Impedance Spectrum Analysis With Relaxation Time Resetting
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Solution Overview
Problem
Existing methods for analyzing impedance spectrum data, particularly for batteries and corrosive systems, face challenges in reproducing measured data when impedance values do not converge to a constant value with frequency decrease, and struggle with components like capacitors and inductors.
Innovation Solution
A method involving the determination and resetting of logarithmic relaxation time values, combined with regularized least squares analysis, to accurately analyze parameters and reproduce impedance spectrum data using the formula Z(fp) ≈ R∞ + T2πfpj + 2πfpL + ∑l=1M Rl1+2πj exp(ln τl) exp(ln fp) |Δ ln τ|, considering capacitor and inductor components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the conventional formulas (a) and (b) are applied to analyze impedance spectrum data, then the analysis can be performed for standard samples, but the method fails to reproduce measured data when impedance values do not converge to a constant value with frequency decrease or when inductor components are present
Solution Approach 1:
The patent modifies the conventional impedance analysis formulas by adding inductor component parameters (L and its derivative) to the mathematical model. This parameter expansion allows the formula to represent systems with inductive characteristics and non-converging impedance behavior, thereby resolving the contradiction between maintaining reproduction accuracy for standard cases and achieving adaptability for previously inapplicable cases.
2Measurement precision
If the number of divisions M of logarithmic relaxation time is increased to improve analysis precision, then the reproduction accuracy improves, but the calculation complexity and time increase
Solution Approach 1:
The patent employs an iterative optimization approach where the regularized least squares method repeatedly adjusts parameters including the number of divisions M, comparing calculated impedance spectra with measured data. This feedback loop allows the system to automatically determine the optimal M value that achieves sufficient reproduction accuracy without unnecessarily increasing calculation time, balancing precision and computational efficiency.
Data Source
AI summary
This method for analysis processing by using measured impedance spectrum data includes: a step for determining whether to reset the maximum value and/or the minimum value of logarithmic relaxation time corresponding to a measured logarithmic frequency on the basis of the measured impedance spectrum data; a step for setting the number of equal-interval divisions within the range of the logarithmic relaxation time set in the determination step; and a step for analyzing parameters R∞, T, L, and Rl for the range of the set logarithmic relaxation time so as to satisfy a prescribed expression (A) by applying a regularized least-squares method.