AL



AL , AL value , inductance factor , inductance per turn , inductance per square turn - reciprocal of magnetic reluctance , characteristic for a given magnetic core (type, size, gap, etc.), often provided by the manufacturer. The AL value is commonly used in the design of electronic transformers based on ferrite cores, and on the data sheets of is given in nanohenries.

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 turns (nH/N2).

Therefore, to calculate inductance the AL value must be multiplied by the square of the number of turns N, because it is defined as:

(1)   $$ A_L = \frac{L}{N^2}$$

If the AL value is not known for a given core then it can be easily calculated from equation (1), if the number of turns is known and the inductance can be measured.

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 very quick calculation of the required number of turns for a given core size.

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:

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

where: N - number for 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)

We can rewrite the equation (3) as:

(4)  $$ L = N^2 \cdot C$$

where:

(4)  $$ C = \frac{\mu_0 \cdot \mu_r \cdot A}{l}$$

And by comparing equations (2) and (4) we can see that the value C = AL, and it is constant for a given magnetic core of fixed parameters.

Therefore, if the manufacturer provides the AL this greatly simplifies the calculations.

A typical notation "AL=160 nH ±3%" will likely mean that the core is gapped with such an air gap that AL = 160 nH (per turn squared). 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 the the tolerance would be as wide as ±25%. The same applies for ungapped cores.

Data sheet
An example of data sheet giving the AL value: