Understanding the true meaning of dielectric constant
August 9, 2010
John Coonrod is a Market Development Engineer for Rogers Corporation, Advanced Circuit Materials Division. John has 23 years of experience in the Printed Circuit Board industry. About half of this time was spent in the Flexible Printed Circuit Board industry doing circuit design, applications, processing and materials engineering. The past ten years have been spent supporting circuit fabrication, providing application support and conducting electrical characterization studies of High Frequency Rigid Printed Circuit Board materials made by Rogers. John has a Bachelor of Science, Electrical Engineering degree from Arizona State University.
Understanding the true meaning of dielectric constant
Dielectric constant (Dk or relative permittivity) is a parameter that design engineers use constantly, often without fully understanding it. Every material has a dielectric constant, even air (slightly more than unity). And the parameter is commonly used by circuit designers to compare different printed-circuit-board (PCB) materials, typically by referring to a fixed value for a given frequency, found on a product data sheet. However, the number can vary for most PCB materials, regardless of material quality. Variations in the Dk value actually have less to do with quality and more to do with how the material is used and tested.
Commercial PCB materials are typically characterized by Dk values in their x, y, and z directions at one or more reference (test) frequencies. Some microwave designs generate electric fields more across the x-y plane (length and width) than use the z-axis (thickness). For example, edge-coupled circuit designs have electric fields that use a PCB laminate’s x-y plane, whereas a transmission line mostly uses the z-axis plane. Since few PCB materials are isotropic, most have Dk values that are different for each axis. A microstrip edge-coupled design and a transmission line both fabricated on the same laminate can exhibit different apparent Dk characteristics, due to the anisotropic effects of the PCB material and the circuit is designed.
Designing circuits with specific PCB materials assumes that Dk values are accurately known, and this depends on proper measurement practices by each material supplier. But characterizing the Dk of a high-frequency laminate material is not trivial; in fact, more than 20 different measurement approaches are used to evaluate a material’s Dk. Most materials suppliers use a measurement approach accepted as an industry standard, and that also supports high-volume testing to minimize measurement time and cost.
High-frequency laminate suppliers typically use test methods defined by the International Printed Circuit (IPC) organization (www.ipc.org), the large electronic interconnect industry association. One of these test methods is based on a loosely coupled balanced homogeneous stripline resonator at 10 GHz, resulting in many data sheets with Dk values at 10 GHz. For designs that resemble this test circuit and operating frequency, the Dk value determined by this test method should provide accurate results when used for modeling purposes, such as in computer design software. But for designs at different frequencies, or with different circuit structures, the Dk values determined by a different test method, such as the stripline method, may provide more accurate simulation results when used in a design program.
Even when a circuit design is similar to the test structure and method used to characterize a material’s Dk, other differences in the test procedure may not agree closely with the way the circuit is designed and fabricated. For this reason, materials suppliers often provide a suggested Dk value for modeling purposes that may be different than the material’s nominal Dk value. It is also why materials suppliers stress the need to fully evaluate a material for a given application, even to the extent of building multiple prototype circuits with slightly different geometries to better understand the electromagnetic (EM) field interactions with the material and the designed circuit structures.
Several basic material properties can cause variations in a PCB laminate’s nominal Dk value. For example, values appearing on a product data sheet are based on a specific material thickness and copper type. However, materials suppliers typically offer many different dielectric and copper laminate thicknesses for a given product, and the dielectric constant can vary with the thickness of the dielectric and the thickness of the copper. In fact, even the surface roughness of the copper can have an impact on the Dk value. In a paper recently published by Dr. Al Horn of Rogers Corporation, the roughness of the copper on a PCB laminate was found to play a significant role in the apparent Dk of the material. Dr. Horn’s research found that the copper roughness can alter the propagation constant and affect the apparent permittivity of the laminate. The effects of copper surface roughness are less pronounced for thicker laminates, more so for thinner laminates.
When a dielectric material is subjected to an electric field, the field causes polarization of atoms and molecules within the material to create electric dipole moments. These moments supplement the electric flux and are related to the material’s electrical susceptibility. For a truly uniform medium, such as a vacuum, the dielectric constant is consistent and well understood. But most PCB materials are composites of different materials, each with its own Dk value. Each of these materials can have dissimilar electrical susceptibilities and even differing polarization potentials when subjected to an electric field. Because of the difficulty of truly understanding the Dk behavior of a PCM material, the Dk values presented on its data sheet should be considered approximate values and used as guidelines rather than strict rules when creating a high-frequency circuit design.