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# 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 of said coil and the flux of the magnetic field.

Faraday stated that the magnitude of the emf generated is proportional to the rate of change of magnetic flux.

The flux linkage (measured in Vs (volt second) or weber-turns) is used in self inductance or mutual inductance as a measure of the linkage of an inductor to itself or another and is the product of magnetic flux (φ), and the number of turns (N) linked by that flux. It is usually denoted as λ (lambda) or ψ (psi).

Because of Faraday's relation the flux linkage of a winding can be expressed as the time integral of the voltage over the winding.

$\lambda=\int_\, v\, dt$

This can also be written in differential form as

$v = \frac{d\lambda}{dt}$

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.