Solutions for Measuring Permittivity and Permeability with LCR Meters and Impedance Analyzers

Introduction 

Recently, electronic equipment technology has dramatically evolved to the point where an electronic component’s material characteristics become a key factor in a circuit’s behavior. For example, in the manufacture of high capacitance multilayer ceramic capacitors (ML-CCs), which are being used more in digital (media) appliances, employing high κ (dielectric constant) material is required. In addition, various electrical performance evaluations, such as frequency and temperature response, must be performed before the materials are selected.

In fields outside of electronic equipment, evaluating the electrical characteristics of materials has become increasingly popular. This is because the composition and chemical variations of materials such as solids and liquids can adopt electrical characteristic responses as substituting performance parameters.

A material evaluation measurement system is comprised of three main pieces. These elements include precise measurement instruments, test fixtures that hold the material under test, and software that can calculate and display basic material parameters, such as permittivity and permeability. Various measurement methods for permittivity and permeability currently exist (see Table 1). However, this note’s primary focus will be on methods that employ impedance measurement technology, which have the following advantages: 

• Wide frequency range from 20 Hz to 1 GHz
• High measurement accuracy
• Simple preparations (fabrication of material, measurement setup) for measurement 

This note begins by describing measurement methods, systems, and solutions for permittivity in Section 2, followed by permeability in Section 3. The resistivity measurement system and the permittivity measurement system for liquids are described later in the appendix.

Table of Contents:

• Permittivity Evaluation
  • Definition of permittivity
  • Parallel plate measurement method of measuring permitivity
  • Permittivity measurement system
  • Measurement system using the 16451B dielectric test fixture
  • Measurement system using the 16453A dielectric material test fixture
• Permeability Evaluation
  • Definition of permeability
  • Inductance measurement method
  • Permeability measurement system
  • Measurement system using 16454A magnetic material test fixture
• Conclusion
  

Permittivity Evaluation

Definition of permittivity 

Permittivity describes the interaction of a material with an electric field. The principal equations are shown in Figure 1. Dielectric constant (κ) is equivalent to the complex relative permittivity (εr*) or the complex permittivity (ε*) relative to the permittivity of free space (ε0). The real part of the complex relative permittivity (εr´) is a measure of how much energy from an external field is stored in a material; εr´ > 1 for most solids and liquids.

The imaginary part of the complex relative permittivity (εr´´) is called the loss factor and is a measure of how dissipative or lossy a material is to an external field. εr´´ is always> 0 and is usually much smaller than εr´. The loss factor includes the effects of both dielectric loss and conductivity.

When complex permittivity is drawn as a simple vector diagram as shown in Figure 1, the real and imaginary components are 90° out of phase. The vector sum forms an angle δ with the real axis (εr´). The tangent of this angle, tan δ or loss tangent, is usually used to express the relative “lossiness” of a material. The term “dielectric constant” is often called “permittivity” in technical literature. In this application note, the term permittivity will be used to refer to dielectric constant and complex relative permittivity.