Method of determining the impedance of an electrochemical system

• US 20060091892A1
• Filed: 07/11/2003
• Published: 05/04/2006
• Est. Priority Date: 07/15/2002
• Status: Active Grant

• Current Assignee: Institut National Polytechnique de Grenoble
• Original Assignee: Institut National Polytechnique de Grenoble
• Inventors: Petrescu, Bogdan, Petit, Jean-Pierre, Poignet, Jean-Claude
• Granted Patent: US 7,253,631 B2
• Time in Patent Office: Days
• US Class Current: 324/433
• CPC Class Codes: G01R 27/02 Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant by measuring phase angle only G01R25/00

Abstract

The invention relates to a method of determining the complex impedance Z(f_m) of a non-steady electrochemical system, comprising the following steps consisting in: bringing the system to a selected voltage condition and applying a sinusoidal signal with frequency f_m thereto; immediately thereafter, measuring successive values for voltage and current at regular time intervals ?T; calculating the discrete Fourier transforms for voltage (E(f)) and current (I(f)), the voltage transform being calculated for the single frequency f_m of the sinusoidal signal and the current transform being calculated for frequency f_m and for two adjacent frequencies f_m−1 and f_m+1 on either side of frequency f_m; and calculating the impedance using the following formula: Z(f_m)=E(f_m)/I*(f_m), wherein I* denotes a corrected current such that Re[I*(f_m)]=Re[I(f_m)]−{Re[I(f_m+1)]+Re[I(f_m−1)]}/2, Im[I*(f_m)]=Im[I(f_m)]−{Im[I(f_m+1)]+Im[I(f_m−1)]}/2.

Claims

1. A method for determining the complex impedance Z(f_m) of a non-stationary electrochemical system, characterized in that it comprises the steps of:

setting the system to a selected voltage state and applying a sinusoidal signal of frequency f_m thereto,

measuring, immediately after, successive values of the voltage and of the current at regular time intervals Δ

T,

calculating the discrete Fourier transforms of the voltage (E(f)) and of the current (I(f)), the voltage transform being calculated for the sole frequency f_m of the sinusoidal signal and the current transform being calculated for frequency f_m and for two adjacent frequencies f<sub>m−

1</sub> and f_m+1 on either side of frequency f_m, and

calculating the impedance according to the following formula;

Z(f_m)=E(f_m)/I*(f_m)

where I* designates a corrected current such that;

Re[I*(f_m)]=Re[I(f_m)]−

{Re[I(f_m+1)]+Re[I(f<sub>m−

1</sub>)]}/2
Im[I*(f_m)]=Im[I(f_m)]−

{Im[I(f_m+1)]+Im[I(f<sub>m−

1</sub>)]}/2.

2. The method of claim 1, characterized in that it is repeated for a succession of excitation frequencies.