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The development of impedancebased array devices is hindered by a lack of robust platforms and methods upon which to evaluate and interrogate sensors. One aspect to be addressed is the development of measurementtime efficient techniques for broadband impedance spectroscopy of large electrode arrays. The objective of this work was to substantially increase the low frequency impedance measurement throughput capability of a large channel count array analyzer by developing true parallel measurement methods. The goal was achieved by Fourier transformbased analysis of simultaneouslyacquired multichannel timebased current and voltage data. Efficacy and quantitative analysis of the parallel approach at frequencies less than
Impedancebased measurement approaches, which are noninvasive, can substantially improve the selectivity and sensitivity [
Commerciallyavailable, general purpose multichannel analyzers capable of DC and AC impedance interrogation of arrays with up to 100 electrodes have been used to study complex electrochemical phenomenon such as metallurgical and spatiotemporal interactions in localized corrosion [
To date, impedance spectroscopy measurements of arrays have been based on sequential interrogation of each array element at each frequency [
There are numerous reasons why timeefficient methods are required for impedance spectroscopy of large electrode arrays. First, there is a need to be able to make the measurement in an experimentally practicable duration. It is beyond the patience of most researchers and experimental systems to spend hours or even days to conduct a single experiment, as is conceivable when performing impedance spectroscopy measurements at subHertz frequencies sequentially on arrays with a large number of elements (see discussion on section 1.1). Second, one criteria for valid impedance measurements is a stable, unchanging system. That is, the system must be stable over the timeframe of the experiment. When the impedance of each array element is determined by sequential interrogation of each element at each frequency prior to moving to the next lowest frequency, it becomes increasingly difficult to satisfy the stability criteria because of the extended time required to complete the experiment. Similarly, transient events are more likely to either be missed or misinterpreted (due to failure to meet the stability criteria) when the measurement takes a long time to perform. Finally, some applications are restricted in their power availability and/or are required to function for an extended period of time on a fixed energy budget. Such applications include batterypowered or lowpower sourced sensor array systems as well as systems for space exploration. For these applications, it is highly desirable if not essential to minimize the measurement duration. Thus, there are various reasons to address development of measurementtime efficient techniques for broadband impedance spectroscopy for large electrode arrays.
The objective of this work was to substantially increase the low frequency impedance measurement throughput capability of a large channel count array analyzer by developing true parallel measurement methods. The goal of true parallel impedance measurement at frequencies less than ∼ 10 Hz was achieved through development of Fourier transformbased analysis of simultaneouslyacquired timebased multichannel current and voltage data. In addition, we demonstrate a twopronged measurement approach consisting of the standard sequential measurement method at high frequencies (∼ 1 kHz to 10 Hz) combined with the parallel method at low frequencies (< 10 Hz) for measurementtime efficient broadband impedance spectroscopy of large arrays. Arrays of resistorcapacitor dummy cells exhibiting frequencydependent complex impedance characteristics consistent with chemiresistor and other sensors were used to demonstrate the efficacy of the approach.
The current stateoftheart array analyzer is the Model 910 Multichannel Microelectrode Analyzer (MMA, Scribner Associates, Inc.). The MMA is a general purpose instrument capable of DC and AC impedance interrogation of arrays with up to 100 electrodes or sensors [
However, the limitation of this approach is that at low frequency (less than ∼ 1 Hz), the data acquisition time can be substantial when interrogating large numbers of array elements (∼ 10s of minutes to 10s of hours). As an example, it takes 100 seconds
As will be demonstrated below, 10 Hz is a reasonable choice for the transition frequency from the standard sequential method to the parallel technique.
It is obvious from the results shown in
As demonstrated by the results in
To achieve this, we developed and evaluated a fast Fourier transform (FFT)based method [
The method is based on the wellestablished FFT algorithm approach to calculate the complex impedance
Here,
The fundamental equations are the Fourier transform coefficients [
All experimental work was performed using a using a commercially available PCcontrolled Multichannel Microelectrode Analyzer, MMA (Model 910, Scribner Associates Inc.). Application software for the MMA instrument (MMALive®, Scribner Associates Inc.) was modified by the authors to implement the measurement schemes presented below. For all tests described below, all 100 channels of the MMA were monitored while the AC signal was applied to the array. Timestamped multichannel current and singlechannel voltage data were acquired at a rate of ∼ 22 frames/second. That is, the current from each of the 100 channels and the common voltage signal were sampled more then 20 times per second.
The MMA incorporates a digital signal processor (DSP)based impedance analyzer with a frequency range of 10 kHz to 1 mHz and a measurable impedance range of 500 to 10^{7} Ω. The standard sequential impedance measurement method is based on the singlesine digital correlation technique used in many commercial impedance analyzers. Synchronization of the generator and analyzer is critical to ensure that signals of frequency not being generated are strongly rejected by the analyzer as noise. A small AC voltage signal of known frequency is simultaneously imposed on each array element for which the impedance is to be measured and the AC current response of each electrode sequentially evaluated by the impedance analyzer. Impedance spectroscopy measurements are performed sequentially from highest to lowest frequency. In other words, the instrument sequentially interrogates the impedance response of each electrode at a single frequency before stepping to the next lower frequency. In this way, the majority of the data is obtained for each electrode over a relative short period of time (
Because the focus of this work is evaluation of the performance of the analytical instrumentation and developed measurement techniques, testing was conducted using arrays of dummy cells. Dummy cells composed of electrical components (resistors and capacitors) have the advantage that the impedance of the circuit is known. Therefore, the performance of the analytical instrument and measurement methods can be accurately judged. As described below, a variety of dummy cells were employed in this work.
For the initial experiments, two of the dummy cells consisted of a 1 MΩ resistor, one was an open circuit condition (
A second array consisted of one hundred 100 kΩ (±1 % rated accuracy) resistors while a third array consisted of 98 resistors ranging from 1 MΩ to 10 MΩ. During these experiments, for each frequency down to 0.2 Hz, all 100 channels were measured for 5 seconds; for frequencies less than 0.2 Hz, up to 10 second acquisition time was required to get at least one full cycle.
For the second part of this work, described in section 3.2, circuits composed of resistors and capacitors were used to evaluate impedance measurement of test elements with frequencydependent complex impedance values consistent with typical chemiresistor sensors [
Five replicates each of 4 different dummy circuits were fabricated using resistors and capacitors with rated accuracy of ±1 %.
The authors recognize that for highly nonlinear systems, such as an electrochemical system, 50 or 250 mV AC perturbation is a large excitation signal that may result in violation of the criteria for linearity. This excitation signal was selected based on the range of impedances under investigation in relation to the dynamic range and resolution of the current measuring circuitry. Of course, impedance measurement of real systems would necessitate an AC voltage perturbation that did not displace the system from its steadystate condition in violation of the criteria for linearity. As discussed in section 3.2, this will require matching the dynamic range of the current measuring circuitry with the expected range of impedances for a given (acceptable) AC voltage perturbation signal.
The results of this work are presented in two parts. First we describe implementation and demonstration of the parallel multichannel impedance measurement approach detailed in section 1.1. The benefits and challenges associated with practicable implementation of the parallel method, such as measurement time efficiency and time skew, respectively, are presented. The second part describes experiments designed to demonstrate the efficacy of a combined sequential + parallel measurement approach on dummy cells composed of resistorcapacitor networks that mimic in their frequencydependent impedance response typical sensor and/or electrochemical systems.
The parallel multichannel impedance measurement approach described in Section 1.1 was implemented in the MMA. Initial tests were performed on 4 simple dummy cells: two of the dummy cells consisted of a 1 MΩ resistor, an open circuit condition reproduced a very high impedance condition, and the final dummy cell was a 1 nF capacitor. Multichannel current and the common voltage signal were acquired at a rate of approximately 22 samples/second.
Note that an exact sampling rate is not necessary, and in fact could be detrimental. It is very important to know exactly when a signal was sampled, but sampling at a particular frequency is not required. That is, sampling at
There are two relatively simple approaches to dealing with the need for a nonperfect sampling. The first is to incorporate a small (∼ 0.01 second) random delay to the triggering of each frame. An alternative approach would use a precise sample rate that is not a multiple of the applied AC frequency. For example, sampling for 10 s at 20.01 frames/second would spread the data for any given channel over 0.1 s within the reconstructed timebase. Thus, although an exact sampling rate is not required, there is a constraint to know precisely
Within the reconstructed timebase of
To address the issue of time skew between channels, we determined a series of correction factors by measuring the time delay between each current sample and the voltage sample, determining the order in which each channel of current and the voltage was sampled, and assessing how the number of channels sampled influenced the time skew between samples. The MMA application software was modified to use these correction factors to automatically account for time skew between measurements in the raw timebased data. As presented below, testing with 100element resistor arrays verified the efficacy of this approach.
The effect of time skew is particularly evident by comparing the phase angle
We can quantify the accuracy of the parallel method by comparing its results to that obtained with the standard method.
Three frequencies were analyzed: 10, 1 and 0.2 Hz. Good agreement between the two methods is observed at the lowest frequencies, 0.2 and 1 Hz. In fact, close observation of the data sets at these frequencies reveals that they essentially overlap and are only slightly displaced from the 1:1 line. For these frequencies, there is less than 1 % difference between the mean of the result obtained from the parallel method and the standard method (see “%
At 10 Hz, the parallel method produced slightly greater values than the standard method. This is indicated by the larger positive %
As further demonstration of the efficacy and advantage of the FFTbased parallel method for low frequency impedance measurement of electrode or sensor arrays, the impedance of an array composed of 100 resistors ranging from 1 MΩ to 50 MΩ was determined using the parallel and “standard” sequential approach. Recall that in the standard approach, at each frequency the impedance of each electrode within the array is determined before stepping to the next lower frequency. While this approach is efficient at high frequency, at low frequency the experimental time becomes significant.
Bode plots showing the impedance magnitude and phase angle (theta) as a function of frequency for both the standard sequential and parallel techniques are shown in
It is worth reiterating the benefit of the parallel approach to low frequency impedance spectroscopy in multichannel systems. The following conditions were used to measure the impedance of the two types of 100element resistor arrays presented above: 1 kHz to 0.1 Hz; 10 steps/decade; duration: 5 second per frequency for parallel method, minimum of 0.3 second or 1 cycle for standard method. For these conditions, the parallel measurement method required 7 minutes of data acquisition time whereas the standard sequential method required 120 minutes. Thus, a 17fold reduction in experimental time was achieved by the parallel measurement method. The increase in timeefficiency of the parallel method as compared to the standard method was derived at frequencies less than about 10 Hz.
Despite the forgoing discussion, it should be recognized that ultimately one probably would not want to apply the parallel method at frequencies greater than about 10 Hz because the advantages of the parallel method, with respect to measurement time efficiency gains, are not realized at higher frequencies and because errors caused by limitations in timebased measurement accuracy are exacerbated at higher frequencies. It is better to use the standard method of impedance measurement at frequencies greater than about 10 Hz and the parallel method at frequencies less than about 10 Hz. Implementation of the optimum solution to broad frequency sweep impedance measurement of large arrays will involve the use of the standard, sequential approach at high frequencies combined with a transition to the parallel approach for the low frequency range. This hybrid or twopronged approach to timeefficient impedance spectroscopy of large arrays is addressed in the next section.
Here, we assess the performance of a multichannel impedance analyzer with an array of dummy cells that exhibit frequencydependent response and with impedance and reactance values consistent with typical chemiresistor sensors [
The results for the parallel low frequency impedance method are shown in
Noise in the data is evident, in particular at low frequencies and for the cells with very high impedance (
The array analyzers' ZRA circuitry has a limited number of ranges which it can use to optimize measurement of the current, thus limiting the measurable range of impedance to ∼ 5 to 6. As such there is an inherent challenge when one type of ZRA circuit is called upon to measure the impedance over 8 orders of magnitude. Fortunately, if the impedance range of a given sensor (or electrode system under study) is known, the current measuring circuitry and possibly the AC voltage perturbation can be selected for optimum measurement accuracy and resolution over the full range of the system response.
As indicated in the experimental section, two types of impedance experiments were conducted: the standard sequential measurement approach and the parallel low frequency approach described in detail above. The results of the equivalent circuit dummy cell impedance testing using the parallel approach are presented above. Next, we merged the results of the standard method covering the high frequency range (10 kHz to 10 Hz) with the results of the parallel method restricted to the low frequency range (10 Hz to 0.1 Hz) to demonstrate the efficacy of efficiently obtaining broadband impedance spectra.
The results of equivalent circuit fitting of the combined standard + parallel experimental impedance data provide an indication of the accuracy of the measurement. The results of the fit along with the nominal dummy cell resistor and capacitor values for one of each of the four different types of circuit are shown in
There was, however, a > 10 % error in the fitted value of the 1 kΩ series resistor (R_{s}) used in the Type A and B dummy cells, which was observed in other experiments as well, and only occurs when measuring a dummy cell containing a parallel resistorcapacitor (R_{p}‖C_{p}) element. That is, this error is not evident when measuring a resistor alone. Neither was this error observed when R_{s} ≫ 1 kΩ,
The results demonstrate that, in general, the largechannel count array analyzer used here was capable of accurately measuring the impedance of dummy cells designed to simulate typical chemiresistor (and other) sensors [
This work demonstrates the technical feasibility of implementing an enhanced, timeefficient approach to low frequency impedance measurement of large channelcount electrodes and sensor arrays. When the impedance of a 100electrode array was measured to 0.1 Hz, the measurement time was reduced nearly twentyfold by the parallel method in comparison to the standard sequential method without sacrificing accuracy. To our knowledge, this is the first implementation of such an approach to electrode arrays. The use of the described parallel impedance measurement approach at subHertz frequencies, which are required for some applications, yields significant gains in measurementtime efficiency.
Dummy cells that mimic a simple electrical / electrochemical cell or sensor were used to probe the impedance measurement capability of the general purpose laboratory multichannel array analyzer. Four different dummy cells covering four orders of magnitude in resistance were used (1 kΩ to 10 MΩ); the resistor and capacitor values were consistent with typical chemiresistortype sensors. The results demonstrated that the array analyzer technology and measurement approaches were capable of accurately determining the impedance of dummy cells designed to mimic such sensors. Employing the combined standard + parallel measurement approaches significantly reduced by more than an order of magnitude the data acquisition time in comparison to using the standard method alone. Finally, equivalent circuit fit results of experimental data acquired using the combined standard + parallel approach resulted in most cases in predicted values of the dummy cell circuit components within a few percent of the nominal value used to fabricate the dummy cell.
This work was funded by the United States National Aeronautics and Space Administration (NASA) under contract # NNC07QA56P. The technical support of F.J. Grunthaner (Jet Propulsion LaboratoryCalifornia Institute of Technology) and R. Quinn (NASAAmes/SETI Institute) are gratefully acknowledged. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.
Typical experimental setup for electrical or electrochemical testing of a microelectrode or sensor array. The setup is similar to a traditional 3electrode configuration consisting of a working electrode (WE), counter electrode (CE) and reference electrode (RE) with the exception that the single WE is replaced with
Key to placement of twenty equivalent circuit dummy cells across array analyzer segments and groups (10 groups of 10 segments/group).
(a) Raw current I(x,y) and voltage data acquired at ∼ 22 frames/second with the MMA instrument imposing a 10 Hz, 0.25 V AC signal. The frequencydependence of the data is not apparent in the raw data. (b) PostFFT data processing, the timedependent AC response is reproduced with the expected 0.1 second period. Time skew between the individual current channel data and the voltage channel data is apparent in the reconstructed data set.
Low frequency impedance of an array of one hundred 100 kΩ resistors determined from DC timebased I_{k}(ω),V(ω) data. (a) Without time skew correction factor the phase error approached 180° at 10 Hz. (b) With time skew correction factors the phase error is less than 2.5° at 10 Hz. Application of the time skew correction significantly improves the accuracy and decreases the phase angle error at all but the lowest frequencies.
Real(Z) by standard
Low frequency impedance of an array of one hundred resistors ranging from 1 MΩ to 50 MΩ. (a) Complex impedance obtained from parallel FFT method in 7 minutes. With time skew correction factors applied the phase error is less than 2.5° at 10 Hz indicating that the parallel measurement method can be used to simultaneously obtain the impedance of large array. (b) Complex impedance determined using standard sequential measurement approach in 120 minutes.
Complex plane plots (Z″
Impedance plots for standard method (○) + parallel (□) measurement method for one of each of 4 types of equivalent circuit dummy cells. This page: Type A and B, next page: Type C and D. Standard Method: 10 kHz to 10 Hz; Parallel Method: 10 Hz to 0.1 Hz. See text for impedance measurement conditions.
Time required to measure the impedance of 100 electrodes
 

26  46  264  2452  
26  29  33  55  
1.0×  1.6×  8×  45× 
Key to the nominal resistor and capacitor values used to fabricate the equivalent circuit dummy cells (±1 % rated accuracy).
1 kΩ  100 kΩ  0.1 μF  
1 kΩ  1 MΩ  0.1 μF  
1 MΩ  10 MΩ  0.1 μF  
1 MΩ  100 kΩ  0.1 μF 
Real component of the impedance Z′ at three frequencies via the parallel and standard impedance measurement method (N = 98).
 

101,659  100,673  100,670  99,927  99,998  99,926  
101,680  100,550  100,550  99,904  99,905  99,905  
547  1051  1233  81  753  83  
0.54  1.04  1.22  0.08  0.75  0.08  


1.7  0.7  0.7 
The difference, expressed as a percentage, in the real component of the impedance at a specific frequency obtained by the two methods = [Real(Z)_{parallel} – Real(Z)_{standard}] / [Real(Z)_{standard}]
Comparison of measurement time for the impedance measurement parameters reported in the experimental section using just the standard sequential approach and a combined standard sequential (10 kHz to 10 Hz) plus the parallel method (10 Hz to 0.1 Hz).
254  
16 + 7 = 23 
Fit results for the 4 equivalent circuit dummy cells shown in
1×10^{3}  1×10^{5}  0.1  1.14×10^{3}  0.99×10^{5}  0.103  
1×10^{3}  1×10^{6}  0.1  1.12×10^{3}  1.02×10^{6}  0.103  
1×10^{6}  1×10^{7}  0.1  1.01×10^{6}  1.08×10^{7}  0.098  
1×10^{6}  1×10^{5}  0.1  1.00×10^{6}  1.09×10^{5}  0.107 