The modified inductance element La – Battery – Application Note 42

Abstract

A Constant Phase Element (CPE) can be physically interpreted as an effect of the surface roughness of the sample, leading to a heterogeneity of the capacitance. On the other hand, the modified inductance, La, can be used to represent the presence of an unusual inductance in the Nyquist diagram. The expression of the impedance of an inductance is ZL(f) = Lj2πf. The expression of the impedance of the modified inductance La is ZLa(f) = La(j2πf)a with L and La the value of the inductance in H and of the modified inductance in H s(a-1), respectively, with 0<a≤1.
This application note introduces a few practical cases for which the modified inductance component can lead to a much better fit of impedance data. The new element La is a modified inductance element. It can be used to fit impedance characteristics related to either an unusual connection inductance at high frequencies (i.e. mostly visible in batteries or a heterogeneous adsorption mechanism) or at low frequencies (i.e. mostly visible in corrosion).

Introduction

It is convenient to use a Constant Phase Element (CPE) instead of a capacitor when for instance the Nyquist diagram of the impedance of a system shows a semi-circle whose center is located below the Real axis, instead of on the Real axis. The difference between a capacitor C and a CPE Q is that the expression of the impedance of a CPE contains an additional parameter a…

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