Setting up a Multi sine impedance measurement Case study: how do I setup a Multi Sine impedance measurement? 1 Single sine vs Multi sine Traditional electrochemical impedance spectroscopy measurements are based on a single sine approach, during which the frequency is scanned from a starting frequency to a stop frequency and each frequency is applied separately. It is common practice to start at high frequency and to stop at low frequency. The drawback of this method is that the low frequency part of the spectrum affects the duration of the measurement, significantly. This is shown in Figure 1, where a frequency scan was conducted from 100 khz to 1 mhz, using 6 points per decade. Figure 1 Frequency vs time plot for a single sine measurement Figure 1 shows that the last decade of frequencies accounts for about 80% of the measurement time. The intrinsic instability of electrochemical systems dictates that the duration of the measurement should be as small as possible. Autolab instruments fitted with a FRA32M or a FRA2 impedance analyzer module are able to perform multi sine measurements as an alternative to single sine measurements or to combine single sine and multi sine waveforms in the same measurement. 1 Page
NOVA Technical note 20 In a multi sine measurement, several frequencies are applied at once 1. The perturbation applied on the cell is a combination of individual single sine components. The response from the cell carries the contribution at each applied frequency. The acquisition time for each multi sine signal is defined by the lowest frequency in the signal. An example of a multi sine signal is provided in Figure 2. Figure 2 Example of a multi sine measurement (blue: potential, red: current) The multi sine waveform shown in Figure 2 contains a base frequency of 0.1 Hz and four higher harmonics of the base frequency (0.3, 0.5, 0.7 and 0.9 Hz). The duration of the measurement is defined by the base frequency of 0.1 Hz, which translates into 10 seconds, or one period. Converting the multi sine signals from the time domain to the frequency domain through FFT reveals the five frequency components (see Figure 3). 1 S.C. Creason, D. E. Smith, J. Electroanal. Chem. 36 (1972), 1. 2 Page
Figure 3 Frequency domain plot of the multi sine measurement shown in Figure 2 The advantage of a multi sine measurement is that multiple data points can be acquired at the same time, reducing the total measurement time. The disadvantage of multi sine measurements is that the individual accuracy of the data points recorded using the multi sine method is lower than the accuracy of the same data points recorded using the single sine method. The multi sine versus single sine method therefore boils down to a trade-off: accuracy versus speed. In this technical note, all these aspects will be explored. 2 Multi sine methods Two different multi sine techniques are supported in NOVA: 5 Sines: the generated waveform contains a base frequency, ωω and 4 additional higher harmonics of the base frequency (3ωω, 5ωω, 7ωω and 9ωω). 15 Sines: the generated waveform contains a base frequency, ωω and 14 additional higher harmonics of the base frequency (3ωω, 5ωω, 7ωω, 9ωω, 13ωω, 19ωω, 25ωω, 33ωω, 41ωω, 51ωω, 61ωω, 73ωω, 87ωω and 99ωω). 3 Page
NOVA Technical note 20 3 Hardware limitations The multi sine method can only be used at low frequencies. Depending on the impedance analyser module, the lowest frequency at which the multi sine method is available is different (see Table 1). Module 5 sines frequency limit 15 sines frequency limit FRA32M 320 Hz 32 Hz FRA2 3472 Hz 315.7 Hz Table 1 Frequency limitations for the FRA32M and FRA2 module 4 Setting up the measurement To setup a multi sine measurement, it is necessary to keep in mind that each multi sine waveform contains 5 or 15 frequencies and that these frequencies cover one or two decades, respectively. In order to make the most of the acquisition time benefit, it is necessary to setup the frequency scan properly. In this tutorial, the default FRA impedance potentiostatic procedure will be used. The frequency scan parameters are defined in the FRA editor. To open this editor, click the button located in the procedure editor, as shown in Figure 4. Figure 4 Opening the FRA editor 4 Page
The FRA editor dialog will be displayed. The frequency scan parameters are shown in the Frequency section of this window (see Figure 5). Figure 5 The FRA editor window For example, a frequency scan from 100 khz to 1 mhz will be used, with 6 frequencies per decade. Using these parameters, the estimated duration of the scan, indicated in the lower left corner of the FRA editor will be 1 hour and 47 minutes (see Figure 6). 5 Page
NOVA Technical note 20 Figure 6 The parameters of the frequency scan (based on a single sine scan) In this example, a 5 sine multi sine waveform will be used to reduce the acquisition time. A FRA32M module will be assumed. According to Table 1, the lowest possible frequency for this experimental setup is 320 Hz. The frequency scan will be programmed in the following way: From 100 khz to 1 khz, 6 frequencies per decade, single sine. From 100 Hz to 0.001 MHz, 1 frequency per decade, 5 sine. This will give a total of total of 43 frequencies, compared to 49 frequencies using a single sine frequency scan as shown in Figure 6. To define the frequency scan according to the distribution shown above, the single sine part must first be defined, as shown in Figure 7. 6 Page
Figure 7 Setting up the single part of the frequency scan Note It is noteworthy to see that the first part of the spectrum has an estimated duration of 33 seconds. To extend the existing frequency scan with the multi sine part, select the Summary section of the FRA editor. The button can be clicked to add extra frequencies to the existing frequency scan (see Figure 8). 7 Page
NOVA Technical note 20 Figure 8 It is possible to extend the frequency scan in the Summary section Clicking the button brings up a new dialog that can be used to extend the frequency scan. In this example, the frequency scan will be extended from 100 Hz to 0.001 Hz, using 1 frequency per decade and 5 sines (see Figure 9). 8 Page
Figure 9 Extending the frequency scan Click the button to validate the modification of the frequency scan. The total duration of the measurement will increase to 38 minutes (see Figure 10). The duration of the frequency scan is now about 1 hour shorter than the single sine equivalent. 9 Page
NOVA Technical note 20 Figure 10 The final scan parameters Click to close the editor and validate the scan parameters. 5 Running the measurement The procedure can be executed on the normal Autolab dummy cell (a) circuit. The data obtained with the procedure used in this technical note is displayed in Figure 11. Figure 11 Measured data obtained using the multi sine method The data is comparable with data obtained using a single sine measurement. 10 Page
Note The distribution of the data points in the multi sine part of the frequency scan is not logarithmic. It is defined by the coefficients used in the combination of single sines in the multi sine waveform. 5.1 Actual duration The duration of the multi sine measurement is 439.11, which compared to the single sine equivalent (2308.8 seconds), is about half an hour shorter. The improvement to the acquisition time is significant using the multi sine method. 5.2 Acccuracy Both a single sine measurement and the multi sine measurement can be fitted with the expected R(RC) equivalent circuit. The residual values are higher for the multi sine measurements compared to the single sine measurement, as shown in Figure 12. Figure 12 Residual plots for the Z values for the single sine (red curve) and multi sine (blue curve) measurements on dummy cell (a) Although the values are comparable, the accuracy of the measurements performed with multi sine measurements are lower than the same measurement performed with a single sine approach. The source of this difference stems from the fact that the FRA modules need to process all of the signals carried by a multi sine waveform using the same amount of memory as in the case of a single sine measurement. 11 Page