# How do I measure/calculate the permittivity constant of materials?

## Main Question or Discussion Point

Hi,

I am trying to figure out how to calculate the permeability constant of a lot of plastics by making solenoid (because that seemed to be the best method of doing so). I am currently using: μ=Ll/((N^2)A) to calculate that constant. Using this method I will only need an induction meter which can easily be a part of an LCR meter but is this the method you would advise me use?

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I am doing some research for work and I was wondering how you would go about calculating the permittivity constant for a few plastics. I did some research a while ago and found that the dielectric value of the material was only a constant multiplier different from the permittivity constant. Therefore I have decided that I am going to make a parallel plate capacitor with the plastic in the center of the two metal plates and with the capacitance and the dimensions of the capacitor I can use this: C = k*ε_0*A/d to find the dielectric value(k). However is that the correct method and how do i calculate the permittivity constant from the dielectric value.

I understand that in order to calculate the dielectric constant I will need to use the same frequency of electricity that is within the radio frequency range I am using because the frequency affects the permittivity constant.

berkeman
Mentor
Hi,

I am trying to figure out how to calculate the permeability constant of a lot of plastics by making solenoid (because that seemed to be the best method of doing so). I am currently using: μ=Ll/((N^2)A) to calculate that constant. Using this method I will only need an induction meter which can easily be a part of an LCR meter but is this the method you would advise me use?
I am doing some research for work and I was wondering how you would go about calculating the permittivity constant for a few plastics. I did some research a while ago and found that the dielectric value of the material was only a constant multiplier different from the permittivity constant. Therefore I have decided that I am going to make a parallel plate capacitor with the plastic in the center of the two metal plates and with the capacitance and the dimensions of the capacitor I can use this: C = k*ε_0*A/d to find the dielectric value(k). However is that the correct method and how do i calculate the permittivity constant from the dielectric value.

I understand that in order to calculate the dielectric constant I will need to use the same frequency of electricity that is within the radio frequency range I am using because the frequency affects the permittivity constant.

Welcome to the PF.

Yes, you would generally use inductance to help you measure the magnetic permeability of a material, and capacitance to help you measure the dielectric constant.

Since this is your own research, you should do some reading on the web and in textbooks about the equations that you will use, and what kind of error factors you will need to account for and try to minimize.

What is the equation relating dielectric constant and permittivity, for example? What errors will you need to minimize in the capacitance measuring setup, and how will you do it? What about losses and complex permittivity?

Thank you for the information,
My research was done on the web, so I should be able to find out more about the equations and their error factors. Most of the error factors will probably be included in the tools used although calipers and micrometers should lessen the error. The equation I am using is just the equation used to calculate the capacitance of a parallel plate capacitor using the cross-sectional area of the material, dielectric value, and distance between the parallel plates.

I do not know much about complex permittivity, but I am guessing that I should do some research about that because I am going to need to be working with about 900 MHz to 1 GHz.

berkeman
Mentor

Thank you for the information,
My research was done on the web, so I should be able to find out more about the equations and their error factors. Most of the error factors will probably be included in the tools used although calipers and micrometers should lessen the error. The equation I am using is just the equation used to calculate the capacitance of a parallel plate capacitor using the cross-sectional area of the material, dielectric value, and distance between the parallel plates.

I do not know much about complex permittivity, but I am guessing that I should do some research about that because I am going to need to be working with about 900 MHz to 1 GHz.
If you need to do these measurements up near 1GHz, then you have a whole different set of problems and issues to deal with. The parasitics and transmittion line characteristics of your setup will dominate other error sources. Do you have much experience working with GHz signals? You can't just make an LCR measurement at 1GHz...

no I have not, I have only finished 1 year of college. I am currently working with RFID tags and after some research I found that the permittivity constant and the permeability constant were the two factors that affected radio waves. Therefore in order to get those values about the materials that my work is encapsulating the RFID tags so that the materials I am using can be directly compared with other materials before any testing is done with them, I have decided to try to do a little testing.
this is the reason I am asking these questions.
the reason I am working between that frequency range is because that is the range or radio frequency I am working with. This a big learning experience

I did see some searching online and found some (quite expensive) LCR meters which read up to 3 GHz so I did not think much of it.

berkeman
Mentor

no I have not, I have only finished 1 year of college. I am currently working with RFID tags and after some research I found that the permittivity constant and the permeability constant were the two factors that affected radio waves. Therefore in order to get those values about the materials that my work is encapsulating the RFID tags so that the materials I am using can be directly compared with other materials before any testing is done with them, I have decided to try to do a little testing.
this is the reason I am asking these questions.
the reason I am working between that frequency range is because that is the range or radio frequency I am working with. This a big learning experience
I did see some searching online and found some (quite expensive) LCR meters which read up to 3 GHz so I did not think much of it.
There's a reason they are quite expensive Also, take a look at the fixtures they use to hold components when measuring them. Even with those fixtures, you need to calibrate the instrument+fixture before usinng it to measure the impedance of the component in the fixture...

just to make sure I am thinking correctly, my results would not be relevant if I used a lower frequency than the frequency of the rf wave, if it would not be relevant I might just give-up on testing for that property of the material and leave that up to a more scientific company.
Another thought would the frequency affect the permeability value?

berkeman
Mentor

Okay. Since your application is encapsulating RFID tags in some plastic material, you do not need to worry about the magnetic permeability of the material. The relative permeability will be unity, unless the plastic has some ferrous material embedded in it, which would be strange.

So the main issue is how the dielectric constant alters the characteristics of the antenna. Mostly the higher capacitance resulting from being embedded in plastic will change the resonant frequency of the antenna. You should be able to use the DC dielectric constant of the plastic as a good first-order number, and then use antenna modelling software to see how varying the dielectric constant and the thickness of the plastic affects the resonant frequency.

The bottom line will be that the antenna can be made slightly smaller when embedded in plastic. That's a common effect when you put an antenna in a weatherproof plastic tube, for example...

this is more going to be applied to the encapsulation of passive RFID tags. I have noticed after doing a frequency sweep of a lot of tags when they were in free air and compared to sandwiched between some of my plastics it did shift their optimum frequency's reading. I am now trying to specify that shift with a specific property of the plastic, which can be directly related to other plastics. This way it would save my company time and money with testing and not knowing what the new plastic would do to the readability of the tag.

berkeman
Mentor

this is more going to be applied to the encapsulation of passive RFID tags. I have noticed after doing a frequency sweep of a lot of tags when they were in free air and compared to sandwiched between some of my plastics it did shift their optimum frequency's reading. I am now trying to specify that shift with a specific property of the plastic, which can be directly related to other plastics. This way it would save my company time and money with testing and not knowing what the new plastic would do to the readability of the tag.
You should be able to characterize this experimentally fairly well, IMO. The dielectric constant of the plastic and the thickness will be the main variables for you to take into account. Since you are able to run RF sweeps of the antenna characteristics already, just try it with several different plastics with different dielectric constants and whatever thicknesses you anticipate using in production. You should be able to plot some good correlations, and base decisions on the plots when considering other materials with other dielectric constants.

thank you very much for your help I will try to do that.

"You should be able to use the DC dielectric constant of the plastic as a good first-order number, and then use antenna modelling software to see how varying the dielectric constant and the thickness of the plastic affects the resonant frequency."
Most Capacitance meters work by creating an RC circuit and it sends ac through the circuit, from that set up the time-constant can be measured. since T = RC, the capacitance can then be easily calculated with the known resistance value. Then how would a DC capacitance meter work? would it be using stepped ac current instead of a sign-wave?

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berkeman
Mentor

Most Capacitance meters work by creating an RC circuit and it sends ac through the circuit, from that set up the time-constant can be measured. since T = RC, the capacitance can then be easily calculated with the known resistance value. Then how would a DC capacitance meter work? would it be using stepped ac current instead of a sign-wave?
Yeah, there's no such thing as a DC capacitance meter.

how did you propose to measure the dc dielectric constant? Would you propose using a very low frequency that would be approaching 0 Hz?

berkeman
Mentor
how did you propose to measure the dc dielectric constant? Would you propose using a very low frequency that would be approaching 0 Hz?
LOL. Look it up on the material's datasheet.

By DC dielectric constant, I meant low-frequency. I don't think you need to try to see if it varies much up near 1GHz from its low-frequency value.

The one exception to that would be if the dielectric were lossy at higher frequencies. You could make a small capacitor with the material, and sweep it on your impedance analyzer to see how it looks...