ZSim and ZFit as learning tools. IV. The effect of high frequency inductance.Latest updated: January 6, 2022
Sometimes high-frequency inductance is just removed, which is not good
Sometimes in the literature, we can encounter battery impedance graphs that are plotted only in the capacitive half-plane as shown in Fig. 1a. However, most battery impedance graphs show a high-frequency inductive behavior as shown in Fig. 1b .
Figure 1: Nyquist impedance graph of a Li-ion battery a) plotted only in the capacitive half-plane; b) complete plot .
The influence of the value of the inductance L on the shape of the Nyquist impedance graph.
The analysis of the inductance influence on the measured electrochemical impedance was presented a long time ago . The high-frequency depressed semi-circle shown in Fig. 1 can be simply modeled by the following circuit: L1 + R1 + C2/R2.
In the animation shown in Fig. 2, the evolution of the impedance graphs of the circuit defined above is shown for a certain range of values of the parameter L, the values of the other parameters being constant.
Figure 2: Impedance graphs of the circuit L1 + R1 + C2/R2 with R1 = 1 Ω, R2 = 4 Ω, C2 = 0.1 F
and L varying from a) 10-3 to 10-2 and b) 0.0316 to 0.1 H.
For a small inductance value (Fig. 2a), the impedance shows a semi-circle and a vertical line from low to high frequencies. It shows an accumulation of data points around Im Z = 0.
For a large inductance value (Fig. 2b), the arc is deformed and the data points move away from each other when the sign of Im Z is changing.
Partially fitting the data without accounting for high-frequency inductance leads to wrong values.
In Fig. 3, the impedance graph of the circuit L1 + R1 + C2/R2 with R1 = 1 Ω, R2 = 4 Ω, C2 = 0.1 F, L = 0.1 H was simulated with 8 points per frequency decade. This graph shows a deformed arc, which means a large inductance value.
If the inductance is neglected and the low-frequency arc is fitted with an R1 + C2/R2 circuit as it is shown in Fig. 3, all the calculated values are wrong: R1 and C2 are overestimated, R2 is underestimated.
Figure 3: Simulated impedance graph of the L1 + R1 + C2/R2 with R1 = 1 Ω, R2 = 4 Ω, C2 = 0.1 F, L = 0.1 H and
fitting of the low frequency arc with R1 + C2/R2. The calculated values are wrong.
Always fit impedance data completely and never fit partially.
When an impedance graph shows a high-frequency inductance, a good practice is to plot the graph completely and to avoid truncating the graph at high frequencies. Fitting the graph without including the high-frequency inductance can lead to erroneous values determination of the parameters of the chosen equivalent circuit.
 B. Savova-Stoynov and Z. B. Stoynov J. Appl. Electrochem., 17 1987 1150 – 1158.
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ZSim and ZFit as learning tools. Part II. Why circle fitting is wrong.
ZSim and ZFit as learning tools. Part III How to detect an inductive behaviour at low frequencies
ZFit (impedance fitting) tutorials for potentiostats and battery cyclers