Time Domain Analysis on Current Response of Equivalent Circuit Involving Constant Phase Element
(1) The pulse voltage V (t) in the time domain including the data of the 2N unit is converted into the voltage V (ω) in the frequency domain by a fast Fourier transform (FFT).
(2) The impedance Z (ω) is calculated as a complex number at each frequency from the equivalent circuit involving CPE.
(3) The current I (ω) in the frequency domain is calculated by dividing Z (ω) by V (ω) in the frequency domain.
(4) I (ω) is converted into the time domain current I (t) by an inverse fast Fourier transform (IFFT)
(5) The number and value of the time constant of I (t) are determined by curve fitting of the ladder equivalent circuit.
(6) The impedance spectrum calculated by (5) is compared with that by the equivalent circuit involving CPE.
The calculated results indicate that the current response by the equivalent circuit involving CPE is a sum of those with plural time constants. It was found that the distribution of time constants is concerned with the CPE index (p) remarkably. In addition, the relation between the CPE constant (TCPE) and Cdl was discussed.
 Z. Kener, T. Pajkossy, J. Electroanal. Chem. 448 (1998) 139.
 C. A. Schiller, W. Strunz, Electrochim. Acta 46 (2001) 3619.
 G. J. Burg, V. D. Eeden, M. Sluyters-Rehbach, J. H. Sluyters, J. Electroanal Chem., 176 (1984) 275.