Reconciling Static Field Solvers with High-Frequency TDR Reflection Curves
Reconciling static field solvers with TDR curves requires transforming 2D RLGC parameters into causal, broadband S-parameters with instrument rise-time filtering.
Huray Surface Roughness
Loss Approximation
A mathematical representation of the skin-effect loss on printed circuit board traces models the copper surface as a collection of stacked hemispherical nodules. Integrating the Huray surface roughness calculation allows high-frequency simulators to predict conductor attenuation across multi-gigahertz digital signals.
Physical Model
The model replaces traditional surface-profile parameters with physical dimensions based on copper foil manufacturing technology. Instead of using a single average roughness value, it utilizes the radius of the nodules, the number of nodules per unit area, and the thickness of the treatment layer. This physical approach reflects the actual microstructure of the electrodeposited copper foil, where treatment is applied to enhance adhesion to the resin.
As signal frequencies increase, current is forced closer to the bumpy copper surface, which increases the effective resistance and signal loss.
Calculation Limit
Accuracy in loss prediction is achieved by avoiding overestimation of attenuation in the ten to fifty gigahertz range, where simpler models often fail. Process engineers and designers rely on these predictions to choose the correct foil type, such as very low profile or ultra-low profile copper, for high-speed laminates. Incorrect modeling leads to over-designing the circuit or failing signal integrity tests during prototype evaluation.
By providing a closer match to measured laboratory data, the calculation improves the success rate of first-pass board designs.