ConstantDielectric

class pmrf.materials.ConstantDielectric(ep_r: Any = 1.0, tand: Any = 0.0, sigma: Any = 0.0, mu_r: Any = 1.0, *, name: str | None = None, metadata: Any = None)

Bases: AbstractDielectric

Non-dispersive dielectric with a constant permittivity and loss tangent.

This is the default material. It is not causal - a constant loss tangent cannot satisfy the Kramers-Kronig relations - but it is the conventional choice in a frequency-domain package. For a popular causal wideband alternative, see DjordjevicSarkarDielectric.

Mathematical Formulation

\[\varepsilon_r(\omega) = \varepsilon_r' \left(1 - j\tan\delta\right) - j\frac{\sigma}{\omega\varepsilon_0} \qquad \mu_r(\omega) = \mu_r\]

Example

import pmrf as prf
from pmrf.materials import ConstantDielectric

fr4 = ConstantDielectric(ep_r=4.3, tand=0.02)
freq = prf.Frequency(start=1, stop=10, npoints=101, unit='ghz')
eps = fr4.properties(freq).ep_r

References

Pozar, D. M. (2011). Microwave Engineering (4th ed.), Section 1.3. Wiley.

Parameters:

  • ep_r (Param, default=1.0) – Real relative permittivity.

  • tand (Param, default=0.0) – Dielectric loss tangent.

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

  • mu_r (Param, default=1.0) – Relative permeability of the medium.

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_r: Param = 1.0

Real relative permittivity

mu_r: Param = 1.0

Relative permeability of the medium

sigma: Param = 0.0

Static bulk conductivity in S/m

tand: Param = 0.0

Dielectric loss tangent