# Data modeling

1. Apr 15, 2015

### labd0001

Hi all,

I am trying to obtain an empirical equation/model having 2 inputs (frequency and S11) and one output (a physical parameter)
I have done various simulations using CST of the System and now I am trying to relate S11 and frequency to a physical parameter. Any suggestions of how I should go about it?

I have tried using system identification tool in Matlab but the results I obtained are rather confusing and I am not sure whether the approach is correct.

Thanks

2. Apr 15, 2015

### Simon Bridge

You have described a box with three wires (I'm guessing it's electronic, it could be three tubes or three nerves or something - you havn't actually said) coming out of it.
Two are labelled "input" and one "output" ... the input wires are further labelled "frequency" and "S11".
There is no description of what is in the box or what these labels actually refer to.

You want the "output" to be something to do with a physical parameter" but you don't know which parameter and you have not said what would count - presumably the signal that comes from the output is not, itself, a physical parameter.

Basically the request is too wide open for any answer to be useful.
Usually, the act of describing your problem is sufficient detail and specificity to get a useful answer will result in an answer occuring to you.

3. Apr 15, 2015

### labd0001

I would like to relate (empirically) the reflection coefficient of a material with a physical property being length, electrical properties etc for specific frequencies. That is why the input of the model/equation will be the frequency and reflection coefficient (at that particular frequency) and the output is the physical property I am relating to.

4. Apr 15, 2015

### Simon Bridge

OK - you you want your box to tell you some length given the reflection coefficent and frequency?
You have said that the reflection coefficient is for a material - presumably the material surface?
What is the frequency of: incoming light perhaps? You have to say. The software you are using is a tad general.
Finally, "length" of what?

I don't know what " electrical properties etc for specific frequencies" means in this context - please be specific.

5. Apr 15, 2015

### labd0001

frequency of incident signal. I am doing a sweep from 8-15GHz and recording the S11.
What i did is the following, I simulated a material (with known electrical properties) and calculated the S11 for 8-15GHz. Therefore I have the S11 for particular frequencies and their corresponding electrical properties. Now I would like to obtain a model so if I do measurements of S11 in the laboratory using the same system I used in the simulation, I can calculate the electrical properties.

I hope this makes it clearer.

6. Apr 16, 2015

### Staff: Mentor

It would be clearer to me if I knew what a 511 is.

7. Apr 16, 2015

### labd0001

S11 is the reflection coefficient measured using a vector network analyser

8. Apr 16, 2015

### Simon Bridge

OK - you have a computer model already that takes some "known electrical properties" (whatever that means) and gives you the reflection coefficient as a function of incident frequency.

But what you want another model that goes the other way ... takes the data for S11(f) and tells you the "electrical properties".

It is unlikely that this is possible - in general, the reverse mapping won't be unique.

Inside the computer model is a set of calculations ... to get the reverse model, you need to reverse the calculations.
For more information on how to get a model (in your case, the "electrical properties") from data, have a look at "inverse problems" from S.M.Tan, here: http://home.comcast.net/~szemengtan/ [Broken] ... that should give you an idea of how much vital information you have left out.