Meaning
Empirical correction formulas estimate the rise in microstrip line attenuation that occurs when the conductor surfaces are not perfectly smooth. The hammerstad bekkadal model uses the root-mean-square roughness value to scale the theoretical smooth-wall attenuation coefficient of a transmission line. This multiplier represents the increase in effective resistance caused by the longer path that current must travel over a rough surface.
The correction works best when the roughness is smaller than the skin depth of the signal. In plated plastics, the resulting attenuation can dictate the success of the polymer component.
Roughness Correction
High frequency signals concentrate in a thin skin on the conductor surface. If the hammerstad bekkadal model is applied to high-frequency designs, it scales the loss predictions according to the ratio of surface roughness to skin depth. The mathematical form of the model incorporates an exponential function that rises to a maximum factor of two.
Tooling Effect
Thermoplastic substrates molded in rough tooling produce plated parts with high attenuation factors. Moulders use the hammerstad bekkadal model to determine if the molded part requires a higher polish on the tool steel or if the current finish is acceptable. This ensures that tool wear is caught before part attenuation exceeds specified limits.
Limit Condition
The model underestimates signal attenuation when the operating frequency rises above twenty gigahertz and the surface roughness exceeds the skin depth. At these extreme frequencies, the current profile cannot follow the rough contours, and the assumptions of the formula break down. Designers then turn to more advanced models that account for the three-dimensional geometry of the roughness.
