MultipoleDebyeDielectric

class pmrf.materials.MultipoleDebyeDielectric(ep_inf: Any = 1.0, poles: Any = (), sigma: Any = 0.0, *, name: str | None = None, metadata: Any = None)

Bases: AbstractDielectric

N-pole Debye dielectric, with every coefficient fittable.

Mathematical Formulation

\[\varepsilon_r(f) = \varepsilon_\infty + \sum_{n} \frac{\Delta\varepsilon_{r,n}}{1 + jf/f_{r,n}} - j\frac{\sigma}{\omega\varepsilon_0}\]

Example

from pmrf.materials import MultipoleDebyeDielectric

material = MultipoleDebyeDielectric(ep_inf=2.0, poles=[(1.0, 1e9), (0.5, 1e10)])

References

Debye, P. (1929). Polar Molecules. Chemical Catalog Company.

Parameters:

• ep_inf (Param, default=1.0) – High-frequency limit of the relative permittivity.

• poles (tuple of DebyePole, default=()) – The Debye poles. (dep_r, f_relax) pairs are coerced automatically.

• sigma (Param, default=0.0) – Static bulk conductivity in S/m.

properties(freq: Frequency) → DielectricProperties

Evaluate the dielectric properties over a frequency axis.

Parameters:

freq (Frequency) – The frequency axis to evaluate over.

Returns:

Complex permittivity, permeability, and static conductivity.

Return type:

jnp.ndarray

ep_inf: Param = 1.0

High-frequency limit of the relative permittivity

poles: tuple[DebyePole, ...] = ()

The Debye poles

sigma: Param = 0.0

Static bulk conductivity in S/m