# A Capacitance-to-Time Converter-Based Electronic Interface for Differential Capacitive Sensors

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}and C

_{2}of the differential capacitive sensor. In particular, the mixer also allows for reducing the measurement time, since the period of the output pulsed signal V

_{MIX}is equal to a semi-period (i.e., a double frequency) of the internal square wave signal V

_{COMP2}generated by the closed loop oscillator composed by the integrator and the two comparators. The mixer, in fact, receives at its input terminals the two square wave signals, V

_{COMP1}and V

_{COMP2}, generating a further square waveform V

_{MIX}whose period T

_{1}(that is half period of V

_{COMP1}and V

_{COMP2}) and pulse width T

_{2}(that is the overlapping time between V

_{COMP1}and V

_{COMP2}, when they have both positive or negative values) have to be measured so as to estimate and calculate the capacitance values C

_{1}and C

_{2}. Moreover, it is possible to easily set the interface working range (i.e., the sensor variation range) through the employed resistors, which also allow for fixing the desired detection sensitivity of the overall conditioning circuit.

_{1}and the pulse width T

_{2}of the generated output square waveform V

_{MIX}can be expressed, as follows:

_{1}and C

_{2}) of the differential capacitive sensor as a function of the other circuit parameters and the time values T

_{1}and T

_{2}:

_{1}and C

_{2}impose the starting oscillating period T

_{1}and duty-cycle T

_{2}of the output signal. Nevertheless, through the seven resistors it is possible to change these initial values, even if it acts also on the circuit detection range, sensitivity, and resolution. On the other hand, according to Equations (1) and (2), T

_{1}and T

_{2}are mostly/directly conditioned by resistor R

_{7}, which mainly regulates the charge/discharge of C

_{1}and C

_{2}. Therefore, when dealing with small sensor capacitances (in the range of few pF), R

_{7}is required to be high in order to set T

_{1}and T

_{2}in a range (e.g., in the order of μs or ms), which is more suitable for subsequent signal conditioning/processing stages as well as to optimize/maximize the circuit response/performance (i.e., the detectable capacitive variation range and the detection sensitivity/resolution of the interface circuit). For moderate detection of sensitivities/resolutions and/or high capacitive ranges (in the range of hundreds pF), the value of R

_{7}can be reduced. Finally, if C

_{1}= C

_{2}, the relationship between T

_{1}and T

_{2}can be simply expressed, as follows:

_{2}/T

_{1}taking into account the effects due to the variation of both the sensor capacitive elements C

_{1}and C

_{2}(i.e., the differential variation) is evaluated by extracting the DC level of the output pulsed signal V

_{MIX}(i.e., its mean value that is proportional to the differential capacitive sensor variation (C

_{1}− C

_{2})/(C

_{1}+ C

_{2})) whose value can be ideally calculated, as follows:

_{SAT+}and V

_{SAT−}the output saturation levels of the mixer reached by V

_{MIX}signal. In this last case, the overall circuit can be consequently classified as a C-V converter.

## 3. Results

#### 3.1. Simulations

_{1}= C

_{2}= C

_{0}= 2.2 pF, 10 pF, 100 pF, and 180 pF), so to demonstrate the circuit suitability with different kind of commercial and ad-hoc integrated sensors (with responses linear, hyperbolic, etc.). In Figure 4, the simulation results are reported and compared with the related theoretical values (from Equations (1) and (2)) of the period T

_{1}and the pulse width T

_{2}of output square waveform V

_{MIX}as a function of the relative variation the differential capacitive sensor (i.e., 100 × (C

_{1}− C

_{2})/(C

_{1}+ C

_{2})) showing high linearity (i.e., R

^{2}= 0.9997) and high sensitivity S (i.e., S

_{T}

_{1}= 0.145 ms/pF; S

_{T}

_{2}= 0.071 ms/pF). In particular, Figure 4a shows an example of the time response of the circuit when considering the voltage signals at its main nodes for C

_{1}= 5 pF and C

_{2}= 15 pF (i.e., considering C

_{0}= 10 pF and a differential capacitance variation equal to −50%). In addition, Figure 4b reports the T

_{1}and T

_{2}time values that were achieved when considering a sensor baseline C

_{1}= C

_{2}= C

_{0}= 10 pF (i.e., the central/initial value) and its relative variation of ±50%, so that the differential capacitance (i.e., C

_{1}− C

_{2}) is changed from −10 pF to +10 pF. In particular, C

_{1}changes from 5 pF to 15 pF, while C

_{2}varies from 15 pF to 5 pF with a differential capacitance variation step equal to 2 pF (i.e., each single capacitive element varies in opposite way with a step of 1 pF). Moreover, the reported results have been achieved by setting the circuit resistors, as follows: R

_{1}= 1 kΩ, R

_{2}= 3 kΩ, R

_{3}= 20 kΩ, R

_{4}= 1 kΩ, R

_{5}= 15 kΩ, R

_{6}= 1 kΩ and R

_{7}= 10 MΩ.

_{1}and C

_{2}, the resulting maximum relative variations of T

_{1}and T

_{2}at −20 °C is lower than 0.6%, while at +85 °C it is lower than 9%. These values correspond to maximum relative errors that are lower than 10% at −20 °C and lower than 7% at +85 °C in the estimation of C

_{1}and C

_{2}values.

#### 3.2. Preliminary Experimental Measurements

_{1}− C

_{2}) is varied from −15.8 pF to +15.8 pF using commercial high-precision high-accuracy discrete capacitors, calibrated/measured by using an ISO-TECH LCR821 high-precision high-accuracy LCR-meter (accuracy better than 0.5%) verifying the maximum deviation from the capacitance nominal value lower than 1%. In particular, C

_{1}has been changed from 2.2 pF to 18 pF (i.e., 2.2 pF, 4.7 pF, 8.2 pF, 10 pF, 12 pF, 15 pF, 18 pF) and C

_{2}from 18 pF to 2.2 pF (i.e., 18 pF, 15 pF, 12 pF, 10 pF, 8.2 pF, 4.7 pF, 2.2 pF), while keeping constant the total capacitance value C

_{1}+ C

_{2}at about 20 pF (C

_{0}= 10 pF). In order to get oscillating periods of few milliseconds and to achieve better results, the following resistance values have been chosen: R

_{1}= 1 kΩ, R

_{2}= 1.2 kΩ, R

_{3}= 15 kΩ, R

_{4}= 1 kΩ, R

_{5}= 47 kΩ, R

_{6}= 1 kΩ, R

_{7}= 10 MΩ. The parasitic capacitance of the resistors was measured, giving values below 0.5 pF. The resulting measurements of the period T

_{1}and the pulse width T

_{2}have been performed while employing a GPIB-based experimental setup and a National Instruments LABVIEW-based automatic acquisition system, including conventional instrumentations, such as a frequency-meter Agilent 34970A (accuracy better than 0.01%), a Data Acquisition/Switch Unit, and digital multimeter Agilent 34401A (accuracy better than 0.01%), as well as an oscilloscope Tektronix TPS2024R.

_{MIX}) and the corresponding measured values of T

_{1}(i.e., CH1 Period in the right part of each picture) and T

_{2}(i.e., CH1 Pos Width in the right part of each picture) for three different sets of C

_{1}and C

_{2}values: Figure 5a, C

_{1}= 2.2 pF and C

_{2}= 18 pF; Figure 5b, C

_{1}= C

_{2}= 10 pF; Figure 5c, C

_{1}= 18 pF and C

_{2}= 2.2 pF. The overall measurement results are reported in Figure 5d showing the oscillation period T

_{1}and the pulse width T

_{2}as function of the differential capacitance variation (i.e., 100 × (C

_{1}− C

_{2})/(C

_{1}+ C

_{2})), which are in a good agreement with the theoretical calculations according Equations (1) and (2) and with the related simulation results achieved with the same operating conditions. In this case, the achieved sensitivities with respect to T

_{1}and T

_{2}are S

_{T}

_{1}= 0.982 ms/pF and S

_{T}

_{2}= 0.491 ms/pF, respectively (linearity correlation coefficient R

^{2}of about 0.999). On the other hand, taking into account the measured values of T

_{1}and T

_{2}, Figure 5e reports on the estimated values of C

_{1}and C

_{2}capacitances calculated through the Equations (3) and (4). The corresponding relative error, evaluated between the measured/estimated capacitance values and its nominal/real values, is lower than 3%. Finally, the maximum averaged RMS jitter level, measured on the rising/falling edges of the output square wave signal V

_{MIX}, results to be always lower than 50 ns, so that the resulting estimated minimum detectable differential capacitance variation (i.e., the best theoretical detection resolution of the circuit) is about 0.1 fF. The average power consumption of the overall electronic interface circuit is about 68 mW.

#### 3.3. Relative Humidity (RH) Sensor

_{1}has been fixed to a value equal to 180 pF (i.e., C

_{0}= 180 pF), while performing a sweep of the C

_{2}capacitance in the variation range [160 pF–197 pF] by means of a fixed 150 pF capacitor in parallel with others having smaller different values (i.e., C

_{2}= 150 pF + [10 pF; 12 pF; 15 pF; 18 pF; 22 pF; 27 pF; 30 pF; 33 pF; 39 pF; 47 pF]). In this case, the following resistance values have been set so to optimize the interface circuit response: R

_{1}= 470 Ω, R

_{2}= 560 Ω, R

_{3}= 2.2 kΩ, R

_{4}= 470 Ω, R

_{5}= 4.7 kΩ, R

_{6}= 470 Ω, R

_{7}= 47 kΩ. The employed experimental set-up and measurement instrumentations are those ones already previously reported and described in Section 3.1.

_{MIX}, including the corresponding measured values of the period T

_{1}(i.e., CH1 Period in the right part of each picture) and the pulse width T

_{2}(i.e., CH1 Pos Width in the right part of each picture). They demonstrate the proper performances of the circuit for an operating configuration with a fixed value of C

_{1}= 180 pF and three different values of C

_{2}: Figure 6a, C

_{2}= 160 pF; Figure 6b, C

_{2}= 180 pF; Figure 6c, C

_{2}= 197 pF.

_{1}and the pulse width T

_{2}as function of the relative capacitance variation (i.e., 100 × (C

_{1}− C

_{2})/(C

_{1}+ C

_{2})) achieved by changing C

_{2}in the range [160 pF–197 pF]. The collected data confirm the correct functionalities of the interface circuit agreeing with the theoretical calculations, from Equations (1) and (2), and also with the corresponding simulations performed when considering the same circuit parameters. From these results, the two detection sensitivities S

_{T}

_{1}= 0.001 ms/pF and S

_{T}

_{2}= 0.0006 ms/pF with respect to T

_{1}and T

_{2}, respectively, have been calculated (linearity correlation coefficient R

^{2}of about 0.999) so as to evaluate/estimate the performances of the circuit, especially in terms of the minimum detection resolution of differential capacitance variations that, in this case, is about 83 fF (considering a maximum averaged RMS jitter level, measured on the rising/falling edges of V

_{MIX}, lower than 50 ns). Finally, starting from these results and by employing Equations (3) and (4), the values of C

_{1}and C

_{2}capacitances have been estimated/calculated, as reported in Figure 6d showing a relative error, evaluated between the measured/estimated capacitance values and its nominal/real values, lower than 0.5 %.

_{2}capacitor has been replaced by the commercial HS1101LF RH capacitive sensor, so performing through the controlled climatic chamber a sweep in the RH from 35% to 75%, with steps of 5% and room temperature set to 25 °C. The achieved results are reported in Figure 7 comparing the calculated/estimated RH% with the fixed nominal values as well as with the values that were achieved from direct measurement of the sensor by using the ISO-TECH LCR821 high-precision high-accuracy LCR-meter and extracting the data from sensor datasheet. The reported data have been extracted starting from the measurement of the time period T

_{1}and the pulse width T

_{2}as a function of the RH% variation with detection sensitivities of about S

_{T}

_{1}= 0.0004 ms/RH% and S

_{T}

_{2}= 0.0002 ms/RH% with respect to T

_{1}and T

_{2}, respectively. Subsequently, the values of the capacitances C

_{1}and C

_{2}have been estimated/calculated by employing Equations (3) and (4). Finally, from the information reported in the datasheet of the used commercial capacitive sensor, the RH% values have been extracted employing the reverse polynomial response equation reported in the same device datasheet. In this case, the relative error, evaluated between the measured/estimated values and nominal/real values, is lower than 3% and the minimum estimated detection resolution in terms of the RH% variation is about 0.25% (considering a maximum averaged RMS jitter level, measured on the rising/falling edges of V

_{MIX}, lower than 50 ns).

#### 3.4. Liquid Level

_{1}and the other with the air providing the capacitor C

_{2}.

_{1}and C

_{2}capacitance values. Moreover, in order to optimize the interface circuit response, the following resistance values have been considered: R

_{1}= 1 kΩ, R

_{2}= 1.2 kΩ, R

_{3}= 15 kΩ, R

_{4}= 1 kΩ, R

_{5}= 47 kΩ, R

_{6}= 1 kΩ, R

_{7}= 10 MΩ. The overall experimental measurement results are reported in Figure 8, when considering that the two capacitors C

_{1}and C

_{2}have been connected to the circuit both, as depicted in Figure 8 (see results of Figure 9a) and by interchanging their positions/connections (i.e., C

_{1}used as C

_{2}, and vice versa; see results of Figure 9b). In particular, by measuring the time period T

_{1}and the pulse width T

_{2}values of the circuit main output signal V

_{MIX}as a function of the liquid level, the C

_{1}and C

_{2}capacitance values have been calculated/estimated through the Equations (3) and (4) and compared with the capacitive values of the same elements achieved from direct measurements through the ISO-TECH LCR821 high-precision high-accuracy LCR-meter. In this last case, the resulting relative error, as calculated among the obtained experimental data, is always lower than 5%, both for the capacitor with higher values and for the capacitor with lower values. The minimum estimated detection resolution in terms of the liquid level variation is about 0.01 mm (considering a maximum averaged RMS jitter level, measured on the rising/falling edges of V

_{MIX}, lower than 50 ns). Additional simulation analyses have been also performed, so demonstrating a low sensitivity to common-mode noise and disturbances as well as, in particular, an excellent immunity to additional parasitic capacitances at the main circuit sensing nodes. More in detail, at each terminal node of the differential capacitive sensor connected to the circuit (i.e., the three main input nodes of the interface), a 10 pF grounded capacitor has been considered and added as an external parasitic component (i.e., as a parasitic capacitance provided by a differential capacitive sensor, as those ones related to the plates of C

_{1}and C

_{2}of the box shown in Figure 8). In this sense, referring to the circuit set-up considered for the simulation results reported in Section 3.1, and thus considering the capacitive variation range of 5–15 pF for C

_{1}and C

_{2}, the resulting maximum relative variation of T

_{1}and T

_{2}is lower than 0.25% that, on the other hand, corresponds to a maximum relative error lower than 8% in the estimation of C

_{1}and C

_{2}values.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Yuan, J.S.; Bi, Y. Process and temperature robust voltage multiplier design for RF energy harvesting. Micorelectron. Reliab.
**2015**, 55, 107–113. [Google Scholar] [CrossRef] - Bi, Y.; Gaillardon, P.E.; Hu, X.S.; Niemier, M.; Yuan, J.S.; Jin, Y. Leveraging Emerging Technology for Hardware Security—Case Study on Silicon Nanowire FETs and Graphene SymFETs. In Proceedings of the 2014 IEEE 23rd Asian Test Symposium, Hangzhou, China, 16–19 November 2014; pp. 342–347. [Google Scholar] [CrossRef]
- Bi, Y.; Shamsi, K.; Yuan, J.S.; Jin, Y.; Niemier, M.; Hu, X.S. Tunnel FET Current Mode Logic for DPA-Resilient Circuit Designs. IEEE Trans. Emerg. Top. Comput.
**2017**, 5, 340–352. [Google Scholar] [CrossRef] - Chen, X.; Brox, D.; Assadsangabi, B.; Ali, M.S.M.; Takahata, K. A stainless-steel-based implantable pressure sensor chip and its integration by microwelding. Sens. Actuators A Phys.
**2017**, 257, 134–144. [Google Scholar] [CrossRef] - Apigo, D.J.; Bartholomew, P.L.; Russell, T.; Kanwal, A.; Farrow, R.C.; Thomas, G.A. An Angstrom-sensitive, differential MEMS capacitor for monitoring the milliliter dynamics of fluids. Sens. Actuators A Phys.
**2016**, 251, 234–240. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rivadeneyra, A.; Fernández-Salmerón, J.; Agudo-Acemel, M.; López-Villanueva, J.A.; Capitan-Vallvey, L.F.; Palma, A.J. Printed electrodes structures as capacitive humidity sensors: A comparison. Sens. Actuators A Phys.
**2016**, 244, 56–65. [Google Scholar] [CrossRef] - Aydemir, A.; Terzioglu, Y.; Akin, T. A new design and a fabrication approach to realize a high performance three axes capacitive MEMS accelerometer. Sens. Actuators A Phys.
**2016**, 244, 324–333. [Google Scholar] [CrossRef] - Rahman, M.D.T.; Rahimi, A.; Gupta, S.; Panat, R. Microscale additive manufacturing and modeling of interdigitated capacitive touch sensors. Sens. Actuators A Phys.
**2016**, 246, 94–103. [Google Scholar] [CrossRef] - Liu, Y.T.; Kuo, Y.L.; Yan, D.W. System integration for on-machine measurement using a capacitive LVDT-like contact sensor. Adv. Manuf.
**2017**, 5, 50–58. [Google Scholar] [CrossRef] - Bai, Y.; Lu, Y.; Hu, P.; Wang, G.; Xu, J.; Zeng, T.; Li, Z.; Zhang, Z.; Tan, J. Absolute position sensing based on a robust differential capacitive sensor with a grounded shield window. Sensors
**2016**, 16, 680. [Google Scholar] [CrossRef] - Park, S.H.; Kim, H.S.; Bang, J.S.; Cho, G.H.; Cho, G.H. A 0.26-nJ/node, 400-kHz Tx driving, filtered fully differential readout IC with parasitic RC time delay reduction technique for 65-in 169 × 97 capacitive-type touch screen panel. IEEE J. Solid-State Circuits
**2017**, 52, 528–542. [Google Scholar] [CrossRef] - Liu, X.; Peng, K.; Chen, Z.; Pu, H.; Yu, Z. A new capacitive displacement sensor with nanometer accuracy and long range. IEEE Sens. J.
**2016**, 16, 2306–2316. [Google Scholar] [CrossRef] - Ciccarella, P.; Carminati, M.; Sampietro, M.; Ferrari, M. Multichannel 65zF RMS resolution CMOS monolithic capacitive sensor for counting single micrometer-sized airborne particles on chip. IEEE J. Solid-State Circuits
**2016**, 51, 2545–2553. [Google Scholar] [CrossRef] - Wu, X.; Deng, F.; Hao, Y.; Fu, Z.; Zhang, L. Design of a humidity sensor tag for passive wireless applications. Sensors
**2015**, 15, 25564–25576. [Google Scholar] [CrossRef] [PubMed] - Arefin, M.S.; Redouté, J.M.; Yuce, M.R. A MEMS interface IC with low-power and wide-range frequency-to-voltage converter for biomedical applications. IEEE Trans. Biomed. Circuits Syst.
**2016**, 10, 455–466. [Google Scholar] [CrossRef] [PubMed] - Constandinou, T.G.; Georgiou, J.; Toumazou, C. A micropower front-end interface for differential-capacitive sensor systems. In Proceedings of the 2008 IEEE International Symposium on Circuits and Systems, Seattle, WA, USA, 18–21 May 2008; pp. 2474–2477. [Google Scholar] [CrossRef]
- Mochizuki, K.; Watanabe, K.; Masuda, K. A high-accuracy high-speed signal processing circuit of differential-capacitance transducers. IEEE Trans. Instrum. Meas.
**1998**, 47, 1244–1247. [Google Scholar] [CrossRef] [Green Version] - Singh, T.; Saether, T.; Ytterdal, T. Current-mode capacitive sensor interface circuit with single-ended to differential output capability. IEEE Trans. Instrum. Meas.
**2009**, 58, 3914–3920. [Google Scholar] [CrossRef] - Royo, G.; Sánchez-Azqueta, C.; Gimeno, C.; Aldea, C.; Celma, S. Programmable low-power low-noise capacitance to voltage converter for MEMS accelerometers. Sensors
**2017**, 17, 67. [Google Scholar] [CrossRef] [PubMed] - Scotti, G.; Pennisi, S.; Monsurro, P.; Trifiletti, A. 88-μA 1-MHz stray-insensitive CMOS current-mode interface IC for differential capacitive sensors. IEEE Trans. Circuits Syst.
**2014**, 61, 1905–1916. [Google Scholar] [CrossRef] - Kyriakis-Bitzaros, E.D.; Stathopoulos, N.A.; Pavlos, S.; Goustouridis, D.; Chatzandroulis, S. A reconfigurable multichannel capacitive sensor array interface. IEEE Trans. Instrum. Meas.
**2011**, 60, 3214–3221. [Google Scholar] [CrossRef] - Wang, S.; Koickal, T.J.; Hamilton, A.; Mastropaolo, E.; Cheung, R.; Abel, A.; Smith, L.S.; Wang, L. A power-efficient capacitive read-out circuit with parasitic-cancellation for MEMS cochlea sensors. IEEE Trans. Biomed. Circuits Syst.
**2016**, 10, 25–37. [Google Scholar] [CrossRef] - Ignjatovic, Z.; Bocko, M.F. An interface circuit for measuring capacitance changes based upon capacitance-to-duty cycle (CDC) converter. IEEE Sens. J.
**2005**, 5, 403–410. [Google Scholar] [CrossRef] - De Marcellis, A.; Ferri, G.; Mantenuto, P. A CCII-based non-inverting Schmitt trigger and its application as astable multivibrator for capacitive sensor interfacing. Int. J. Circuit Theory Appl.
**2016**, 45, 1060–1076. [Google Scholar] [CrossRef] - Bruschi, P.; Nizza, N.; Piotto, M. A current-mode, dual slope, integrated capacitance-to-pulse duration converter. IEEE J. Solid-State Circuits
**2007**, 42, 1884–1891. [Google Scholar] [CrossRef] - Tan, Z.; Shalmany, S.H.; Meijer, G.C.M.; Pertijs, M.A.P. An energy-efficient 15-bit capacitive-sensor interface based on period modulation. IEEE J. Solid-State Circuits
**2012**, 47, 1703–1711. [Google Scholar] [CrossRef] - He, Y.; Chang, Z.Y.; Pakula, L.; Shalmany, S.H.; Pertijs, M.A.P. A 0.05 mm
^{2}1 V capacitance-to-digital converter based on period modulation. In Proceedings of the IEEE International Solid-State Circuits Conference (ISSCC), San Francisco, CA, USA, 22–26 February 2015; pp. 1–3. [Google Scholar] [CrossRef] - Nizza, N.; Dei, M.; Butti, F.; Bruschi, P. A low-power interface for capacitive sensors with PWM output and intrinsic low pass characteristic. IEEE Trans. Circuits Syst.
**2013**, 60, 1419–1431. [Google Scholar] [CrossRef] - Lu, J.H.L.; Inerowicz, M.; Joo, S.; Kwon, J.K.; Jung, B. A low-power wide-dynamic-range semi-digital universal sensor readout circuit using pulsewidth modulation. IEEE Sens. J.
**2011**, 11, 1134–1144. [Google Scholar] [CrossRef] - Sheu, M.L.; Hsu, W.H.; Tsao, L.J. A capacitance-ratio-modulated current front-end circuit with pulsewidth modulation output for a capacitive sensor interface. IEEE Trans. Instrum. Meas.
**2012**, 61, 447–455. [Google Scholar] [CrossRef] - Arefin, M.S.; Redouté, J.M.; Yuce, M.R. A low-power and wide-range MEMS capacitive sensors interface IC using pulse-width modulation for biomedical applications. IEEE Sens. J.
**2016**, 16, 6745–6754. [Google Scholar] [CrossRef] - Brookhuis, R.A.; Lammerink, T.S.J.; Wiegerink, R.J. Differential capacitive sensing circuit for a multi-electrode capacitive force sensor. Sens. Actuators A Phys.
**2015**, 234, 168–179. [Google Scholar] [CrossRef] - Aezinia, F.; Bahreyni, B. Low-power parasitic-insensitive interface circuit for capacitive microsensors. IET Circuits Device Syst.
**2016**, 10, 104–110. [Google Scholar] [CrossRef] - De Marcellis, A.; Cubells-Beltrán, M.D.; Reig, C.; Madrenas, J.; Zadov, B.; Paperno, E.; Cardoso, S.; Freitas, P.P. Quasi-digital front-ends for current measurement in integrated circuits with GMR technology. IET Circuits Device Syst.
**2014**, 8, 291–300. [Google Scholar] [CrossRef] - Mohan, N.M.; Shet, A.R.; Kedarnath, S.; Kumar, V.J. Digital converter for differential capacitive sensors. IEEE Trans. Instrum. Meas.
**2008**, 57, 2576–2581. [Google Scholar] [CrossRef] - Reverter, F.; Casas, O. Interfacing differential capacitive sensors to microcontrollers: A direct approach. IEEE Trans. Instrum. Meas.
**2010**, 59, 2763–2769. [Google Scholar] [CrossRef] - Nabovati, G.; Ghafar-Zadeh, E.; Mirzaei, M.; Ayala-Charca, G.; Awwad, F.; Sawan, M. A new fully differential CMOS capacitance to digital converter for lab-on-chip applications. IEEE Trans. Biomed. Circuits Syst.
**2015**, 9, 353–361. [Google Scholar] [CrossRef] [PubMed] - Omran, H.; Arsalan, M.; Salama, K.N. An integrated energy-efficient capacitive sensor digital interface circuit. Sens. Actuators A Phys.
**2014**, 216, 43–51. [Google Scholar] [CrossRef] [Green Version] - Shin, D.Y.; Lee, H.; Kim, S. A delta–sigma interface circuit for capacitive sensors with an automatically calibrated zero point. IEEE Trans. Circuits Syst. II Express Briefs
**2011**, 58, 90–94. [Google Scholar] [CrossRef] - Alhoshany, A.; Omran, H.; Salama, K.N. A 45.8 fJ/step, energy-efficient, differential SAR capacitance-to-digital converter for capacitive pressure sensing. Sens. Actuators A Phys.
**2016**, 245, 10–18. [Google Scholar] [CrossRef] - Tan, Z.; Daamen, R.; Humbert, A.; Ponomarev, Y.V.; Chae, Y.; Pertijs, M.A.P. A 1.2-V 8.3-nJ CMOS humidity sensor for RFID applications. IEEE J. Solid-State Circuits
**2013**, 48, 2469–2477. [Google Scholar] [CrossRef] - Oh, S.; Lee, Y.; Wang, J.; Foo, Z.; Kim, Y.; Blaauw, D. Dual-slope capacitance to digital converter integrated in an implantable pressure sensing system. In Proceedings of the 40th European Solid State Circuits Conference (ESSCIRC), Venice, Italy, 22–26 September 2014; pp. 295–298. [Google Scholar] [CrossRef]

**Figure 2.**Schematic circuit of the proposed electronic interface for differential capacitive sensors.

**Figure 3.**Example of the time response of the proposed interface evaluating the voltage signals at its main nodes.

**Figure 4.**(

**a**) Example of the time response of the circuit; and, (

**b**) simulation results together with the corresponding theoretical data of the period T

_{1}and the pulse width T

_{2}of output square waveform V

_{MIX}as a function of the relative variation the differential capacitive sensor for C

_{1}= C

_{2}= C

_{0}= 10 pF.

**Figure 5.**Measured main output signals of the circuit for (

**a**) C

_{1}= 2.2 pF and C

_{2}= 18 pF, (

**b**) C

_{1}= C

_{2}= 10 pF, and (

**c**) C

_{1}= 18 pF and C

_{2}= 2.2 pF; (

**d**) measured, simulated and theoretical oscillation periods T

_{1}and pulse widths T

_{2}as a function of the relative differential capacitance variation; (

**e**) calculated/estimated capacitance values.

**Figure 6.**Oscillograms showing the output voltage signal V

_{MIX}that demonstrates the proper performances of the circuit for a configuration employing a fixed C

_{1}= 180 pF and (

**a**) C

_{2}= 160 pF, (

**b**) C

_{2}= 180 pF, and (

**c**) C

_{2}= 197 pF; (

**d**) measured, simulated, and theoretical oscillation periods T

_{1}and pulse widths T

_{2}as a function of the relative differential capacitance variation; (

**e**) calculated/estimated capacitance values.

**Figure 7.**Experimental results concerning the measurement of RH% performed by employing a commercial capacitive sensor.

**Figure 9.**(

**a**) Experimental results achieved by using the developed liquid level meter as differential capacitive sensor reported in Figure 8, (

**b**) after interchanging C

_{1}and C

_{2}.

**Table 1.**Main performance parameters of the proposed circuit as compared to other similar solutions based on C-T conversion.

Ref. | Sensor Topology | Circuit Typology | Circuit Realization | Output Format | Detection Range | Sensitivity | Resolution |
---|---|---|---|---|---|---|---|

[25] | Single element | A/D mixed signal | On chip integration | PWM | 0.8–1.2 pF | 47 μs/pF @ 20 kHz 15 μs/pF @ 50 kHz | 0.9 fF |

[26] | Single element | A/D mixed signal | On chip integration | PM | 1.8–6.8 pF | 1.12 ms/pF | 0.2 fF |

[27] | Single element | A/D mixed signal | On chip integration | PM | 0–8 pF | n.a. | 1.4 fF |

[28] | Single element | Analogue | On chip integration | PWM | 16–256 fF | 32 μs/pF | 0.8 fF |

[29] | Single element | Analogue | On chip integration | PWM | 0.013 fF–9 pF | 1.82 μs/pF | 0.013 fF |

[30] | Single element | Analogue | On chip integration | PWM | 2.5–2.8255 pF | 3.88 μs/pF | 2.8 fF |

[31] | Single element | Analogue | On chip integration | PWM | 1–22 pF | 3.62 μs/pF | 0.011 fF |

[32] | Differential element | Analogue | Discrete components | PM | 0–19.8 pF (single) −19.8 ÷ +19.8 pF (differential) | 0.49 μs/pF (differential) | 2 fF (differential) |

[33] | Differential element | A/D mixed signal | On chip integration | PWM | 40–60 fF (single) −20 ÷ +20 fF (differential) | 127 μs/pF (differential) | 0.16 fF (differential) |

[35] | Differential element | A/D mixed signal | Discrete components | PM | 400 pF (±50%) | n.a. | 10 pF |

This work | Single or Differential element | Analogue | Discrete components | PWM PM | 2.2–197 pF (single) [−15.8 ÷ +15.8 pF] (differential) | 1 μs/pF (single) 982 μs/pF (differential) | 83 fF (single) 0.1 fF (differential) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Marcellis, A.; Reig, C.; Cubells-Beltrán, M.-D.
A Capacitance-to-Time Converter-Based Electronic Interface for Differential Capacitive Sensors. *Electronics* **2019**, *8*, 80.
https://doi.org/10.3390/electronics8010080

**AMA Style**

De Marcellis A, Reig C, Cubells-Beltrán M-D.
A Capacitance-to-Time Converter-Based Electronic Interface for Differential Capacitive Sensors. *Electronics*. 2019; 8(1):80.
https://doi.org/10.3390/electronics8010080

**Chicago/Turabian Style**

De Marcellis, Andrea, Càndid Reig, and María-Dolores Cubells-Beltrán.
2019. "A Capacitance-to-Time Converter-Based Electronic Interface for Differential Capacitive Sensors" *Electronics* 8, no. 1: 80.
https://doi.org/10.3390/electronics8010080