# Inductor and transformer with open magnetic core

I have some troubles to understand the principle of: 1-> open core inductor 2-> open core transformer

Let us talk about open core inductor as the one above:

If we think about it as an equivalent magnetic circuit, we get:

And the reluctance of the air is rougly bigger than the reluctance of the core and then the reluctance of the core is negligible. So the flux into the inductance does not depends on the core. And as the inductance is proportionnal to the flux, why do not just remove the core?

So it is probably a problem of coupling? But I do not understand what is the purpose to have a great coupling between the windings of the core? It is an inductance, so it will just add some "leakage" inductance? Inductance + leakage inductance = inductance. What is the problem?

1. Then here is a transformer with an open core:

This is actually an induction coil. Nevertheless there is two coils which are wound around a common core. For having a good transformer we need to have a large variation of magnetic flux according to the time as indicated by Faraday, but in this case, we reduce the maximum of flux as we have some of the flux which has to travel through the air. So for the same number of turn and the same intensity, we have a flux which is lower than it could be if the core were closed. It might be better to have less turn (or less intensity) and a core closed for doing the same experiment? Did I do a mistake? In this case I understand that we need to have a good coupling ;)

Thank you very much :)

• That's generally called an "unshielded" inductor, rather than "open". Jul 4, 2022 at 20:06

as the inductance is proportionnal to the flux, why do not just remove the core?

Even though the air gap permeability dominates the calculation for inductance, with a reasonably high permeability core, you can still rely on the flux that is made by one turn, coupling nearly 100% to all the other turns. This means that this well-known formula is still true: -

$$L = k\cdot N^2$$

So, it's easy to calculate the number of turns for a given final inductance.

If there wasn't a core, the above formula gets more complex and winding overlaps and spacing becomes a factor. Not so with a half-decent permeability core.

For having a good transformer we need to have a large variation of magnetic flux according to the time as indicated by Faraday, but in this case, we reduce the maximum of flux as we have some of the flux which has to travel through the air.

That's not true; a large variation of flux is not needed for a transformer. What is needed is that the primary and secondary couple with each other close to 90% or more (usually 98% or more for good transformers).

That's what makes a good power transformer even if all of the flux is exposed to a long air-gap. Of course, for a proper power transformer we don't want much leakage flux because that can create power losses in nearby conductive materials (eddy-current losses).

So for the same number of turn and the same intensity, we have a flux which is lower than it could be if the core were closed.

Mainly untrue. With an open core, the primary magnetization inductance is going to be much smaller and hence the current flow for a given excitation voltage and frequency is going to be much higher. This means that magneto motive force (MMF or ampere-turns) are much greater and although an open core usually creates a longer average path for the magnetic field lines to travel around, there will be a significant H-field increase.

It might be better to have less turn (or less intensity) and a core closed for doing the same experiment?

Fewer turns means less inductance and a greater intensity magnetic field (H filed) strength ironically. Think of it like this, if 1000 turns makes 1 henry then 500 turns makes 0.25 henries and that means 4 times the current for a given excitation voltage (same frequency). 4 times the current and half the turns means MMF = twice as much and, given that the field travels the same distance through the core and around the air gap, the H-field doubles.

• Thank you for your comment. It helps me a lot for the inductor. For the transformers, i still have some questions, what is the purpose to close the core on the majority of the transformers ?
– Jess
Jul 5, 2022 at 6:50
• You mean that the coupling coefficient is lower with an open core ? and so when you close the core, you have less leakage inductance and this is why we close the transformer ?
– Jess
Jul 5, 2022 at 6:54
• (1) To avoid "escaping" flux affecting nearby conducting objects and causing power losses due to eddy currents and induction. (2) No I don't - if I have said that please tell me where and I shall correct it @Jess Jul 5, 2022 at 7:08
• The eddy currrent can still circulate into the core ? I do not understand why it reduces the eddy current to have a core open or a core closed . It would be better if the eddy current "circulates" in the air as the resistance of the air is infinite which is not the case of a core. If the coupling coefficient is not affected whatever if it is closed or not, the induction problem are only coming from the fact, as you said, that the inductance is reduced with an open core. Is this what you want to explain to me ? I agree for the problem of magnetic field escaping.
– Jess
Jul 5, 2022 at 10:03
• Cores are designed to have minimum eddy currents. An open core can cause unwanted eddy currents to occur in close-by (but otherwise unconnected) conductive materials through air-coupling. I'm unsure what you mean by "induction problem" @Jess Jul 5, 2022 at 12:51

Leakage means flux not shared between primary and secondary, thus less energy that is deposited into the primary is available at the secondary.

It can be harnessed, or at least canceled out, under certain conditions, namely with resonant circuits. So, Tesla coils, resonant switching supplies, etc.

The open core design by the way, increases the air gap path, increasing the current flow at a given flux: energy storage goes up. This reduces inductance, which doesn't counter that, it's the point (notice E = 0.5 L I^2 so L goes down but I goes up double, thus energy goes up). The windings need to be placed close together to avoid losing flux through the air gap.