Zahner — RoboInd Global

Overview

Whether you need to measure a lot of samples down to low frequencies during high throughput tests, or you need to analyze the difference of successive EIS measurements while your device under test (DUT) is changing (desired, such as charging of a battery - or undesired, such as degradation), the duration of an EIS can be a limiting factor. An impedance spectrum that reaches into the millihertz range is expensive in time, and nearly all of that time is spent on its last few frequency points.Multisine excitation addresses exactly that part of the spectrum and is able to significantly speed up EIS measurements. Instead of measuring one frequency after another, all frequencies of the low-frequency range are excited at the same time and evaluated from a single recording.The IM7 offers a multisine implementation for 1 to 5 decades. Thereby, one wave is used to excite all frequencies at once. The length of this wave is the period of the fundamental frequency (the lowest frequency of the multisine measurement). One wave is enough to calculate an impedance spectrum from the excitation and response signals. For example, a measurement from 10 mHz to 1 Hz (2 decades) can be done in 100 s providing 13 frequency points.The results are pretty impressive. The outstanding accuracy is achieved by careful engineering of the measurement device and software. One crucial factor is the high precision provided by the 24 bit resolution of the measurement channel of the IM7, which allows for significantly higher precision than many other devices.Amplitude is a challenge because the available excitation amplitude needs to be shared between all excited frequencies. We apply a crest factor optimization (crest factor: ratio between peak and RMS) that increases the amplitude for all frequencies in the multisine excitation significantly, while keeping the total amplitude below a given maximum. This is done by optimizing the phases of the applied Harmonics.In Fig. 1, a direct comparison of a single-sine EIS (solid line) and a multisine EIS (markers) is shown. In this application note, the galvanostatic single-sine EIS sweep is treated as a reference sweep. The reference sweep is recorded from 100 kHz down to 10 mHz, recording 100 points with one pre-wave, and two measured waves per point, these settings are already chosen for speed. The reference sweep consists of 12 points per decade above 66 Hz and 8 points per decade at the lower frequency limit. The second measurement is a Galvanostatic Multisine EIS with identical frequency range and amplitude. It is configured to cover the lowest 3 decades with one multisine excitation, starting at the first harmonic, with no multisine pre-wave and one multisine wave. The crossover frequency is therefore 10 Hz: single-sine mode above, multisine mode below. Both spectra were recorded on the same cell within half an hour of each other.Fig. 1: Single-sine EIS (line) and multisine EIS (markers) spectra of the 40 Ah LiFePO4 cell. Comparison of the two measurements in the two common representations. Left: Bode plot, impedance magnitude (blue) and phase (red) against frequency. Right: Nyquist plot, imaginary against real part of the impedance, frequency increasing from the upper right toward the lower left. For the multisine EIS measurement, 21 lowest frequencies between 10 mHz and 10.07 Hz originate from a single multisine recording.Single-sine and multisine lie almost perfectly on top of each other. In the Bode plot as well as in the Nyquist plot, the results of the multisine cannot be told apart from those measured through the single-sine sweep. How far apart the two actually are, and what that difference should be judged against, is analyzed in detail further down, but we will have a look at the measurement time first.The runtime of a single-sine sweep is set by the period of each frequency, and the arithmetic is unforgiving: one period at 100 Hz lasts 10 ms, one period at 10 mHz lasts 100 s, and each of those periods buys exactly one point of the spectrum. Both measurements therefore start identically and require less than 10 s to sweep from the start frequency up to 100 kHz and back down to 11.13 Hz. From there the two diverge.The reference sweep continues frequency by frequency, and the growing period pulls its points apart along the time axis. The first 71 points were all recorded within the first 9.3 s. The remaining 29 points, the three decades from 9.06 Hz down to 10 mHz, consumed the other 19 min 30 s (1169.7 s), that is 99.2 % of the total runtime. The 10 mHz point alone accounts for 5 min (300 s) of it, exactly the one pre-wave and two measured waves it was asked for.Speeding up an impedance measurement therefore is done in its lowest decades. In this example, everything above 10 Hz was measured below 10 s with little potential to save additional time, and that is precisely why the multisine covers only the lowest decades instead of the whole spectrum. Extending it upward would not save significantly more time. Considering the data quality, adding more frequencies to the multisine would decrease the amplitude of every excited frequency because all of them share one peak amplitude. Keeping the multisine confined to the decades where a sweep is genuinely slow is what keeps that price small.The multisine range here replaces 19 min 30 s of sweeping with 1 min 40 s of measurement. What is traded in is spectral detail and amplitude per point: 21 frequencies (multisine) instead of 29 (single-sine) in the same three decades, and each excited with about one seventh of the total amplitude in multisine mode (see Crest Factor section for more detail), while single-sine mode measures each frequency with the total amplitude.<img src="https://www.roboind.com/file/upload/company/profile_web_remaining_20261029/910103452-1.jpg" alt="Bode plot of the 40 Ah LiFePO4 cell from 10 mHz to 100 kHz, comparing the single-sine reference sweep drawn as solid lines with the multisine measurement drawn as markers. Blue shows the impedance magnitude, which falls from 2.8 milliohms at 10 mHz to a minimum below 1 milliohm near 2 kHz and rises to 11 milliohms at 100 kHz; red shows the phase, which rises from -20 degrees at 10 mHz to +82 degrees at 100 kHz. The markers of the multisine measurement lie on the solid reference curves over the whole frequency range."><img src="https://www.roboind.com/file/upload/company/profile_web_remaining_20261029/910103452-2.jpg" alt="Nyquist plot of the same data, imaginary against real part of the impedance, with the single-sine reference sweep drawn as a solid line and the multisine measurement as markers. The low-frequency end lies at the lower right at 2.7 milliohms real and -1 milliohm imaginary, the curve runs to the left through a flat capacitive arc with a local maximum near 2 milliohms real, crosses the zero line near 0.9 milliohms real and then rises steeply into the inductive branch at high frequencies. The markers follow the solid line everywhere."><img src="https://www.roboind.com/file/upload/company/profile_web_remaining_20261029/910103452-3.jpg" alt="Frequency versus elapsed measurement time for both measurements. Blue circles show the single-sine sweep: the high frequencies are recorded within the first seconds, then the points spread out increasingly along the time axis and the last point at 10 mHz is reached only after about 1180 seconds, almost 20 minutes. Red squares show the multisine measurement: the same high frequencies appear within the first seconds, and the 21 frequencies from 10 Hz down to 10 mHz then all appear at once as a vertical column at about 110 seconds, not quite 2 minutes."><img src="https://www.roboind.com/file/upload/company/profile_web_remaining_20261029/910103452-4.jpg" alt="Residual plot with three panels sharing a logarithmic frequency axis from 10 mHz to 100 kHz. The top panel shows the impedance magnitude of the reference sweep, which stays between 0.9 and 11 milliohms over the whole spectrum. The middle panel shows the deviation of the multisine measurement from the reference in percent, the bottom panel the deviation in phase in degrees. Filled markers are the 21 multisine frequencies below 10 hertz, which scatter within about 0.5 percent and 0.2 degrees around zero, with a single outlier of minus 1.3 percent at the 10 millihertz fundamental. Open markers are the swept frequencies above 10 hertz, which both measurements contain and which scatter by a comparable 0.4 percent and 0.25 degrees. A grey band across the multisine range marks the interpolation floor of the comparison, which reaches about 0.3 percent and 0.09 degrees.">