sensors Article

Cable Crosstalk Suppression with Two-Wire Voltage Feedback Method for Resistive Sensor Array Jianfeng Wu *, Shangshang He, Jianqing Li and Aiguo Song School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China; [email protected] (S.H.); [email protected] (J.L.); [email protected] (A.S.) * Correspondence: [email protected]; Tel.: +86-153-6600-6069 Academic Editor: Vittorio M. N. Passaro Received: 3 December 2015; Accepted: 16 February 2016; Published: 19 February 2016

Abstract: Using a long, flexible test cable connected with a one-wire voltage feedback circuit, a resistive tactile sensor in a shared row-column fashion exhibited flexibility in robotic operations but suffered from crosstalk caused by the connected cable due to its wire resistances and its contacted resistances. Firstly, we designed a new non-scanned driving-electrode (VF-NSDE) circuit using two wires for every row line and every column line to reduce the crosstalk caused by the connected cables in the circuit. Then, an equivalent resistance expression of the element being tested (EBT) for the two-wire VF-NSDE circuit was analytically derived. Following this, the one-wire VF-NSDE circuit and the two-wire VF-NSDE circuit were evaluated by simulation experiments. Finally, positive features of the proposed method were verified with the experiments of a two-wire VF-NSDE prototype circuit. The experiment results show that the two-wire VF-NSDE circuit can greatly reduce the crosstalk error caused by the cables in the 2-D networked resistive sensor array. Keywords: networked resistive sensor array; measurement error; one-wire VF-NSDE circuit; two-wire VF-NSDE circuit

1. Introduction Resistive sensor arrays are important for tactile sensing [1–8], infrared sensing [9,10], light sensing [11], etc. For limited space in sensitive areas, many resistive sensor arrays used in robotic applications are connected with their test circuits with different length cables. Fernando et al. [1] designed a 16 ˆ 9 force sensor patch with its test cable’s length more than 55 mm to cover large distances within robots and machines for interacting with human beings. Speeter [2] reported a flexible sensing system with its test cable’s length more than 60 mm and achieved a sampling rate of more than 60 Hz in scanning 16 ˆ 16 resistive taxels. Fernando et al. [3] realized and compared three circuits of networked piezoresistive sensor arrays with test cable length longer than 70 mm based on standard microcontrollers, programmable systems on chip, and field programmable gate arrays. Yang et al. [4] designed a 32 ˆ 32 flexible array with a test cable length longer than 70 mm using PI-copper films within a 160 mm ˆ 160 mm temperature and tactile sensing area, which could be used to recognize large objects of different shapes. Zhang et al. [5] reported a 3 ˆ 3 thin tactile force sensor array with its test cable length longer than 95 mm based on conductive rubber. Castellanos-Ramos et al. [6] reported a 16 ˆ 16 tactile sensor array with its test cable length greater than 100 mm based on conductive polymers with screen-printing technology. Kim et al. [7] reported a new concept of a flexible tactile sensor array with more length capable of sensing contact force and position with high performance and high spatial resolution. Lazzarini et al. [8] reported a 16 ˆ 16 tactile sensor array for practical applications requiring manipulation with its test cable’s length of 500 mm. Saxena et al. designed a 16 ˆ 16 bolometer array of IR detectors [9,10] and a 16 ˆ 16 imaging array of light-dependent Sensors 2016, 16, 253; doi:10.3390/s16020253

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resistors [11]. With longer flexible test cables, the resistive sensor array modules are more flexible for robotic operations and easier to be connected with their test circuits. In connected cables with fewer wires (M + N wires for a M ˆ N resistive array), sensor modules of networked resistive arrays in shared row-column fashion were connected with their test circuits [11]. With equal length and the same material, wires of long cables had similar wire resistances which increased with the increase of cables’ length. Between the plugs of the connected cables and the sockets of the test circuits, there existed contacted resistances which varied in the range from 0 ohms to several ohms with the change of the contacted conditions caused by mechanical vibration and time variation. As for the voltage feedback circuits of the resistive networked sensor arrays in shared row-column fashion, the voltage differences between the circuits’ test ports and the sensor modules’ ports of the same connected wires were caused by the similar wire resistances and the different contacted resistances. Thus, the ideal feedback conditions in the voltage feedback circuits of the 2-D networked resistive sensor arrays were destroyed and crosstalk caused by the test cables existed. As such, good cable crosstalk suppression methods should be further studied. For this purpose, we present a novel cable crosstalk suppression method with less cost for the 2-D networked resistive sensor arrays in the row-column fashion. This paper begins with an overview of the application fields of the 2-D networked resistive sensor arrays. Secondly, a novel cable crosstalk suppression method will be proposed and its equivalent resistance expression of the element being tested will be analytically derived. Followed, experiments will be implemented to evaluate this method with different parameters such as the wire resistances and contacted resistances of the cables, the array size, the measurement range of the EBT, and the adjacent elements’ resistances of 2-D networked resistive sensor arrays. Finally, the results of experiments will be analyzed and conclusions for the method will be given. 2. Principle Analysis With the row-column fashion, few wires were use in the 2-D networked resistive circuits. However, these circuits suffered from the crosstalk for parasitic parallel paths in the 2-D networked resistive sensor arrays, and some theoretical analyses had been implemented for suppressing it. Fernando et al. [1,3–8,12–14] suppressed the crosstalk caused by the adjacent elements and the multiplexers with larger number of op-amps using virtual ground technique. With the Improved Isolated Drive Feedback Circuit (IIDFC) [15], Wu et al. depressed the crosstalk error caused by the adjacent column elements. With the Improved Isolated Drive Feedback Circuit with Compensation (IIDFCC) [16], Wu et al. reduced the influence on the EBT caused by parasitic parallel paths for the multiplexers’ channel resistor and the adjacent elements. In these methods, the measurement accuracy of the EBT still suffered from the interferences of cables’ parameters, such as wire resistances and contacted resistances. Liu et al. [17] defined the voltage feedback method including the voltage feedback non-scanned-electrode (VF-NSE) method, the voltage feedback non-scanned-sampling-electrode (VF-NSSE) method, and the voltage feedback non-scanned-driving-electrode (VF-NSDE) method. Wu et al. [18] proposed a general voltage feedback circuit model for the two-dimensional networked resistive sensor array. In this analysis, a VF-NSDE circuit was taken as the example. A traditional VF-NSDE circuit of a resistive networked sensor array in a shared row-column fashion is shown as Circuit A in Figure 1a. In Circuit A, R11 in the M ˆ N resistive array was the element being tested (EBT); only one connected wire was used for every row line and every column line between the array and the circuit; only one equal current M:1 multiplexer was used between the sampling resistor (Rs ) and the row lines of the sensor module. On the column lines of the circuit, 2:1 multiplexers had multiplexer switch resistances (Rsc s); column wires had column resistances (R Lc s) including column wire resistances and contacted resistances. On row lines of the circuit, the equal current M:1 multiplexers had multiplexer switch resistances (Rsr s); row wires had row resistances (R Lr s) including row wire resistances and contacted resistances. Thus, the Circuit A had one voltage feedback op-amp, N 2:1 multiplexers, and M + N wires.

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(a)

(b)

(c)

(d)

Figure 1. (a) One-wire VF-NSDE circuit (Circuit A); (b) simplified measurement circuit of a one-wire

Figure 1. (a) One-wire VF-NSDE circuit (Circuit A); (b) simplified measurement circuit of a one-wire VF-NSDE circuit (Circuit B); (c) two-wire VF-NSDE circuit (Circuit C); and (d) simplified VF-NSDE circuit (Circuit (c) two-wire VF-NSDE (Circuit C); and (d) simplified measurement measurement circuit ofB); a two-wire VF-NSDE circuitcircuit (Circuit D). circuit of a two-wire VF-NSDE circuit (Circuit D). Under an ideal condition, all Rscs and all RLcs were omitted. Thus, the voltage (Vcy) on the column lineideal of EBT was equal all to the voltage (VI),sand the voltages on non-scanned column lines Under an condition, Rscset s and all R Lc were omitted. Thus, the voltage (Vcy ) on the were equal to the feedback voltage (VF). At the same time, all Rsrs and all RLrs were omitted. Thus, column line of EBT was equal to the set voltage (V I ), and the voltages on non-scanned column lines the voltage (Vsg) on Rs was equal to the voltage (Vrx) on the row line of EBT. Under the effect of the were equal to the feedback voltage (VF ). At the same time, all Rsr s and all R Lr s were omitted. Thus, ideal op-amp, VF followed the change of Vsg. Thus, VF, Vrx, and Vsg were equal. As the voltages on the voltage (Vsg ) column on Rs was to thetovoltage thethe row line ofrow EBT. Underofthe effect rx ) on on non-scanned linesequal were equal Vrx, the (V currents adjacent elements EBT wereof the idealequal op-amp, VF At followed thetime, change of Vsg .on Thus, VF , Vrx , andinput Vsg were As the was voltages to zero. the same the current the non-inverting of theequal. ideal op-amp on non-scanned column lines were equal to V , the currents on the adjacent row elements omitted for its infinite input impedance, the current (Ixy) on the EBT was equal to the current (Is of = EBT rx sg/Rs = (V − Vrx)/RAt xy =the (VI same − Vsg)/Rtime, xy) on the Rs. As VI andon Rs were known, Vsg = VFinput could of be the measured by wereVequal toI zero. current the non-inverting ideal op-amp ADC, so the value (Rxy) the of the EBT in(Ithe could beequal calculated with was omitted for equivalent its infiniteresistance input impedance, current on the A EBT was to the current xy ) Circuit Equation (1): (Is = V /R = (V ´ V )/R = (V ´ V )/R ) on R . As V and R were known, V = V could sg s rx xy sg xy s s sg I

I

I

F

be measured by ADC, so the equivalent Rresistance be xy = (VI − VFvalue ) × Rs/V(R F xy ) of the EBT in the Circuit A could (1) calculated with Equation (1): Rxy “ pV I ´ VF q ˆ Rs {VF (1)

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However, under real conditions, as shown in Figure 1b, Vcy was not equal to V I for Rsc and R Lc , and Vsg was not equal to Vrx for Rsr and R Lr . The ideal feedback condition was destroyed by the row wires and the column wires, so extra measurement errors of the EBT occurred. For suppression crosstalk of the cables in the 2-D networked resistive arrays, we proposed a two-wire voltage feedback method as shown in Figure 1c. In the Circuit C, we used two wires for every row line and every column line between the sensor module and the test circuit; also we used one column driving op-amp for every column line and one equipotential M:1 multiplexer between the row lines and the voltage feedback op-amp. Thus, Circuit C had one voltage feedback op-amp, N column driving op-amps, N 2:1 multiplexers, two M:1 multiplexers, and 2(M + N) wires. Every column line in the sensor module was connected with the output of its column driving op-amp by one driving wire and it was also connected with the inverting input of its column driving op-amp by one driving sampling wire. The non-inverting input of every column driving op-amp was connected with the common port of its column 2:1 multiplexer, thus every non-inverting input was connected with V I or VF . The non-inverting input of the EBT’s column driving op-amp was connected with V I while the non-inverting inputs of other column driving op-amps were connected with VF . As the input impedance of every column driving op-amp was much bigger than its Rsc , the effect of all Rsc s could be omitted. Thus, the voltage on the non-inverting input of its column driving op-amp was equal to the input voltage (V I or VF ) on its 2:1 multiplexer. If the column driving op-amps had sufficient driving ability, the voltage on every column line followed the change of the voltage on the non-inverting input of its column driving op-amp. So Vcy was equal to V I , and the voltages on non-scanned column lines were equal to VF . Thus the crosstalk effect of R Lc s and Rsc s were suppressed. By one equal current wire, every row line in the sensor module was connected with one channel of the equal current M:1 multiplexer with its common port connected with Rs . In the equal current M:1 multiplexer, only the row line of EBT was gated and all other non-scanned lines were suspended. So, only the row line of the EBT was connected with Rs . By one equipotential wire, every row line in the sensor module was also connected with one channel of the equipotential M:1 multiplexer with its common port connected with the non-inverting input of the voltage feedback op-amp. In the equipotential M:1 multiplexer, only the row line of EBT was gated and all other non-scanned lines were suspended. Only the row line of the EBT was connected with the non-inverting input of the voltage feedback op-amp. From the EBT’s column driving op-amp, the test current firstly flowed through the EBT, then it flowed through the equal current wire, followed it flowed through the equal current M:1 multiplexer, finally it flowed through Rs to ground. As the input impedance of the voltage feedback op-amp was much larger than its series resistances including the switch-on resistance of the equipotential M:1 multiplexer, and the wire resistance and the contacted resistance of the equipotential, the voltage on the non-inverting input of the voltage feedback op-amp was equal to the voltage (Vrx ) of the EBT’s row line. Under the effect of the voltage feedback op-amp, VF followed the change of Vrx . Thus, VF was equal to Vrx . As the input impedance of the voltage feedback op-amp was much larger than its parallel resistances, such as Rs, Rsr , and RLr , the leak current on the non-inverting input of the voltage feedback op-amp could be omitted, as the voltage on every non-scanned column line was equal to VF , which was equal to Vrx . Thus, the currents on the EBT’s (N ´ 1) row adjacent elements were zero. The current (Is ) on Rs was equal to the current (Ixy ) on the EBT. The current with equal value also flowed through Rsr and RLr . As Rs was known and Is was equal to Ixy , we know Ixy if the voltage (Vsg ) on Rs and the voltage (Vxy = Vcy ´ Vrx = V I ´ Vrx ) on the EBT were known. Then we could get Rxy of the EBT. However, Vsg was not equal to VF = Vrx for Rer (Figure 1d) which was the crosstalk caused by the row wire. Thus, extra measurement error of the EBT was created. From the above discussion, we could know that the currents on Rxy , Rs , and Rer had equal values. We could use Equation (2) to calculate Rxy in the Circuit C. We could find that no Rer existed in Equation (2). As V I and Rs were known, Vsg

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the Circuit C could be calculated with Equation (2). Thus, the crosstalk caused by the row wires was suppressed. Sensors 2016, 16, 253

Rxy = (VI − VF) × Rs/Vsg

(2) 5 of 12

From the above discussion, the two-wire voltage feedback method can suppress the crosstalk caused by the row wires and the column wires, such as Rsrs, RLrs, Rscs, and RLcs.

and VF could be measured by ADC, so the equivalent resistance value (Rxy ) of the EBT in the Circuit C Experiments could3.be calculatedand withDiscussion Equation (2). Thus, the crosstalk caused by the row wires was suppressed. 3.1. Simulation Experiments in NI Multisim Rxy “ pV I ´ VF q ˆ Rs {Vsg

(2)

To emulate the performance of our method, a precise op-amp, OP07, was selected as the From the above two-wire voltage feedback the crosstalk macro-model of discussion, the op-amp the (from the datasheet, the offset method voltage, can the suppress bias current, the caused by the row wires and the column wires, such as R s, R s, R s, and R s. sr sc gain-bandwidth, and the gain are equal to 10 μV, 0.3 nA, 0.6 MHz, and 112 dB,Lcrespectively) in the Lr simulation experiments using National Instrument (NI) Multisim 12. In the simulation experiments, VI 3. Experiments was 5.0 V. and Discussion

3.1. Simulation Experiments inExperiment NI Multisim 3.1.1. R0 Effect Simulation in NI Multisim To emulate the performance our method, a precise OP07, The performances of the 2-Dofnetworked resistive circuits op-amp, were affected by Rwas 0 (R0 selected = Rer = Recas ), the includingofthe resistance contacted resistance caused the by bias cables. As shown in Figure 1, macro-model thewire op-amp (fromand thethe datasheet, the offset voltage, current, the gain-bandwidth, thegain switch-on resistance of the in the VF-NSDEincircuit was also included and the are equal to 10 µV, 0.3M:1 nA,multiplexers 0.6 MHz, and 112two-wire dB, respectively) the simulation experiments in R er (R0 = Rer). Thus, the resistance of R0 could be several hundred ohms. We investigated the effect using National Instrument (NI) Multisim 12. In the simulation experiments, V I was 5.0 V.

of R0, including wire resistance and contacted resistance on the one-wire VF-NSDE circuit and the two-wire circuit in NI Multisim. simulations, we fixed some parameters, including the 3.1.1. R0 EffectVF-NSDE Simulation Experiment in NI In Multisim resistance value of the sampling resistor and all elements in the resistive sensor array at 10 kΩ, and The performances the circuits werewith affected by resistance R0 (R0 = value Rer = Rec ), M and N at 8, R0 = Rerof =R ec in2-D the networked sensor arraysresistive varied synchronously the same including theΩ–100 wire resistance and theresults contacted by cables. As shown in Figure Figure2.1, the from 0.1 Ω. The simulation of the resistance two circuitscaused in NI Multisim 12 were shown in Figureof 2, the withM:1 R0 varied from 0.1inΩthe to 100 Ω, Rxy VF-NSDE errors in the one-wire circuitin Rer switch-onFrom resistance multiplexers two-wire circuit wasVF-NSDE also included showed a large change (from 0.006% to 8.958%) with an obvious positive coefficient, while R xy errorsof R0 , (R0 = Rer ). Thus, the resistance of R0 could be several hundred ohms. We investigated the effect in the two-wire VF-NSDE circuit showed a tiny change (from −0.003% to −0.002%). Thus, the including wire resistance and contacted resistance on the one-wire VF-NSDE circuit and the two-wire two-wire VF-NSDE circuit has a better performance than the one-wire VF-NSDE circuit when R0 is VF-NSDE circuit in NI Multisim. In simulations, we fixed some parameters, including the resistance varied from 0.1 Ω to 100 Ω; the absolute Rxy errors in the one-wire VF-NSDE circuit are small enough value of the sampling resistor and all elements in the resistive sensor array at 10 kΩ, and M and N to be negligible (less than 0.087% for the one-wire VF-NSDE circuit) when R0 is less than 1 Ω; the at 8, R =xyRerrors sensor arrays varied synchronously with the same resistance value from ec in the 0 = Rer R absolute in the two-wire VF-NSDE circuit are small enough to be negligible (less than 0.1 Ω–100 Ω. The simulation results of the two circuits in than NI Multisim 0.003% for the two-wire VF-NSDE circuit) when R0 is less 100 Ω. 12 were shown in Figure 2.

Figure 2. Effect of R0 on the Rxy errors in the one-wire VF-NSDE circuit and the two-wire VF-NSDE Figure 2. Effect of R0 on the Rxy errors in the one-wire VF-NSDE circuit and the two-wire VF-NSDE circuit where M = N = 8. circuit where M = N = 8.

From Figure 2, with R0 varied from 0.1 Ω to 100 Ω, Rxy errors in the one-wire VF-NSDE circuit showed a large change (from 0.006% to 8.958%) with an obvious positive coefficient, while Rxy errors in the two-wire VF-NSDE circuit showed a tiny change (from ´0.003% to ´0.002%). Thus, the two-wire VF-NSDE circuit has a better performance than the one-wire VF-NSDE circuit when R0 is varied from 0.1 Ω to 100 Ω; the absolute Rxy errors in the one-wire VF-NSDE circuit are small enough to be negligible (less than 0.087% for the one-wire VF-NSDE circuit) when R0 is less than 1 Ω; the absolute

investigated the effect of M and N on the one-wire VF-NSDE circuit and the two-wire VF-NSDE circuit in NI Multisim. In simulations, we fixed some parameters including the resistance value of the sampling resistor and all elements in the resistive sensor array at 10 kΩ, M or N at 8, R0 at 2 Ω, N or M was one number in (8, 15, 29, 57, 83, 98, 113, 225, and 449). The array size effect on the one-wire VF-NSDE circuit and the two-wire VF-NSDE circuit was simulated in NI Multisim and the results were shown in Figure 3. 16, 253 Sensors 2016, 6 of 12 From Figure 3, the absolute Rxy errors in both circuits increased with the increase of the row number or the column number; with the increase of the column number, the Rxy errors in the one-wire had a circuit positiveare coefficient (from 0.178% 8.85%) while thethan Rxy errors in for the Rxy errors in theVF-NSDE two-wirecircuit VF-NSDE small enough to betonegligible (less 0.003% the two-wire VF-NSDE circuit had a negative coefficient (from −0.002% to −0.162%), and the absolute two-wire VF-NSDE circuit) when R0 is less than 100 Ω. Rxy errors in the two-wire VF-NSDE circuit had been reduced significantly comparing with the absolute Rxy errors in the one-wire VF-NSDE circuit. 3.1.2. Array Size Effect Simulation Experiment From Figure 3, with the increase of the row number, the Rxy errors in the two-wire VF-NSDE circuit were to the Rxy such errorsas inthe the row one-wire VF-NSDE circuit; the row number changed Parameters ofsimilar the array size, number (M) and thewith column number (N), were proved in the range from 8 to 98, the Rxy errors in both circuits changed small (from 0.178% to 0.231% for the to have effects on the performance of the 2-D networked resistive sensor arrays [9–17]. We investigated one-wire VF-NSDE circuit, from −0.002% to 0.077% for the two-wire VF-NSDE circuit); but when the the effect of M and N on the one-wire VF-NSDE circuit and the two-wire VF-NSDE circuit in NI row number changed in the range from 113 to 449, the Rxy errors in both circuits changed greatly Multisim. In simulations, some parameters including resistance value the sampling (from 1.23% to 462%we for fixed the one-wire VF-NSDE circuit, from the 1.65% to 517% for the of two-wire resistor VF-NSDE and all elements in the resistive 10 lines, kΩ, M N at 8, Rof Ω, N or M was circuit). While both circuitssensor had tooarray manyatrow theorhypothesis the2 op-amps’ 0 at virtualinshort was every had effect a limited ability in driving one number (8, 15, 29,not 57,correct 83, 98,as113, 225,column-driving and 449). Theop-amp array size on the one-wire VF-NSDE current. Thus, in the two-wire VF-NSDE circuit, the influence of the arrayand sizethe on the Rxy error circuit and the two-wire VF-NSDE circuit was simulated in NI Multisim results werehas shown in been decreased greatly; fewer row numbers and greater column numbers are preferred for good Figure 3. performance.

Figure 3. Array size effect on the Rxy errors in the one-wire VF-NSDE circuit and the two-wire

Figure 3. Array size effect on the Rxy errors in the one-wire VF-NSDE circuit and the two-wire VF-NSDE VF-NSDE circuit where R0 = 2 Ω and Rother = 10 kΩ. circuit where R0 = 2 Ω and Rother = 10 kΩ. 3.1.3. The Adjacent Elements Effect Simulation Experiment

From Figure 3, the absolute Rxy errorselements in bothofcircuits with athe increase ofinthe row In the literatures [9–17], the adjacent all otherincreased elements played significant role the measurement the EBT. In fixed some numberaffecting or the column number;accuracy with theofincrease ofsimulations, the columnwe number, theparameters, Rxy errorsincluding in the one-wire thecircuit resistance of non-adjacent elements all other elements M and at two-wire 8, VF-NSDE hadvalue a positive coefficient (fromand 0.178% to adjacent 8.85%) while theatR10xykΩ, errors in N the R0 at 2 Ω, Rs at 10 kΩ. The resistance value of the EBT and one adjacent element varied in the range VF-NSDE circuit had a negative coefficient (from ´0.002% to ´0.162%), and the absolute Rxy errors in from 0.1 kΩ to 1 MΩ. The adjacent element could be an adjacent row element (Radjr) or an adjacent the two-wire VF-NSDE circuit had been reduced significantly comparing with the absolute Rxy errors in the one-wire VF-NSDE circuit. From Figure 3, with the increase of the row number, the Rxy errors in the two-wire VF-NSDE circuit were similar to the Rxy errors in the one-wire VF-NSDE circuit; with the row number changed in the range from 8 to 98, the Rxy errors in both circuits changed small (from 0.178% to 0.231% for the one-wire VF-NSDE circuit, from ´0.002% to 0.077% for the two-wire VF-NSDE circuit); but when the row number changed in the range from 113 to 449, the Rxy errors in both circuits changed greatly (from 1.23% to 462% for the one-wire VF-NSDE circuit, from 1.65% to 517% for the two-wire VF-NSDE circuit). While both circuits had too many row lines, the hypothesis of the op-amps’ virtual short was not correct as every column-driving op-amp had a limited ability in driving current. Thus, in the two-wire VF-NSDE circuit, the influence of the array size on the Rxy error has been decreased greatly; fewer row numbers and greater column numbers are preferred for good performance. 3.1.3. The Adjacent Elements Effect Simulation Experiment In the literatures [9–17], the adjacent elements of all other elements played a significant role in affecting the measurement accuracy of the EBT. In simulations, we fixed some parameters, including

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the resistance value of non-adjacent elements and all other adjacent elements at 10 kΩ, M and N at 8, R0 at 2 Ω, Rs at 10 kΩ. The resistance value of the EBT and one adjacent element varied in the range from 0.1 kΩ to 1 MΩ. The adjacent element could be an adjacent row element (Radjr ) or an adjacent Sensors 2016, 16,(R 253 12 column element two-wire adjc ). The simulation results of the one-wire VF-NSDE circuit and the7 of Sensors 2016, 16, 253 7 of 12 VF-NSDE circuit in NI Multisim are shown in Figures 4–7. column element (Radjc). The simulation results of the one-wire VF-NSDE circuit and the two-wire From Figures 4–7(R the Rxy in theresults EBT with a greater more easily to be column element adjc). Theerrors simulation of the one-wireresistance VF-NSDE value circuit were and the two-wire VF-NSDE circuit in NI Multisim are shown in Figures 4–7. interfered by one R or one R with a smaller resistance value. In both circuits, the changes of the VF-NSDE circuit in NI Multisim are shown in Figures 4–7. adjr 4–7, the Radjc From Figures xy errors in the EBT with a greater resistance value were more easily to From Figures 4–7, the R xy errors in the EBT with a greater resistance value were more easily to Rxy errors for the change Radjr than the changes the change of xy errors be interfered by one Rof adjrone or one Radjcwere with larger a smaller resistance value. of In the bothRcircuits, thefor changes of be.R interfered by onechange Radjrone or of one Radjc with afrom smaller resistance value.the In the changes of (with one Radjc With onefor Radjr or Radjc varied 0.1than kΩ the to 1changes MΩ, changes of the errors the xy errors the one Radjr were larger of both the Rcircuits, xy errors for R the xy change the RxyRerrors forone the R change of one adjr were larger than the changes of the Rxy errors for the change one adjc . With adjr one RadjcRfor varied kΩ from to 1 MΩ, the changes of the for Rxy errors Rxy at of 1 MΩ, from ´9.72% toor´19.1% onefrom Radjc0.1and ´9.67% to ´65.1% one R(with adjr ) in the of one R adjc. With one Radjr or one Radjc varied from 0.1 kΩ to 1 MΩ, the changes of the Rxy errors (with R xy at 1 MΩ, from −9.72% to −19.1% for one Radjc and from −9.67% to −65.1% for one Radjr) in the one-wire VF-NSDE circuit weretosignificant, while those (with Rxy at 1 MΩ, from ´0.290% to ´0.289% Rxy at 1 VF-NSDE MΩ, fromcircuit −9.72%were −19.1% for one Radjcthose and (with from −9.67% −65.1% one Rto adjr) in the significant, while Rxy at 1 to MΩ, from for −0.290% −0.289% for oneone-wire R and from ´0.247% to ´4.34% for one R ) in the two-wire VF-NSDE circuit were small. adjc adjr (with Rxy at 1 MΩ, from −0.290% to −0.289% one-wire VF-NSDE circuit were for one Radjc and from −0.247% tosignificant, −4.34% for while one Rthose adjr) in the two-wire VF-NSDE circuit were small. Thus, in the two-wire VF-NSDE circuit, the influence of the adjacent elements on the R error has for one adjc and from −0.247% to −4.34% for one Radjr) in the two-wire VF-NSDE circuit were xy small. Thus, in R the two-wire VF-NSDE circuit, the influence of the adjacent elements on the Rxy error has Thus, in the two-wire VF-NSDE circuit, the influence of the adjacent elements on the Rxy error has been decreased greatly. been decreased greatly. been decreased greatly.

Figure 4. The Radjc effect on Rxy errors in the one-wire VF-NSDE circuit.

4. The effect errors ininthe VF-NSDE circuit. FigureFigure 4. The RadjcRadjc effect ononRRxyxy errors theone-wire one-wire VF-NSDE circuit.

Figure 5.5.The RRadjr effect on xy one-wire VF-NSDE circuit. Figure The adjr effect onRRRxy xy errors errors in ininthe the one-wire VF-NSDE circuit. Figure 5. The Radjr effect on errors the one-wire VF-NSDE circuit.

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Figure 6. R effect on xy errors in the two-wire VF-NSDE circuit. Figure 6. The Radjc effect errorsin inthe thetwo-wire two-wire VF-NSDE circuit. Figure 6. The The Radjc adjc effecton onRR Rxy xy errors VF-NSDE circuit.

Figure 7. The Radjr effect on Rxy errors in the two-wire VF-NSDE circuit.

Figure 7. The Radjr effecton onRRxy xy errors in the two-wire VF-NSDE circuit. Figure 7. The Radjr effect errors in the two-wire VF-NSDE circuit.

3.2. 3.2. Test Test Experiments Experiments with with the the Two-Wire Two-Wire VF-NSDE VF-NSDE Prototype Prototype Circuit Circuit

3.2. Test Experiments with the Two-Wire VF-NSDE Prototype Circuit

A A VF-NSDE VF-NSDE prototype prototype circuit circuit based based on on the the two-wire two-wire voltage voltage feedback feedback method method was was designed. designed. In In

the prototype circuit, and OPA2209 (from the the offset the current, A circuit based on the two-wire voltage method was designed. theVF-NSDE prototype prototype circuit, OPA4209 OPA4209 and OPA2209 (from the datasheet datasheet the feedback offset voltage, voltage, the bias bias current, the gain-bandwidth, and the gain are equal to ±150 μV, ±1 nA, 18 MHz, and 120 dB, respectively) In thethe prototype circuit, OPA4209 andare OPA2209 the datasheet the offset the bias current, gain-bandwidth, and the gain equal to(from ±150 μV, ±1 nA, 18 MHz, and voltage, 120 dB, respectively) were op-amps, MAX4619 the datasheet the on-resistance, the the gain-bandwidth, and the gainMAX4617 are equaland to ˘150 µV, ˘1(from nA, 18 and 120 respectively) were used used as as the the op-amps, MAX4617 and MAX4619 (from theMHz, datasheet the dB, on-resistance, thewere on-resistance match between channels, and the on-resistance flatness are equal to 8 Ω, 0.2 Ω, and 11 on-resistance match between channels, and the on-resistance flatness are equal to 8 Ω, 0.2 Ω, and used as the op-amps, MAX4617 and MAX4619 (from the datasheet the on-resistance, the on-resistance Ω, respectively) were used as the multiplex switches, and the resistance of the sampling resistor was respectively) were used as the multiplex switches, resistance of 0.2 the Ω, sampling resistor was matchΩ,between channels, and the on-resistance flatnessand arethe equal to 8 Ω, and 1 Ω, respectively) 10 kΩ. In the prototype circuit, M and N were 16 and 8, respectively, and 48 lines were necessary for 10 kΩ. In the prototype circuit, M and N were 16 and 8, respectively, and 48 lines were necessary for were the used as the multiplex switches, and thelines resistance of the of sampling resistor was 10 kΩ.the In the prototype circuit. A cable with 50 core and its length 400mm was used to connect the prototype circuit. A cable with 50 core lines and its length of 400mm was used to connect the prototype circuit, M and N were 16 and 8, respectively, and 48 lines were necessary for the prototype circuit. A cable with 50 core lines and its length of 400mm was used to connect the resistive sensor array modules with the circuit. The remaining two lines connected to ground were used as the shield

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resistive sensor array modules with the circuit. The remaining two lines connected to ground were used as the shield lines. In the prototype circuit, VI was 3.30 V and a micro control unit (MCU) with lines. In the prototype circuit, VI was 3.30 V and a micro control unit (MCU) with an embedded an embedded 8-channel, 12-bit analog-to-digital converter (ADC) was used. 8-channel, 12-bit analog-to-digital converter (ADC) was used. 3.2.1. The The R Rxy Measurement Experiment with the Two-Wire VF-NSDE Prototype Circuit 3.2.1. xy Measurement Experiment with the Two-Wire VF-NSDE Prototype Circuit In the the experiment, experiment, the the EBT EBT was was replaced replaced by by aa precision precision resistance resistance box box with with its its smallest smallest step step In resistance value at 0.1 Ω, all non-scanned elements were precision resistors at 4.7 kΩ or 5.1 kΩ. resistance value at 0.1 Ω, all non-scanned elements were precision resistors at 4.7 kΩ or 5.1 The kΩ. resistance value of the EBT was varied from 10 Ω to 100 kΩ, and the results of with the two-wire The resistance value of the EBT was varied from 10 Ω to 100 kΩ, and the results of with the two-wire VF-NSDE prototype prototype circuit circuit were were shown shown in in Figure Figure8. 8. VF-NSDE

Test Results of Rxy (kΩ)

100

2-wires VF-NSDE circuit

10

1

0.1

0.01 0.01

0.1

1

10

Rxy with non-scanned elements at 4.7kΩ or 5.1kΩ (kΩ)

100

Figure Results of of the Figure 8. 8. Results the EBT EBT varied varied from from 10 10 Ω Ω to to 100 100 kΩ kΩ in in the the prototype prototype circuit. circuit.

From the theresults results in Figure we found the two-wire had a good From in Figure 8, we8,found that thethat two-wire VF-NSDEVF-NSDE circuit hadcircuit a good performance performance in of a wide range ofbeing the element being tested.we Additionally, we found thecircuit output of in a wide range the element tested. Additionally, found that the outputthat of the was the circuit wasthe unstable theresistance EBT of a larger resistance value (R xy > 50 kΩ). The reason could be unstable with EBT of with a larger value (R > 50 kΩ). The reason could be the nonlinearity xy the nonlinearity and of thethe circuit noise of the voltage and the circuit noise voltage feedback circuit. feedback circuit. 3.2.2. The Adjacent Elements Effect Experiments with with the Two-Wire Two-WireVF-NSDE VF-NSDEPrototype PrototypeCircuit Circuit In the experiments, experiments, the EBT was replaced by a precision resistance box with its smallest step resistance was also replaced byby a precision resistance box,box, andand the resistance value valueat at0.1 0.1Ω, Ω,one oneadjacent adjacentelement element was also replaced a precision resistance other non-scanned elements were precision resistors withwith eacheach resistance value at 4.7 the other non-scanned elements were precision resistors resistance value at kΩ 4.7 or kΩ5.1 or kΩ. 5.1 The resistance value of the EBT varied in the range from 5 kΩ to 100 kΩ and the resistance value of kΩ. The resistance value of the EBT varied in the range from 5 kΩ to 100 kΩ and the resistance value one adjacent element varied in the from 10 Ω to kΩ. adjacent elementelement could becould an adjacent of one adjacent element varied inrange the range from 101 Ω to The 1 kΩ. The adjacent be an row element ) or an adjacent column element (R ). The results of the two-wire VF-NSDE circuit adjacent row(Relement (R adjr ) or an adjacent column element (R adjc ). The results of the two-wire adjr adjc were shown in Figures 9 and 10. VF-NSDE circuit were shown in Figures 9 and 10. From the 1010, in the two-wire VF-NSDE prototype circuit, we found that the results resultsininFigures Figures9 9and and in the two-wire VF-NSDE prototype circuit, we found the adjacent row element with small resistance value (R < 100 Ω) had a significant effect on that the adjacent row element with small resistance value on adjr(Radjr < 100 Ω) had a significant effectthe measurement errorerror of the WithWith a smaller resistance valuevalue of oneofrow element, the effect the measurement ofEBT. the EBT. a smaller resistance oneadjacent row adjacent element, the was While the adjacent columncolumn elementelement with small value (Rvalue effectmore wassignificant. more significant. While the adjacent withresistance small resistance (RadjcΩ) < adjc < 100 had insignificant effect on the measurement error of the EBT. In simulation experiment results, similar 100 Ω) had insignificant effect on the measurement error of the EBT. In simulation experiment variations were also found were in Figures 6 and 7. in thethe two-wire VF-NSDE results, similar variations also found in However, Figures 6 the andvariations 7. However, variations in the prototype circuit were smaller, circuit which might be caused by the larger featurecurrent in the two-wire VF-NSDE prototype were smaller, which might be current caused driving by the larger

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op-amp offeature OPA4209. From the results in Figures andresults 10 wein also found99 that the we output the circuit driving in op-amp of From Figures and also found that driving feature in the the op-amp of OPA4209. OPA4209. From9 the the results in Figures and 10, 10, we also of found that the output of the circuit was unstable with the EBT of a larger resistance value (R xy > 50 kΩ). was unstable with the EBT of a larger resistance value (R > 50 kΩ). xy the output of the circuit was unstable with the EBT of a larger resistance value (Rxy > 50 kΩ). 0.06 0.06

Rxy error error with with M=16 M=16 and and N=8 N=8 (%) (%) Rxy

0.04 0.04 0.02 0.02 0.00 0.00 -0.02 -0.02 -0.04 -0.04 -0.06 -0.06

Rxy=5kΩ Rxy=5kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=10kΩ Rxy=10kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=30kΩ Rxy=30kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=50kΩ Rxy=50kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=100kΩ Rxy=100kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit

-0.08 -0.08 -0.10 -0.10 -0.12 -0.12 -0.14 -0.14 -0.16 -0.16

10 10

100 100

1000 1000

One One Radjc Radjc with with other other Radj Radj at at 4.7kΩ 4.7kΩ or or 5.1kΩ 5.1kΩ (Ω) (Ω) Figure The adjc effect VF-NSDE prototype circuit. Figure 9. 9. The errorsin thetwo-wire two-wire VF-NSDE prototype circuit. Figure 9. TheRR R adjc effect effect on R Rxy xy errors ininthe the two-wire VF-NSDE prototype circuit. xyerrors adjc 0.0 0.0

Rxy error error with with M=16 M=16 and and N=8 N=8 (%) (%) Rxy

-0.5 -0.5 -1.0 -1.0 -1.5 -1.5 -2.0 -2.0

Rxy=5kΩ Rxy=5kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=10kΩ in 2-wires Rxy=10kΩ in 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=30kΩ Rxy=30kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=50kΩ Rxy=50kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit Rxy=100kΩ Rxy=100kΩ in in 2-wires 2-wires VF-NSDE VF-NSDE circuit circuit

-2.5 -2.5 -3.0 -3.0 -3.5 -3.5 -4.0 -4.0 -4.5 -4.5 -5.0 -5.0 -5.5 -5.5 -6.0 -6.0 -6.5 -6.5 -7.0 -7.0

10 10

100 100

One One Radjr Radjr with with other other Radj Radj at at 4.7kΩ 4.7kΩ or or 5.1kΩ 5.1kΩ (Ω) (Ω)

1000 1000

Figure The adjr effect VF-NSDE prototype circuit. Figure 10.10. The errorsin thetwo-wire two-wire VF-NSDE prototype circuit. Figure 10. TheRR R adjr effect effect on R Rxy xy errors ininthe the two-wire VF-NSDE prototype circuit. xyerrors adjr

Discussion 3.3. Discussion 3.3.3.3. Discussion As shown in Figure the one-wire VF-NSDE circuit one voltage feedback op-amp, N 2:1 shown Figure1,1, 1,the theone-wire one-wireVF-NSDE VF-NSDE circuit circuit had had NN 2:12:1 AsAs shown inin Figure had one onevoltage voltagefeedback feedbackop-amp, op-amp, multiplexers, and M ++ N wires; the two-wire VF-NSDE circuit had one voltage feedback op-amp, N multiplexers, and M N wires; the two-wire VF-NSDE circuit had one voltage feedback op-amp, N multiplexers, and M + N wires; the two-wire VF-NSDE circuit had one voltage feedback op-amp, column driving op-amps, N 2:1 multiplexers, two M:1 multiplexers, and 2(M + N) wires. Thus, more column driving driving op-amps, N)N) wires. Thus, more N column op-amps, N N 2:1 2:1 multiplexers, multiplexers,two twoM:1 M:1multiplexers, multiplexers,and and2(M 2(M+ + wires. Thus, more components components were were used used in in the the two-wire two-wire VF-NSDE VF-NSDE circuit. circuit. components were used in the two-wire VF-NSDE circuit.

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As shown in Figure 1, the two-wire VF-NSDE circuit had two M:1 multiplexers, which had the switch-on resistance of several hundred milliohms to several hundred ohms. The switch-on resistance of the M:1 multiplexers was included in Rer (R0 = Rer ). In practical circuits, the M:1 multiplexers with their switch-on resistances of small value, for example, 2 ohms, were preferred. From the results in Figure 2, we found that the multiplexers with the switch-on resistance of one hundred ohms could also be used in the circuits with the proposed method. From the results in Figures 6, 7, 9 and 10 with the change of one adjacent element, similar variations of the Rxy error were found in the simulation circuit and the prototype circuit. However, the variations in the two-wire VF-NSDE prototype circuit were smaller, which might be caused by the larger current driving feature in the OPA4209 op-amp. Thus, a precision op-amp with large current driving features may better for a good performance of the two-wire voltage feedback circuit. From the results in Figures 2 and 3 and Figures 6–10 the good performance of the two-wire VF-NSDE circuit was verified with simulation experiments and practical circuit experiments. From the results in Figures 8–10 we also found that the output of the circuit was unstable with the EBT with a larger resistance value (Rxy > 50 kΩ). The reason could be the nonlinearity and the circuit noise of the voltage feedback circuit. From the experiment results, the two-wire voltage feedback method was verified to be efficient in suppressing the VF-NSDE circuit’s crosstalk caused by the row wires and the column wires. The two-wire voltage feedback method could also be useful for depressing the cable crosstalk in other voltage feedback circuits such as the VF-NSE circuit, and the VF-NSSE circuit. It should be noted that all conclusions were correct under the assumption that the column driving op-amps had sufficient driving ability and the voltage feedback op-amp had very large input impedance on its non-inverting input. From the results in Figures 3, 6 and 7 the two-wire VF-NSDE circuit failed to work normally with too large a row number, and its Rxy error increased with the increase of the EBT’s resistance and the decrease of the adjacent element’s element. If the resistances of the adjacent elements in a resistive sensor array were too small, or the array size was too large for the column driving op-amps’ limited driving ability, Vcy would be not equal to V I and the voltages on non-scanned column lines would not equal to VF . At the same time, if the voltage feedback op-amp did not have very large input impedance or the elements in the resistive sensor array had very large resistance values for the voltage feedback op-amp’s input impedance, VF would be not equal to Vrx . Thus, the ideal work conditions would be destroyed for the two-wire VF-NSDE circuit and the Rxy error would be significant. 4. Conclusions Firstly, a two-wire VF-NSDE method of the 2-D networked resistive sensor array was proposed in this paper. Secondly, the formula was given for the equivalent resistance expression of the element being tested in the networked resistive sensor array by principle analysis. Thirdly, the effects of some parameters on the measurement accuracy of the EBT were simulated with the National Instrument Multisim 12, the parameters including wire resistances and contacted resistances of the long cables, the column number, the row number, and the adjacent elements of the 2-D resistive sensor array. Following this, a two-wire VF-NSDE prototype circuit was designed and its performance was tested by experiments. The experiment results show that the two-wire voltage feedback method is efficient in suppressing the crosstalk caused by the row wires and the column wires; in the 2-D networked resistive sensor array with the two-wire VF-NSDE circuit, the influence of the adjacent column elements and the adjacent row elements on the measurement error of the element being tested has been reduced greatly; fewer rows and more columns are preferred for good performance in accessing all elements individually in the 2-D resistive sensor array. Acknowledgments: This study was supported by the Specialized Research Fund Program for the Doctoral Program of Higher Education (No. 20130092110060). This study was also supported by the scientific research fund project of Nanjing Institute of Technology (No. CKJB201405), the Open Fund of the Key Laboratory of remote measurement and control technology in Jiangsu Province (No. YCCK201401, YCCK201006), the National Major Scientific Equipment R&D Project (Grant No. ZDYZ2010-2), and NSAF (No. U1230114).

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Author Contributions: J.W. conceived and designed the experiments; J.W. and S.H. performed the experiments; J.W., J.L. and A.S. analyzed the data; J.L. and A.S. contributed analysis tools; J.W. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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