WheelerCurrentDistribution

class pmrf.models.components.lines.microstrip.WheelerCurrentDistribution(slab_impedance: AbstractSurfaceImpedance = <factory>)

Bases: AbstractCurrentDistribution[MicrostripCrossSection]

Wheeler’s incremental-inductance current distribution.

This implements Wheeler’s 1942 skin-effect rule. It is distinct from the 1977 quasi-static impedance approximation implemented by WheelerMicrostripFormulation.

Mathematical Formulation

\[k_c = \frac{2}{W}\exp\left[-1.2\left(\frac{\Re(Z_c)}{Z_0}\right)^{0.7}\right]\]

Here \(W\) is the physical trace width and \(Z_c\) is the solved characteristic impedance. An unspecified thickness uses HalfSpaceSurfaceImpedance; otherwise, the distribution uses slab_impedance. The returned weight is in inverse metres.

Validating against an external 3D solver

slab_impedance defaults to RootSumSquareSlabSurfaceImpedance, which corrects for finite strip thickness. 3D solvers commonly run with a skin-effect approximation that neglects thickness in the current distribution, applying a plain half-space

\[Z_s = (1+j)\sqrt{\pi f \mu_0 / \sigma}\]

instead; this has been confirmed on the exported surface impedance of at least one widely used commercial tool. It is not universal, and most solvers allow the approximation to be turned off, so check what the tool was actually run with. Where it is in force, over \(t/\delta\) = 3.7-6.0 the two models differ by 2-5%, so a cross-tool comparison that leaves the default in place charges the solver for a thickness correction it never applied and attributes the resulting 2-5% discrepancy to one tool or the other when it is purely a difference in surface-impedance model. Pass slab_impedance=HalfSpaceSurfaceImpedance() explicitly for such a comparison, and check where your band sits relative to that \(t/\delta\) range before deciding whether it matters.

This is not a defect in the default: RootSumSquareSlabSurfaceImpedance is the more defensible physics and remains the default. It is a trap only for cross-tool validation.

References

Wheeler, H. A. (1942). Formulas for the Skin Effect. Proceedings of the IRE, 30(9), 412-424.

cross_section_type

alias of MicrostripCrossSection

slab_impedance: AbstractSurfaceImpedance

Finite-thickness surface impedance. The default matches the dc and strong-skin limits under Wheeler’s geometry weight. Validating against an external half-space solver needs HalfSpaceSurfaceImpedance() passed here explicitly; see the class docstring. See AbstractSurfaceImpedance for normalisation details.