Effective permittivity of coplanar transmission line when distance is less than thickness

Under the conditions described below, the effective permittivity of a coplanar line can be calculated directly from the relative permittivity of the substrate.

Conditions:

  1. \(h \ge \frac{d}{4}\) where \(h\) is the thickness of the substrate, and \(d\) is the distance between the first and last electrodes.

effective_permittivity

Effective relative_permittivity of the coplanar line. See Effective permittivity of coplanar line.

Symbol:

epsilon_eff

Latex:

\(\varepsilon_\text{eff}\)

Dimension:

dimensionless

relative_permittivity

relative_permittivity of the dielectric substrate of the coplanar line.

Symbol:

epsilon_r

Latex:

\(\varepsilon_\text{r}\)

Dimension:

dimensionless

law

epsilon_eff = (1 + epsilon_r) / 2

Latex:
\[\varepsilon_\text{eff} = \frac{1 + \varepsilon_\text{r}}{2}\]