HammerstadRoughness

class pmrf.materials.HammerstadRoughness(rms: Any = 0.0, *, name: str | None = None, metadata: Any = None)

Bases: AbstractRoughness

Hammerstad-Jensen surface-roughness correction.

Mathematical Formulation

\[K(\omega) = 1 + \frac{2}{\pi}\arctan\left(1.4\left(\frac{\Delta}{\delta}\right)^2\right)\]

where \(\Delta\) is the RMS surface roughness and \(\delta\) the skin depth. The factor saturates at \(2\), which is the well-known limitation of the model.

Validity

A Roughness is a correction to conductor behaviour, not a line formulation: it scales a smooth surface impedance and produces no state of its own. The skin depth is derived here from frequency, conductivity and permeability rather than being part of the conductor interface, so the correction is meaningful only for a conductor whose loss is genuinely skin-effect limited – RoughConductor therefore extends BulkConductor rather than the abstract conductor, and a non-bulk conductor cannot silently acquire one. The arctangent fit is empirical and saturates at \(2\): it understates loss once \(\Delta/\delta\) exceeds roughly unity, which is the documented limitation of the Hammerstad-Jensen form rather than a rejected input.

References

Hammerstad, E., & Jensen, O. (1980). Accurate Models for Microstrip Computer-Aided Design. IEEE MTT-S International Microwave Symposium Digest, 407-409.

Parameters:

rms (Param, default=0.0) – RMS surface roughness in meters.

factor(freq: Frequency, sigma, mu_r) → Array

Return the multiplier applied to a smooth surface impedance.

rms: Param = 0.0

RMS surface roughness in meters