Alternating current impedance calculations

Under alternating current (AC), the equivalent capacitance C and the equivalent series resistance R depend on the frequency. Generally, these two parameters are determined by impedance spectroscopy. This technique enables us to measure the real part and the imaginary part of the supercapacitor s impedance. An initial approximation is to consider that Ri is the real part of the impedance, and the equivalent capacitance C is calculated using the following expression [RAF 07 GUA07] ... 

Impedance is a measure of the ability of a circuit to resist the flow of an alternating current. It is usually measured by applying an AC potential to an electrochemical cell and measuring the current through the cell. The current response to a sinusoidal potential will be a sinusoid at the same frequency but shifted in phase. The impedance of the system can be calculated as an expression analogous to Ohm s Law as ... 

As well as CV and GCD analysis, another characterisation method that is often used to characterise supereapacitor materials is electrochemical impedance spectroscopy (EIS), or alternating current (AC) impedance spectroscopy. The following equation can be used to calculate the capacitance value from impedance measurements ... 

In electrochemical impedance spectroscopy (EIS) measurements a membrane is placed in an electrolyte solution of specified concentration. Two electrodes are located on the membrane surface, and a small alternating current of known frequency and with small amplitude is applied to the system. The phase difference and the amplitude of the simultaneous electrical potential that develops across the membrane are measured. A wide frequency range is used in the measurements, and the membrane is assumed to be a plane capacitor. As a result, the resistances and capacitances of the membrane are obtained and the thickness of the membrane can be evaluated. By using knowledge of the dielectric constant of water and the membrane material, the porosity of the membrane can be evaluated from the capacitance values. Impedance can be calculated from the values for resistance and... 

A more recent alternative for looking at cytotoxicity in adherent cultured cells involves the use of real-time cell electronic sensing (RT-CES) equipment. Cells are plated into special multiwell plates through which a current is passed at defined time intervals. The impedance of that current is correlated to the density of adherent cells in the well through calculation of a cell index that is measured over the duration of the experiment. The RT-CES assay has an advantage over... 

The impedance simulation of the dynamics was carried out with Finite Difference Method (FDM) implemented in MATLAB. Alternatively, the discretization of equations can be performed by use of Finite Element Method (FEM), wavelets techniques, etc. [15,16]. Electrodes were positioned on 2 sides of the 10 mm square tissue model, current was inserted and voltages were calculated for each case of 60 time-steps. Electric impedance maps with resolution 35 x 35 x 1 were derived from the dynamic vascular network (Figure 4). 

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