The absolute accuracy of 2D field solvers: built product is no baseline for absolute accuracy.
And no, it is not true that 3D field solvers will be more accurate than 2D field solvers in stackup design. When interconnects are uniform transmission lines; i.e., uniform in cross-section, a 2D field solver can be more accurate, and much easier to use.
The absolute accuracy of the results of a field solver can be evaluated with three tests: comparison to exact analytic for mulae, comparison to measurements on well-characterized test vehicles, and comparison to measurements on real product.
The third test is used by most engineers to verify the accuracy of a 2D field solver. In fact, this only tests the variation in as-manufactured product. While it is important to know this, it is not a test of the absolute accuracy of the field solver.
The second test is important, as it is our final anchor to reality. Knowing the absolute accuracy of the dimensions of the test board, especially the dielectric constant of the insulator, is usually what limits the accuracy to which the field solver can be checked.
The first test allows a measure of the ultimate accuracy the tool is capable of achieving. There are only three fundamental transmission line structures with exact analytic expressions relating their geometry and material properties to characteristic impedance. These are for two round rods, a rod over an infinite plane and a coax.
What makes one field solver more accurate than another is typically the number and size of the mesh elements it uses to divide up the space around the conductors. In each small mesh element, Maxwell's equations are solved, assuming the electric and magnetic fields change linearly in the mesh element. The smaller the mesh elements, the more accurate the calculation, but the longer it will take to calculate.
The absolute accuracy of a 2D field solver can be evaluated by comparing the calculated characteristic impedance of two round rods to the results of the analytic equation. FIGURES 1a and 1b shows this comparison for the Ansoft 2D field solver. Also shown is the absolute error using the exact expression as the reference. The absolute error can be less than 0.5%. By adjusting the tool's features, this error can be even further reduced.
[FIGURE 1 OMITTED]
Not all field solvers allow calculation of round structures. Using the Ansoft tool as the reference, the predicted characteristic impedance for a microstrip structure calculated with two other popular field solvers can be evaluated. FIGURE 2 shows the absolute error of the field solver embedded in Mentor Graphics' HyperLynx and Polar Instruments' SI8000.
[FIGURE 2 OMITTED]
It is possible for simple, easy-to-use 2D field solvers to provide absolute errors less than 1%. At this level, the chief practical limit to the predicted accuracy of characteristic impedance is the accuracy of the dielectric constant of the laminate.
Additional online lectures and tutorials on 2D field solvers can be viewed from Bogatin's Web site, www.BogEnt.com.
Ed.: Many of the details on this and related topics can be found in Bogatin's new book, Signal Integrity--Simplified, (Prentice Hall).
ERIC BOGATIN is CTO of Synergetix. He is scheduled to speak at PCB Design Conference East in October. He can be reached at eric@BogEnt.com.
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|Title Annotation:||No Myths Allowed|
|Publication:||Printed Circuit Design & Manufacture|
|Date:||Jul 1, 2004|
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