4.0.1 What is a multisine EIS signal?
One of the criticisms of EIS is the prolonged testing time when measuring at low frequencies and sequentially exciting one frequency at a time. This process can take between minutes or even hours depending on the prescribed frequency range. This raises issues with stability as over longer periods of time the system may drift from its steady state due to internal or environmental factors. This also prevents the application of dynamic EIS which measures impedance while the system is operating. Since the system’s state of charge is changing during charing or discharging the EIS measurement must be fast to remain stationary. The use of multisine signals can help combat these issues by providing quicker measurements.
Multisine EIS operates by measuring impedance at various frequencies simultaneously. Applying multiple frequencies at a once cuts down on testing time opening up more potential use-cases for EIS. In multisine EIS the waves are superimposed upon one another with each individual sinusoid having the same amplitude but differing phases [2]. Figure depicts the resulting multisine signal when individual sine waves at different frequencies are summed. The peak amplitude of the multisine wave must be considered when initializing the experiment. The following section will advise on proper testing practices when experimenting with multisine EIS to ensure accurate measurements.
4.0.2 Crest factor optimization
The individual signal phases is crucial to ensure the system remains linear during testing as compounding signals can result in constructive interference. There is a trade-off here between single, and mutlisine EIS, as the amplitude must be sufficiently low to ensure constructive interference is reduced, while also maintaining a suitable signal-to-noise ratio. Multisine can help relieve added noise due to the lower amplitudes by taking multiple measurements over a short period of time [1].
To maximize the signal-to-noise ratio and minimize the constructive interference of the multisine signal, crest factor optimization is employed. The crest factor refers to the ratio between the height of the peaks in the multisine signal in comparison to the average amplitude. The phases of the superimposed EIS signals are selected to minimize the crest factor, this can be done by assigning random phases from a uniform distribution, or, using more sophisticated mathematical algorithms. Shroeder’s optimization algorithm is one of the most popular methods for logarithmic spaced frequencies as it focuses on phase positioning to promote destructive interference using the frequency’s harmonics.
4.0.3 Converting time domain to the frequency domain
Synthesizing multisine EIS data is more complex in comparison to sequential EIS due to the presence of multiple frequencies responding at once. To deconstruct this complex waveform a fast Fourier transform (FFT) is applied to convert the data from the time domain into the frequency domain. The FFT is a mathematical algorithm that breaks down the multisine wave into its individual frequency components. The FFT is foundational for periodic data analysis in many different fields from electrical engineering, to audio and image processing. With the voltage and current data from the individual frequencies, the impedance is calculated as the ratio between the voltage and current spectra using Ohm’s law [1].
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