# Transformer core inductor: E vs EI shape inductance relation

I have an EI laminated iron core inductor (with gap) of 32mH of inductance with the coil winded on the central leg.

I need to reduce the inductance using the same component without touching the winding. So I removed the "I" shape lamination.

Now I have an E core inductor (or an EI core inductor but with infinite gap) and I measured an inductance of 8mH, that is about one-fourth of the original.

Is there any relation formula of the inductance between the two shapes (EI vs E) so I could rougtly predict the new value?

Is there any pro and cons using E core vs EI core with gap, a part the cons of different size efficiency?

Are the up and dw legs still useful in the new E core shape? simulate this circuit – Schematic created using CircuitLab

• Air gap is very roughly the gap between legs. As you had 32mH at 2mm (2 * 1mm) air gap, and now 8mH, that suggests 4x the air gap, or 8mm. How wide are those slots? Oct 18, 2021 at 16:08
• The "I" lamination I removed is 12,5 mm wide (104mm long and 50mm heigh) Oct 26, 2021 at 5:07

Are the up and dw legs still useful in the new E core shape?

Yes, the field seeks to travel shortest path through the low permeability medium (air), so it will close in on itself from the upper and lower tips of the E to the central tip.

Removing the top and bottom bars of the E would reduce permeance (and inductance) a lot more because you would enlarge the airgap by much larger a distance than what you did be removing the I.

Conversely, if you want to achieve an inductance intermediate between the E and EI, you could add the I back, but place few millimeter thick low-permeability shim in the gap to hold it open.

Is there any relation formula of the inductance between the two shapes (EI vs E) so I could rougtly predict the new value?

Sort of. The inductance is proportional to the core permeance. Getting familiar with permeance is a rewarding topic if you need to calculate cores often. If the core permeability is much higher than that of the surrounding medium (as in: steel vs. air), the permeance is essentially proportional to the air gap cross-section divided by air gap length.

Therefore, also inductance would be proportional to the cross-section of the air gap divided by the length of the air gap. If you saw the inductance decrease only by a factor of 4, that means that the airgap in the EI shape was considerable already.

Let's say, if you use a shim to enhance the air gap from 1 mm to 2 mm the factor of reduction would be pretty close to 2. But if you place the E and I further and further apart, the field will start to close between the bars of the E, so the air gap cross-section will be changed and the prediction will be come more difficult.

This proportionality only holds for appreciable air gaps. If air gaps become rather small, the permeance will be less and less reduced due to the air gap, but instead will be limited by the shape of the core itself.

• So there was no way to predict this factor reduction of 4? Could be any value like 20, 10 or 100 etc? In the new E core, how much would be the air gap lenght to consider? Oct 18, 2021 at 6:47
• @GianlucaG It is possible to guess the order of magnitude but determining the exact factor is difficult without a field solver. You carefully look at the residual air gap in the E-I-assembly, and measure its length and cross-section. Then for the E core, the length is approximately the distance from either top/bottom bar to the middle bar. The cross- section will be much larger though. It is the area between top-middle and the area between bottom-middle. Oct 18, 2021 at 6:50
• @GianlucaG Let's say, if you use a shim to enhance the air gap from 1 mm to 2 mm the factor of reduction would be pretty close to 2. But if you place the E and I further and further apart, the field will start to close between the bars of the E, so the air gap cross-section will be changed and the prediction will be come more difficult. Oct 18, 2021 at 6:52
• Could you please better claryfy how to take the measures/distances: "for the E core, the length is approximately the distance from either top/bottom bar to the middle bar. The cross- section ......is the area between top-middle and the area between bottom-middle" Oct 20, 2021 at 6:59
• @GianlucaG For the E core, the flux lines travel (mostly) from the outer tips of the E towards the central tip of the E. But they also 'shortcut' right between the the outer and central legs. So there is no precise value for the length that the flux lines travel through the airgap. There is also no well defined area through which the flux lines travel. This is why you would need a field solver for this complex scenario. However, you can get an order of magnitude estimate by assuming that the flux lines travel straight from the outer legs through air to the inner leg. Oct 20, 2021 at 7:20

The gap is not infinite, but it is harder to calculate as it's no longer more or less parallel to the faces of the E legs. As the inductance measurement tells you, the effective gap is now about four times the old gap, which looking at your sketch sounds entirely reasonable. To calculate the new gap, you'd need to do a field-solve around the ends of E legs.