# Encyclopedia Magnetica

Encyclopedia of magnetics and electromagnetics.

al_value

# AL value

 Stan Zurek, AL value, Encyclopedia-Magnetica.com, {accessed on 2020-06-02}

AL1), AL value2), inductance factor3), inductance per turn4), inductance per square turn5) and also permeance6) - reciprocal of magnetic reluctance7), characteristic for a given magnetic core (type, size, air gap, etc.), often provided by the manufacturer. The AL value is commonly used in the design of electronic transformers based on ferrite cores, for which the value is often given in nanohenries.8)

A ferrite core RM8 gapped by the manufacturer so that the inductance factor AL=250nH/turn2 (the A250 inscription on the core) by S. Zurek, E. Magnetica, CC-BY-3.0

The AL value is used widely with relation to magnetic cores made of soft ferrite. The name permeance is physically and mathematically synonymous with AL value, but is a more general term referring to a property of a given magnetic circuit.9)

## Units and equations

Mathematically, the AL 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/turn2.10)11)

Therefore, to calculate inductance the AL 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/turn2) = (H)

So the AL value for a given core can be calculated if the number of turns is known and the inductance can be measured.

## 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)

AL value =       number of turns N =

L=

(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 AL value allows for a quick calculation of the required number of turns for a given core size.

It should be noted that the AL 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 AL value and inductance is not proportional, due to the squared turns.

The AL 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:12)

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

where: N - number of turns, μ0 - magnetic permeability of free space (H/m), μr - relative permeability of the material (unitless), A - cross-section area (m2), l - magnetic path length (m).

The above equation can be rewritten as:

 $L=N^2 ⋅ C_x$ (W)

where:

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

And by comparing the equations it can be seen that the value $C_x = A_L$ 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 AL this simplifies the calculations.

A typical notation AL=160 nH ±3% means that the core is gapped with such an air gap that AL = 160 nH (per square turn). For the core ER14.5-3-7 this is synonymous with an air gap of 150 μm.

The tight tolerance of ±3% is possible to attain for proportionally larger gaps. In the example above 150 μm is a relatively large values 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.13)

## Example of data sheet

An example of data sheet giving the AL value. 