# Three Coupled Inductors

Description of the Three Coupled Inductors passive linear component block available in Schematic Editor.

Three coupled inductors are implemented as inductors and voltage controlled voltage sources.

Table 1. Three coupled inductors component in the Schematic Editor core library
component component dialog window component parameters

Three coupled inductors

• General
• ${L}_{1}$ - inductance
• ${I}_{\mathrm{1_0}}$ - initial current
• ${R}_{1}$ - resistance
• ${L}_{2}$ - inductance
• ${I}_{\mathrm{2_0}}$ - initial current
• ${R}_{2}$ - resistance
• ${L}_{3}$ - inductance
• ${I}_{\mathrm{3_0}}$ - initial current
• ${R}_{3}$ - resistance
• ${k}_{\mathrm{12}}$ - ${L}_{1}$ and ${L}_{2}$ coupling coefficients
• ${k}_{\mathrm{13}}$ - ${L}_{1}$ and ${L}_{3}$ coupling coefficients
• ${k}_{\mathrm{23}}$ - ${L}_{2}$ and ${L}_{3}$ coupling coefficients

## Description

Three coupled inductors are represented by matrix $\left[\begin{array}{ccc}L& M& M\\ M& L& M\\ M& M& L\end{array}\right]$ where off diagonal elements are calculated as ${M}_{ij}={M}_{ji}={k}_{ij}*\sqrt{{L}_{i}*{L}_{j}}$