TescheRodSurfaceImpedance

class pmrf.materials.TescheRodSurfaceImpedance

Bases: AbstractSurfaceImpedance

Solid round conductor, via Tesche’s equivalent circuit.

Mathematical Formulation

Tesche’s circuit combines the dc resistance and internal inductance,

\[R_{dc} = \frac{1}{\pi a^2\sigma},\qquad L_{int} = \frac{\mu}{8\pi},\]
as \(Z = R_{dc} + \zeta_c/2\pi a\big/[1 + (\zeta_c/2\pi a)/(j\omega L_{int})]\). The equivalent surface impedance \(2\pi aZ\) is
\[Z_s = R_{dc,sq} + \frac{\zeta_c}{1+\zeta_c/(j\omega L_{int,sq})}, \qquad R_{dc,sq}=\frac{2}{a\sigma},\quad L_{int,sq}=\frac{\mu a}{4}.\]

Validity

This is an interpolation, not an exact finite-frequency solution. Its strong-skin limit is \(\zeta_c+R_{dc,sq}\) and omits the \(1/(2\gamma a)\) curvature term in the exact SchelkunoffRodSurfaceImpedance expansion. Prefer the exact formulation unless Bessel evaluation cost is prohibitive.

References

Tesche, F. M. (2007). A Simple Model for the Line Parameters of a Lossy Coaxial Cable Filled With a Nondispersive Dielectric. IEEE Transactions on Electromagnetic Compatibility, 49(1), 12-17.

impedance(omega, conductor: ConductorProperties, *, a, **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