920 IEEE SENSORS JOURNAL, VOL. 11, NO. 4, APRIL 2011

Analysis of Crosstalk in NetworkedArrays of Resistive Sensors

Raghvendra Sahai Saxena, Navneet Kaur Saini, and R. K. Bhan

Abstract—In this paper, we present the analysis of the crosstalklimitation in 2-D resistive sensor arrays that utilize shared row andcolumn connections for simplified interconnections. The mathe-matical expression for crosstalk among all of the elements intro-duced due to the interconnection overloading has been analyti-cally derived and verified by the circuit simulations. Based on thisanalysis, we examined and proved that the solution of crosstalkand snapshot capability cannot be achieved simultaneously in net-worked resistive sensor arrays.

Index Terms—Crosstalk, resistive sensor, sensor array, snapshot.

I. INTRODUCTION

T HE RESISTIVE sensor arrays, due to ease in implemen-tation, are used in many applications, such as electronic

nose, biometric sensing, nuclear electronics, and thermalimaging based on infrared (IR) sensors, etc. [1]–[12]. As thesize of these arrays increases, they face two problems: 1) in-creased number of interconnections, usually two interconnectsper sensor and 2) increased time to access all of them. Also,in some applications, where the sensed parameter may changequickly, it is important to capture the complete information ata single instant, called snapshot capability. For example, in theimaging of a fast-moving target, if we sequentially collect theinformation, the target may change its position before scanningall of the sensors, resulting in a degraded image.

The sharing of rows and columns is a technique that can beused to reduce the interconnect complexity from to

in these arrays as shown in Fig. 1 for the case of a 4 4array. In these rays, called hereafter as networked arrays, thescanning rate will be higher due to fewer nodes. However, in-terconnect overloading results in an undesired crosstalk amongthe elements, resulting in the spread of information.

Various methods have been proposed in the literature to sup-press the crosstalk in networked resistor arrays either by usingthe zero potential method or voltage feedback method [2]–[8].However, the basic limitation of the crosstalk and its quantifi-cation had not been discussed earlier. Since the methods ofsuppressing the crosstalk suffer from the slower scanning ofthe array and set a compromise between the interconnect com-plexity and readout rate, it is desirable to have the quantitative

Manuscript received June 26, 2010; accepted July 26, 2010. Date of publi-cation September 23, 2010; date of current version February 09, 2011 The as-sociate editor coordinating the review of this manuscript and approving it forpublication was Prof. Ralph Etienne Cummings.

The authors are with the State Physics Laboratory, Timarpur 110054, Delhi,India (e-mail: rs_saxena@yahoo.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2010.2063699

Fig. 1. Networked array of sensors with shared rows and shared columns.

idea of the crosstalk in snapshot mode so that the priority my beset properly by the array designer.

In this paper, we present the mathematical analysis of thecrosstalk in networked arrays that allows us to quantify theamount of information spreading in the uncorrected snapshotmode of readout. The analysis may also be used to investigatethe effectiveness of various crosstalk suppressing methods.

II. UNIFORM BIASING OF NETWORKED RESISTOR ARRAY

In a networked array of identical sensors (having same re-sistance, and uniform response to the same excitation), theuniform biasing of all the elements is also important. However,when we apply a constant current bias between a row and acolumn node, the elements at other locations in the array alsoget some amount of current and, therefore, maintaining the biasuniformity becomes difficult.

According to the distribution of bias current, we can dividethe whole array in four zones as shown in Fig. 2. Here, zone-1contains the element being biased, zone-2 contains the elementssharing the same row of the biased element, zone-3 contains theelements sharing the same column of the biased element, andzone-4 contains the elements having no direct connection withthe biased element. It may be seen that elements of a particularzone have exact circuital symmetry and, therefore, obtain theuniform current. Therefore, if we make our sensor arrayas a subarray of an externally created resistorarray by putting additional elements of an additionalrow (row 0) and column (column 0) and bias it in a way thatour sensor array become zone-4, the uniform biasing problemwill be solved. Here, the additional elements at zone-1, zone-2,and zone-3 are the externally connected fixed resistors havingresistances that are the same as that of our sensors that are inzone-4. By a simple circuit analysis, it may be shown that thecurrent flowing in the different zones will have the followingrelation [9]–[13]:

(1)

1530-437X/$26.00 © 2010 IEEE

SAXENA et al.: ANALYSIS OF CROSSTALK IN NETWORKED ARRAYS OF RESISTIVE SENSORS 921

Fig. 2. Biased networked array showing that the elements in different zonesget different current.

Here, is the current flowing in zone-K elements. Again,equating the potential drop between row-0 and column-0 viatwo different paths (path1: col-0 to row-0, path2: col-0 to row-1to col-1 to row-0), we get

(2)

Here, R is the resistance of the elements. Now, using (1) and(2), we may obtain

(3)

(4)

Here, represents the bias current of our sensor elements,which is the same as .

III. CROSSTALK ANALYSIS

Initially, before sensing is done, all of the elements havethe same potential difference across their terminals and aftersensing action, the resistances of some sensor elements changewith different amounts that have to be monitored. However, dueto networking, the apparent potentials of all accessible nodesare affected simultaneously even when one sensor undergoesthe change.

The apparent change in the potentials will be the functions ofthe actual change in all of the element resistances. Let us assumethat the resistance of an element changes by an amount “r.” Toanalyze its effect on the other nodes and branches of the circuit,we may use compensation network theorem [13] by connecting

a current source of compensation current in parallel to it,where

(5)

Only a fraction of flows through its parent element becauseit will also be distributed over the array governed by the samerelation as it is for the bias current, depicted in (3), giving the-following relation among the measured voltage change of theelements in different zones:

(6)

In usual cases and the relation may be simplified asin (3). Thus, we see that when the resistance of a single elementchanges, its effect is observed in the potentials of all nodes. Thisis what we call information spreading or crosstalk. Now, let ussuppose that the resistances of two elements change simulta-neously. The compensation current of both individual elementswill be distributed over the array following the relation of (3) andthe total effect will be the superposition of the two componentsin all branches. Therefore, in general, individual compensationcurrents can now be associated with all of the elements and dueto linearity, the total effect on the node potentials will be the su-perposition of all individual effects. Therefore, if we representthe change in resistance of element (i, j) as , the measuredvoltage change at location (1, 1) will be

(7)

where K is proportionality constant. Here, all changes in fixedresistors, that is, (for i: 0 to N) and (for j: 0 to M) havebeen ignored since they are zero. The negative sign appears dueto the reversed direction of the compensation current in

sensors that do not have direct connection withthe element (1, 1) (i.e., zone-4 for element (1, 1)).

Now, we can construct equations for all of the sensorelements similar to (7). The set of those simultaneous equationswill be the amount of crosstalk among the sensor elements. Forillustration, if we select 2, the simultaneous equationswill be

922 IEEE SENSORS JOURNAL, VOL. 11, NO. 4, APRIL 2011

Fig. 3. Circuit simulated in PSPICE, showing two cases. (a) Case 1, where one resistance R6 at location (1, 1) is changed from 1 k to 1.1 k, (b) Case 2, where tworesistances R6 and R12 have changed from 1 k to 1.2 k and 1.1 k.

In matrix form, these equations will be

(8)

The coefficients of the simultaneous equations may be com-bined as crosstalk matrix [C] and then the equation may bewritten as

(9)

Similarly, by constructing the crosstalk matrix for 3,we obtain

(10)

The rank of is found to be 3 and the rank ofis 5. In general, for any array, the rank of its

crosstalk matrix (i.e., ) will be only, indicating a lack of equations. This

limitation comes fundamentally because there are actuallynodes and they may only give independent nodal

equations [13]. If we monitor the potentials of onlynodes, as we do in the snapshot mode, the individual responsecan be obtained.

IV. SIMULATION RESULTS AND DISCUSSION

To verify the amount of crosstalk predicted by the crosstalkmatrix, we have simulated that in PSPICE circuit simulationtool. A 3 3 array of 1-k resistors (representing the sensors)has been constructed with an additional seven elements makingrow-0 and column-0 as biasing network. The resistances of a fewresistors have been changed slightly and the potentials at all ofthe nodes have been monitored. The actual simulated potentialsand the calculated values using the crosstalk matrix of (10) havebeen compared and we found they agree within the acceptablelimits. This verifies the model. Results of some sample caseswill be discussed.

First, we have simulated the circuit with all 1-k resistorsand stored the node potentials. We obtained 187.5 mV for allrow nodes and 250 mV for all of the columns except the refer-ence column, which is kept at ground potential. Following this,we changed resistance values at different locations. In snapshotmode, one has to acquire the complete data in a single instant.We did the same for the following cases.

A. Case 1

Here, resistance R6 of location (1, 1) changes by 10%.Now, in (8), the normalized resistance-difference vector forthis case will be . The correspondingvoltage-difference vector can be computed by multiplyingthe resistance-difference vector with the crosstalk matrix.That gives the theoretically computed voltage-differencevector to be . Now, we shallcompare this theoretical result with the simulated one. Thesimulated voltage-difference vector can be constructed using

SAXENA et al.: ANALYSIS OF CROSSTALK IN NETWORKED ARRAYS OF RESISTIVE SENSORS 923

the values shown in Fig. 3(a). By doing so, we get it to be. It may be

seen that the simulated voltage-difference vector is the replicaof the calculated one with conversion factor of 0.7 mV.

B. Case 2

Now, we change two resistances with different amounts. The,resistance R6 of location (1, 1) changes by 200 , whereas R12of location (2, 3) changes by 100 , as shown in Fig. 3(b).In this case, the normalized resistance-difference vector willbe , with a corresponding voltage-differ-ence vector . The simulated voltagevector is , which isalso an approximate replica of the calculated voltage vector witha conversion factor of 0.3461.

The agreement in the computed and simulated values verifiesthe analysis. The little variation in the computed and simulatedvalues in the aforementioned cases is due to the fact that thetheory assumes identical resistances of all the sensors whereasa few sensor resistances have been changed here by 10% and/or20% in these cases.

Now, it is clear that the snapshot acquisition of the data willnot serve to reconstruct the actual resistance changes occurredover the array due to the lack of equations. Toobtain the complete set of equations, one has to performmutually independent measurements. It is also desirablethat the crosstalk matrix become a diagonal matrix or at leastdiagonal elements should be very high compared to the otherelements, so that one can get rid of solving the equations afteracquiring the data without sacrificing the accuracy. This leadsto the ideas of shorting the unaccessed rows and/or columnswhile reading an element. This allows access of one elementat a time, keeping the shorted nodes to either zero potential [3],[11], [12] or at some specific fed-back potential [2], [8], giving

equations with an almost diagonal crosstalk matrix.

V. CONCLUSION

The networked resistive sensor arrays have been investi-gated mathematically for their crosstalk. The crosstalk matrixrepresenting the total crosstalk among various elements hasbeen derived. By investigating the rank of crosstalk matrix, wehave shown that the network arrays have lessequations, due to which the snapshot mode of data acquisitioncannot provide the actual sensor response. To obtain all re-quired equations, one has to incorporate changes in thecircuit from outside and perform a total of measurementson these arrays.

ACKNOWLEDGMENT

The authors would like to thank the Director of SSPL, Dr.R. Muralidharan, for his continuous support, guidance, and en-couragement to carry out this work and granting permission topublish it.

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Raghvendra Sahai Saxena received the B.E. degreein electronics and communication engineering fromG. B. Pant Engineering College, Pauri Garhwal,India, in 1997, the M.Tech. degree in microelec-tronics from the Indian Institute of Technology,Bombay, India, in 2003, and is currently pursuingthe Ph.D. degree in electrical engineering, IndianInstitute of Technology, New Delhi, India.

Since 1998, he has been a Scientist with the SolidState Physics Laboratory, Delhi, working on the de-sign, modeling, and characterization of infrared de-

tectors and their readout circuits. His current fields of interest are power-elec-tronic devices, nanoscale very-large scale integrated devices, and infrared de-tectors. He has published many papers in various international refereed journalsand conference proceedings in the aforementioned fields. He has also been areviewer for the journals IEEE TRANSACTIONS ON ELECTRON DEVICES, IEEEELECTRON DEVICE LETTERS, IEEE SENSORS JOURNAL, Elsevier-Measurement,Elsevier-Sensors and Actuators A: Physical, IOP-Semiconductor Science andTechnology, Journal of Electrical and Electronics Engineering Research andMapan (Journal of Meteorological Society of India), and Recent Patents onElectrical Engineering.

Mr. Saxena is a corporate member of the Institution of Electronics andTelecommunication Engineers, India; Institution of Engineers, India; and theInternational Association of Engineers.

Navneet Kaur Saini received the B. Tech. degree in electronics and commu-nication engineering from Guru Teg Bahadur Institute of Technology, GuruGovind Singh Indra Prastha University, Delhi, India, in 2007.

Since 2008, she has been a Scientist in the Solid State Physics Laboratory,Delhi, and is currently involved in the measurement of cooled infrared (IR) de-tectors and circuit simulations of their readout circuits. Her research interestsinclude characterization of IR focal plane arrays, IR sensors, and their readoutcircuits.

924 IEEE SENSORS JOURNAL, VOL. 11, NO. 4, APRIL 2011

R. K. Bhan received the M.Sc. degree in physicsfrom Kashmir University, Srinagar, India, in 1982and the Ph.D. degree in physics from Delhi Univer-sity, New Delhi, in 1994.

He was initially Junior Research Fellow in the“Center for Applied Research in Electronics” at theIndian Institute of Technology, New Delhi, from1982 to 1984. He joined the Solid State PhysicsLaboratory, Delhi, as a Scientist in 1984, where he iscurrently involved in infrared (IR) detector charac-terization. His research interests include metal–oxide

semiconductor physics, charge-coupled devices, IR detectors, and focal planearrays. He has published many research papers in international journals.