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy
2
INO-CNR (National Institute of Optics—National Research Council), Via Branze 45, 25123 Brescia, Italy
*
Author to whom correspondence should be addressed.
Electronics 2019, 8(6), 675; https://doi.org/10.3390/electronics8060675
Received: 14 May 2019 / Revised: 3 June 2019 / Accepted: 11 June 2019 / Published: 14 June 2019
(This article belongs to the Section Microwave and Wireless Communications)

Abstract

This paper presents a contactless measurement system for a mixed array of resistive and capacitive sensors exploiting a low-frequency radio-frequency identification (RFID)-based approach. The system is composed of a reader unit which provides power to and exchanges measurement data with a battery-less sensor unit. The sensor unit is based on a transponder operating at 134.2 kHz and a microcontroller. The microcontroller sequentially measures the elements of the sensor array composed of n capacitive and m resistive sensors which share a common terminal. The adopted technique measures the charging time of a resistor–capacitor (RC) circuit, where the resistor or the capacitor can be either the sensing element or a reference component. With the proposed approach, the measured values of the resistive or capacitive elements of the sensor array are first-order independent from the supply voltage level. A prototype has been developed and experimentally tested with resistive elements in the range 400 kΩ–1.2 MΩ and capacitive elements in the range 200 pF–1.2 nF showing measurement resolution values of 1 kΩ and 5 pF, respectively. Operative distances up to 3 cm have been achieved, with readings taken faster than one element of the array per second.
Keywords: low-frequency RFID; capacitive and resistive sensors; contactless interrogation; power transfer low-frequency RFID; capacitive and resistive sensors; contactless interrogation; power transfer

1. Introduction

The presence of sensors in everyday life and devices is becoming ubiquitous, among other reasons due to the emerging IoT (internet of things) scenario, where objects can become nodes of an intercommunicating network [1]. In this context, wired connections between nodes would be impractical, and hence wireless solutions are the preferred choice. At the same time, supplying power to the nodes is extremely challenging, also considering the scenario of disposable objects [2]. Especially in this latter case, batteries do not seem to be an option due to ecological and recycling issues and the maintenance required for battery replacement.
Energy harvesting solutions have received significant development and research efforts over the last decades, whereby mechanical configurations, energy conversion principles and electronic energy management circuits have been extensively investigated [3,4,5]. Specifically, energy can be harvested from vibrations, movement, thermal gradients and other sources. Harvesting energy from vibrations or movement can be achieved by means of converters generally based on piezoelectric, electrostatic or electrodynamic effects [6]. Several strategies have been adopted to increase the amount of energy harvested from broadband vibrations, overcoming the limitations of linear energy harvesters which best operate at their resonant frequency [7,8,9,10,11,12,13]. On the other hand, harvesting energy from thermal spatial gradients or time variations is typically based on thermoelectric [14] or pyroelectric effects [15], respectively. Energy harvesting is attractive but, though offering in principle an unlimited operation lifetime, demands an adequate amount of environment energy to be effectively harvested to supply the sensor unit.
Alternatively, contactless techniques can be adopted to interrogate passive sensors. One approach for passive mechanical resonators, which are required to be only electrically conductive, exploits externally induced eddy-currents [16]. Similarly, contactless interrogation can be achieved through an electromagnetic link between two coupled coils [17,18]. In [19,20,21,22], a primary coil is connected to the interrogation circuit, while a secondary coil is connected to a resonant sensor; i.e., a mechanical resonator such as a quartz crystal microbalance (QCM), a micro electro-mechanical system (MEMS) or an electrical resonant sensor such as an LC-tank circuit. The measurement principle can exploit both frequency-domain and time-domain techniques [21,22]. This approach relies on completely passive sensors; i.e., they do not require any active electronic circuits on board to operate.
A different approach exploits RFID technologies in the low frequency (LF), high frequency (HF) and ultra-high frequency (UHF) ranges [23]. In these cases, the reader energizes the sensor unit with an on-board transponder and they exchange data, exploiting the wireless link. The transponder can harvest energy through the RF link and operate as a bus bridge towards other devices, such as microcontrollers or digital sensors [24,25,26,27,28]. When a microcontroller is available, the number of sensors can be larger, provided that the energy budget is adequate to power them. Different microcontroller-based configurations have been proposed to interface resistive or capacitive sensors with low-power approaches [29,30,31,32,33,34,35]. Resistive and capacitive sensors are very attractive for disposable devices, because they can be adopted for the measurement of physical quantities, such as temperature and humidity, or chemical quantities, using them as gas sensors that can be applied to monitor, for example, food spoilage. In particular, low-cost gas sensors have been demonstrated in [36].
In this paper, a contactless system for a capacitive and resistive mixed sensor array is presented. By exploiting an RF link, the interrogation unit transfers energy and exchanges data with the sensor unit composed of a RFID transponder, a microcontroller and the sensor array. A measurement technique based on the charging time of suitable RC circuits advantageously allows to measure both the resistive and capacitive elements of the array. The RF link enables a complete contactless measuring technique. The prototyped system has been characterized and successfully applied to the measurement of both humidity and temperature of the air inside a package under different operating conditions.

2. System Description

Figure 1 shows the block diagram of the proposed RFID-powered contactless interface operating at the frequency of 134.2 kHz. The interface is composed of the reader unit (RU) and the sensor unit (SU) to which the resistive and capacitive mixed sensor array is connected. The RU consists of a RFID reader that manages both power transfer and data communication with the SU through the same RF link. The RU is based on a TMS3705 (Texas Instruments, Dallas, TX, USA) device that can be interfaced with a personal computer for commands and data management.
The SU includes an RF transponder and a microcontroller. The transponder is based on a TMS37157 (Texas Instruments, Dallas, TX, USA) device which collects the energy received through the RF link and operates as a serial peripheral interface (SPI) bridge towards the microcontroller. In particular, the transponder exploits the inductor LT, tuned with the capacitor CT to set the operating frequency at 134.2 kHz, for both power transfer and data communication. The RF input of the transponder rectifies the voltage across the LT-CT tank and stores the collected energy into the capacitor CL. The 3.3 V voltage regulator MCP1700-3V3 (Microchip Technology, Chandler, AZ, USA) regulates the voltage VCL, generating the voltage VDD on the capacitor CS. The voltage VDD then supplies both the digital interface of the transponder and the microcontroller.
To implement the measurement procedure and transfer the measurement information to the transponder, an ultra-low-power microcontroller MSP430G2553 (Texas Instruments, Dallas, TX, USA) has been specifically selected since it embeds subsystems and functionalities required to interface the mixed sensor array, such as an analog comparator, counters, and low-power working modes [37]. The microcontroller interfaces the transponder through a SPI bus which allows the bidirectional communication of commands and measurement data. In particular, the commands sent to the microcontroller include the request to operate the measurement of a specific sensor element of the array.
Figure 2 shows the microcontroller sensor interface for the measurement of the elements of a mixed array of n capacitive and m resistive sensors. The resistive and capacitive sensors of the array have one common terminal, while the other terminal of each Ci capacitive and Rj resistive sensor is connected to a different I/O pin of the microcontroller, named PCi and PRj, respectively, with i = 1 to n and j = 1 to m. The common terminal of the array is connected to ground through a reference capacitor CM and to two I/O pins through a reference resistor RREF and a discharge resistor RDIS. The voltage VM across the capacitor CM is fed to the non-inverting input of the comparator inside the microcontroller, while the inverting input is connected to an internal voltage reference at VDD/2. The proposed configuration allows the measurement of the values of both Rj and Ci through the same technique based on the measurement of the charging time of either CM or CM + Ci.
Figure 3a shows the relevant signals in the measurement cycle of the x-th resistive sensor Rx. The measurement starts by configuring the pins PCi (with i = 1, …, n), PRj (with j = 1, …, m, with jx), PREF, and PDIS as inputs, i.e., setting them in the high-impedance state, while the pin PRx is configured as output, i.e., in the low-impedance state. The logic level of PRx is set to high to charge the capacitor CM through Rx. Simultaneously, an internal timer is triggered to measure the time TRx elapsed between the charge starting time and the time when the voltage VM reaches VDD/2, causing the switching of the comparator output OC to the high logic level. This condition triggers the discharge of the capacitor CM through the resistor RDIS whereby PDIS is configured as the output and set to low, while the pin PRx is configured as the input. The same charge–discharge sequence is then repeated by activating the pin PREF and charging the capacitor CM through RREF to measure the reference charge time TREF. Accordingly, Rx can be determined as
R x = R R E F T R x T R E F = R R E F N R x N R E F ,
where NRx = TRxfCK and NREF = TREFfCK are the timer counts corresponding to the charging times through Rx and RREF, respectively, and fCK is the clock frequency of the timer. Equation (1) shows that the proposed measurement technique is independent of the values of the capacitance CM and the power supply voltage VDD. In the following, the value of VDD will be assumed to be constant during the measurement cycle.
Similarly, Figure 3b shows the relevant signals in the measurement cycle of the x-th capacitive sensor Cx. The measurement technique of the capacitive sensors consists in the measurement of the charging time of the selected x-th capacitive sensor Cx of the array through the known resistor RREF. The measurement starts by configuring all the pins PCi, PRj, and PDIS as inputs, while the pin PREF is configured as output. The logic level of PREF is set to high to charge the capacitor CM through RREF. Simultaneously, the internal timer is started to measure the time TREF elapsed between the charge starting time and the time when the voltage VM reaches VDD/2. This condition triggers the discharge of CM through the resistor RDIS whereby the pin PREF is configured as input while PDIS is configured as output and set to low. Subsequently, the pin PCx is configured as output and set to low, keeping the other pins PRx, PCx, and PDIS configured as inputs. This connects the capacitor Cx between the common terminal of the array and ground and thus in parallel with CM. The pin PREF is set to high in order to measure the charging time TMx of the equivalent capacitance Cx + CM through RREF. Accordingly, the times TREF and TMx can be expressed as
T R E F = ln ( 2 ) R R E F C M ,
T M x = ln ( 2 ) R R E F ( C x + C M ) .
Then, the Cx can be determined as
C x = T M x T R E F ln ( 2 ) R R E F = 1 f C k N M x N R E F ln ( 2 ) R R E F ,
where NREF and NMx are the timer counts corresponding to the charging times of CM and the equivalent capacitance Cx + CM, respectively. Equation (4) shows that the proposed measurement technique is independent from the values of the capacitance CM and the power supply voltage VDD.
Different combinations of the values for CM and RREF can be adjusted with respect to those of the resistors and capacitors of the sensor array to set the measurement range avoiding the timer overflow. The measurement accuracy depends on the accuracy of the reference resistor RREF, and the capacitance measurement additionally depends on the accuracy of the clock frequency fCK.
To improve the measurement accuracy for capacitive sensors, the effect of the parasitic capacitance associated to the microcontroller pins has been considered. Figure 4a,b shows the effect of the parasitic capacitances during the measurement of the charging times of CM and CM + Cx, respectively. When the pins PCi are configured as inputs, their parasitic capacitances CPi are connected in series with the corresponding Ci, giving the contribution CAi = CiCPi/(Ci + CPi). As a consequence, during the measurements of the charging times, the capacitances CAi add in parallel to CM or CM + Cx. Specifically, during the measurement of CM, all the pins are configured as inputs and TREF becomes
T R E F = ln ( 2 ) R R E F ( C M + i = 1 n C i C P i C i + C P i ) .
During the measurement of CM + Cx, the pin corresponding to Cx is set to low and the effect of the parasitic capacitance CPx can be neglected. Hence, the time TMx becomes
T M x = ln ( 2 ) R R E F ( C x + C M + i = 1 n C i C P i C i + C P i C x C P x C x + C P x ) .
Consequently, the resulting calculated capacitance C x is
C x = T M x T R E F ln ( 2 ) R R E F = C x C x C P x C x + C P x .
As a simplifying assumption, if all the CPi can be considered equal, their undesired effect can be compensated through a calibration procedure. The calibration requires the measurement of a known reference capacitor CK. Connecting CK to the pins PCi, i.e., with Cx = CK, the corresponding CPx can be calculated from the measured value C K by inverting Equation (7) as
C P x = C K C K ( C K C K ) .
Subsequently, from Equation (7), the known values of CPx can be used to calculate the unaffected value of Cx from the measured C x as
C x = C x + C x 2 + 4 C x C P x 2 .
As far as the measurement of the resistive sensors is concerned, the effect of the parasitic capacitances can be neglected. In fact, the parasitic capacitances, in the order of few picofarads, combined with the resistors of the array, in the order of several hundreds of kiloohms, result in time constants which are much lower than those formed by the resistors of the array with the reference capacitance in the order of nanofarads.

3. Experimental Results

3.1. Description of the System Prototype

Figure 5 shows a picture of the developed system prototype comprising the SU and the RU. The proposed SU consist of a 20 × 20 mm printed circuit board (PCB) which includes the transponder and the microcontroller-based interface. The transponder adopts a chip coil with inductance LT = 2.85 mH tuned to the nominal operating frequency of 134.2 kHz by means of a capacitor CT = 470 pF. Suitable external connections are provided to the capacitive and resistive mixed sensor array. A TMS37157 development tool (Texas Instruments, Dallas, TX, USA) was used as the RU which exploits a 43-mm diameter circular coil with LR = 442 μH measured at 134.2 kHz.
The topology of the mixed sensor array is preconfigured in the RU which manages both the procedure for the measurement of each sensor and the complete measurement cycle of the mixed sensor array. In general, for a single measurement of Rx or Cx the RU sends to the SU the request to trigger a single measurement of the charging times TRx and TREF for Rx, or TMx and TREF for Cx. When the SU is powered by the RF field, the voltage regulator and the transponder turn on, while the microcontroller switches into sleep mode to save energy. Subsequently, the received command is transferred to the microcontroller through the SPI interface. The microcontroller wakes up, enters the active mode and in turn forces the transponder into sleep mode by sending the corresponding command through the SPI interface. The microcontroller performs the measurement of the requested charging time, reactivates the transponder and transfers the measurement data. As the final step, the reader turns off the RF field, and the transponder sends the data received from the microcontroller; i.e., the counts NRx, NMx or NREF. The value of Rx is computed using Equation (1), while the value of Cx is computed using Equations (7) and (9) taking into account the parasitic capacitance CPx estimated during the calibration phase.
For the complete measurement cycle of the mixed sensor array, the reader sends a request every 500 ms and waits for a reply from the transponder within a preset time window of 300 ms. To avoid deadlock events, i.e., a missing reply, up to 5 consecutive attempts are performed before switching to the next sensor of the array.
A set of n = 3 fixed capacitors and m = 3 fixed resistors was connected to the microcontroller-based interface for the preliminary experimental characterization. With reference to the block diagrams of Figure 1 and Figure 2, the voltages VCL, VDD, VM, the current IMC and the RF field were simultaneously measured. The current IMC was measured by a shunt resistor connected in series to the supply pin of the microcontroller. The RF field was sensed by an external probing coil placed closed to the reader coil. The distance between the RU and SU coils was set to 2 cm.
Figure 6 shows the signals acquired at the beginning of the sequential measurements. It can be observed that, for the first two requests—i.e., the first two bursts of the RF field—not enough energy is stored into the capacitors CL and CS to allow the SU to power-up. In fact, the waveform of the current IMC shows that the microcontroller does not enter the active mode. During the second burst, the voltage VDD on the capacitor CS reaches the regulated level of 3.3 V, and the corresponding amount of energy is available for the following request. After the third burst, the measurement procedure is executed as it can be seen from the value of microcontroller current absorption and in the second short activation of the RF field by the RU, which confirms that data have been sent by the SU.
An enlarged view of the signals corresponding to a successful single measurement cycle is shown in Figure 7a. When the RF field is switched on, the voltage VCL has an initial step of about 4 V followed by an incremental increase up to about 6 V, while the voltage VDD is kept fixed at 3.3 V by the voltage regulator. After 80 ms, the command transmission is completed and the transponder activates the microcontroller, as confirmed by the current IMC that increases up to about 2.5 mA; i.e., the current absorption in active mode. The power consumption of the microcontroller causes the discharge of the capacitor CL with a corresponding decrease of the voltage VCL. After 20 ms from the onset of the active mode, VCL goes below 3.4 V and the voltage regulator turns off. However, as shown in Figure 7b, the energy stored into the capacitor CS allows the microcontroller to stay powered to complete the operation. The time duration for a single measurement cycle is about 27 ms. Figure 7b shows two subsequent charge–discharge cycles of CM during which VDD is kept constant, ensuring the effectiveness of the applied method, as discussed in Section 2.
To evaluate the measurement repeatability of the proposed system, two different arrays were tested for a total of six different resistors and six different capacitors. In the experimental tests, the values of CM, RREF and RDIS were set to 4.7 nF, 1 MΩ and 1 kΩ, respectively.
Each resistor, chosen in the range between 390 kΩ and 1.2 MΩ, was consecutively measured N = 40 times. and the corresponding average value R j ¯ was compared with the reference value Rj measured by a multimeter Fluke 8840A (Fluke Corporation, Everett, WA, USA). Table 1 reports the reference values Rj, the average values R j ¯ , and the corresponding standard deviations σRj, respectively. The repeatability for the resistive measurements, which sets the resolution, is estimated at σRj, resulting in between 0.5 kΩ to 1 kΩ. The relative resolution σRj/Rj is about 0.1%.
The relative errors eRj = ( R j ¯ Rj)/Rj have been calculated as an estimation of the resistance measurement accuracy. Figure 8 reports the relative errors as a function of the measured reference values Rj, evidencing eRj less than 0.6% in the considered range.
Similarly, each capacitance, chosen in the range between 220 pF and 1.2 nF, was consecutively measured N = 40 times, and the corresponding average value C i ¯ was compared with the reference value measured by a capacitance meter E4981A (Keysight Technologies, Santa Rosa, CA, USA) at the frequency of 120 Hz. Table 2 reports the reference values Ci, the average values C i ¯ and the corresponding standard deviations σCi, respectively. The repeatability for the capacitive measurements, which sets the resolution, is estimated at σCi resulting in between 1 pF to 5 pF. The relative resolution σCi/Ci is in the range between 0.12% and 1.8%.
The relative errors eCi = ( C i ¯ − Ci)/Ci were calculated as an estimation of the capacitance measurement accuracy. Figure 9 reports the relative errors as a function of the measured reference values Ci, evidencing eCi lower than 1% in the considered range.

3.2. Array of Temperature and Humidity Sensors

The proposed system was experimentally validated with a sensor array composed of two resistive temperature sensors and two humidity capacitive sensors. The temperature sensors are NTCG16QH334 (TDK, Chuo, Japan) NTC thermistors with a resistance given by RT = R0eB(1/T−1/T0), where R0 = 330 kΩ at T0 = 298 K, B = 4662 K and T is the temperature in Kelvin. The relative humidity (RH) sensors are H6000 (Gefran S.p.A., Provaglio d’Iseo, Italy) devices with a nominal capacitance of 500 pF at 75% RH and sensitivity of about 1 pF/% RH.
In the first test, the four sensors were measured during sequential exposures to a hot air jet and a high-humidity air jet, respectively, in order to evaluate the system response to temperature and humidity. Figure 10a,b shows the measured resistance values and the corresponding temperature trends versus time, and the measured capacitance values and the corresponding RH trends versus time, respectively. As can be observed, a reading is received from the SU every 0.5 s, which corresponds to a measurement rate for each sensor of one reading every 2 s.
As a final test application, the contactless monitoring of the temperature and humidity inside a hermetic food box was investigated. A temperature and humidity sensor pair NTCG16QH334 (TDK, Chuo, Japan) and H6000 (Gefran S.p.A., Provaglio d’Iseo, Italy) were placed inside the box, while an additional pair of identical sensors were kept outside to monitor the ambient temperature and humidity. A humidified sponge was placed inside the box as a humidity source. The monitoring of the temperature and humidity was performed by activating the SU placed outside the box every 2 min and collecting N = 10 consecutive measurements for each sensor. Figure 11 shows the temperature and humidity values measured by each of the four sensors during the test.
The test was divided into four phases. At the beginning, the box with the sponge inside is sealed. The humidity sensor inside the box detects an increase of RH up to about 80% RH, while the response of the external sensor remains almost constant, as it will be throughout all the duration of the test. Subsequently, the box is placed on a heater. An increase of temperature inside the box up to about 40 °C is detected by the internal temperature sensor, with a corresponding measured internal humidity decrease down to 50% RH, as expected. In the next phase, the box is removed from the heater and a corresponding decrease of the internal temperature and increase of the humidity up to 100% RH were detected. In the last phase, the box is opened, and a corresponding decrease of the measured internal humidity was consistently detected.

4. Discussion and Conclusions

A contactless system for the measurement of resistive and capacitive mixed sensor arrays has been presented. Contactless operation has been achieved by the exploitation of a low-frequency RFID link operating at 134.2 kHz. An external reader unit (RU) energizes the battery-less sensor unit (SU) and exchanges measurement data which can subsequently undergo post-processing elaboration. The SU is based on a RFID transponder and a microcontroller devoted to the measuring process and connected to a resistive and capacitive mixed sensor array. The SU was designed with the constraint of a minimum count of on-board electronic components in order to minimize power consumption. A key step in the development was the adoption of low-power ratiometric sensor measurement techniques based on the charging time of suitable RC circuits unaffected by the specific value of the supply voltage.
The prototyped SU is as small as 2 × 2 cm, ensuring the possibility of embedding it in disposable or portable sensorized objects to be monitored on-demand without any physical connection or on-board energy sources. The maximum working distance is about 3 cm and depends on the reader-transmitted power, the dimension/alignment and the presence of metallic objects near to the transmitting and receiving coils.
The proposed system was validated on reference resistors and capacitors, showing maximum relative deviations with respect to reference values of 0.6% and 1.2%, respectively. In particular, the accuracy in the measurement of the capacitive elements was improved thanks to dedicated calibration procedures. Other systems reported in the literature based on the measurement of charging time can achieve deviations of the measured resistors with respect to reference values as low as 0.03% [31] and 0.05% [32,34] in the resistive range of up to about 150 kΩ. However, it has to be noted that such systems rely on wired connections to the sensor unit, involve complex circuits based on analog switches or operational amplifiers and have no restrictions on power consumption.
The prototyped system has been successfully applied to the contactless monitoring of the temperature and humidity inside a hermetic food box, adopting a resistive temperature sensor and a capacitive humidity sensor. The results show the ability to track the variations of the two quantities in the ranges 20–40 °C and 20–100% RH, respectively.

Author Contributions

M.D. contributed in the design and development of the system, experimental activity, analysis of experimental data, and in writing the paper. M.B. worked on the design and development of the system, contributed in the experimental activity, analysis of experimental data, and in writing and revising the paper. S.D. contributed in the development of the system and in revising the paper. M.F. contributed in revising the paper. V.F. coordinated the research and contributed in revising the paper.

Funding

This research received no external funding.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Block diagram of the radio-frequency identification (RFID) data and power transfer circuitry for capacitive and resistive mixed sensor array.
Figure 1. Block diagram of the radio-frequency identification (RFID) data and power transfer circuitry for capacitive and resistive mixed sensor array.
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Figure 2. Microcontroller sensor interface for the capacitive and resistive mixed sensor array.
Figure 2. Microcontroller sensor interface for the capacitive and resistive mixed sensor array.
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Figure 3. Operation of the microcontroller-based interface: (a) measurement cycle for the resistive sensor Rx (the charging times of CM through Rx and RREF are sequentially measured); (b) measurement cycle of the capacitive sensor Cx (the charging times of CM and of Cx + CM through RREF are sequentially measured).
Figure 3. Operation of the microcontroller-based interface: (a) measurement cycle for the resistive sensor Rx (the charging times of CM through Rx and RREF are sequentially measured); (b) measurement cycle of the capacitive sensor Cx (the charging times of CM and of Cx + CM through RREF are sequentially measured).
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Figure 4. Effect of the parasitic capacitance CPx of the microcontroller-based interface: (a) equivalent circuit during measurement with CM and (b) during measurement with CM + Cx.
Figure 4. Effect of the parasitic capacitance CPx of the microcontroller-based interface: (a) equivalent circuit during measurement with CM and (b) during measurement with CM + Cx.
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Figure 5. Picture of the developed system composed of the reader unit and the contactless interface.
Figure 5. Picture of the developed system composed of the reader unit and the contactless interface.
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Figure 6. VCL, VDD, IMC signals and RF field correspondent to the startup of sequential measurement cycles.
Figure 6. VCL, VDD, IMC signals and RF field correspondent to the startup of sequential measurement cycles.
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Figure 7. (a) RF field and VCL, VDD, IMC signals during a single measurement cycle; (b) detailed view of IMC, VDD and VM during the measurement.
Figure 7. (a) RF field and VCL, VDD, IMC signals during a single measurement cycle; (b) detailed view of IMC, VDD and VM during the measurement.
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Figure 8. Average values R j ¯ calculated over 40 repeated measurement and relative errors eRj versus the measured reference values Rj of the resistors.
Figure 8. Average values R j ¯ calculated over 40 repeated measurement and relative errors eRj versus the measured reference values Rj of the resistors.
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Figure 9. Average values C i ¯ calculated over 40 repeated measurement and relative errors eCi versus the measured reference values Ci of the capacitors.
Figure 9. Average values C i ¯ calculated over 40 repeated measurement and relative errors eCi versus the measured reference values Ci of the capacitors.
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Figure 10. Continuous measurement of temperature and relative humidity (RH) with the system prototype: (a) measured resistance and temperature trends versus time; (b) measured capacitance and relative humidity trends versus time.
Figure 10. Continuous measurement of temperature and relative humidity (RH) with the system prototype: (a) measured resistance and temperature trends versus time; (b) measured capacitance and relative humidity trends versus time.
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Figure 11. Temperature and humidity trends measured from the sensor unit (SU) placed into a food box during the test, composed of four different phases.
Figure 11. Temperature and humidity trends measured from the sensor unit (SU) placed into a food box during the test, composed of four different phases.
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Table 1. Reference values Rj, average values R j ¯ , standard deviations σRj and relative resolution σRj/Rj estimated over N = 40 repeated measurements obtained with the system prototype.
Table 1. Reference values Rj, average values R j ¯ , standard deviations σRj and relative resolution σRj/Rj estimated over N = 40 repeated measurements obtained with the system prototype.
Reference Value RjAverage Measured Value R j ¯ Standard Deviation σRjRelative Resolution σRj/Rj
390.98 kΩ392.2 kΩ0.5 kΩ0.13%
467.08 kΩ468.8 kΩ0.4 kΩ0.09%
678.14 kΩ681.5 kΩ0.6 kΩ0.13%
828.03 kΩ832.7 kΩ0.9 kΩ0.11%
1.0012 MΩ1.001 MΩ1 kΩ0.10%
1.2012 MΩ1.201 MΩ1 kΩ0.08%
Table 2. Reference values Ci, average values C i ¯ , standard deviations σCi and relative resolution σCi/Ci estimated over N = 40 repeated measurements obtained with the system prototype.
Table 2. Reference values Ci, average values C i ¯ , standard deviations σCi and relative resolution σCi/Ci estimated over N = 40 repeated measurements obtained with the system prototype.
Reference Value CiAverage Measured Value C i ¯ Standard Deviation σCiRelative Resolution σCi/Ci
221.2 pF224 pF4 pF1.8%
318.1 pF317 pF4 pF1.3%
459.3 pF458 pF5 pF1.1%
552.1 pF551 pF1 pF0.12%
915.5 pF914 pF3 pF0.33%
1.179 nF1.191 nF2 pF0.17%
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