effective_magnetic_permeability

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effective_magnetic_permeability [2020/07/02 22:34] 127.0.0.1 external edit |
effective_magnetic_permeability [2020/07/27 23:11] (current) stan_zurek [Equations and calculations] |
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+ | ===== Definition ===== | ||

**Effective magnetic permeability** (also **apparent magnetic permeability**[([[http:// | **Effective magnetic permeability** (also **apparent magnetic permeability**[([[http:// | ||

[([[http:// | [([[http:// | ||

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+ | {{page> | ||

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===== Effect of air gap ===== | ===== Effect of air gap ===== | ||

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[[Magnetic permeability]] of a [[magnetic material]] is linked to the slope of a [[B-H curve]] or (or [[B-H loop]]). With increasing [[air gap]] the slope is reduced, and changes caused by non-linearity of the material (due to variations in [[flux density]], temperature, | [[Magnetic permeability]] of a [[magnetic material]] is linked to the slope of a [[B-H curve]] or (or [[B-H loop]]). With increasing [[air gap]] the slope is reduced, and changes caused by non-linearity of the material (due to variations in [[flux density]], temperature, | ||

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===== Equations and calculations | ===== Equations and calculations | ||

- | <30% right # | + | |

- | [[Flux fringing]] (red arc) around an [[air gap]] of an [[inductor]] slightly increases the effective permeability but also the [[magnetic loss|magnetic losses]] | + | <40% right # |

- | [[file/fringing_flux_magnetica.png|{{fringing_flux_magnetica.png}}]] | + | [[Gapped core]] with: total [[magnetic path length]] $l$ (orange), length of core $l_{core}$ (blue) and length of gap $l_g$ (red) |

+ | [[file/gapped_core_magnetica.jpg|{{gapped_core_magnetica.jpg}}]] | ||

{{page> | {{page> | ||

</ | </ | ||

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There are several assumptions: | There are several assumptions: | ||

- | * the cross section area of the magnetic circuit is constant at every point of the circuit, and is the same for the core and for the gap | + | * the cross section area of the [[magnetic circuit]] is constant at every point of the circuit, and is the same for the core and for the gap |

- | * the length of the air gap is much shorter than the total [[path length]] of the magnetic core | + | * the length of the air gap is much shorter than the [[path length]] of the magnetic core |

- | * the magnetisation is uniform and [[fringing effect]] is neglected | + | * the magnetisation is uniform and [[flux fringing|fringing effect]] is negligible |

* permeability of the core material is much greater than the permeability of air gap | * permeability of the core material is much greater than the permeability of air gap | ||

- | | + | * [[relative permeability]] of the medium in the air gap is assumed to be unity (i.e. the same as [[permeability of free space|vacuum]]). |

- | {{page> | + | |

The equation is derived by using the concept of [[magnetic reluctance]][(Finke)] and with the assumptions listed above. All values of permeability (input and output) are given as [[relative permeability]] (so the value of " | The equation is derived by using the concept of [[magnetic reluctance]][(Finke)] and with the assumptions listed above. All values of permeability (input and output) are given as [[relative permeability]] (so the value of " | ||

- | Equations can also be derived for multi-path or non-uniform magnetic circuits, but these are obviously configuration-dependent and must be calculated for each specific structure.[(Finke)] | + | Equations can also be derived for multi-path or non-uniform magnetic circuits, but these are obviously configuration-dependent and must be calculated for each specific structure.[(Finke)] For example, in a three-leg core (as shown in the image) the path length is considered to be only around one window (e.g. just the orange path). |

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+ | {{page> | ||

===== Composite materials ===== | ===== Composite materials ===== | ||

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===== See also ===== | ===== See also ===== | ||

- | * [[magnetic permeability]] | + | * [[Magnetic permeability]] |

- | * [[air gap]] | + | * [[Air gap]] |

- | * [[magnetic core]] | + | * [[Magnetic core]] |

===== References ===== | ===== References ===== |

effective_magnetic_permeability.1593722094.txt.gz · Last modified: 2020/07/02 22:34 by 127.0.0.1