Electrochemical impedance spectroscopy (EIS) is a critical tool for battery characterization, providing insights into internal processes such as charge transfer, diffusion, and interfacial phenomena. The choice of excitation signal design significantly impacts the quality and efficiency of data acquisition. Two primary approaches exist: traditional single-sine EIS and multi-sine EIS. The comparison between these methods revolves around measurement speed, harmonic analysis capabilities, nonlinear behavior detection, and the associated challenges in data interpretation and signal processing.

Single-sine EIS applies a sinusoidal perturbation at one frequency at a time, sweeping across the desired frequency range sequentially. This method is well-established, with standardized protocols for data collection and analysis. The primary advantage lies in its simplicity and the direct interpretation of linear system responses. However, its sequential nature results in prolonged measurement times, particularly for low-frequency sweeps, which may take hours to complete. For battery testing, this becomes a limitation when rapid characterization is needed, such as in quality control or dynamic state-of-health monitoring.

Multi-sine EIS, in contrast, employs a composite signal containing multiple sine waves at different frequencies simultaneously. By exciting the battery with a broadband signal, the entire frequency range is measured in a single acquisition, drastically reducing testing time. Where a single-sine sweep might require hours, multi-sine EIS can achieve comparable results in minutes or even seconds, depending on the frequency resolution and signal-to-noise requirements. This acceleration is particularly valuable for high-throughput applications, such as production-line testing or real-time performance validation.

The speed advantage of multi-sine EIS comes with increased complexity in signal processing. The composite signal must be carefully designed to avoid spectral leakage and intermodulation distortion. Techniques such as phase optimization and amplitude scaling are employed to ensure minimal interference between frequency components. Additionally, the system must handle higher peak-to-average power ratios, which can strain the excitation hardware if not properly managed. Despite these challenges, modern signal processing algorithms and hardware capabilities have made multi-sine EIS increasingly practical for battery diagnostics.

A key strength of multi-sine EIS is its ability to perform harmonic analysis. Batteries exhibit nonlinear behavior, especially at high currents or extreme states of charge. Traditional single-sine EIS assumes linearity, limiting its ability to detect nonlinear distortions. Multi-sine excitation, however, can capture harmonic responses, providing additional information about kinetic and transport processes that deviate from ideal behavior. By analyzing higher-order harmonics, researchers can identify nonlinearities linked to side reactions, phase transitions, or inhomogeneous current distributions. This capability is particularly useful for studying degradation mechanisms or extreme operating conditions where linear assumptions break down.

Nonlinear behavior detection is further enhanced by the broadband nature of multi-sine signals. Since the excitation covers multiple frequencies at once, transient nonlinearities are more likely to be captured compared to the step-wise probing of single-sine methods. This is especially relevant for batteries, where processes like lithium plating or solid-electrolyte interphase (SEI) growth exhibit time-dependent nonlinear responses. Multi-sine EIS can thus provide a more comprehensive picture of dynamic battery behavior without requiring repeated sweeps.

However, the interpretation of multi-sine EIS data is more complex than single-sine analysis. The simultaneous excitation of multiple frequencies introduces coupling effects that must be decoupled during post-processing. Advanced algorithms, such as Fourier transform-based deconvolution or multisine-specific fitting routines, are necessary to extract accurate impedance values. Misinterpretation can occur if harmonic distortions are incorrectly attributed to linear processes or if intermodulation products are not properly accounted for. These challenges necessitate rigorous validation against single-sine benchmarks, particularly when establishing new testing protocols.

Signal processing requirements for multi-sine EIS are also more demanding. The acquisition system must have sufficient dynamic range and sampling rate to resolve all frequency components without aliasing. Anti-aliasing filters and windowing functions must be carefully selected to prevent artifacts in the impedance spectra. Additionally, the signal-to-noise ratio must be maintained across all frequencies, which may require adaptive amplitude scaling or noise-reduction techniques. These factors increase the computational burden compared to single-sine EIS, where each frequency is processed independently.

Single-sine EIS remains advantageous in scenarios requiring high precision at specific frequencies or when testing highly nonlinear systems where multi-sine excitation could introduce excessive distortion. Its straightforward implementation and well-established analysis frameworks make it the preferred choice for fundamental research or calibration purposes. However, for applications prioritizing speed and comprehensive nonlinear analysis, multi-sine EIS offers clear benefits.

In summary, the choice between multi-sine and single-sine EIS depends on the specific requirements of the battery testing application. Multi-sine methods excel in rapid characterization and nonlinear behavior detection but require sophisticated signal processing and careful interpretation. Single-sine techniques provide simplicity and precision at the cost of slower measurement speeds. As battery diagnostics increasingly demand faster and more detailed insights, multi-sine EIS is likely to see broader adoption, provided that advancements in hardware and algorithms continue to address its inherent complexities.