Bhavna,

Check out http://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1536.pdf

Page 79 has the problem I believe you're working on.

Greg.

Dear Bhavna,

If you are using lsqnonlin in MATLAB , which basically solves nonlinear least-squares problems, including nonlinear data-fitting problems. Then you should get a equation of S11 in which e(permittivity) should be there. it should be staright forward to obtain e ( real n complex values). 

Thank you for your response Sir.

Attached is my matlab code and permittivity profile I'm getting. I don't know where I'm going wrong

Bhavna,

If i understand correctly what u mean is :

a. First, you have a measured data of S11 with frequency

b. Second , you are trying to fit a equation of S11 as a function of frequency and permittivity.

c. finally you are trying to extract the permittivity from the fit equation.

please tell what is the chi square or R square of the fit ??

you can send email to [email protected], it will be much better than discussing here.

Hi Bhavna,

I rewrote your code and it is attached.  I couldn't test it because I don't have your data files or the optimization toolbox.  Also, I'm not really sure what physical quantity you're trying to extract.  So, I just assumed it's relative permittivity. Therefore, the attached files are meant to give you a starting point from which you make modifications.  Although I believe the attached code is close to completion, don't expect it to run as is.

Since I don't have the optimization toolbox, I looked over some online documentation:  http://www.mathworks.com/help/optim/ug/lsqnonlin.html

The main point is that you don't need a lot of different functions (i.e. myfun1, myfun2,... etc).  You just need one function (providing a residual vector).  I placed it in a file separate from the main script.  I made a guess as to what this function should be based on your script try7.m. You  may need to modify it.

Hopefully, you'll find my coding recommendations useful. I believe it will help you stay more organized and make it easier to debug. 

Sincerely,

Greg.

Dear Sir,

Thanks for your valuable suggestions. I'll follow them religiously.

Besides, You are very right. I'm trying to extract relative permittivity which for FR4 should be closer to 4.3-0.1075 i.

Sir, I'll try now . Thanks a lot for your help.

Attached are the data files.

Hi Bhavna,

Since the permittivity you're looking to extract has a negative imaginary part, the time convention you're interested in is exp(+jwt), as opposed to exp(-iwt).  This will have an effect on the equations you use to extract permittivity from S11.

Also effecting the equations you use is the measurement system.  Did you use a free space measurement system?  Did you use a rectangular wave guide measurement system? The resulting S parameters are very different from one another for these two cases.  Based on the data you provided, I'm guessing it came from an X-band rectangular wave guide system.  Is that correct?

Finally, before applying an extraction algorithm, S parameter data has to have been calibrated. Has your S11 data been calibrated?  Depending on how you calibrate the data, the phase of S11 may need to be adjusted prior to applying the extraction algorithm.

Greg.

Sir, I'm using free space measurement system.

And Sir, S11 data has been obtained through simulation using CST microwave studio. But I have done the de-embedding to compute it at the correct reference plane.

I have simulated a 5*5*2mm Fr4 sample backed by a metal plate in free space. From there I have obtained the S11 data.

I'm still not getting the correct results :(

Bhavna,

Now that I know what you're trying to do, I can be of a little more help.  If you model an infinite non-magnetic dielectric in CST (not metal backed, normal incidence) then the attached are the equations you need to invert using lsqnonlin.m.  Also attached is an updated code that should be close to what you want.  As before, it's untested since I don't have the optimization toolbox.  You will have to debug it.

Since your FR4 sample is very small (5mm x 5mm x 2 mm), I don't think there is a simple set of equations you can invert (metal backed or not).  For such problems, you can use CST itself to extract material parameters from S parameters, but that will be a lot of work.

Greg.

Sir, 

Matlab code for short circuit approach is working now. It's giving good results. Attached is the extracted permittivity profile for FR4 sample.

Sir, but when I place a short at a distance of lamda/4 from the sample(creating open circuit) and try to extract permittivity profile from reflection data, results are not coming out to be correct. I have attached the matlab code and obtained results. Please guide me regarding the same. 

Also Sir,

I saw a webinar in which the method to extract material parameters from CST has been described.

They explained ring resonator approach in which resonance frequency and S21 (insertion loss) were used to extract permittivity. Final aim of my project is to characterize metamaterials. Is that approach valid (or could be extended) for metamaterials?

Bhavna,

I'm happy to learn that you were able to make the appropriate changes to obtain a working code, at least for your initial case.  I'm afraid I won't be of much help for your second case.

You may be interested in extracting the so called "bulk" material parameters from a measured metamaterial. These are just complex permittivity and permeability that would result from a homogeneous sample with the same S parameters as the metamaterial.  In that case, you can use CST itself as part of a forward process that's inverted by lsqnonlin.

You could write a MATLAB script that interfaces with CST via MATLAB's invoke command.  The CST code provides theoretical S parameters (as a function of mu and eps) which are subtracted from measured S parameters, thus providing a residual vector for lsqnonlin.m as before.  There would be stumbling blocks along the way, not the least of which is the occurrence of multiple solutions; that is, multiple pairs (eps,mu) with each pair producing theoretical S parameters that match the measured S parameters. It would be quite a project, particularly the programming aspect, but it is definitely doable.

Best of luck.

Greg.

Dear Sir,

I have tried another method for computing the permittivity and permeability profile for material under test. Attached is the PDF file documenting the used set of equations and also the Matlab Code for calculation of reflection data.

Sir, I don't know where I'm going wrong. Please help.

Bhavna,

Check out http://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1536.pdf

Page 79 has the problem I believe you're working on.

Greg.

How do I extract parameters profiles using the lsqnonlin optimization algorithm in Matlab?

I am very delighted to writing to you.

I am working now on build the model for Lithium ion battery to represent the V- I (voltage and current) performance.

I'm not able to extract the correct parameters from my model.

I am not perfect to write code to extract my parameters.

I have one equation with six variables and the constants changing with time.

also I have calculated the Jacobians for this equations.

Please any help.

any advice.

Thanks