# Dielectric permittivity measurement of solid materials using capacitors

#### tlemsalim

Joined Feb 15, 2021
6
Hi,

I am currently doing some research work on different ways to measure permittivity of materials. In particular, I want to measure the permittivity of FR4 materials of PCB, and of an aluminium oxide block of approximately 0.5 cm^3, at 2.45 GHz.

One idea I want to explore is how to measure the dielectric permittivity of solid materials using capacitors. However, I don't know which type of capacitor is best suited for the measurement, since I want to test it under high frequencies (2.45 GHz). I know that by using a simple parallel plates capacitor under high frequencies, the measurement won't be accurate. I was advised to use an interdigitated capacitor because it is more suited to high frequencies, but then how do I put the material between the "teeth" (or plates) of an interdigitated capacitor since the space between the plates is so small? Is there another type of capacitor which is more suited to do this task?

Here is why I want to try it out with a capacitor:

On one hand, let’s consider a random material with an unknown dielectric permittivity. The material consists in the formation of molecules relatively randomly arranged. These molecules which are composed of a certain number of atoms bounded together in a specific configuration. At its formation, molecules often form dipole moments and hence are charged positively on one pole, and negatively on the other pole.

On the other hand, let’s consider a simple capacitor. This capacitor consists in two parallel plates. One plate is charged positively while the other is charged negatively. Therefore, the capacitor creates an electric field between the two plates.

By putting the material between the two capacitor plates, the electric field goes through the material, inducing the polarization of the material’s molecules. This phenomenon (the polarization of the material’s molecules) alters the molecules spatial arrangement by aligning the dipole moments in such a way that the dipole moments form another electric field that resists the capacitor’s electric field. In fact, in the new spatial configuration (under the capacitor’s electric field), the dipoles are parallel to each other so that they can resist to the electric field.
The permittivity of the material can hence be determined since the higher the permittivity of the dielectric (i.e the material between the two parallel plates), the greater the capacitance.

Sorry for the long text, and thank you for your time and consideration.

#### tlemsalim

Joined Feb 15, 2021
6

#### tlemsalim

Joined Feb 15, 2021
6
For those who are interested in the solution, using an interdigital capacitor can be a solution. After doing further research, I realised that my lack of knowledge led me to the assumption that like for a parallel plate capacitor, the dielectric material has to be put in the middle of the interdigital capacitor fingers, which is completely wrong. In fact, the dielectric has to be on top of the capacitor, covering all the interdigital capacitor. The challenge here would then be to vary the dimensions of the interdigital capacitor in order to orientate the electromagnetic field in such a way that the field goes through the dielectric.

To do so, I am thinking of designing a 2 poles strip line with the interdigital capacitor (and maybe even an inductor since I've read somewhere that it could make it easier to measure the dielectric permittivity with an inductor than without, but it needs more investigation). Each component will be respectively separated by a gap as follows: microstrip line left pole, gap, interdigital capacitor, gap, microstrip line right pole. The device will be simulated on a software (EMPro). The software will provide the scattering parameters for the three parts of the device (microstrip line left pole, interdigital capacitor, microstrip line right pole). The S-parameters can then be converted into ABCD matrices. By simply multiplying the 3 ABCD matrices can be obtained one global ABCD matrix of the whole device. By doing some maths (contact me for more details), you end up with an accurate measure of the permittivity.

I hope that this is useful to anyone reading this.