You can get the complex impedance,  f is the frequency in Hertz and C is the capacitor's value in Faradic current.   You can get and calculate faradic capacitance value from EIS (Impedance spectra).

Calculate the complex capacitance from the admittance, i.e. divide Y-imag by j.omega and plot this in a double log plot versus frequency. This will show the (approximate) capacitance plateaus. You can also analyze the impedance with a Nonlinear least Squares program that gives you an equivalent circuit. True capacitance will be obvious, but when you encounter a constant phase element (CPE or symbol 'Q' with Y=Y0.(j.omega)^n) in parallel with a resistance you can calculate an apparent capacitance using the following formula: C-app = [(R.Y0)^(1/n)]/R.

Best regards,

Bernard A. Boukamp 

As far as I understood, you have EIS data from which you can construct Z'-Z" plot (i.e., Nyquist Plot). From this plot, you have to determine Z" (imaginary component of impedance) at any frequency inside the semi-circle (arc). From this relation, capacitance = -1 / (angular frequency * Z"), you can easily calculate the value of capacitance, C. As you know, angular frequency = 2 * pi* frequency (in Hz used for measurement of EIS).

Best of luck.

For the above equation, choose the frequency from the capacitive region. generally 10,000 Hz is chosen. [ if you are running multi frequency EIS]

Otherwise you can also run a single frequency EIS at higher frequency and use the formula above.

 Ideally, the equation C=1/(2*pi*frequency*Z'') only applies for the simple R-C series (i.e. without considering mixed kinetic and diffusion control). For a real case, a higher frequency (no lower than 100 kHz) is chosen to omit diffusion control.

Be attention to the applied potential and frequency you use, the calculated capacitance varies accordingly. Based on my experience, a higher frequency leads to shorter testing time and lower capacitance (maybe not right, considering a faster-scan-rate CV). The applied potential should be in the region where only capacitance process occurring in order to omit any faradaic response.

how will you choose the capacitance value for calculating the complex dielectric value for a wide range of frequency i.e., 1Hz to 1MHz?

Md. Mominul Islam would you please give a reference of given calculation?

@Md. Mominul Islam, I have seen another formula for calculating C'.

C' = (-Z''/ ω )*|Z|2

Where |Z| is SQRT((Z'2 + -Z''2 )).

Which one is correct?? In your formula, is C real or total??

In the introduction of the paper "On Mott-Schottky analysis interpretation of capacitance measurements in organometal Perovskite solar cells" your doubt is completely solved

Depending on the situation, there are many ways for calculating capacitance from impedance data. One may consult with the following book:

Impedance Spectroscopy: Theory, Experiment, and Applications, 2nd Edition

Evgenij Barsoukov (Editor), J. Ross Macdonald (Editor)

ISBN: 978-0-471-64749-2

Mithun Sarkar Xinxin Xiao Md. Mominul Islam . Thank you all for the very fruitful discussion. Could anyone please suggest an article for reference?

Md Saiful Alam Refer to this paper by P. Taberna, Electrochemical Characteristics and Impedance Spectroscopy Studies of Carbon-Carbon Supercapacitors, Journal of The Electrochemical Society.

@Saiful Alam , From Bode plot also you can determine capacitance...See the screenshot.

Dear Rajamanickam Ragavan ,

My answer is based on the the directly previous answer of Mithun Sarkar ,

The first point is that you you curve is a semi circle terminated at in finite frequency at the real impedance = Rs which is the series resistance of an equivalent circuit composed of a parallel resistance Rp and capacitance Cp and the parallel combination is in series with a resistance Rs.

The half circle diagonal is equal to Rp. Then it remains only to determine Cp.

If you choose the point on the circle such that R=X , the angle phi of z will be 45 degrees where R= Rp/2 and X= 1/wC. Then at this point Rp/2= 1/wC,

since w is known and Rp is known one can get C.

For the shape of the impedance curves of a forward biased p-n junction please follow the paper:Article A distributed SPICE-model of a solar cell

Best wishes

http://www.consultrsr.net/resources/eis/cpecalc.htm

Use this link, hope it will help you..

Article Conversion of a Constant Phase Element to an Equivalent Capacitor

This paper describes a few methods to calculate Cdl. Hope this helps!

Dear Mr. Mithun Sarkar, could you please write the name of the book you did in the screenshot? I thank you in advance.

Best regards,

Tanzila

Dear Tanzila Nurjahan I took the screenshot from it: Peer reviewed: electrochemical impedance spectroscopy for better electrochemical measurements

SM Park, JS Yoo - 2003 - ACS Publications

Dear Mr. Mithun Sarkar,

I thank you very much for providing the article name.

Best regards,

Tanzila