Just How Constant Is the Dielectric Constant of PCB Materials?

One of the crucial material factors that we address in our classes is the dielectric constant or relative dielectric constant, e_r. This is sometimes called Dk by laminate suppliers. Sometimes, product developers are not clear as to the role the dielectric constant of PCB materials plays in a design, how to measure it, how to account for it, how it varies with frequency, and how to know if the dielectric constant data provided by the laminate manufacturer is accurate and reliable. This article will address the foregoing topics and describe why the dielectric constant of PCB materials will play a significant role in determining the overall success of a given design.

Overview: Dielectric Constant of PCB Materials

The dielectric constant of a vacuum is, by definition, 1. The dielectric constants of laminate materials, other than a vacuum, are compared to a vacuum. This comparison results in a relative dielectric constant, e_r, that expresses the effects of these materials on the capacitance of a structure such as a parallel plate capacitor as compared to a vacuum. Dielectrics also slow down electromagnetic fields traveling through them. Salient points to keep in mind include:

• The dielectric constant of a vacuum is 1. All laminate materials have dielectric constants higher than 1.
• The common method for measuring e_r is the parallel plate method at 1 MHz. As shown below, for transmission line design, a more useful method is to calculate the e_r by determining the signal velocity in the dielectric.
• The dielectric constant varies with frequency in all PCB materials.
• The dielectric constant in a laminate is a function of the glass-to-resin ratio. If there is more resin, the e_r goes down. If there is less resin, the e_r goes up. That’s why it’s important to know the glass-to-resin ratio as that will help determine the e_r
• The terms Dk and e_r are used interchangeably and they mean the same thing.
• The dielectric constant is really a complex number, and there is an imaginary part that is sometimes called the dissipation factor, or Df. Dk and Df together determine the loss tangent. For now, we'll focus only on Dk as it is normally a starting point for most designs.

Calculating the er

Equation 1 is the equation used for determining the e_r of a given material. You can use the velocity of a test signal and the speed of light in vacuum to calculate e_r:

Here, V is the velocity at a given frequency, e_r is the relative dielectric constant and C is the speed of light. Note that the square root of this quantity is the refractive index of the material (again, we've ignored Df here for simplicity), which most are probably familiar with from physics classes.

To solve this equation, you take a transmission line of some known mechanical length and put a sine wave down it. Then, you measure how long it takes the sine wave to get to the other end. A simple way is to calculate the velocity from a time domain reflectometry (TDR) trace. You can easily calculate the velocity of a signal being sent down a trace on a test coupon that is open or shorted at the far end. Once you calculate the velocity from TDR data, you can then calculate the e_r.

Table 1 shows dielectric constants of PCB materials and their corresponding wave velocities.

Notice the qualifier at the bottom of this figure states that the dielectric constant is a function of the glass-to-resin ratio and the signal frequency. The measurements in this slide were made with a resin constant of 55% at 2 GHz (more about this below).

Figure 1 shows the e_r versus frequency of various laminates.

These are the classic four types of materials along with that somewhat confusing catchall thing called FR-4.  This chart shows that the dielectric constant goes down as the frequency goes up (note that this plot only extends up to 6 GHz). It should be noted that the thin lines represent a resin content of 42% (this is how all cheap materials are made). It’s from this measurement that the standard value e_r = 4.7 was determined because, at 1 MHz, the e_r is approximately 4.9. In reality, no real material has this dielectric constant.

As can be seen, with a 55% resin content, the e_r goes down. As noted below, 55% is no longer what
would be designated as a high resin content. As can be seen in Figure 2 the dielectric constant versus frequency curve goes down with frequency and it flattens out at about 2 GHz.

A note of caution: If you use the e_r value at 1 MHz to calculate impedance, but your product will be operating at 2 GHz, you are starting out your design process with an error and that error will be propagated throughout the entire design process. It used to be a challenge to decide which frequency should be used for a particular design but the speed of modern edges is so fast now (2 GHz and higher) that this is no longer a factor of concern.

If a product developer uses the e_r calculations from a PCB fabrication facility, it’s important to know what frequency that fabricator is using for their stated dielectric constants. If that facility is not using 2 GHz and higher it’s wise not to have any confidence in their numbers. In order to ensure that a design will operate as specified, it’s mandatory that the fabricator provides specific frequency information along with the specific resin content for the cited laminates.

What Laminate Manufacturers Provide

All laminate manufacturers publish the  e_r for  laminate materials they produce. Figure 3 provides an example of the types of information, including e_r data, for a variety of materials offered.

Figure 3 represents the typical laminate table that an engineer needs to have in order to create a good, workable stackup that results in an accurate impedance for a PCB under development. The information contained in this figure contains reliable data and it demonstrates how the e_r varies with frequency. Note that the Dk value is only provided at 3 different frequencies in this case. Also note that the e_r varies with laminate thickness because different thickness laminates have different glass-to-resin ratios.

It’s important to note that there is no value under 100 MHz in this table. Good laminate manufacturers know that data under that number is of no value. In fact, if the laminate manufacturer cites data that they designate as 1 MHz, it’s a good idea not to trust that information and it’s time to find a more reliable laminate supplier.

Another important point is that laminate manufacturers do not use a TDR trace to calculate the dielectric constant of PCB materials. You can certainly do this your self with a test coupon at a few frequencies, but this is not ideal. More sophisticated methods that are specified in IPC standards, and the value reported for the laminate's e_r value depends on the measurement method. Take a look at this podcast with Jon Coonrod to learn more about the Dk and Df values quoted in laminate datasheets.

Summary

Understanding the elements that factor into the dielectric constant of PCB materials is key to ensuring the correct laminate is selected for the product being designed. The data provided by laminate suppliers is a good place to start and it can be trusted as long as the frequency and resin content are correct.

When you need to calculate the effect of e_r on transmission line impedance in your next PCB, you can use Altium Designer and the integrated field solver from Simberian. This integrated field solver uses standard models to determine e_r and impedance in your layer stackup, and it helps you perfectly size your transmission lines to have required impedance.

Would you like to find out more about how Altium can help you with your next PCB design? Talk to an expert at Altium or discover more about materials science.

References

• Ritchey, Lee W., and Zasio, John J., “Right The First Time, A Practical Handbook on High Speed PCB and System Design,” Volume 1.
• Ritchey, Lee W., Course Slides, “2-Day Signal Integrity and High Speed System Design,” training class.