Basics of Measuring the Dielectric Properties of Materials

Introduction

A wide variety of industries need a better understanding of the materials they are working with to shorten design cycles, improve incoming inspection, process monitoring, and quality assurance. Every material has a unique set of electrical characteristics that are dependent on its dielectric properties. Accurate measurements of these properties can provide scientists and engineers with valuable information to properly incorporate the material into its intended application for more solid designs or to monitor a manufacturing process for improved quality control. 

A dielectric materials measurement can provide critical design parameter information for many electronics applications. For example, the loss of a cable insulator, the impedance of a substrate, or the frequency of a dielectric resonator can be related to its dielectric properties. The information is also useful for improving ferrite, absorber and packaging designs. More recent applications in the area of aerospace, automotive, food and medical industries have also been found to benefit from knowledge of dielectric properties. 

Keysight Technologies, Inc. offers a variety of instruments, fixtures, and software to measure the dielectric properties of materials. Keysight measurement instruments, such as network analyzers, impedance analyzers, and LCR meters range in frequency up to 1.1 THz. Fixtures to hold the material under test (MUT) are available that are based on coaxial probe, parallel plate, coaxial/waveguide transmission lines, free space, and resonant cavity methods. The table below shows product examples that can be measured by Keysight’s material test solutions. 

Dielectric Theory  

The material properties that will be discussed here are permittivity and permeability. Resistivity is another material property that will not be discussed here. Information about resistivity and its measurement can be found in the Solutions for Measuring Permittivity and Permeability with LCR Meters and Impedance Analyzers application note. It is important to note that permittivity and permeability are not constant. They can change with frequency, temperature, orientation, mixture, pressure, and molecular structure of the material. 

Dielectric constant

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 the 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. 

Permeability

Permeability (μ) describes the interaction of a material with a magnetic field. A similar analysis can be performed for permeability using an inductor with resistance to represent core losses in a magnetic material (Figure 4). If a DC current source is placed across an inductor, the inductance with the core material can be related to permeability. 

Some materials such as iron (ferrites), cobalt, nickel, and their alloys have appreciable magnetic properties; however, many materials are nonmagnetic, making the permeability very close to the permeability of free space (μr = 1). All materials, on the other hand, have dielectric properties, so the focus of this discussion will mostly be on permittivity measurements.  

Electromagnetic Wave Propagation

In the time-varying case, such as a sinusoidal signal, electric and magnetic fields appear together and form an electromagnetic wave. This wave can propagate through free space at the speed of light, c = 3 × 10⁸ m/s, or through materials at a slower speed.

Electromagnetic waves exist at various wavelengths. The wavelength, λ, of a signal is inversely proportional to its frequency, f, according to the relationship λ = c/f. As the frequency increases, the wavelength decreases. For example, in free space, a 10 MHz signal has a wavelength of 30 m, while a 10 GHz signal has a wavelength of only 3 cm.

Wave Propagation Through Materials

Many aspects of wave propagation depend on the permittivity and permeability of a material. To understand dielectric behavior from an “optical view,” consider a flat slab of material under test (MUT) in space, with a TEM wave incident on its surface, as shown in Figure 5.

When the electromagnetic wave reaches the material, there are incident, reflected, and transmitted waves. Because the impedance of the wave in the material, Z, differs from the free-space impedance, η (or Z₀), an impedance mismatch occurs, creating a reflected wave. Part of the electromagnetic energy penetrates the sample.

Once inside the slab, the wave velocity, v, is slower than the speed of light, c. As a result, the wavelength in the material, λd, is shorter than the free-space wavelength, λ₀, according to the equations below.

Because the material will always have some degree of loss, the wave experiences attenuation, or insertion loss, as it propagates through the sample. For simplicity, the impedance mismatch at the second boundary is not considered.

Figure 6 depicts the relation between the dielectric constant of the Material Under Test (MUT) and the reflection coefficient |G| for an infinitely long sample (no reflection from the back of the sample is considered). For small values of the dielectric constant (approximately less than 20), there is a lot of change of the reflection coefficient for a small change of the dielectric constant. In this range dielectric constant measurement using the reflection coefficient will be more sensitive and hence precise. Conversely, for high dielectric constants (for example between 70 and 90) there will be little change of the reflection coefficient and the measurement will have more uncertainty.

Dielectric Mechanisms

A material may have several dielectric mechanisms, or polarization effects, that contribute to its overall permittivity. A dielectric material contains electric charge carriers that can be displaced by an applied electric field. These charges become polarized in response to the electric field, with positive and negative charges moving 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 that rotate to follow an alternating electric field. These mechanisms are relatively lossy, which explains why food heats in a microwave oven.

Atomic and electronic mechanisms are relatively weak and are usually constant throughout the microwave frequency region. Each dielectric mechanism has a characteristic cutoff frequency. As frequency increases, the slower mechanisms drop out in turn, leaving the faster mechanisms to contribute to ε′ (the real part of permittivity). Correspondingly, the loss factor, ε″, peaks at each critical frequency.

The magnitude and cutoff frequency of each dielectric mechanism vary depending on the material. Water, for example, has a strong dipolar effect at low frequencies, but its dielectric constant decreases dramatically around 22 GHz. PTFE, on the other hand, has no significant dipolar mechanisms, so its permittivity remains remarkably constant well into the millimeter-wave region.

A resonant effect is typically associated with electronic or atomic polarization, while a relaxation effect is typically associated with orientation polarization.

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