Flux linkage
Encyclopedia
Flux linkage is a property of a coil of conducting wire and the magnetic field through which it passes. It is determined by the number of turns in the coil and the flux
of the magnetic field.
The definition of the flux linkage is the total flux passing through a surface (i.e. normal to that surface) formed by a closed conducting loop. i.e.
where
is the flux density
, or flux per unit area at a given point in space.
The simplest example of such a system is a single circular coil of conductive wire immersed in a magnetic field of constant magnitude at every point and with a direction perpendicular to the surface formed by the loop. In this case the flux linkage is simply the flux density passing through the loop multiplied by its surface area, i.e.
. If several turns of the wire are made, this becomes 
where N is the number of turns. In this case, the surface through which the magnetic flux is passing has been increased by a factor of 
.
Faraday
showed that the magnitude of the emf
generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop (Faraday's law
). The flux linkage of a coil is simply an alternative term for this total flux, used for convenience in engineering applications. Therefore, the flux linkage can also be expressed as the time integral of the voltage over the winding and measured in Vs (volt second).
Because of Faraday's relation the flux linkage of a winding .
This can also be written in differential form as
Due to the simplicity of these formulas flux linkage is commonly used to estimate the magnetic flux of an AC machine
. However, errors in the voltage measurement and the resulting drift problem of the integral cause the ideal integral to often be replaced with a low-pass filter
approximation.
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
of the magnetic field.
The definition of the flux linkage is the total flux passing through a surface (i.e. normal to that surface) formed by a closed conducting loop. i.e.
where
is the flux densityFlux density
-Formal Statement:The flux density is simply defined as the amount of flux passing through a unit-area. -Mathematical Statement:The flux density would essentially be the number of field lines passing through a defined unit-area...
, or flux per unit area at a given point in space.
The simplest example of such a system is a single circular coil of conductive wire immersed in a magnetic field of constant magnitude at every point and with a direction perpendicular to the surface formed by the loop. In this case the flux linkage is simply the flux density passing through the loop multiplied by its surface area, i.e.
. If several turns of the wire are made, this becomes where N is the number of turns. In this case, the surface through which the magnetic flux is passing has been increased by a factor of .Faraday
Michael Faraday
Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....
showed that the magnitude of the emf
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...
generated in a conductor forming a closed loop is proportional to the rate of change of the total magnetic flux passing through the loop (Faraday's law
Faraday's law of induction
Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...
). The flux linkage of a coil is simply an alternative term for this total flux, used for convenience in engineering applications. Therefore, the flux linkage can also be expressed as the time integral of the voltage over the winding and measured in Vs (volt second).
Because of Faraday's relation the flux linkage of a winding .
This can also be written in differential form as
Due to the simplicity of these formulas flux linkage is commonly used to estimate the magnetic flux of an AC machine
AC motor
An AC motor is an electric motor driven by an alternating current.It commonly consists of two basic parts, an outside stationary stator having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor attached to the output shaft that is given a torque by the...
. However, errors in the voltage measurement and the resulting drift problem of the integral cause the ideal integral to often be replaced with a low-pass filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
approximation.