To achieve a certain value of the magnetizing inductance (Lm), we can adjust the transformer air gap.

Air gap calculation formula:

There is no particular information on this, but I assumed that:

```
u0 = Vacuum permeability (4π×10−7 H/m)
N - primary turns? (x18)
Ae effective area (PQ5050) = 328mm2 (Core datasheet)
Lm = magnetic inductance (my goal - 60uH)
```

Substituting these values into the formula, I got 2.2 meters of the gap, which is clearly **incorrect**.

```
(0.000001257 * 324(18^2) * 0.328) / 0.00006
```

Next, I tried replacing N with the transformation ratio (n = 1.5), I got 15.46mm of the gap. This is closer to true, but still a very large gap.

```
(0.000001257 * 2.25(1.5^2) * 0.328) / 0.00006
```

I also tried to remove the square from N, but this is still a very large gap.

**Question:** what is my mistake? I assumed that the matter is in N (it is not clear whether this is the number of turns of the primary winding, or this is the transformation ratio (but it is denoted by a small n))

Perhaps there are other formulas with which you can get the Air gap value, the desired value of the magnetizing inductance?

## Best Answer

Well, you have the ferrite core-set data sheet and you have the ferrite material spec; 3C95 so let's proceed from there. The important formulas to know are these: -

The effective permeability of a core set when gapped$$\mu_e = \dfrac{\mu_i}{\mu_i\cdot\dfrac{\ell_g}{\ell_e}+1}$$

If you plug-in the numbers with a gap of 1 mm, \$\mu_e\$ equals 108.17 and this is used in the next formula for inductance: -

Inductance of the gapped core set$$L = \dfrac{\mu_0\cdot\mu_e \cdot N^2 \cdot A_e}{\ell_e + \ell_g}$$

effectivecross sectional area in m² (328 mm² or 3.28 x \$10^{-4}\$ m²)So, if you plug in the numbers now (1 mm gap) you get 126.7 μH

Given the above, I reckon you should be able to figure out the reverse process to get the inductance you require (about 2 mm).

SummaryYou will also have to double check that you have provided enough of a gap so that the peak magnetic flux density remains significantly less than 400 mT. I usually aim for 200 mT but, in the Cree document that you linked, they appear to be aiming for 120 mT. This is fairly easy to check remembering that \$B = \mu_0\cdot \mu_e\cdot H\$ where \$H\$ is the peak current multiplied by number of turns and then divided by \$\ell_e\$.

Or, \$H = \dfrac{MMF}{\ell_e}\$