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In the late 1970s, when one of the authors (Rautio) first got started in microwaves, one of his first tasks was to design filters on alumina for Landsat IV. The design was carefully performed using the commonly assumed substrate dielectric constant of 9.8. Even so, several design iterations were required. “Get used to it,” he was told. “Multiple design iterations are a fact of microwave design life.” Or so it was thought.

Fast forward to 2007. EM analysis is a mainstream design tool. Dielectric Laboratories (Casenovia, NY) is having good success with rapid fire design of filters using commercial, 3D planar EM analysis. Success on first fabrication is now normal, except for certain cases. The troublesome cases use a nearly exactly zero temperature coefficient ceramic, and that ceramic is anisotropic. Figure 1 illustrates the problem. For this filter, pretending that the substrate dielectric constant is isotropic means a re-design is required. With anisotropy included, the filter is ready for production.¹

Anisotropy means that the dielectric constant depends on the direction of the electric field. The obvious work-around for not being able to analyze anisotropy using EM is to assume a constant dielectric constant in all directions (isotropy) and to use an average dielectric constant. A percentage of a transmission line’s electric field is parallel to the substrate surface and the rest is perpendicular to the substrate surface. Therefore, a weighted average of the horizontal and vertical dielectric constants is used, and the average is weighted according to the percentage of horizontal and vertical electric fields.

This works well as long as only single transmission lines are used, all with the same width. If the width is changed, the percentage of horizontal and vertical electric field has to be changed as well. A different weighted average is needed. If the difference is not so large, maybe just one isotropic dielectric constant can be used and one can still get the designs to work.