Short circuit inductance of microstrip line

To create a short circuit based on a microstrip line, a metallized hole can be made in the line. Such an opening will have a certain inductance, which can be calculated.

Notation:

1. \(\mu_0\) (mu_0) is vacuum_permeability.

inductance

inductance of a metallized hole in a microstrip line.

Symbol:

L

Latex:

\(L\)

Dimension:

inductance

substrate_thickness

thickness of the substrate of the microstrip line.

Symbol:

h

Latex:

\(h\)

Dimension:

length

radius

radius of the metallized hole.

Symbol:

r

Latex:

\(r\)

Dimension:

length

law

L = mu_0 / (2 * pi) * (h * log((h + sqrt(r^2 + h^2)) / r) + 1.5 * (r - sqrt(r^2 + h^2)))

Latex:

\[L = \frac{\mu_0}{2 \pi} \left(h \log \left( \frac{h + \sqrt{r^{2} + h^{2}}}{r} \right) + 1.5 \left(r - \sqrt{r^{2} + h^{2}}\right)\right)\]