Rectangle Loop Inductance

Calculate the Inductance of a Rectangle Loop

Introduction

The rectangle loop is often found in windings for transformers or ferrite cores.

Rectangle Inductance Description

The inductance of a rectangle loop has three geometric variables:

• W – rectangle long side
• h – rectangle short side
• d – wire diameter

Rectangle Loop Inductance Model.

The inductance for a rectangle loop is:

L_{rec}=\frac{\mu _{o}\mu _{r}}{\pi }\left [ -2\left ( w+h \right )+2\sqrt{h^{2}+w^{2}}+temp \right]

where

temp=-h\ln \left ( \frac{h+\sqrt{h^{2}+w^{2}}}{w} \right )-w\ln \left ( \frac{w+\sqrt{h^{2}+w^{2}}}{h} \right)+h \ln \left ( \frac{2h}{d} \right )+w \ln \left ( \frac{2h}{d} \right )