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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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 | //[[user/Stan Zurek]], Effective magnetic permeability, [[http://Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]], {accessed on @YEAR@-@MONTH@-@DAY@}// | | //[[user/Stan Zurek]], Effective magnetic permeability, [[http://Encyclopedia-Magnetica.com|Encyclopedia-Magnetica.com]], {accessed on @YEAR@-@MONTH@-@DAY@}// |
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 +===== Definition =====
  
 **Effective magnetic permeability** (also **apparent magnetic permeability**[([[http://google.com/books?isbn=9781566775601|M. Bedenbecker, Z. Celinski, H.H. Gatzen, Directional permeability dependence in electroplated patterned permalloy layers, The Electrochemical Society Transactions, 3 (25), 2007, ISBN 9781566775601, p. 123]])]), often denoted as **//μ<sub>e</sub>//**, **//μ<sub>eff</sub>//** or **//μ<sub>a</sub>//** - a term used in analysis of magnetic performance of [[gapped core|gapped cores]]. For a non-homogeneous core (e.g. gapped or composed of powder-like particles) this would be the value of [[magnetic permeability]] of a hypothetical homogeneous material which would exhibit the same permeability. **Effective magnetic permeability** (also **apparent magnetic permeability**[([[http://google.com/books?isbn=9781566775601|M. Bedenbecker, Z. Celinski, H.H. Gatzen, Directional permeability dependence in electroplated patterned permalloy layers, The Electrochemical Society Transactions, 3 (25), 2007, ISBN 9781566775601, p. 123]])]), often denoted as **//μ<sub>e</sub>//**, **//μ<sub>eff</sub>//** or **//μ<sub>a</sub>//** - a term used in analysis of magnetic performance of [[gapped core|gapped cores]]. For a non-homogeneous core (e.g. gapped or composed of powder-like particles) this would be the value of [[magnetic permeability]] of a hypothetical homogeneous material which would exhibit the same permeability.
 [([[http://www.intl-magnetics.org/pdfs/SFG-98.pdf|Soft Ferrites, A User's Guide, Magnetic Materials Producers Association, 1998, p. 37]])] [([[http://www.intl-magnetics.org/pdfs/SFG-98.pdf|Soft Ferrites, A User's Guide, Magnetic Materials Producers Association, 1998, p. 37]])]
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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, bias, time, etc.) are reduced.[([[http://www.ferronics.com/files/Toroid.pdf|Toroids, Design considerations, Ferronics Inc., {accessed 24 Jun 2013}]])] [[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, bias, time, etc.) are reduced.[([[http://www.ferronics.com/files/Toroid.pdf|Toroids, Design considerations, Ferronics Inc., {accessed 24 Jun 2013}]])]
  
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 ===== Equations and calculations  ===== ===== Equations and calculations  =====
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-[[Flux fringing]] (red arc) around an [[air gap]] of an [[inductor]] slightly increases the effective permeability but also the [[magnetic loss|magnetic losses]] +<box 40% right #f0f0f0> 
-[[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}}]]
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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>calculator/effective_permeability_from_air_gap}}+
  
 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 "1" means permeability of the air gap itself). The length of the core and the gap must be given in the same units. For instance, if the core length is given in millimetres, then also the air gap length must be given in millimetres. But the equation holds for any other length units: inches/inches, metres/metres, etc. 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 "1" means permeability of the air gap itself). The length of the core and the gap must be given in the same units. For instance, if the core length is given in millimetres, then also the air gap length must be given in millimetres. But the equation holds for any other length units: inches/inches, metres/metres, etc.
  
-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>calculator/effective_permeability_from_air_gap}}
  
 ===== 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

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