Effective permittivity of microstrip line when width is less than thickness

Under the conditions described below, the effective permittivity of the microstrip line can be calculated from its relative permittivity and physical dimensions.

Conditions:

1. The thickness \(h\) of the substrate of the microstrip line should be greater than or equal to the width \(w\) of the microstrip.

relative_permittivity

relative_permittivity of the dielectric substrate of the microstrip line.

Symbol:

epsilon_r

Latex:

\(\varepsilon_\text{r}\)

Dimension:

dimensionless

effective_permittivity

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

Symbol:

epsilon_eff

Latex:

\(\varepsilon_\text{eff}\)

Dimension:

dimensionless

width

Width (see length) of the microstrip line.

Symbol:

w

Latex:

\(w\)

Dimension:

length

thickness

thickness of the microstrip line.

Symbol:

t

Latex:

\(t\)

Dimension:

length

substrate_thickness

thickness of the substrate.

Symbol:

h

Latex:

\(h\)

Dimension:

length

law

epsilon_eff = (1 + epsilon_r) / 2 + (epsilon_r - 1) / 2 * (1 / sqrt(1 + 12 * h / w) + 0.04 * (1 - w / h)^2) - (epsilon_r - 1) / 4.6 * t / h * sqrt(h / w)

Latex:

\[\varepsilon_\text{eff} = \frac{1 + \varepsilon_\text{r}}{2} + \frac{\varepsilon_\text{r} - 1}{2} \left(\frac{1}{\sqrt{1 + \frac{12 h}{w}}} + 0.04 \left(1 - \frac{w}{h}\right)^{2}\right) - \frac{\varepsilon_\text{r} - 1}{4.6} \frac{t}{h} \sqrt{\frac{h}{w}}\]