Impedance Calculation
Characteristic resistance of a conductor whose cross-section is narrower at the top than at the bottom accounts for the real-world effects of chemical etching on signal propagation. The trapezoidal trace impedance is a more accurate representation of high-speed signal behavior than the idealized rectangular model often used in basic design software. As signal frequencies increase, the specific shape of the conductor becomes more influential in determining the reflections and losses in the circuit.
Geometry Effect
Etching chemistry naturally removes more copper from the top of the trace where it is exposed to the solution for a longer period. This creates a slope on the sidewalls, which changes the total capacitance and inductance of the trace compared to a perfectly rectangular design. To achieve the target trapezoidal trace impedance, engineers must specify the etch factor and the expected top and bottom widths in their field solver tools.
Maintaining a consistent etch factor across the panel is essential for minimizing impedance variations in differential pairs.
Modeling Precision
Variations in the etching process can lead to fluctuations in the slope of the sidewalls, which causes the impedance to vary along the length of the conductor. Manufacturers use time-domain reflectometry to measure the actual trapezoidal trace impedance on test coupons included on the production panel. Aligning the measured results with the simulated model is a central part of the quality assurance process for high-speed digital boards.