Why Add an Air Gap to an Inductor? BH Curve Analysis

Script Below for those who can’t understand English:

BH curve air gap video

In this video I will be giving a brief overview on BH curves and how introducing an air gap can be advantageous for power electronics applications.


Consider the case where we need to create an inductor for our DC-DC converter. Shown here is a crappy boost converter.

We know that in a nutshell, the whole reason this DC-DC converter works is that when Q1 is closed, and Q2 opens, a current flows through the inductor and energy is stored in the inductor. When Q2 is closed and Q1 opens, the energy from the inductor is transferred to the load. Bam

We also know that along with the number of turns, IL plus delta IL determines the amount of energy stored.

Now, let’s look at how the magnetic flux density through the inductor’s core is affected by the amount of current we pump through the windings.

Now it is time to define some terms that may be confusing. H, or the field ______, can be thought of like the amount of excitation we are giving the inductor. The more H we provide, the more storage in the form of magnetic flux we expect to have. H is proportional to the current, turns, and tight-spacing of the wire around the core.

The actual amount of magnetic flux is hard to measure. however, B, or the magnetic flux density, is more easily measured, and is just a scaled version of the total flux based on the area.

Here is where drawing the BH curves starts to come in handy. Every time I have learned about them, there is always so much math that eclipses just how intuitive it is, so I’m going very light on the math right now.

(START DRAWING VIRGIN CURVE)

As we excite the coil of wire around the magnetic core by providing current through the turns, we align magnetic dipoles within the core and actually magnetize the core. If we keep providing more H, eventually, the core cannot become any more magnetized. The maximum B is typically 1.5 Tesla for Steel, and maybe half of a tesla for ferrites.

Next, let’s assume we remove any current through the coil. We slowly reduce the amount of excitation until no H remains. According to the BH curve, even with zero excitation, the material is providing a magnetic flux. The B remaining is called the remanence.

In order to coerce the material to become de-magnetized, we actually need to provide current flowing the opposite way through the coil. The amount of H we need to provide to completely de-magnetize it is called the coercivity of the material.

We can see the same thing happens with reverse polarity if we increase H in the reverse direction. We eventually run out of dipoles to magnetize, there is remanence, and so on. We need to increase H positively to get to zero magnetization again. This loop is called hysteresis.

The area of the hysteresis loop is indicative of how much energy it wastes to keep demagnetizing and re-magnetizing. In our case, we constantly ride this hysteresis curve in order to store energy in the inductor. For something like a transformer working at 50 or 60 Hertz, the losses may be acceptable. But for power electronics applications, at 100 kilohertz, you would want something with much smaller losses. Such materials are called “Soft magnetic materials”. Conversely, materials with large coercivity and hysteresis are called “Hard magnetic materials”. For a permanent magnet, you would want a large remanence so that it stays on your fridge better without you having to hook a battery up to it or something.

So, why do we need an air gap? Well, let’s go over to these hysteresis curves.

Adding an air gap does not lower the saturation magnetism of the core’s material, but it does lower the magnetic permeability. The slope of B over H in the linear range is a constant µ called the permeability. the permeability of steel is thousands of time larger than just air.

So, let’s go back to the original circuit. We see the current through the inductor from this graph. That can be thought of as the H through the core. So, if the design of the circuit allows for a large inductor current ripple, that means the H through the core will be large.

Looking at the hysteresis curve for the core without the gap, we see that we would enter saturation way too early with our given inductor ripple current. However, if we add an air gap, we allow for more storage of energy in the core before it reaches saturation.

Adding the gap adds reluctance. This means for the same MMF, or amp-turns flowing into the core, we get less flux.

this also means that the air gap reduces the inductance. This is because inductance can also be thought of as how much flux you get for a given current through the coils.

So yeah, that’s what I learned today about the air gap, leave any comments below. Thanks.