Fitting impedance of simple randles circuit to Fourier transform formula

I have this simple circuit that i want to find parameters of,

and its real-world magnitude frequency response derived from impedance spectroscopy.

(magnitude frequency response.Frequency is 10-10000Hz with 10Hz step.)

Now, i have derived the fourier transform of this impedance:

Whose magnitude i found:

However trying to fit this last equation with matlab CFTOOL gives nonsense. What am i doing wrong??

Answer 1

[David Goodmanson]

Hi F^2

I believe you are trying to fit an incorrect magnitude, which can of course lead to nonsense. The correct expression is

absZ = sqrt( ((r1+r2)^2 + r1^2*r2^2*w^2*c^2)/(1 + r2^2*w^2*c^2) );

If you plug some numbers into your expression and compare to

absZ = abs((r1+r2 +i*w*c*r1*r2)/(1+i*w*c*r2))       (a) 

there is going to be disagreement.

When using fctool, is there any reason you can't do this an easier way and just fit (a) above?

[Frizstyler Friz]

Well, i had used a sketchy formula indeed. Anyway, tried your formulas and the same result comes out. I changed the frequencies to rad/s ,too.

Here i supply the measurements too in excel sheet, if anyone's interested i'd highly appreciate.

Answer 2

[Frizstyler Friz]

The problem was solved by tweaking the fitting options. Constraining the lower limits and startpoint values was important. Scaling the capacitor with 1e-7 or less in front worked. I also reduced function termination tolerance to 1e-10, seems to affect the fit somewhat?