Practical Tips | What is the inductor saturation that engineers often talk about?

Latest update time：2020-10-17

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Do you understand the meaning of the term "inductor saturation" that you hear all the time? In addition to the phenomena of current bending and distortion and device burnout, what does "saturation" actually mean in physics?

Inductance, temperature resistance, saturation current, size, price - these five are the basic coordinates for our inductor selection. Of course, we will also consider the shape of the coil and core, the magnetic material, and the installation and welding method. The most annoying thing in the selection process is to find a suitable inductor among dozens of inductors, only to find that one of the parameters does not meet the requirements, or that the saturation current is insufficient due to the extremely low probability of peak power, resulting in excessive design margin.

The Secret of Sensibility

The reason why the inductor is inductive is that the current flowing through the inductor lags behind the current applied to the inductor (in fact, it lags by 90 degrees):

Because of Lenz's law, inductance is like a naughty child grabbing a pet at home and hindering the pet's progress (change in current). You have to put some pressure on the naughty child, so he will be reluctant at first, and then let the pet (current) go (we make full use of this disobedient characteristic to achieve the purpose of our choke); inductance is also like a spring. When you apply pressure, it stores part of the energy in its body and transmits the remaining energy. When the spring is compressed to the extreme, it can no longer store more energy, that is, saturation occurs, all the added energy is transmitted, and the inductance loses its hysteresis effect.

In physics, the spring example might be more appropriate, as shown in the following textbook answer found online:

Electrons rotate around several layers of orbits in the outer layer of atoms. Each layer of electrons will generate a weak magnetic field according to Lenz's law. The magnetic force of each layer is different and the direction is different, but the net force is zero, and there is no magnetism. When a coil is energized, a magnetic field is generated according to Lenz's law. The magnetic lines of force pass through the magnetic material (iron core), and the electrons of the atoms in the magnetic material begin to turn to offset the magnetic lines of force generated by the coil. The greater the coil current, the more the rotation direction of the electrons in the magnetic material changes. When the rotation direction of all the electrons in the magnetic material is the same, it is magnetic saturation.

Causes and Theoretical Analysis of Inductor Saturation

When we superimpose a common rotation direction on all electrons, like a well-organized military formation, its magnetic force reaches a certain level, and when the magnetic force cannot be increased any further, it is called saturation. This description is vivid enough to explain the concept of saturation qualitatively, but qualitative analysis may not satisfy you. The charm of physics goes far beyond qualitative analysis.

The physical meaning of inductor saturation

When we talk about inductor saturation, we are actually talking about iron core saturation. Air core inductors will never saturate. The intuitive question at this time is: why not use air core inductors? This must start with the calculation formula of inductance (here we directly draw the conclusion, the specific derivation will be mentioned in the next section):

In the formula, L is the inductance, magnetic permeability μ, equivalent number of winding turns N, equivalent cross-sectional area of the magnetic circuit S, and equivalent magnetic circuit length of the inductor coil is ɭ.

Obviously, to increase the inductance, you can increase the numerator μ, N, S and reduce the denominator ɭ. N is often limited by volume (especially for power inductors with very thick wires, each turn will greatly increase the volume, and increasing N will also increase), wire resistance (heating), and parasitic capacitance (especially for EMC inductors, parasitic capacitance will greatly weaken its high-frequency suppression ability).

Under the same dimensions, increasing μ is almost the only way. The magnetic permeability of air is almost equal to the magnetic permeability μ0 in a vacuum, while the μ of excellent magnetic materials can reach 2000μ0. The inductance value of an air-core inductor differs by thousands of times compared to an inductor with a magnetic core.

Magnetization curves of 9 ferromagnetic materials showing magnetic saturation

(1. Steel plate 2. Silicon plate 3. Steel casting 4. Tungsten steel 5. Magnetic steel 6. Cast iron 7. Nickel 8. Cobalt 9. Magnetite)

"Success or failure depends on Xiao He." μ helps us obtain high inductance, but it also brings us saturation problems. The relationship between magnetic field intensity H and magnetic induction intensity B can be expressed by magnetic permeability:

The magnetic permeability of magnetic materials is not a constant quantity, but depends on the magnetic field strength H. In metals that are subject to magnetic saturation, as the current through the inductor increases, the relative permeability μ reaches a maximum value with the increase of the magnetic field strength H, and then decreases with its saturation, and finally becomes 1, so the corresponding inductance L also tends to be an air-core inductor.

In other words, it becomes a wire, which is the physical meaning of inductor saturation. The inductor will not disappear, but will only degenerate into a hollow inductor.

The BH curve (in many textbooks it has another name: hysteresis loop, of course, the hysteresis loop has three other quadrants) is shown in the figure below. At the right limit of H, all materials will tend to the same straight line. This is the physical convergence of nature:

Due to magnetic saturation, the magnetic permeability μf of ferromagnetic materials will rise to a maximum value as the magnetic field strength increases, and then gradually decrease.

Calculate everything with Maxwell's equations - All electromagnetic related physical quantities can be derived from Maxwell's equations. Inductance is no exception:

The physical definition of inductance (only self-inductance is considered here) is:

It describes the rate of change of unit current:

One of the most puzzling facts in physics is that the definition formula is often not the formula used for design. For the latter, we will have a more commonly used calculation formula. Let's derive it as follows: According to Faraday's law (one of Maxwell's equations), the induced electromotive force is equal to

the rate of change of magnetic flux ( ). If it is a multi-turn coil, the equivalent number of winding turns must also be considered:

Combined with the definition of inductance, we have

: Integrating both sides with respect to time, we can obtain

BS, B = μH, assuming the current flowing into the inductor is I, according to the full current law (one of Maxwell's equations) Hɭ = NI combined with the definition of inductance, we can get:

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