TescheCoaxialFormulation

class pmrf.models.components.lines.coaxial.TescheCoaxialFormulation(inner_impedance: AbstractSurfaceImpedance = TescheRodSurfaceImpedance(), shield_impedance: AbstractSurfaceImpedance = TescheTubeSurfaceImpedance())

Bases: AbstractCoaxialFormulation

Coaxial line formulation using Tesche’s equivalent-circuit approximation.

Mathematical Formulation

The external per-unit-length inductance and the shunt admittance follow from the coaxial geometry and the complex permittivity \(\varepsilon = \varepsilon_0 \varepsilon_r\):

\[L' = \frac{\mu_0 \mu_r}{2\pi} \ln\left(\frac{b}{a}\right) \qquad Y = \frac{j\omega 2\pi\varepsilon}{\ln(b/a)}\]

Each conductor contributes \(Z_s/(2\pi r)\). The defaults are TescheRodSurfaceImpedance and TescheTubeSurfaceImpedance. An unspecified shield thickness uses the infinite-wall limit. Complex \(\varepsilon_r\) and \(\mu_r\) account for dielectric and magnetic loss.

Validity

The conductor circuit interpolates between dc resistance and half-space impedance but omits the exact \(1/(2\gamma a)\) curvature term. Use SchelkunoffCoaxialFormulation for the exact cylindrical solution. The TEM line model applies below the TE11 cutoff \(f_c \approx c / \left[\pi (a + b) \sqrt{\varepsilon_r \mu_r}\right]\).

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.

Schelkunoff, S. A. (1934). The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields. Bell System Technical Journal, 13(4), 532-579.

immittance(freq: Frequency, *, d_in, d_out, dielectric: DielectricProperties, conductor: ConductorProperties, outer_conductor=None, shield_thickness=None) → ImmittanceResult

Calculate the per-unit-length immittance.

Parameters:

  • freq (Frequency) – The frequency axis.

  • d_in (ArrayLike) – Inner conductor diameter in meters.

  • d_out (ArrayLike) – Outer conductor inner diameter in meters.

  • dielectric (DielectricProperties) – Evaluated relative permittivity and permeability.

  • conductor (ConductorProperties) – Evaluated inner-conductor properties.

  • outer_conductor (ConductorProperties | None, default=None) – Evaluated shield properties, or None to reuse conductor.

  • shield_thickness (ArrayLike | None, default=None) – Shield wall thickness, or None for an infinitely thick shield.

Returns:

The series impedance and shunt admittance.

Return type:

ImmittanceResult

inner_impedance: AbstractSurfaceImpedance = TescheRodSurfaceImpedance()

Surface-impedance formulation for the inner conductor

shield_impedance: AbstractSurfaceImpedance = TescheTubeSurfaceImpedance()

Surface-impedance formulation for the shield, called with the shield’s inner radius and its wall thickness, infinite when none is given