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Frequency dependent permittivity

Posted Jun 7, 2011, 2:17 p.m. EDT Studies & Solvers 18 Replies

John Bordelon
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Hey all,

I have tried searching the forums for a similar question but can find none.
I am trying to model a blood cell and and need to model its permittivity as frequency dependent.

I am wondering if it is possible to somewhere plug in an equation like this:

eps_tot = 4 + 50/((1 + i*freq*2*pi)^(.1))

and get the real and imaginary parts of eps_tot.

I have tried plugging this into the relative permittivity but it gives me errors.
I have tried defining a material function, using the same format that the built-in Temperature dependent values use, but cannot get it to work.

Any examples or advice is appreciated.

-John
18 Replies Last Post Jun 10, 2011, 2:15 p.m. EDT
John Bordelon
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Posted: 1 decade ago Jun 7, 2011, 4:05 p.m. EDT
Hey all,

I have included a copy of my attempt.

If you go to the materials section, then 'Blood Cell (original was water)'
and in the relative permittivity to real_eps (which is a material function I defined) then it will run.

I have also searched through (I think) every material and cannot find a frequency dependant relative permittivity for one of them.

Any help is really, really appreciated.

John
Hey all, I have included a copy of my attempt. If you go to the materials section, then 'Blood Cell (original was water)' and in the relative permittivity to real_eps (which is a material function I defined) then it will run. I have also searched through (I think) every material and cannot find a frequency dependant relative permittivity for one of them. Any help is really, really appreciated. John
John Bordelon
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Posted: 1 decade ago Jun 7, 2011, 4:08 p.m. EDT
sorry for double post, the above glitched with no attachment
sorry for double post, the above glitched with no attachment

Attachments:

Peijun Guo
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Posted: 1 decade ago Jun 7, 2011, 5:48 p.m. EDT
Hi, as far as I know, defining a complex function won't be very safe. I have met this problem before.
I would define two analytic functions at the global definitions, for both the real part and the imaginary part. And then at the material property section i will specify the real or imag permittivity as functions of freq, where the function names are what you defined at the beginning.
Hi, as far as I know, defining a complex function won't be very safe. I have met this problem before. I would define two analytic functions at the global definitions, for both the real part and the imaginary part. And then at the material property section i will specify the real or imag permittivity as functions of freq, where the function names are what you defined at the beginning.
John Bordelon
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Posted: 1 decade ago Jun 7, 2011, 8:07 p.m. EDT
Thanks. Do you know if using the Transient Electromagnetic Wave physics with Solver step of Time Domain Analysis by default solves for 'freq', or do I have to specify that in some way? Because even using this as a variable in a simple example (I set the relative permittivity to freq*10e-9) still gives the same error.

Thanks,

John
Thanks. Do you know if using the Transient Electromagnetic Wave physics with Solver step of Time Domain Analysis by default solves for 'freq', or do I have to specify that in some way? Because even using this as a variable in a simple example (I set the relative permittivity to freq*10e-9) still gives the same error. Thanks, John
Edgar Kaiser
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Posted: 1 decade ago Jun 8, 2011, 2:58 a.m. EDT
Hi,

in a transient study you must define the time dependency of the study by yourself. There is no specific frequency variable.
If you want to study the frequency response of your model and the time dependency is purely harmonic, you should use a frequency domain study and there you have the frequency variable.
However, this will only give you a steady state result.

Cheers
Edgar
Hi, in a transient study you must define the time dependency of the study by yourself. There is no specific frequency variable. If you want to study the frequency response of your model and the time dependency is purely harmonic, you should use a frequency domain study and there you have the frequency variable. However, this will only give you a steady state result. Cheers Edgar
John Bordelon
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Posted: 1 decade ago Jun 8, 2011, 2:12 p.m. EDT
Thanks for the reply.

So does this mean COMSOL cannot simulate a transient event dealing with a frequency dependent electrical permittivity?

Thanks,

John
Thanks for the reply. So does this mean COMSOL cannot simulate a transient event dealing with a frequency dependent electrical permittivity? Thanks, John
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jun 9, 2011, 4:12 a.m. EDT
Hi

Well how do you link the frequency dependent permittivity to a transient response (I mean how do you want to write out the equations) ?

Once you have that you can impelment it ontop of the existing COMSOL physics

--
Good luck
Ivar
Hi Well how do you link the frequency dependent permittivity to a transient response (I mean how do you want to write out the equations) ? Once you have that you can impelment it ontop of the existing COMSOL physics -- Good luck Ivar
John Bordelon
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Posted: 1 decade ago Jun 9, 2011, 9:50 a.m. EDT
Thanks Ivar.

Is there a way to tell COMSOL to Fourier transform the fields at each time step? I cannot find FFT anywhere in the documentation although I did read this about COMSOL 4.1

"Transient models in particular will benefit from the max, min, and average time-series operations as well as the fast Fourier transform to the frequency domain." -- which sounds exactly like what I want.

Again any help is appreciated. Does anyone have a example that involves computing the Fourier transform (even if it has nothing to do with electromagnetics?)

Thanks again,

John
Thanks Ivar. Is there a way to tell COMSOL to Fourier transform the fields at each time step? I cannot find FFT anywhere in the documentation although I did read this about COMSOL 4.1 "Transient models in particular will benefit from the max, min, and average time-series operations as well as the fast Fourier transform to the frequency domain." -- which sounds exactly like what I want. Again any help is appreciated. Does anyone have a example that involves computing the Fourier transform (even if it has nothing to do with electromagnetics?) Thanks again, John
John Bordelon
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Posted: 1 decade ago Jun 9, 2011, 10:02 a.m. EDT
Hey Ivar,

I am trying a few different things now. Do you know if what I am looking for is under Model Couplings (perhaps coupling the time dependence to frequency dependence)?

Again, any help or examples are greatly appreciated.

-John Bordelon (LA Tech)
Hey Ivar, I am trying a few different things now. Do you know if what I am looking for is under Model Couplings (perhaps coupling the time dependence to frequency dependence)? Again, any help or examples are greatly appreciated. -John Bordelon (LA Tech)
Edgar Kaiser
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Posted: 1 decade ago Jun 9, 2011, 10:20 a.m. EDT
Hi,

the time steps of a transient model do not explicitely depend on time. So you cannot transform them to frequency domain.
Only the whole transient model (all the steps together) is a function of time and can be transformed to frequency domain by an FFT.

One thought: In case your model is linear you could consider to decompose the transient excitation you want to apply into spectral components (by FFT), run frequency domain studies and add them up using appropriate weights you gained from the spectral analysis. This way you can implement your frequency dependent permittivity into the frequency domain studies.

Then you could transform the model back to time domain by FFT and obtain the transient.

You probably need Matlab to finally add the frequency components in this approach, but I am not sure about that.

Cheers
Edgar
Hi, the time steps of a transient model do not explicitely depend on time. So you cannot transform them to frequency domain. Only the whole transient model (all the steps together) is a function of time and can be transformed to frequency domain by an FFT. One thought: In case your model is linear you could consider to decompose the transient excitation you want to apply into spectral components (by FFT), run frequency domain studies and add them up using appropriate weights you gained from the spectral analysis. This way you can implement your frequency dependent permittivity into the frequency domain studies. Then you could transform the model back to time domain by FFT and obtain the transient. You probably need Matlab to finally add the frequency components in this approach, but I am not sure about that. Cheers Edgar
John Bordelon
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Posted: 1 decade ago Jun 9, 2011, 10:25 a.m. EDT

Only the whole transient model (all the steps together) is a function of time and can be transformed to frequency domain by an FFT.


Thanks a bunch! Do you know how to access the FFT in COMSOL (I have tried searching the help but can find nothing)?

-John
[QUOTE] Only the whole transient model (all the steps together) is a function of time and can be transformed to frequency domain by an FFT. [/QUOTE] Thanks a bunch! Do you know how to access the FFT in COMSOL (I have tried searching the help but can find nothing)? -John
Edgar Kaiser
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Posted: 1 decade ago Jun 9, 2011, 10:33 a.m. EDT

I think they announced that for 4.2. I am still on 4.1 and expecting the update.

Cheers
I think they announced that for 4.2. I am still on 4.1 and expecting the update. Cheers
Jeff Hiller COMSOL Employee

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Posted: 1 decade ago Jun 9, 2011, 11:19 a.m. EDT
Search the v4.1 User's Guide manual for "FFT". You'll find it.
Search the v4.1 User's Guide manual for "FFT". You'll find it.
John Bordelon
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Posted: 1 decade ago Jun 9, 2011, 3:19 p.m. EDT
Is a seperate FFT module needed? I can't find anything about it in help, even going through each Fourier entry seperately.

Is a seperate FFT module needed? I can't find anything about it in help, even going through each Fourier entry seperately.
Jeff Hiller COMSOL Employee

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Posted: 1 decade ago Jun 9, 2011, 3:26 p.m. EDT
No, I am talking about the User's Guide for COMSOL Multiphysics base package. Search for "FFT" on that document and you'll get several hits (page 687, 716, etc)
No, I am talking about the User's Guide for COMSOL Multiphysics base package. Search for "FFT" on that document and you'll get several hits (page 687, 716, etc)
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jun 10, 2011, 1:29 a.m. EDT
Hi

the FFT is linked to "tables" and analyiss of data therein, its a nice feature, note that in v4.1 the fft is not normalised, so you must do that yourself. Normalisation was planned for 4.2 I have heard, but I havent had time yet to check

--
Good luck
Ivar
Hi the FFT is linked to "tables" and analyiss of data therein, its a nice feature, note that in v4.1 the fft is not normalised, so you must do that yourself. Normalisation was planned for 4.2 I have heard, but I havent had time yet to check -- Good luck Ivar
Edgar Kaiser
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Posted: 1 decade ago Jun 10, 2011, 3:33 a.m. EDT
Hi,

and it looks like FFT is not available in frequency domain studies, so we can't transform back to time domain. Will 4.2 provide that?

Cheers
Edgar
Hi, and it looks like FFT is not available in frequency domain studies, so we can't transform back to time domain. Will 4.2 provide that? Cheers Edgar
John Bordelon
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Posted: 1 decade ago Jun 10, 2011, 2:15 p.m. EDT
Thanks all for the help. It looks like this is going to require some work.

I am wondering if you could recommend the best physics/studies settings to model a transient pulse traveling through non-dispersive media, generating heat.

I have tried using the previously posted model, by fixing the permittivity, and including microwave heat transfer physics, but continue to get a stiffness matrix error.

Any help is greatly appreciated,

John, LA Tech
Thanks all for the help. It looks like this is going to require some work. I am wondering if you could recommend the best physics/studies settings to model a transient pulse traveling through non-dispersive media, generating heat. I have tried using the previously posted model, by fixing the permittivity, and including microwave heat transfer physics, but continue to get a stiffness matrix error. Any help is greatly appreciated, John, LA Tech

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