# Wire Over Plane Inductance

Calculate the Inductance of a Wire Over a Plane

## Wire Over Plane Inductance Calculator

### Inputs

Wire Diameter
D
Height Above Plane
H
Length of Wire
L
Relative Permeability
μR

### Outputs

Inductance:

#### Introduction

The wire over plane is a transmission line that is common. One place that it is used is in modifications to existing circuit boards. In some instances one might be interested in only the inductance.

#### Description

The inductance calculated in this tool is the loop inductance created with the wire and its return path on the ground plane. It is important to notice this is not the self inductance of the wire but a closed loop. The inductance allows one to understand the amount of energy that can be stored in magnetic fields. The only variables used in this calculation are the height of the wire from the reference plane, the radius of the wire, and the relative permeability of the medium around the wire. The permeability of air is 1 for all practical purposes. The permeability of a vacuum is exactly 1.

#### Wire over Plane Inductance Model.

The inductance of the loop created with the wire and plane.

L_{wire}\approx \frac{\mu _{o}\mu _{r}}{2\pi}\cosh^{-1}\left ( \frac{h}{a} \right )

where

\left ( h> > a \right )