HalfSpaceSurfaceImpedance

class pmrf.materials.HalfSpaceSurfaceImpedance

Bases: AbstractSurfaceImpedance

Leontovich half-space boundary.

Mathematical Formulation

\[Z_s = \zeta_c\]

Validity

Exact for a half-space. Approximates a curved surface when its radius of curvature is large relative to the skin depth.

References

Leontovich, M. A. (1948). Approximate boundary conditions for the electromagnetic field on the surface of a well-conducting medium, in Investigations of Radiowave Propagation, Part II, 5-12. Academy of Sciences, USSR.

impedance(omega, conductor: ConductorProperties, **geometry) → Array

Return the surface impedance of this cross-section, in ohm per square.

Parameters:

  • omega (ArrayLike) – Angular frequency in rad/s. w is reserved for strip width.

  • conductor (ConductorProperties) – Evaluated metal properties. conductor.zs is the surface prefactor, including any surface treatment, and conductor.gamma(omega) is the bulk diffusion constant. Treat them as independent: \(\gamma=\sigma\zeta_c\) holds only for a smooth bulk conductor.

  • **geometry – Cross-section-specific dimensions in metres. Implementations ignore dimensions they do not use.

  • weight (ArrayLike, optional) – Caller’s geometry weight in inverse metres. Only RootSumSquareSlabSurfaceImpedance uses it to express its dc limit in the caller’s normalisation.

Returns:

Surface impedance in ohm per square.

Return type:

jnp.ndarray