CoaxialLine

class pmrf.models.components.lines.uniform.CoaxialLine(length: Any, din: Any = 0.00112, dout: Any = 0.0032, epr: Any = 1.0, mur: Any = 1.0, tand: Any = 0.0, rho: Any = 1.68e-08, *, name: str | None = None, metadata: Any = None)

Bases: RLGCLine

Coaxial line defined directly by its physical geometry and material properties.

Mathematical Formulation

Ideal non-dispersive components (\(L'\) and \(C'\)) and dielectric loss (\(G\)) are given by:

\[L' = \frac{\mu_0 \mu_r}{2\pi} \ln\left(\frac{b}{a}\right)\]

\[C' = \frac{2\pi \varepsilon_0 \varepsilon_r}{\ln(b/a)}\]

\[G_{diel} = \frac{2\pi \omega \varepsilon_0 \varepsilon_r \tan\delta}{\ln(b/a)}\]

The internal surface impedance defining frequency-dependent skin resistance (\(R_{skin}\)) and skin inductance (\(L_{skin}\)) is governed by:

\[R_{skin} = \frac{1}{2\pi a} \sqrt{\frac{\omega\mu}{2\sigma_a}} + \frac{1}{2\pi b} \sqrt{\frac{\omega\mu}{2\sigma_b}}\]

\[L_{skin} = \frac{1}{2\pi a} \sqrt{\frac{\mu}{2\omega\sigma_a}} + \frac{1}{2\pi b} \sqrt{\frac{\mu}{2\omega\sigma_b}}\]

Where \(a\) is the inner radius, \(b\) is the outer radius, and \(\sigma\) is the conductor conductivity (\(1/\rho\)). The total per-unit-length inductance is \(L = L' + L_{skin}\).

Example

import pmrf as prf
from pmrf.models import CoaxialLine

phys_cable = CoaxialLine(
    din=0.9e-3,
    dout=2.95e-3,
    epr=1.5,
    tand=0.0004,
    rho=1.72e-8,
    length=0.5
)

freq = prf.Frequency(start=1, stop=20, npoints=101, unit='ghz')
s_phys = phys_cable.s(freq)

Parameters:

din (Param, default=1.12e-3) – Inner conductor diameter in meters.
dout (Param, default=3.2e-3) – Outer conductor inner diameter in meters.
epr (Param, default=1.0) – Relative permittivity of the dielectric.
mur (Param, default=1.0) – Relative permeability.
tand (Param, default=0.0) – Loss tangent of the dielectric.
rho (Param, default=1.68e-8) – Resistivity of the conductors in Ohm-meters.

C_prime(freq: Frequency) → Array

G_diel(freq: Frequency) → Array

L_prime(freq: Frequency) → Array

L_skin(freq: Frequency) → Array

R_skin(freq: Frequency) → Array

Z_skin(freq: Frequency)

rlgc(freq: Frequency) → tuple[Array, Array, Array, Array]

Calculates the frequency-dependent RLGC parameters.

Parameters:: freq (Frequency) – The frequency axis.
Returns:: The R, L, G, and C parameter vectors.
Return type:: tuple

din: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 0.00112: Inner conductor diameter

dout: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 0.0032: Outer conductor inner diameter

epr: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 1.0: Relative permittivity

property eps: Array

property mu: Array

mur: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 1.0: Relative permeability

rho: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 1.68e-08: Resistivity of the conductors

tand: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 0.0: Loss tangent