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frequency dependence of capacitance to examine influence of harmonics

Posted May 4, 2020, 2:54 p.m. EDT Electromagnetics, Low-Frequency Electromagnetics, Studies & Solvers 5 Replies

Jun
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Hello!

I am new to comsol and am still learning a lot of new things, I know my question has probably been asked many times, but I still can't figure a way to solve my problem:

I want to simulate a voltage with two frequencies, such as 50 Hz and 350 Hz to test the influence of the third harmonic on the capacitance/permittivity of my dielectric. I am using the time dependent study and have entered Asin(wt) + A/2sin(3wt) for my voltage electrode, my model looks a little like the AC/DC example of capacitor_ac, except with an additional guard ring. My model works so far, I can see my field lines and have my current values, but I somehow can't simulate the capacitance/permittivity of my dielectric? I have read on this forum that people recommend the frequency domain study to simulate capacitance/permittivity, but I think this study wouldn't be relevant to my problem, since I will be defining my two frequencies. Should I be tackling this problem another way instead? Does somehow maybe have a better idea? Would appreciate help!

Jun

5 Replies Last Post May 7, 2020, 4:02 p.m. EDT
Edgar J. Kaiser Certified Consultant
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Posted: 5 years ago May 4, 2020, 3:37 p.m. EDT
Updated: 5 years ago May 4, 2020, 3:38 p.m. EDT

Jun,

permittivity is a material property that needs to be specified. The model cannot measure it. So unless you specify a frequency-dependent permittivity you won't see any impact of the frequency you apply to the capacitance of the model.

Cheers Edgar

-------------------
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Jun, permittivity is a material property that needs to be specified. The model cannot measure it. So unless you **specify** a frequency-dependent permittivity you won't see any impact of the frequency you apply to the capacitance of the model. Cheers Edgar
Jun
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Posted: 5 years ago May 4, 2020, 3:46 p.m. EDT

Hello Edgar, thanks for the response. Yes that was also a problem of mine and what I intend to solve later, but I am not so sure if it is correct to calculate my model using the time dependent study - since I cannot seem to calculate my capacitance, and comsol doesnt have the equations either? I know how to do it using the frequency domain, but is there a way to do it using the time dependent study (because of my mixed frequencies voltages)? I tried calculating using Z = U(t)/i(t) and C = jw/Z, but my values dont seem right. Am I missing something here? Do you mean that if i specify a frequency dependent permittivity in a time dependent study I would be able to calculate the capacitance (how?) ?

Jun

Hello Edgar, thanks for the response. Yes that was also a problem of mine and what I intend to solve later, but I am not so sure if it is correct to calculate my model using the time dependent study - since I cannot seem to calculate my capacitance, and comsol doesnt have the equations either? I know how to do it using the frequency domain, but is there a way to do it using the time dependent study (because of my mixed frequencies voltages)? I tried calculating using Z = U(t)/i(t) and C = jw/Z, but my values dont seem right. Am I missing something here? Do you mean that if i specify a frequency dependent permittivity in a time dependent study I would be able to calculate the capacitance (how?) ? Jun
Edgar J. Kaiser Certified Consultant
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Posted: 5 years ago May 4, 2020, 4:31 p.m. EDT

Jun,

impedance is a frequency domain concept and not suitable in the time domain. Capacitance is pretty much a geometrical thing. So you can measure it in a frequency domain model at one frequency and if you have the frequency dependent permittivity it is a hand calculation on paper to get it at the harmonic frequency.

Cheers Edgar

-------------------
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Jun, impedance is a frequency domain concept and not suitable in the time domain. Capacitance is pretty much a geometrical thing. So you can measure it in a frequency domain model at one frequency and if you have the frequency dependent permittivity it is a hand calculation on paper to get it at the harmonic frequency. Cheers Edgar
Jun
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Posted: 5 years ago May 7, 2020, 12:36 p.m. EDT

Hello Edgar,

thank you, I have managed to calculate the capacitance using the Frequency Domain study. Although I must say I have doubts about your statement:

'So you can measure it in a frequency domain model at one frequency and if you have the frequency dependent permittivity it is a hand calculation on paper to get it at the harmonic frequency'

In this case are you assuming that the material has a linear behaviour? Let's say by measuring epsr at single frequencies, at 50 Hz my material has an epsr1 = 3 and at 550Hz epsr1 = 6. However, when harmonics are present, eg 50Hz + 550 Hz, how does one 'calculate'/determine the end permittivity of the material at such mixed frequencies 50Hz+550Hz ?

A second question relating to this, considering I have a material that has a relative permittivity which is frequency dependent, is it possible to somehow define this epsr(f) in my material properties? I have tried defining the real part of the permittivity epsr1 and imaginary part epsr2 as a function of frequency as two analytic functions at global definitions but cannot implement them in the material properties table. Is there a way to do this, regardless of the implemented study (time dependent or frequency domain)?

This is an interesting topic for me and I would love to hear other opinions! Jun

Hello Edgar, thank you, I have managed to calculate the capacitance using the Frequency Domain study. Although I must say I have doubts about your statement: > 'So you can measure it in a frequency domain model at one frequency and if you have the frequency dependent permittivity it is a hand calculation on paper to get it at the harmonic frequency' In this case are you assuming that the material has a linear behaviour? Let's say by measuring epsr at single frequencies, at 50 Hz my material has an epsr1 = 3 and at 550Hz epsr1 = 6. However, when harmonics are present, eg 50Hz + 550 Hz, how does one 'calculate'/determine the end permittivity of the material at such mixed frequencies 50Hz+550Hz ? A second question relating to this, considering I have a material that has a relative permittivity which is frequency dependent, is it possible to somehow define this epsr(f) in my material properties? I have tried defining the real part of the permittivity epsr1 and imaginary part epsr2 as a function of frequency as two analytic functions at global definitions but cannot implement them in the material properties table. Is there a way to do this, regardless of the implemented study (time dependent or frequency domain)? This is an interesting topic for me and I would love to hear other opinions! Jun
Edgar J. Kaiser Certified Consultant
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Posted: 5 years ago May 7, 2020, 4:02 p.m. EDT

Jun,

in the frequency domain everything is linear. Again a 'mixed' permittivity is not a suitable concept in the frequency domain. A frequency dependent permittivity can be defined as eps(freq) and it can be complex, such as eps(freq) = f1(freq) + j*f2(freq). Define it under the respective material node.

One thing you may consider to get a known frequency dependent permittivity and mixed frequencies into the time domain is to run an inverse FFT on an appropriately set up frequency sweep with a suitable window function. I have successfully done that in acoustics and it should just work the same way in electromagnetics. However, I can tell you it is not exactly simple.

Good luck, Edgar

-------------------
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Jun, in the frequency domain everything is linear. Again a 'mixed' permittivity is not a suitable concept in the frequency domain. A frequency dependent permittivity can be defined as eps(freq) and it can be complex, such as eps(freq) = f1(freq) + j*f2(freq). Define it under the respective material node. One thing you may consider to get a known frequency dependent permittivity and mixed frequencies into the time domain is to run an inverse FFT on an appropriately set up frequency sweep with a suitable window function. I have successfully done that in acoustics and it should just work the same way in electromagnetics. However, I can tell you it is not exactly simple. Good luck, Edgar

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