The formula to calculate the impedance (Z) of a constant phase element is:
\[ Z = \frac{1}{Q \cdot \omega^{\alpha}} \]
Where:
Let's say the constant phase element coefficient (\( Q \)) is 0.01, the angular frequency (\( \omega \)) is 100 rad/s, and the phase angle (\( \alpha \)) is 0.9. Using the formula:
\[ Z = \frac{1}{0.01 \cdot 100^{0.9}} \]
We get:
\[ Z \approx \frac{1}{0.01 \cdot 79.43} \approx 1.26 \]
So, the impedance (\( Z \)) is approximately 1.26 ohms.
A constant phase element (CPE) is an electrical component used in the modeling of electrochemical systems. It is characterized by a constant phase angle over a wide range of frequencies, which makes it useful for representing non-ideal capacitive behavior in systems such as batteries, fuel cells, and corrosion processes. The CPE is defined by its coefficient (Q) and phase angle (α), and its impedance is frequency-dependent. The CPE can be used to model the behavior of porous electrodes, rough surfaces, and other complex electrochemical interfaces.