On the Sensitivity of the Kramers–Kronig Relations to Nonlinear Effects in Impedance Measurements

Abstract

The Kramers–Kronig relations, which strictly apply for systems that are linear, stable, and causal, provide an essential tool for assessing the internal consistency of impedance data. The Kramers–Kronig relations are understood to be sensitive to failures of causality, but insensitive to failures of linearity. Numerical simulations were performed to explore the conditions under which the Kramers–Kronig relations are sensitive to nonlinear behavior of electrochemical systems. A characteristic frequency was identified below which the Kramers–Kronig relations are satisfied, even for very nonlinear systems. This result is observed for systems with a small ohmic resistance. The Kramers–Kronig relations are not satisfied for measurements which include the characteristic frequency. For systems with a large ohmic resistance, the Kramers–Kronig relations may provide a better tool for assessing the presence of nonlinear behavior as compared to analysis of low frequency Lissajous plots.