Analysis of the electrical circuit


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 …

node potentials

(state variable = node potential)

current sources




mesh currents

(state variable = mesh current)

voltage sources




node integrated potentials

(state variable = node potential integrated in time)

current sources


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)