Z-HIT - A SIMPLE RELATION BETWEEN IMPEDANCE MODULUS AND PHASE ANGLE, PROVIDING A NEW WAY TO THE VALIDATION OF ELECTROCHEMICAL IMPEDANCE SPECTRA

摘要

In the Bode representation of electrochemical impedance spectra one observes that the modulus of the phase angle resembles the first derivative of the impedance modulus course. It is shown that a fundamental law is hidden behind this trivial observation. Using the special properties of the 'two-pole' impedance (Z), an expansion of the logarithmic Hilbert Transform (HIT) leads to the Z-HIT relation. This relation claims that the logarithmic impedance modulus function can in first order be approximated by a simple integral of the phase angle function along the logarithm of the frequency, multiplied by 2/π. A second order approximation with sufficient accuracy for validation purposes can be obtained by subtracting a weighed fraction of the first derivative of the phase angle function. The weighing factor is the second coefficient of the Riemann Zeta function divided by π, that is -π/6 for all examined systems. It is demonstrated how Z-HIT enables detection of steady state violations and instrumentation artifacts when applied to practical impedance measurements. Furthermore results from fuel cell research are presented that show how Z-HIT can be applied for the reconstruction of precise impedance spectra from data affected by steady state violations.