*This post authored by John Coonrod originally appeared on the ROG Blog hosted by Microwave Journal*.

**Dielectric constant **is an important number for specifiers of printed-circuit-board (PCB) materials. As detailed in the **previous blog**, it is often the first number that a circuit designer sees when sorting through PCB materials, and it is a number that designers count on across a wide range of operating frequencies. But what about circuits that must provide reliable performance at lower frequencies, for example in very-high-frequency (VHF) and ultra-high-frequency (UHF) ranges? Does the dielectric constant or Dk of a PCB material behave the same way at lower frequencies as at microwave frequencies?

As mentioned previously, **most PCB materials are anisotropic**, and the Dk of a PCB material can easily be three different values for the three different axes of the material. The Dk value of some PCB materials can also be nonlinear with frequency, with different Dk values at lower frequencies versus higher frequencies. Rogers has characterized its PCB materials extensively through measurements, and developed a set of **Design Dk** values that are average Dk values proven effective when used in design and with software design tools. These Design Dk values can typically be applied over a wide range of frequencies, although they tend to have somewhat different values at lower frequencies than at higher, microwave frequencies. In fact, a curve developed for Design Dk versus frequency (see Figure 1) tends to be linear across most of the frequency range covered, with some nonlinear traits at lower microwave frequencies.

*Figure 1. Plot of a Dk / Df vs. Frequency curve for a generic material. Using a generic material, this plot shows the change in dielectric constant for a PCB material from its lowest frequencies to its highest frequencies, with the effects of the material’s dipole moments.*

Of course, a number of different measurement methods are used to determine the Dk of a PCB material, and those Dk values can differ from lower to higher frequencies, depending upon the test method applied. In reality, the “dielectric constant” for a PCB material is not a constant value but exhibits some nonlinear characteristics. The nonlinear trend of Dk versus frequency at lower frequencies is different for every material, so it is not possible to generalize any type of Dk behavior at lower frequencies, or with different types of copper, or different material thicknesses.

When a dielectric material, such as a PCB material, is exposed to an electric field, the material’s molecules are polarized, creating electric dipole moments and increasing the total electric flux, D, of the material. The equation for D in terms of the electric field intensity, E, is simply:

D = εE

where ε is not necessarily the dielectric constant but represents the complex permittivity of the material. The parameter ε_{r} , of course, is well known as the relative permittivity or dielectric constant. This simple equality for D has other components, such as a polarization vector, associated with the material, as well as a property known as electric susceptibility. Electric susceptibility is a complex variable related to the dielectric material’s storage and dissipative characteristics relative to E. It is a multiplier for the polarization vector, which describes how the dipole moments react to the electric field in regards to the different axes of the dielectric material. A dielectric material known to be anisotropic has a polarization vector with different values for the different axes of the material.

Complex permittivity, ε, is related to the electric susceptibility and has real and imaginary components. The real component is related to the material’s dielectric constant, ε_{r}, while the imaginary component is related to the material’s loss tangent, tanδ, or dissipation factor, Df. In a way, the real component can be thought of as impacting the energy storage capability of the material while the imaginary component is related to the material’s dissipative characteristics.

Most microwave PCB materials are formulated for low dispersion and for minimal change in Dk with frequency. But, as noted, Dk is not really a constant and it will change with frequency. The reason for this is the dipole moments within the material, set up within the molecular structure of the dielectric material and reacting to the presence of an applied electric field. As the electric fields increase and decrease as a function of frequency, the material’s dipole moments will be established and will then relax. At higher frequencies, the electric fields increase and decrease at faster rates, and the time required for the dipole moments to relax becomes significant and the supplemental electric flux due to the dipole moments goes through an adjustment period.

At DC and lower frequencies, the dipole relaxation time has no effect on augmenting the electric field for the dielectric material. At higher, microwave frequencies, however, the effect can be significant. As the simple plot of Dk with frequency for a generic dielectric PCB material shows, the material’s dielectric “constant” will change with frequency and with some of the related, affecting phenomena. The plot shows how dielectric constant can change with frequency, considerably more at higher, microwave and millimeter-wave frequencies than for frequencies in the very-high-frequency (VHF) range from 30 to 300 MHz and the ultra-high-frequency (UHF) range from 300 MHz to 3 GHz.

The simple plot is a curve regarding a generic material. Its Dk is changing more at microwave and millimeter-wave frequencies than at other lower frequencies and can, in fact, be somewhat nonlinear over some of these higher-frequency regions. This is a valid trend for most materials, but materials which are formulated for high-frequency applications have more stable Dk versus frequency trends in the microwave and millimeter-wave frequency regions. The values of Dk presented on PCB material data sheets are frequency-dependent, and the values of Dk and Df for a PCB material can often vary quite widely when the same material is characterized at different test frequencies. It is also important to understand that many microwave PCB materials have E fields that primarily use the z-axis of the material, but some applications may call more for the x-y dimensions of the PCB material. A PCB material’s Dk values are determined not only at different frequencies but with different test methods, some better at lower frequencies and some better at higher frequencies. All of these factors can play a hand in the Dk value appearing on a data sheet for a given dielectric material. Rogers Corporation has performed extensive evaluations of their dielectric PCB materials and has developed curves of Dk with frequency for most of its materials, available free upon request.

The next blog will examine another critical PCB material parameter, the dissipation factor, Df, and how it can be interpreted by high-frequency circuit designers when sorting through their next batch of candidate circuit-board materials.

Do you have a design or fabrication question? John Coonrod and Joe Davis are available to help. Log in to the Rogers Technology Support Hub and “**Ask an Engineer**” today.

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