How to make (almost) anything

A material is classified as “dielectric” if it has the ability to store energy when an external electric field is applied. If a DC voltage source is placed across a parallel plate capacitor, more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates. The dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes, which ordinarily would contribute to the external field. The capacitance with the dielectric material is related to dielectric constant. If a DC voltage source V is placed across a parallel plate capacitor (Figure 1), more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates.

In the image on the right, C and C0 are capacitance with and without dielectric, k' real dielectric constant or permittivity, and A and t are the area of the capacitor plates and the distance between them (Figure 1). The dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes, which ordinarily would contribute to the external field. The capacitance of the dielectric material is related to the dielectric constant as indicated in the above equations.

A material may have several dielectric mechanisms or polarization effects that contribute to its overall permittivity (see image on the right). A dielectric material has an arrangement of electric charge carriers that can be displaced by an electric field. The charges become polarized to compensate for the electric field such that the positive and negative charges move in opposite directions. At the microscopic level, several dielectric mechanisms can contribute to dielectric behavior. Dipole orientation and ionic conduction interact strongly at microwave frequencies. Water molecules, for example, are permanent dipoles, which rotate to follow an alternating electric field. These mechanisms are quite lossy – which explains why food heats in a microwave oven. Atomic and electronic mechanisms are relatively weak, and usually constant over the microwave region. Water (and other polar liquids), has a strong dipolar effect at low frequencies – but its dielectric constant rolls off dramatically around 22 GHz. Teflon, on the other hand, has no dipolar mechanisms and its permittivity is remarkably constant well into the millimeter-wave region.

Relaxation time τ is a measure of the mobility of the molecules (dipoles) that exist in a material. It is the time required for a displaced system aligned in an electric field to return to 1/e of its random equilibrium value (or the time required for dipoles to become oriented in an electric field). Liquid and solid materials have molecules that are in a condensed state with limited freedom to move when an electric field is applied. Constant collisions cause internal friction so that the molecules turn slowly and exponentially approach the final state of orientation polarization with relaxation time constant τ. When the field is switched off, the sequence is reversed and random distribution is restored with the same time constant. Relaxation frequency is the inverse of the relaxation time. At frequencies below relaxation the alternating electric field is slow enough that the dipoles are able to keep pace with the field variations.

In this project I will use a different technique to get the dielectric constant response in the frequency domain. The technique is to send a very sort pulse and sample in time the reponse of the material using a high speed ADC (Analog to Digital Converter) and oversampling. After having the response in time, I will do a Fourier transform to shift to the frequency domain. The maximum frequency I can resolve is the half of the sampling frequency (due to aliasing).

In order to go relatively high in frequency, to start seeing a curve in the dielectric constant, I have to use a very fast ADC. Thus, I selected as my microcontroller the ATXMega32A4U, which for a cost of 3$ in quantity ships with a 2MSPS ADC, capable of performing single ended and differential measurements with a gain up to 64X in the latter case. It can also carry out automatic sample and hold for high impedance sources and perform simultaneous double measurement with its single ADC using a technique that stores temporarily a value in the comparator. Much faster ADC's, in the regime of GHz have not prohibitive costs, around $80 , but I will consider them in the next spiral of this project.