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54 DESIGN007 MAGAZINE I APRIL 2020 The Dk of any dielectric material is fre- quency-dependent. In other words, when test- ing the same piece of material and using the same test method, it should be expected to get slightly different Dk values when testing at dif- ferent frequencies. There is a range of frequen- cies where the Dk changes more with a change in frequency, and that is typically from a few megahertz up to about 5 GHz to 10 GHz. Af- ter about 10 GHz, and out to about 250 GHz, the Dk frequency curve will have a slight neg- ative slope for most low loss circuit materials. Considering this range of frequencies, and de- pending on the degree of polarity of the circuit material, the slight decrease in Dk with an in- crease of frequency is usually in the range of 2% or less. For more accurate circuit model- ing, it is important to use material data that was produced at the same frequency as the cir- cuit being modeled. Another issue, which is typically a little more problematic for Dk values used in circuit sim- ulation, is anisotropy. Most circuit materials are anisotropic, which means the Dk is not the same on the three axes of the material. It is pret- ty common for most circuit materials to have a Z-axis (thickness axis) Dk, which is different from the x-y plane of the material. The X-axis and Y-axis are typically similar for Dk values, but the Z-axis is often quite different. Also, for the testing to determine the Dk of a material, there are common test methods that evaluate the Z-axis of the material only and other test methods that evaluate the X-Y plane only. If a designer uses the Dk information in their model, which was produced by testing the X-Y plane (instead of the Z-axis), it may or may not be appropriate for their particular model. It is good for the designer to be aware of what type of test method was used to determine the Dk, as well as the frequency at which the Dk value was obtained. In the case of most high-frequency circuit materials, which have a Dk around 4 or less, the anisotropy is typically not that significant. In most of these cases, the difference between the Z-axis and the X-Y plane Dk values is 3% or less. However, for non-filled, glass-rein- forced circuit materials, these Dk differences can be much higher. In the case of higher Dk materials, such as materials with Dk values in the range of 6 or higher, there can be much larger differences in the Dk values of the Z-axis when compared to the X-Y plane values. For these materials, it is not uncommon to see Dk differences due to anisotropy of 5–15%, depending on the mate- rial. There are some exceptions, where some high Dk materials are formulated to have mini- mal anisotropy; however, the designer should consider anisotropy when using materials with higher Dk values. Lastly, the designer should use Dk values from a test method that is most similar to their circuit design and at the same frequency as their application. Since there are a limited num- ber of test methods and a very diverse number of circuit applications, it can be difficult for the designer to find a good match between the test method and their model. Regardless, the de- signer should investigate and try to use a Dk value that was generated in a manner that is as close to their model as possible. Further, engage with the material supplier to see if they have other Dk information that may be more appro- priate for their design. DESIGN007 John Coonrod is technical marketing manager at Rogers Corporation. To read past columns or contact Coonrod, click here. For more accurate circuit modeling, it is important to use material data that was produced at the same frequency as the circuit being modeled.

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