### Table of Contents

# AL value

Stan Zurek, AL value, Encyclopedia Magnetica, http://www.e-magnetica.pl/doku.php/al_value |

*A _{L}*

^{1)},

*A*value_{L}^{2)},

**AL factor**,

**inductance factor**

^{3)},

**inductance coefficient**

^{4)},

**inductance per turn**

^{5)},

**inductance per square turn**

^{6)}and also

**permeance**

^{7)}- a value of specific inductance (measured with 1 turn), characteristic for a given magnetic core (type, size, air gap, etc.), often provided by the manufacturer, for ease of calculations.

*A*=250nH/turn

_{L}^{2}(note the

**A25/**inscription on the core,

**3H1**denotes the type of ferrite material)

^{S. Zurek, E-Magnetica.pl, CC-BY-4.0}

The *A _{L}* value is commonly used in the design of electronic transformers based on ferrite cores, for which the value is often given in nanohenries.

^{8)}

The *A _{L}* value is used widely with relation to magnetic cores made of soft ferrite.

The name permeance is physically and mathematically synonymous with *A _{L}* value, but is a more general term referring to a property of a given magnetic circuit.

^{9)}Permaence is a reciprocal of magnetic reluctance

^{10)}

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## Units and equations

Mathematically, the *A _{L}* has the SI unit henry (H), but the the relationship to inductance is non-linear and the practical unit is nanohenry per square turn or nH/turn

^{2}.

^{11)}

^{12)}

Therefore, to calculate inductance the *A _{L}* value must be multiplied by the square of the number of turns

*N*, because it is defined as:

$$A_L = \frac{L}{N^2}$$ | (H/turn^{2}) ≡ (H) |

So the *A _{L}* value for a given core can be calculated if the number of turns is known and the inductance can be measured.

Consequently, the following equations also hold:^{13)}

$$L = A_L · N^2$$ | (H) |

$$N = \sqrt{ \frac{L}{A_L} }$$ | (unitless) |

## Calculator of inductance from AL value and number of turns

If AL value is known then the inductance can be calculated as:

$$ L = A_L ⋅ N^2 $$ | (H) |

*Note: the AL value is typically specified just in the units of inductance e.g. (nH), without the square turns. If this is the case just select the corresponding unit, e.g. (nH/t*

^{2}).
(See also the calculator of **AL value from inductance and number of turns**).

## Practical use

In the design of transformers and inductors for switch mode power supplies the switching parameters and power level dictate the values of inductance required for such component.

Therefore, the value of inductance is known for the next design step. Using the *A _{L}* value allows for a quick calculation of the required number of turns for a given core size.

It should be noted that the *A _{L}* value is often given in the units of (nH) or similar, with the “per square turn” implied. It is important to remember that the relationship between the

*A*value and inductance is not proportional, due to the squared turns.

_{L}
The *A _{L}* value is especially useful when designing with gapped cores, for instance for gapped inductors or flyback transformers. Under normal conditions the air gap stores all the energy and dictates the effective permeability of the magnetic core.

For a simplified case of a uniform magnetic circuit the inductance can be calculated from the following equation:^{14)}

$$ L = \frac{N^2 ⋅ \mu_0 ⋅ \mu_r ⋅ A}{l} $$ | (H) |

where: *N* - number of turns, *μ*_{0} - magnetic permeability of free space (H/m), *μ _{r}* - relative permeability of the material (unitless),

*A*- cross-section area (m

^{2}),

*l*- magnetic path length (m).

The above equation can be rewritten as:

$$ L=N^2 ⋅ x $$ | (H) |

where:

$$ x = \frac{\mu_0 ⋅ \mu_r ⋅ A}{l} $$ | (W) |

And by comparing the equations it can be seen that the value $x = A_L$ and it is a constant for a given magnetic core of fixed parameters, as long as the effective magnetic permeability is not affected (e.g. saturation is avoided).

Therefore, if the manufacturer provides the *A _{L}* this simplifies the calculations.

A typical notation *A _{L}=160 nH ±3%* means that the core is gapped with such an air gap that

*A*= 160 nH (per square turn). For the core ER14.5-3-7 this is synonymous with an air gap of 150 μm.

_{L}The tight tolerance of ±3% is possible to attain for proportionally larger gaps. In the example above 150 μm is a relatively large value for the magnetic path of the core, which is 19 mm. This reduces the effective permeability from over 1000 to around 137 (see also the calculator of effective permeability).

For smaller gaps the influence of the core is increased and the tolerance could be as wide as ±25%. The same applies for ungapped cores.^{15)}

## Example of data sheet

An example of data sheet giving the *A _{L}* value.

File | Description |
---|---|

Datasheet: ER14.5-3-7, Planar ER cores and accessories, Ferroxcube ER14.5-3-7, Planar ER cores and accessories, Ferroxcube |

## See also

## References

^{1), 11), 15)}Datasheet, ER14.5-3-7, Ferroxcube.pdf

^{3), 8), 12)}Inductor and Flyback Transformer Design, Texas Instruments Inc., 2001, p. 5-7, {accessed 24 Jun 2013}

^{4)}Ferrite, Summary, Ferrites, TDK, 2014, 001-01 / 20140308 / ferrite_summary_en.fm, {accessed 2021-09-12}