PhysicalLine

class pmrf.models.components.lines.uniform.PhysicalLine(length: Any, zn: Any = 50.0, epr: Any = 1.0, A: Any = 0.0, fA: Any = 1.0, tand: Any = 0.0, *, name: str | None = None, metadata: Any = None)

Bases: RLGCLine

Transmission line defined by nominal characteristic impedance, relative permittivity, conductor attenuation, and dielectric loss tangent.

Mathematical Formulation

The frequency-dependent attenuation components are computed as:

\[\alpha_c = A \cdot \sqrt{\frac{f}{fA}} \cdot \frac{\ln(10)}{20}\]

\[\alpha_d = \frac{\pi f \sqrt{\varepsilon_r}}{c} \cdot \tan\delta\]

Which yield the per-unit-length parameters:

\[R = 2 z_n \alpha_c\]

\[L = \frac{z_n \sqrt{\varepsilon_r}}{c}\]

\[G = \frac{2 \alpha_d}{z_n}\]

\[C = \frac{\sqrt{\varepsilon_r}}{z_n c}\]

Example

import pmrf as prf
from pmrf.models import PhysicalLine

line = PhysicalLine(
    zn=50.0,
    length=1.0,
    epr=2.2,
    A=0.01,
    fA=1.0,
    tand=0.001
)

freq = prf.Frequency(start=1, stop=10, npoints=101, unit='ghz')
s = line.s(freq)

Parameters:

zn (Param, default=50.0) – Nominal characteristic impedance defining the L/C ratio.
epr (Param, default=1.0) – Relative permittivity.
A (Param, default=0.0) – Conductor loss in dB/m/sqrt(Hz).
fA (Param, default=1.0) – Frequency scaling reference for attenuation in Hz.
tand (Param, default=0.0) – Dielectric loss tangent.

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

A: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 0.0: Conductor loss in dB/m/sqrt(Hz)

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

fA: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 1.0: Frequency scaling reference

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

zn: AbstractVariable | Inexact[jaxlib._jax.Array, '...'] = 50.0: Nominal characteristic impedance