Air Gap Corrections in Clamped Stripline in Plane Permittivity Extraction
Air gap corrections eliminate systematic two to six percent dielectric underestimation in clamped stripline tests, preventing finished board impedance failures.
Wheeler Transform
Geometric Mapping
Mathematical mapping of the physical dimensions of a transmission line to its electrical characteristics allows for the calculation of characteristic impedance. The wheeler transform is used to analyze the relationship between the width of a trace, the thickness of the dielectric and the resulting capacitance. This method provides a way to simplify complex electromagnetic field problems into manageable equations.
Designers use these formulas to create initial layouts before moving to more intensive simulation tools.
Calculation Method
Incremental changes in the trace geometry are related to the change in the impedance through a set of analytical functions. Applying the wheeler transform helps to predict how manufacturing tolerances, such as etching variations, will affect the final performance of the board. These equations are particularly effective for microstrip and stripline configurations on standard substrates.
The accuracy of the method is well established for most common circuit board materials and thicknesses.
Implementation Range
Limitations of the mathematical model occur when the trace width becomes very small or the frequency becomes very high. In these cases, the wheeler transform may be supplemented with full wave electromagnetic solvers to account for higher order effects. Engineers use the transform as a fast way to explore different design options during the early stages of a project.
Final verification of the impedance is always performed with physical measurements on the finished production panels.