# Analysis of the electrical circuit

## Introduction

An electrical circuit comprises various components that can be:

• generic components, such as: sources (of current or of voltage), passive components (resistors, coils, capacitors), semi-conductors (switches, diodes), …
• specific components, concerned by the field - circuit coupling), such as: solid conductors and stranded conductors

## Component description

The components are described by their electrical behavior.

• For the generic components it is the current-voltage characteristic, i.e. the relation between the voltage at the component terminals and the current that flows through the component
• For the specific components it is the differential equation linking the magnetic potential, the electric potential, the current and the voltage

## Description of an electrical circuit: definitions

The topology of an electrical circuit (or of an electrical network) consists of an assembly of nodes and branches that contains one or more series connected electrical components.

A node is a point of the circuit where several branches end.

A mesh comprises of two or more branches that together form a closed loop.

## Equation of the electrical circuit

The description of the equations corresponding to the electrical circuit is based on Kirchoff's laws.

• the nodes law or 1st Kirchoff's law states that: the sum of the currents flowing into a node must equal the sum of the currents flowing out of the node

• the mesh law or 2nd law of Kirchoff states that: for any circuit mesh, the algebraic sum of the voltages at the terminals of branches that form the mesh is null

## Methods of analysis

The common methods used to describe the equations corresponding to an electrical circuit are listed in the table below.

The method of … is well adapted for taking into consideration …
(1)

node potentials

(state variable = node potential)

current sources

resistors

capacitors

(2)

mesh currents

(state variable = mesh current)

voltage sources

resistors

coils

(3)

node integrated potentials

(state variable = node potential integrated in time)

current sources

resistors

coils and capacitors

## … in Flux

Concerning the methods used in Flux:

• the 2D solver uses the mesh current method (2)
• the 3D solver uses the method of node integrated potentials (3)