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Using Cole-Cole expression to solve for frequency dependence of dielectric properties

Posted Jun 2, 2011, 12:15 p.m. EDT RF & Microwave Engineering, Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions Version 4.1 1 Reply

John Bordelon
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Hey all,

I am very new to the software and trying to learn my way around by doing tutorials. However there are some things that I cannot easily find.

I was wondering if anyone knew if it is possible to use the Cole-Cole expression to model the frequency dependence of the dielectric in tissue. The formula (forgive writing formulas in text) is:

e(w) = e(infinity) + SUMMATION(from 1 to 4) expression.

I am also wondering if anyone knows how to set up an electromagnetic wave as a Gaussian pulse. I am trying Transient Electromagnetic Wave physics.

Any help is greatly appreciated,

John
1 Reply Last Post Apr 26, 2012, 9:43 a.m. EDT
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Hello John Bordelon

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Chris Nadovich
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Posted: 1 decade ago Apr 26, 2012, 9:43 a.m. EDT
Cole-Cole permittivity models can be done in the following way on 4.2a

Under

Electromagnetic Waves -> Wave Equation -> Electric Displacement Field -> Electric Displacement Field Model

choose the "Dielectric Losses" option. This will activate the real and imaginary part of relative permittivity
requirement for material properties. You can then enter your cole-cole equations in the material parameters
epsilonBis and epsilonPrim. For example, muscle tissue can be modeled over the microwave band by these equations:

Real part

(55.32+1.0131763650973007E-8*freq^0.875+2.3290263939139233E-18*freq^1.75)/(1.+3.47871713338129E-10*freq^0.875+7.948895542368339E-19*freq^1.75)


Imaginary part

-(-1.3966655477570145E10-4.858604370585691*freq^0.875-1.1101948546745167E-8*freq^1.75-4.581162876363306E-8*freq^1.875)/(freq*(1.+3.47871713338129E-10*freq^0.875+7.948895542368339E-19*freq^1.75))

Be careful that you don't have a "conductivity" defined for the material that is redundant with the Cole Cole model.
I set conductivity to zero and put everything in epsilon. Also, the imaginary part of epsilon is actually the negative of the imaginary part. For most materials, epsilonBis should be a *positive* number in Comsol. Note the extra minus
sign in the formula above for the Imaginary part. Power dissipation should be positive in material. If you see negative power dissipation, you probably have the sign of the imaginary part of permittivity wrong.

As far as Gaussean pulse goes, it sounds to me like you should be using CST rather than COMSOL. Also, if
you use CST the Cole-Cole equations are built in for first and second order models. You just need to enter the parameters. And plane wave illuminations with absorbing boundaries are easier in CST.

But COMSOL makes nicer plots.
Cole-Cole permittivity models can be done in the following way on 4.2a Under Electromagnetic Waves -> Wave Equation -> Electric Displacement Field -> Electric Displacement Field Model choose the "Dielectric Losses" option. This will activate the real and imaginary part of relative permittivity requirement for material properties. You can then enter your cole-cole equations in the material parameters epsilonBis and epsilonPrim. For example, muscle tissue can be modeled over the microwave band by these equations: Real part (55.32+1.0131763650973007E-8*freq^0.875+2.3290263939139233E-18*freq^1.75)/(1.+3.47871713338129E-10*freq^0.875+7.948895542368339E-19*freq^1.75) Imaginary part -(-1.3966655477570145E10-4.858604370585691*freq^0.875-1.1101948546745167E-8*freq^1.75-4.581162876363306E-8*freq^1.875)/(freq*(1.+3.47871713338129E-10*freq^0.875+7.948895542368339E-19*freq^1.75)) Be careful that you don't have a "conductivity" defined for the material that is redundant with the Cole Cole model. I set conductivity to zero and put everything in epsilon. Also, the imaginary part of epsilon is actually the negative of the imaginary part. For most materials, epsilonBis should be a *positive* number in Comsol. Note the extra minus sign in the formula above for the Imaginary part. Power dissipation should be positive in material. If you see negative power dissipation, you probably have the sign of the imaginary part of permittivity wrong. As far as Gaussean pulse goes, it sounds to me like you should be using CST rather than COMSOL. Also, if you use CST the Cole-Cole equations are built in for first and second order models. You just need to enter the parameters. And plane wave illuminations with absorbing boundaries are easier in CST. But COMSOL makes nicer plots.

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