Measurement Model Validation of Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy

Harmonic distortion is a measurable feature of nearly all electrochemical impedance spectroscopy (EIS) experiments. Linearity is generally assumed when total harmonic distortion is below a few percent threshold. A workflow is presented for optimally extracting and using 2nd-harmonic data while ensuring adequate linearity for sound EIS analysis. We prove mathematically that frequency dispersion functions for 2nd-harmonic nonlinear EIS (2nd-NLEIS) satisfy Kramers–Kronig (KK) relations, providing a basis for constructing a measurement model (MM) test of stationarity and causality in both EIS and second-NLEIS data. The performances of cost and confidence interval algorithms for automating MM fitting are evaluated. We illustrate this workflow by analyzing three different batteries to identify optimal current modulations and frequency ranges for analysis. For example, an optimal balance between 2nd-NLEIS signal quality and EIS linearity in a 1.5 Ah NMC||C SamSung cell occurs with a current modulation of Δ I = 0.5 amp. Experiments with commercial pouch and in-house coin cells show these MM tests can distinguish between intrinsic cell-to-cell 2nd-NLEIS variance vs measurements that fail to meet stationarity and causality criteria. Robust optimization and validation of simultaneous EIS and 2nd-NLEIS data opens the door for more reliable frequency-domain model identification, parameterization, and error analysis.