Dear Colleagues, this is actually not an question but a simple aid, as many asked for help in HN fitting. The attached file helps to make the first, approximative steps in fitting Havriliak Negami paramaters to experimental dielectirc data. Into the first worksheet one has to insert the exprimental frequency, permittivity and loss data. The assumed HN parameters (the resonance frequency, the limiting permittivies and the two HN shape parameters) are to be inserted into the second worksheet. The form of the equation was taken from https://en.wikipedia.org/wiki/Havriliak%E2%80%93Negami_relaxation, which is actually somewhat different from other references, here alpha is the non-symmetric (skew) parameter and beta is athe symmetric. In this parametrisation alpha and beta equal to 1 gives the Debye realxation. Instead of omega*tau I used f/f0 which is the same. On the third worksheet the calculation can be done by copying row 2 to the further rows. The eps' and eps" data vs log frequency can be seen on sheet 4, while the Cole-Cole plot can be seen on sheet 5. Of couse, one can change the axis sizes etc. to see better the details. the residuals are also calculated and can be summed up to make the comparison of various fits more quantitative. As I said, this is not a fitting program by itself, but it can be used to get a reasonable initial guess by trial and error and using visual comparison, which can be used in nonlinear fitting programs. It also gives a feeling how does the change of certain parameters change the visual apperance of the simulated curves. Good luck!
Dear professor, kindly let me know if can I use this excel file to fit the electric modulus also
Thank you in advance
Hello Sir, I want to fit data of dielectric spectroscopy of Polyurethane in HN equation, but I don't know about the alpha and beta of the same. Can you suggest how to find alpha and beta which best fit the curve?
Dear Professor Gyorgy Banhegyi, how to find the beta value ? Can you please suggest?
Thanking You
Dear Prof.Banhegyi
I would be grateful if you can refer me to an article suggesting a two-dimensional HN model. I wish you can help me with this by providing a model of 2 simultaneous equations and not one like the usual one. My model should be of the form
Dx(t)=Ax(t)+Bu(t) where A is a matrix and D is the RL differential operator subscrip alpha, beta, omega and superscript gamma so that it is the Prabhakar fractional derivative. Can you provide me with an example of HN involving a matrix A. many thanks
Pro. A. Deif, Cairo univ.
Dear Professor Deif, It is possible that I do not understand exactly your question. Do you want to use the linear combination of two H-N processes (which is relatively straightforward) or to describe a single relaxation process by four parameters? May I ask you to send the functional form in a Word file? Best personal regards Gyorgy
Ok thank you I shall send it by mail. I already sent a mail but I shall resend you a new one
thanks
Can we fit the frequency vs dielectric constant spectra with the HN equation? If it is possible, then could someone please suggest to me some article on it? It will be very much helpful.
Thanking you
Ad Chinmayee: The fitting is always done vs. frequency, the Cole-Cole plot is drawn in the second step only.
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