# Cable Crosstalk Suppression in Resistive Sensor Array with 2-Wire S-NSDE-EP Method

Authors: JianFeng Wu; Lei Wang
Journal: Journal of Sensors
 (2016)

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## Abstract

With long flexible cables connected to the 1-wire setting non-scanned-driving-electrode equipotential (S-NSDE-EP) circuit, the resistive sensor array modules got flexibility in robotic operations but suffered from the crosstalk problem caused by wire resistances and contacted resistances of the cables. Firstly, we designed a new S-NSDE-EP circuit using two wires for every driving-electrode and every sampling-electrode to reduce the crosstalk caused by the connected cables in the 2D networked resistive sensor array. Then, an equivalent resistance expression of the element being tested (EBT) for this circuit was analytically derived. Then, the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit were evaluated by simulations. The simulation results show that the 2-wire S-NSDE-EP circuit, though it requires a large number of wires, can greatly reduce the crosstalk error caused by wire resistances and contacted resistances of the cables in the 2D networked resistive sensor array.


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## Body

## 1. Introduction

Resistive sensor arrays were widely used in tactile sensing [1–8], light sensing [9], infrared sensing [10], and so forth. In robotic applications, long flexible cables were preferred for flexibility and limited space of the sensitive areas. With tested cables of lengths from 55 mm to 500 mm (as shown in Table 1), different modules of resistive sensor arrays were connected to the test circuits through the plugs and the sockets. Vidal-Verdú et al. [1, 3] designed and compared circuits of networked piezoresistive sensor arrays. Speeter [2] designed a flexible sensing system with 16 × 16 resistive taxels. Yang et al. [4] designed a 32 × 32 flexible array within a 160 mm × 160 mm temperature and tactile sensing area. Zhang et al. [5] reported a 3 × 3 thin tactile force sensor array based on conductive rubber. Castellanos-Ramos et al. [6] reported a 16 × 16 tactile sensor array based on conductive polymers with screen-printing technology. Kim et al. [7] reported a flexible tactile sensor array with high performance in sensing contact force. Lazzarini et al. [8] reported a 16 × 16 tactile sensor array for practical applications in manipulation. But cables had different wire resistances which increased with the increase of their lengths. Between the plugs of the connected cables and the sockets of the test circuits, there existed contacted resistances of tens of milliohms to several ohms varying with the variation of mechanical vibration and time. But new methods are still lacking, which can be used to suppress crosstalk caused by long cables.Table 1
Resistive sensor arrays with cables of different lengths.
Literature
Sensor
Array size of sensing elements
Cable length (mm)
Cable crosstalk
[1]
Polymer based FSR
16 × 9
>55
Yes
[2]
FSR
16 × 16
>60
Yes
[3]
FSR
16 × 16
>70
Yes
[4]
Conductive rubber
32 × 32
>70
Yes
[5]
Conductive rubber
3 × 3
>95
Yes
[6]
Conductive polymer
16 × 16
>100
Yes
[7]
Semiconductor strain gage
5 × 5
>100
Yes
[8]
FSR
16 × 16
500
Yes
[9]
Light dependent resistor
16 × 16
—
YesFor this purpose, we present a novel cable crosstalk suppression circuit based on a 2-wire method for the 2D networked resistive sensor arrays in the row-column fashion. This paper begins with an overview of the application fields of the 2D networked resistive sensor arrays. Secondly, a novel cable crosstalk suppression method will be proposed and its equivalent resistance expression of the element being tested (EBT) will be analytically derived. Then simulations will be implemented to evaluate this method with different parameters such as wire resistances and contacted resistances of the cables, the array size, the measurement range of the EBT, and the adjacent elements’ resistances of 2D networked resistive sensor arrays. Finally, the results of experiments will be analyzed and conclusions for the method will be given.


## 2. Principle Analyses

In the row-column fashion, 2D resistive sensor arrays needed few wires but suffered from crosstalk caused by parasitic parallel paths. For suppressing crosstalk, many methods have been proposed and analyzed in literatures, such as the passive integrators method [3], the inserting diode method [11], the resistive matrix array method [12], the voltage feedback methods [2, 13–17], and the zero potential methods (ZPMs) [1, 3–10, 16–20]. Wu et al. have suppressed the crosstalk caused by the adjacent column elements and the adjacent row elements with the Improved Isolated Drive Feedback Circuit (IIDFC) [13] and the Improved Isolated Drive Feedback Circuit with Compensation (IIDFCC) [14]. Wu et al. have also proposed a general voltage feedback circuit model [15] for fast analyzing the performances of different voltage feedback circuits. D’Alessio has analyzed measurement errors in the scanning circuits of piezoresistive sensors arrays [16]. Saxena et al. [18, 19] have suppressed the crosstalk caused by the adjacent column elements with large number of op-amps using the zero potential method. Roohollah et al. [20] have suppressed the crosstalk error caused by the input offset voltage and input bias current of the op-amp with a novel double-sampling technique. In these methods, the measurement accuracy of the EBT still suffered from cable crosstalk.Liu et al. [17] defined the setting non-scanned-electrode zero potential (S-NSE-ZP) method, the setting non-scanned-sampling-electrode zero potential (S-NSSE-ZP) method, and the setting non-scanned-driving-electrode zero potential (S-NSDE-ZP) method for the zero potential methods, in which bipolar power sources were necessary for op-amps and analog digital converters (ADCs). In some circuits [1, 3], the reference voltages were not zero, so op-amps and ADCs with unipolar power sources, which were of less cost and were more convenient for use, could be used. So we defined those equipotential methods as the setting non-scanned-electrode-equipotential (S-NSE-EP) method, the setting non-scanned-sampling-electrode-equipotential (S-NSSE-EP) method, and the setting non-scanned-driving-electrode-equipotential (S-NSDE-EP) method. In this analysis, the S-NSDE-EP circuit was taken for example. Traditional S-NSDE-EP circuit of resistive networked sensor array in shared row-column fashion was shown as Circuit A in Figure 1(a). In Circuit A, the row electrodes and the column electrodes were used as the sampling electrodes and the driving electrodes, respectively. In Circuit A, R11 in the M×N resistive array was the element being tested (EBT); only one connected wire was used for every column and row electrode between the sensor array and the circuit; only one equal current M : 1 multiplexer was used between the current setting resistor (Rset1) and the row electrodes of the sensor module. On column electrodes of the circuit, 2 : 1 multiplexers had multiplexer switch resistances (Rscs); column wires had column resistances (RLcs) including column wire resistances and column contacted resistances. On row electrodes of the circuit, the equal current M : 1 multiplexers had multiplexer switch resistances (Rsrs); row wires had row resistances (RLrs) including row wire resistances and row contacted resistances. Thus Circuit A had one row sampling op-amp, one M : 1 multiplexer, N 2 : 1 multiplexers, and M+N wires.Figure 1
(a) 1-wire S-NSDE-EP circuit (Circuit A). (b) Simplified measurement circuit of 1-wire S-NSDE-EP circuit (Circuit B). (c) 2-wire S-NSDE-EP circuit (Circuit C). (d) Simplified measurement circuit of 2-wire S-NSDE-EP circuit (Circuit D).
(a)
(b)
(c)
(d)Under an ideal condition, allRscs and all RLcs were omitted. Thus the voltage (Vcy1) on the column electrode of the EBT was equal to the feedback voltage (Vxy1), and the voltages on the nonscanned column electrodes were equal to the reference voltage (Vref1). At the same time, all Rsrs and all RLrs were omitted. Thus the voltage (Ve1) on the inverting input of the row sampling op-amp was equal to the voltage (Vrx1) on the row electrode of EBT. Under the effect of the ideal op-amp, Ve1 was equal to Vref1 and the current (Ixy1) on the EBT was following the change of the current (Iset1) on Rset1. As the voltages on the nonscanned column electrodes were equal to Vref1, the currents on the adjacent row elements of EBT were equal to zero. At the same time, the current on the inverting input of the ideal op-amp was omitted for its infinite input impedance, the current (Ixy1) on the EBT was equal to the current (Iset1=(Vxy1-Vref1)/Rxy1=Vref1/Rset1) on Rset1. Thus, Iset1 and Ixy1 were equal. As Vref1 and Rset1 were known, Vxy1 could be measured by ADC, so the equivalent resistance value (Rxy1) of the EBT in Circuit A could be calculated with the following: (1)Rxy1=Vxy1-Vref1×Rset1Vref1.But under the real condition as shown in Figure1(b), Vcy1 was not equal to Vxy1 for Rsc and RLc, and Ve1 was not equal to Vrx1 for Rsr and RLr. The ideal feedback condition was destroyed by the row wires and the column wires, so extra measurement errors of the EBT existed.For suppression cable crosstalk in the 2D networked resistive arrays, we proposed a 2-wire equipotential method (Circuit C, as shown in Figure1(c)). In Circuit C, we used two wires for every row electrode and every column electrode between the sensor module and the test circuit; also we used one column driving op-amp for every column electrode and one more equipotential M : 1 multiplexer between the row electrodes and the row sampling op-amp. Thus Circuit C had one row sampling op-amp, N column driving op-amps, N 2 : 1 multiplexers, two M : 1 multiplexers, and 2(M+N) connected wires.Every column electrode 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 noninverting input of every column driving op-amp was connected with the common port of its column 2 : 1 multiplexer; thus every noninverting input was connected withVxy or Vref. The noninverting input of EBT’s column driving op-amp was connected with Vxy and the noninverting inputs of other column driving op-amps were connected with Vref.As the input impedance of every column driving op-amp was much bigger thanRsc, the effect of Rsc could be omitted. So the voltage on the noninverting input of every column driving op-amp was equal to the input voltage (Vxy or Vref) of its 2 : 1 multiplexer. If the column driving op-amps had sufficient driving ability, the voltage on every column electrode was following the change of the voltage on the noninverting input of its column driving op-amp. So Vcy was equal to Vxy, and the voltages on nonscanned column electrodes were equal to Vref. Thus the crosstalk effect of RLc and Rsc was suppressed.By one equal current wire, every row electrode in the sensor module was connected with one channel of the equal currentM : 1 multiplexer with its common port connected with Rset. In the equal current M : 1 multiplexer, only the row electrode of EBT was gated and all other nonscanned electrodes were suspended. So only the row electrode of the EBT was connected with Rset.By one equipotential wire, every row electrode in the sensor module was also connected with one channel of the equipotentialM : 1 multiplexer with its common port connected with the inverting input of the row sampling op-amp. In the equipotential M : 1 multiplexer, only the row electrode of EBT was gated and all other nonscanned electrodes were suspended. So only the EBT’s row electrode was connected with the inverting input of the row sampling op-amp. From the output port of the EBT’s column driving op-amp, the test current firstly flowed through the EBT, then it flowed through the row equal current wire, then it flowed through the equal current M : 1 multiplexer, and finally it flowed through Rset to ground.As the input impedance of the row sampling op-amp was much bigger than its series resistances such as the switch resistance of the equipotentialM : 1 multiplexer, the wire resistance of the equipotential wire, and the contacted resistance, the voltage on the inverting input of the row sampling op-amp was equal to the voltage (Vrx) of the EBT’s row electrode.Under the effect of the row sampling op-amp, the current (Ixy) on the EBT followed the change of the current (Iset) on Rset. As the input impedance of the row sampling op-amp was much bigger than its parallel resistances such as Rs, Rsr, and RLr, the leak current on the inverting input of the voltage feedback op-amp could be ommited. And the voltage on every nonscanned column electrode was equal to Vref, which was also equal to Vrx. Thus the currents on the EBT’s (N-1) row adjacent elements were zero. So Iset was equal to Ixy. The current with equal value also flowed through Rsr and RLr. As Rset was known and Iset was equal to Ixy, we could know Ixy if the voltage (Ve) on Rset and the voltage (Vxy) on the EBT were known. Thus we could get Rxy of the EBT.ButVe was not equal to Vrx for Rer (as shown in Figure 1(d)) which was the crosstalk caused by the row wire. Thus extra measurement error of the EBT was caused by it. From the above discussion, we could know that the currents on Rxy, Rset, and Rer had equal values. So we could use (2) to calculate Rxy in Circuit C. We found that Rer did not exist in (2). As Vref and Rs were known, Vxy and Ve could be measured by ADC, so the equivalent resistance value (Rxy) of the EBT in Circuit C could be calculated with (2). Thus the crosstalk caused by the row wire was suppressed:(2)Rxy=Vxy-Vref×RsetVe.From the above discussion, the 2-wire S-NSDE-EP method can depress the crosstalk caused by the row wires and the column wires such asRsrs, RLrs, Rscs, and RLcs.


## 3. Simulation Experiments and Discussion

To emulate the performance of our method, OP07 was selected as the macromodel of the op-amp (from the datasheet, the offset voltage, the bias current, the gain-bandwidth, and the gain are equal to 75μV, 2.8 nA, 0.60 MHz, and 126 dB, resp.) in the simulations of National Instrument (NI) Multisim 12. In simulations, Vref was set at 0.1 V, Rset was set at 1 kΩ, the positive voltage source of the op-amps was set at 9 V, and the negative voltage source of the op-amps was set at −6 V.


### 3.1.R0 Effect Simulation in NI Multisim

Cable resistance (R0, R0=Rer=Rec) including the wire resistance and the contacted resistance affected the performance of the 2D networked resistive circuits. We investigated the effect of R0 including wire resistance and contacted resistance on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim. In simulations, we fixed some parameters including all elements in the resistive sensor array at 10 kΩ and M and N at 8, and R0=Rer=Rec in sensor arrays varied synchronously with the same resistance value in 0.1 Ω–100 Ω. The simulation results of the two circuits in NI Multisim 12 were shown in Figure 2. In the results, as shown in Figure 2, the deviation effect of Ve caused by the row line and the row multiplexer was also considered.Figure 2
Effect ofR0 on the Rxy errors in the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit where M=N=8.From Figure2, with R0 varied from 0.1 Ω to 100 Ω, Rxy errors in the 1-wire S-NSDE-EP circuit showed a significant change (from 0.025% to 9.017%) with an obvious positive increase coefficient, while Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve showed a tiny change (from −0.000% to −0.003%). But if the deviation effect of Ve was ignored, Rxy errors in the 2-wire S-NSDE-EP circuit with Ve would be significant (from −0.002% to −9.083%) as shown in Figure 2. Thus, the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve has a better performance than the 1-wire S-NSDE-EP circuit when R0 is varied from 0.1 Ω to 100 Ω; the absolute Rxy errors of the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve are small enough to be negligible when R0 is less than 100 Ω.In the data of the simulation results, we also found the offset value ofVe from Vref was varied from 0.19 mV to 9.08 mV with R0 changing from 2 Ω to 100 Ω.


### 3.2. Array Size Effect Simulation Experiment

Parameters of the array size such as the row number (M) and the column number (N) were proved to have effect on the performance of the 2D networked resistive sensor arrays [9–19]. We investigated the effect of M and N on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim. In simulations, we fixed some parameters including all elements in the resistive sensor array at 10 kΩ, M or N at 8, and R0 at 2 Ω, and N or M was one number in (8, 15, 29, 57, 113, and 225). The results of the array size effect on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit were simulated in NI Multisim and the results were shown in Figure 3. In the results, as shown in Figure 3, the deviation effect of Ve caused by the row line and the row multiplexer was also considered.Figure 3
Array size effect on theRxy errors in the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit where R0=2 Ω and Rother=10 kΩ.From Figure3, with the increase of the column number, the Rxy errors in the 1-wire S-NSDE-EP circuit had a positive coefficient (from 0.196% to 4.722%) while the Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve had a negative coefficient (from −0.000% to −0.044%). But if the deviation effect of Ve was ignored, we found a deviation of Rxy errors (from −0.191% to −0.235%) in the 2-wire S-NSDE-EP circuit with Ve in Figure 3. The absolute Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve had been reduced significantly comparing with the absolute Rxy errors in the 1-wire S-NSDE-EP circuit.From Figure3, with the row number changed in the range from 8 to 113, the Rxy errors in both circuits changed little (from 0.196% to 0.194% for the 1-wire S-NSDE-EP circuit, about 0.000% for the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve, about −0.191% for the 2-wire S-NSDE-EP circuit with Ve); but when the row number changed in the range from 113 to 225, the Rxy errors in both circuits changed clearly (from 0.194% to −0.067% for the 1-wire S-NSDE-EP circuit, from 0.000% to 0.032% for the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve, from −0.191% to −0.159% for the 2-wire S-NSDE-EP circuit with Ve). If every column driving op-amp had a sufficient current driving ability, the row number had less influence on the Rxy errors in both circuits. In the data of the simulation results, we also found the offset value of Ve from Vref was about 0.19 mV with array size changed.Thus, in the 2-wire S-NSDE-EP circuit eliminating the deviation effect ofVe, the influence of array size on the Rxy error has been decreased greatly.


### 3.3. The Adjacent Elements Effect Simulation

In literatures [9–19], the adjacent elements played a significant role in affecting the measurement accuracy of the EBT. In simulations, we fixed some parameters including the resistance value of nonadjacent elements and all other adjacent elements at 10 kΩ, M and N at 8, and R0 at 2 Ω. The resistance value of an 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 column element (Radjc). The simulation results of the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim were shown in Figures 4–7.Figure 4
TheRadjc effect on Rxy errors in the 1-wire S-NSDE-EP circuit.Figure 5
TheRadjr effect on Rxy errors in the 1-wire S-NSDE-EP circuit.Figure 6
TheRadjc effect on Rxy errors in the 2-wire S-NSDE-EP circuit.Figure 7
TheRadjr effect on Rxy errors in the 2-wire S-NSDE-EP circuit.From Figures4–7, the Rxy errors of the EBT of both circuits had negative coefficient when the resistance value of the EBT increased; the Rxy errors of the EBT showed irregular variations when the resistances of the EBT was bigger than a certain value (≥30 kΩ for the 1-wire S-NSDE-EP circuit, ≥50 kΩ for the 2-wire S-NSDE-EP circuit). We found that the output voltages of the row sampling op-amp in both circuits were saturated for a bigger resistance value of the EBT. Under the same power source voltage, the measurement range of the 2-wire S-NSDE-EP circuit was bigger than that of the 1-wire S-NSDE-EP circuit.From Figures4–7, the Rxy errors of the EBT with a bigger resistance value were susceptible to interference from by one Radjr or one Radjc with a smaller resistance value. In both circuits, the changes of the Rxy errors for the change of one Radjr were bigger than the changes of the Rxy errors for the change of one Radjc. With one Radjr or one Radjc varied from 0.1 kΩ to 1 MΩ, the changes of the Rxy errors (with Rxy at 30 kΩ, from −0.307% to −0.048% for one Radjc and from −3.022% to −0.051% for one Radjr) in the 1-wire S-NSDE-EP circuit were significant, while those (with Rxy at 50 kΩ, from −0.006% to −0.006% for one Radjc and from −0.106% to −0.005% for one Radjr) in 2-wire S-NSDE-EP circuit were small. Thus, in the 2-wire S-NSDE-EP circuit, the influence of the adjacent elements on the Rxy error has been decreased greatly.


### 3.4. The Op-Amp’s Offset Voltage Effect Simulation

As many op-amps were used in the 2-wire S-NSDE-EP circuit, the offset voltages of the op-amps would affect the performance of the proposed circuit. In simulations, we fixed some parameters including the resistance value of all other row elements at 10 kΩ,M and N at 8, R0 at 2 Ω, and all Rajcrs at the same resistance value in (100 Ω, 300 Ω, 1 kΩ, and 10 kΩ). The offset voltages of the nonscanned column driving op-amps varied synchronously with the same value in (−75 μV–75 μV), and the 2-wire S-NSDE-EP circuit was simulated in NI Multisim and the results were shown in Figure 8.Figure 8
The op-amp’s offset voltage effect onRxy errors in the 2-wire S-NSDE-EP circuit.From Figure8, we found that the offset voltages of the op-amps and the resistances of the row adjacent elements affected the 2-wire S-NSDE-EP circuit. The smaller these resistances were and the larger the offset voltage was, the larger the Rxy error in the proposed circuit was.


### 3.5. The Op-Amp’s Driving Capability Effect Simulation

The op-amp’s driving capability affected the performance of the 2-wire S-NSDE-EP circuit. The nonscanned elements’ bypass effect on the EBT in the 2D resistive sensor array was obvious when the EBT had large resistance and all nonscanned elements had the small resistances. In the worst case, the EBT had the maximum resistance and all nonscanned elements had the minimum resistances [17]. In the experiments, we were about to simulate the op-amp’s driving capability with all nonscanned elements of different fixed small resistances and the EBT of a large resistance. In simulations, we fixed some parameters including M and N at 8 and R0 at 2 Ω and all non-scanned elements at the same resistance value in (100 Ω, 300 Ω, 500 Ω, 1 kΩ, and 3 kΩ). The resistance value of the EBT varied in the range from 0.1 kΩ to 60 kΩ. The 2-wire S-NSDE-EP circuit with the op-amp of OP07 was simulated in NI Multisim and the results were shown in Figure 9 and Table 2. Also the op-amps of OP07 (Ishort-circuit=30 mA) were replaced by the op-amps of AD797 (Idriving=50 mA), and the 2-wire S-NSDE-EP circuit was simulated.Table 2
The EBT’s maximum resistance of the 2-wire S-NSDE-EP circuit with its op-amp of OP07.
R
non-scanned (kΩ)
The maximum resistance (kΩ)
0.10
3.2
0.30
9.6
0.50
16.0
1.00
32.0
3.00
60.0Figure 9
The op-amp’s driving capability effect onRxy errors in the 2-wire S-NSDE-EP circuit.From Figure9 and Table 2, with the resistances of all nonscanned elements fixed, the 2-wire S-NSDE-EP circuit failed to work normally when the EBT’s resistance exceeded certain values; with the minimum resistances of all nonscanned elements increased, the maximum resistance which could be tested in the 2-wire S-NSDE-EP circuit increased; with a larger op-amp’s driving capability, the 2-wire S-NSDE-EP circuit with its op-amp of AD797 had a larger measurement range.


### 3.6. Discussion

From the results in Figure1, the 1-wire S-NSDE-EP circuit had one voltage feedback op-amp, N 2 : 1 multiplexers, one M : 1 multiplexers, and M+N wires; the 2-wire S-NSDE-EP circuit had one voltage feedback op-amp,N column driving op-amps, N 2 : 1 multiplexers, two M : 1 multiplexers, and 2(M+N) wires. Thus more components and more wires were used in the 2-wire S-NSDE-EP circuit.From the results in Figure2, the 2-wire S-NSDE-EP method was verified to be efficient in depressing the crosstalk caused by the row wires and the column wires such as Rsr, RLr, Rsc, and RLc. It should be noticed that all conductions were right under the assumption that the column driving op-amps had sufficient driving ability and the row sampling op-amp had very big input impedance on its inverting input.From the results in Figures3, 6, and 7, the 2-wire equipotential circuit was failed to work normally with too much big resistance value of the EBT. If the resistance of the adjacent elements in resistive sensor array was too small, the absolute Rxy errors of the EBT would increase significantly. At the same time, if the row sampling op-amp did not have very big input impedance or the elements in resistive sensor array had very big resistance values for the row sampling op-amp’s input impedance, Ixy would be not equal to Iset. Thus the ideal work conditions were destroyed for the 2-wire S-NSDE-EP circuit and the Rxy error would be significant.From the results in Figures2, 3, and 8, Ve in the 2-wire S-NSDE-EP circuit had a significant effect on the Rxy error when the resistances such as the wire resistance, the contacted resistance, and the switch-on resistance of the equal current M : 1 multiplexer were large. Thus the deviation value of Ve, mainly caused by the connected cable and the equal current M : 1 multiplexers should be carefully considered in the 2-wire S-NSDE-EP circuit. In the proposed method, the deviation effect of Ve had been eliminated and the 2-wire S-NSDE-EP circuit with good performance was obtained. As the offset value of Ve from Vref was varied from 0.19 mV to 9.08 mV with R0 changing from 2 Ω to 100 Ω, one more op-amp was necessary for amplifying the signal of Ve in the case of using an analog-digital converter with limited resolution in the 2-wire S-NSDE-EP circuit.From the results in Figure8, the offset voltages of the column driving op-amps had an obvious influence on the performance of the 2-wire S-NSDE-EP circuit, and the offset voltage’s effect would be more obvious for the element being tested with its row adjacent elements of smaller resistance values. With the increase of the offset voltage, the Rxy error increased. As the column number of the sensor array had accumulation influence on the conductance values of the row adjacent elements, it would enhance the effect of the offset voltage. Obviously, the offset voltage of the row sampling op-amp had similar influence on the performance of the 2-wire S-NSDE-EP circuit. Thus in the practical circuit, the op-amps with smaller offset voltages were preferred. In the op-amp’s offset voltage effect simulation experiments, the offset voltages of all nonscanned driving op-amps varied synchronously with the same value and their effect was obvious. But, in a practical circuit, the op-amps’ offset voltages would be the uncertain values less than the offset voltage given in their datasheets and their effect would be weaker. In the 2-wire S-NSDE-EP circuit, the double-sampling technique [20] was also useful for eliminating the effect of those nonidealities of the op-amps such as the input offset voltage and the input bias current.From the results in Figure9 and Table 2, the op-amp’s driving capability affected the measurement range of the 2-wire S-NSDE-EP circuit; with the op-amp fixed, there was an approximate linear relation between the minimum resistance and the maximum resistance in the 2-wire S-NSDE-EP circuit. But the maximum resistance which could be tested in the 2-wire S-NSDE-EP circuit was also limited by the test current and the power source voltage. Thus the op-amps with large driving capability were preferred in the 2-wire S-NSDE-EP circuit. But the op-amps with large driving capability always had a large offset voltage. So the contradiction between the driving capability affecting its measurement range and the offset voltage affecting its measurement accuracy should be balanced according to the test requirement.For good performance of the IIDFC [13] and the IIDFCC [14], special compensated resistors with their resistances equal to their multiplexers’ switch-on resistances are necessary. But the multiplexers’ switch-on resistances may vary in the practical circuits, and the ideal performances of the IIDFC and the IIDFCC are difficult to realize. In the 2-wire S-NSDE-EP method, two wires for every row electrode and every column electrode between the sensor module and the test circuit, though it requires a large number of wires, are easier to achieve. The 2-wire S-NSDE-EP method’s performance and its limitation have been verified by simulation experiments. Similar methods can also be used in the S-NSSE-EP circuit and the S-NSE-EP circuit. But these should be verified in future practical application.


## 3.1.R0 Effect Simulation in NI Multisim

Cable resistance (R0, R0=Rer=Rec) including the wire resistance and the contacted resistance affected the performance of the 2D networked resistive circuits. We investigated the effect of R0 including wire resistance and contacted resistance on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim. In simulations, we fixed some parameters including all elements in the resistive sensor array at 10 kΩ and M and N at 8, and R0=Rer=Rec in sensor arrays varied synchronously with the same resistance value in 0.1 Ω–100 Ω. The simulation results of the two circuits in NI Multisim 12 were shown in Figure 2. In the results, as shown in Figure 2, the deviation effect of Ve caused by the row line and the row multiplexer was also considered.Figure 2
Effect ofR0 on the Rxy errors in the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit where M=N=8.From Figure2, with R0 varied from 0.1 Ω to 100 Ω, Rxy errors in the 1-wire S-NSDE-EP circuit showed a significant change (from 0.025% to 9.017%) with an obvious positive increase coefficient, while Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve showed a tiny change (from −0.000% to −0.003%). But if the deviation effect of Ve was ignored, Rxy errors in the 2-wire S-NSDE-EP circuit with Ve would be significant (from −0.002% to −9.083%) as shown in Figure 2. Thus, the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve has a better performance than the 1-wire S-NSDE-EP circuit when R0 is varied from 0.1 Ω to 100 Ω; the absolute Rxy errors of the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve are small enough to be negligible when R0 is less than 100 Ω.In the data of the simulation results, we also found the offset value ofVe from Vref was varied from 0.19 mV to 9.08 mV with R0 changing from 2 Ω to 100 Ω.


## 3.2. Array Size Effect Simulation Experiment

Parameters of the array size such as the row number (M) and the column number (N) were proved to have effect on the performance of the 2D networked resistive sensor arrays [9–19]. We investigated the effect of M and N on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim. In simulations, we fixed some parameters including all elements in the resistive sensor array at 10 kΩ, M or N at 8, and R0 at 2 Ω, and N or M was one number in (8, 15, 29, 57, 113, and 225). The results of the array size effect on the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit were simulated in NI Multisim and the results were shown in Figure 3. In the results, as shown in Figure 3, the deviation effect of Ve caused by the row line and the row multiplexer was also considered.Figure 3
Array size effect on theRxy errors in the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit where R0=2 Ω and Rother=10 kΩ.From Figure3, with the increase of the column number, the Rxy errors in the 1-wire S-NSDE-EP circuit had a positive coefficient (from 0.196% to 4.722%) while the Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve had a negative coefficient (from −0.000% to −0.044%). But if the deviation effect of Ve was ignored, we found a deviation of Rxy errors (from −0.191% to −0.235%) in the 2-wire S-NSDE-EP circuit with Ve in Figure 3. The absolute Rxy errors in the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve had been reduced significantly comparing with the absolute Rxy errors in the 1-wire S-NSDE-EP circuit.From Figure3, with the row number changed in the range from 8 to 113, the Rxy errors in both circuits changed little (from 0.196% to 0.194% for the 1-wire S-NSDE-EP circuit, about 0.000% for the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve, about −0.191% for the 2-wire S-NSDE-EP circuit with Ve); but when the row number changed in the range from 113 to 225, the Rxy errors in both circuits changed clearly (from 0.194% to −0.067% for the 1-wire S-NSDE-EP circuit, from 0.000% to 0.032% for the 2-wire S-NSDE-EP circuit eliminating the deviation effect of Ve, from −0.191% to −0.159% for the 2-wire S-NSDE-EP circuit with Ve). If every column driving op-amp had a sufficient current driving ability, the row number had less influence on the Rxy errors in both circuits. In the data of the simulation results, we also found the offset value of Ve from Vref was about 0.19 mV with array size changed.Thus, in the 2-wire S-NSDE-EP circuit eliminating the deviation effect ofVe, the influence of array size on the Rxy error has been decreased greatly.


## 3.3. The Adjacent Elements Effect Simulation

In literatures [9–19], the adjacent elements played a significant role in affecting the measurement accuracy of the EBT. In simulations, we fixed some parameters including the resistance value of nonadjacent elements and all other adjacent elements at 10 kΩ, M and N at 8, and R0 at 2 Ω. The resistance value of an 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 column element (Radjc). The simulation results of the 1-wire S-NSDE-EP circuit and the 2-wire S-NSDE-EP circuit in NI Multisim were shown in Figures 4–7.Figure 4
TheRadjc effect on Rxy errors in the 1-wire S-NSDE-EP circuit.Figure 5
TheRadjr effect on Rxy errors in the 1-wire S-NSDE-EP circuit.Figure 6
TheRadjc effect on Rxy errors in the 2-wire S-NSDE-EP circuit.Figure 7
TheRadjr effect on Rxy errors in the 2-wire S-NSDE-EP circuit.From Figures4–7, the Rxy errors of the EBT of both circuits had negative coefficient when the resistance value of the EBT increased; the Rxy errors of the EBT showed irregular variations when the resistances of the EBT was bigger than a certain value (≥30 kΩ for the 1-wire S-NSDE-EP circuit, ≥50 kΩ for the 2-wire S-NSDE-EP circuit). We found that the output voltages of the row sampling op-amp in both circuits were saturated for a bigger resistance value of the EBT. Under the same power source voltage, the measurement range of the 2-wire S-NSDE-EP circuit was bigger than that of the 1-wire S-NSDE-EP circuit.From Figures4–7, the Rxy errors of the EBT with a bigger resistance value were susceptible to interference from by one Radjr or one Radjc with a smaller resistance value. In both circuits, the changes of the Rxy errors for the change of one Radjr were bigger than the changes of the Rxy errors for the change of one Radjc. With one Radjr or one Radjc varied from 0.1 kΩ to 1 MΩ, the changes of the Rxy errors (with Rxy at 30 kΩ, from −0.307% to −0.048% for one Radjc and from −3.022% to −0.051% for one Radjr) in the 1-wire S-NSDE-EP circuit were significant, while those (with Rxy at 50 kΩ, from −0.006% to −0.006% for one Radjc and from −0.106% to −0.005% for one Radjr) in 2-wire S-NSDE-EP circuit were small. Thus, in the 2-wire S-NSDE-EP circuit, the influence of the adjacent elements on the Rxy error has been decreased greatly.


## 3.4. The Op-Amp’s Offset Voltage Effect Simulation

As many op-amps were used in the 2-wire S-NSDE-EP circuit, the offset voltages of the op-amps would affect the performance of the proposed circuit. In simulations, we fixed some parameters including the resistance value of all other row elements at 10 kΩ,M and N at 8, R0 at 2 Ω, and all Rajcrs at the same resistance value in (100 Ω, 300 Ω, 1 kΩ, and 10 kΩ). The offset voltages of the nonscanned column driving op-amps varied synchronously with the same value in (−75 μV–75 μV), and the 2-wire S-NSDE-EP circuit was simulated in NI Multisim and the results were shown in Figure 8.Figure 8
The op-amp’s offset voltage effect onRxy errors in the 2-wire S-NSDE-EP circuit.From Figure8, we found that the offset voltages of the op-amps and the resistances of the row adjacent elements affected the 2-wire S-NSDE-EP circuit. The smaller these resistances were and the larger the offset voltage was, the larger the Rxy error in the proposed circuit was.


## 3.5. The Op-Amp’s Driving Capability Effect Simulation

The op-amp’s driving capability affected the performance of the 2-wire S-NSDE-EP circuit. The nonscanned elements’ bypass effect on the EBT in the 2D resistive sensor array was obvious when the EBT had large resistance and all nonscanned elements had the small resistances. In the worst case, the EBT had the maximum resistance and all nonscanned elements had the minimum resistances [17]. In the experiments, we were about to simulate the op-amp’s driving capability with all nonscanned elements of different fixed small resistances and the EBT of a large resistance. In simulations, we fixed some parameters including M and N at 8 and R0 at 2 Ω and all non-scanned elements at the same resistance value in (100 Ω, 300 Ω, 500 Ω, 1 kΩ, and 3 kΩ). The resistance value of the EBT varied in the range from 0.1 kΩ to 60 kΩ. The 2-wire S-NSDE-EP circuit with the op-amp of OP07 was simulated in NI Multisim and the results were shown in Figure 9 and Table 2. Also the op-amps of OP07 (Ishort-circuit=30 mA) were replaced by the op-amps of AD797 (Idriving=50 mA), and the 2-wire S-NSDE-EP circuit was simulated.Table 2
The EBT’s maximum resistance of the 2-wire S-NSDE-EP circuit with its op-amp of OP07.
R
non-scanned (kΩ)
The maximum resistance (kΩ)
0.10
3.2
0.30
9.6
0.50
16.0
1.00
32.0
3.00
60.0Figure 9
The op-amp’s driving capability effect onRxy errors in the 2-wire S-NSDE-EP circuit.From Figure9 and Table 2, with the resistances of all nonscanned elements fixed, the 2-wire S-NSDE-EP circuit failed to work normally when the EBT’s resistance exceeded certain values; with the minimum resistances of all nonscanned elements increased, the maximum resistance which could be tested in the 2-wire S-NSDE-EP circuit increased; with a larger op-amp’s driving capability, the 2-wire S-NSDE-EP circuit with its op-amp of AD797 had a larger measurement range.


## 3.6. Discussion

From the results in Figure1, the 1-wire S-NSDE-EP circuit had one voltage feedback op-amp, N 2 : 1 multiplexers, one M : 1 multiplexers, and M+N wires; the 2-wire S-NSDE-EP circuit had one voltage feedback op-amp,N column driving op-amps, N 2 : 1 multiplexers, two M : 1 multiplexers, and 2(M+N) wires. Thus more components and more wires were used in the 2-wire S-NSDE-EP circuit.From the results in Figure2, the 2-wire S-NSDE-EP method was verified to be efficient in depressing the crosstalk caused by the row wires and the column wires such as Rsr, RLr, Rsc, and RLc. It should be noticed that all conductions were right under the assumption that the column driving op-amps had sufficient driving ability and the row sampling op-amp had very big input impedance on its inverting input.From the results in Figures3, 6, and 7, the 2-wire equipotential circuit was failed to work normally with too much big resistance value of the EBT. If the resistance of the adjacent elements in resistive sensor array was too small, the absolute Rxy errors of the EBT would increase significantly. At the same time, if the row sampling op-amp did not have very big input impedance or the elements in resistive sensor array had very big resistance values for the row sampling op-amp’s input impedance, Ixy would be not equal to Iset. Thus the ideal work conditions were destroyed for the 2-wire S-NSDE-EP circuit and the Rxy error would be significant.From the results in Figures2, 3, and 8, Ve in the 2-wire S-NSDE-EP circuit had a significant effect on the Rxy error when the resistances such as the wire resistance, the contacted resistance, and the switch-on resistance of the equal current M : 1 multiplexer were large. Thus the deviation value of Ve, mainly caused by the connected cable and the equal current M : 1 multiplexers should be carefully considered in the 2-wire S-NSDE-EP circuit. In the proposed method, the deviation effect of Ve had been eliminated and the 2-wire S-NSDE-EP circuit with good performance was obtained. As the offset value of Ve from Vref was varied from 0.19 mV to 9.08 mV with R0 changing from 2 Ω to 100 Ω, one more op-amp was necessary for amplifying the signal of Ve in the case of using an analog-digital converter with limited resolution in the 2-wire S-NSDE-EP circuit.From the results in Figure8, the offset voltages of the column driving op-amps had an obvious influence on the performance of the 2-wire S-NSDE-EP circuit, and the offset voltage’s effect would be more obvious for the element being tested with its row adjacent elements of smaller resistance values. With the increase of the offset voltage, the Rxy error increased. As the column number of the sensor array had accumulation influence on the conductance values of the row adjacent elements, it would enhance the effect of the offset voltage. Obviously, the offset voltage of the row sampling op-amp had similar influence on the performance of the 2-wire S-NSDE-EP circuit. Thus in the practical circuit, the op-amps with smaller offset voltages were preferred. In the op-amp’s offset voltage effect simulation experiments, the offset voltages of all nonscanned driving op-amps varied synchronously with the same value and their effect was obvious. But, in a practical circuit, the op-amps’ offset voltages would be the uncertain values less than the offset voltage given in their datasheets and their effect would be weaker. In the 2-wire S-NSDE-EP circuit, the double-sampling technique [20] was also useful for eliminating the effect of those nonidealities of the op-amps such as the input offset voltage and the input bias current.From the results in Figure9 and Table 2, the op-amp’s driving capability affected the measurement range of the 2-wire S-NSDE-EP circuit; with the op-amp fixed, there was an approximate linear relation between the minimum resistance and the maximum resistance in the 2-wire S-NSDE-EP circuit. But the maximum resistance which could be tested in the 2-wire S-NSDE-EP circuit was also limited by the test current and the power source voltage. Thus the op-amps with large driving capability were preferred in the 2-wire S-NSDE-EP circuit. But the op-amps with large driving capability always had a large offset voltage. So the contradiction between the driving capability affecting its measurement range and the offset voltage affecting its measurement accuracy should be balanced according to the test requirement.For good performance of the IIDFC [13] and the IIDFCC [14], special compensated resistors with their resistances equal to their multiplexers’ switch-on resistances are necessary. But the multiplexers’ switch-on resistances may vary in the practical circuits, and the ideal performances of the IIDFC and the IIDFCC are difficult to realize. In the 2-wire S-NSDE-EP method, two wires for every row electrode and every column electrode between the sensor module and the test circuit, though it requires a large number of wires, are easier to achieve. The 2-wire S-NSDE-EP method’s performance and its limitation have been verified by simulation experiments. Similar methods can also be used in the S-NSSE-EP circuit and the S-NSE-EP circuit. But these should be verified in future practical application.


## 4. Conclusion

Firstly, a 2-wire S-NSDE-EP method of the 2D networked resistive sensor array was proposed. Secondly, the formula was given for the equivalent resistance expression of the element being tested in the networked sensor array by principle analyses. Then, the effects of some parameters on the measurement accuracy of the EBT were simulated with the National Instrument Multisim 12, the parameters including the wire resistances and the contacted resistances of long cables, the array size and the adjacent elements of the 2D resistive sensor array, and the offset voltages of the op-amps. The simulation results show that the 2-wire equipotential method was verified to be efficient in depressing the crosstalk caused by the row wires and the column wires such asRsr, RLr, Rsc, and RLc; in the 2D networked resistive sensor array with the 2-wire S-NSDE-EP 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. Finally, the factors which affected the performance of the 2-wire S-NSDE-EP circuit were discussed and the conclusion was given.



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