For example at room temperature (20ºC) the saturation current is 450mA and with 100ºC the saturation current is 350mA. What causes this?
(Edit) The higher inductance with higher temperatures and lower currents is my biggest question here.
This is a graph for a power inductor. The original video is here: Temperature influence of the saturation current for an inductor
This is mostly a solid-state physics question, but, to boil this down to something that we can answer without going into finesse of core material physics:
Magnetism happens when in a material, you can align the spins of electrons around their core (or more generally, the spin normal of any charged quantum) – in "normal" materials, these are totally randomly oriented, and once you've aligned a lot of the spin axes to point in the same direction, you get a macroscopically observable effect "magnetism".
The ability of cores to store energy energy depends on the "alignability" of these spins.
The hotter any material, the more random the movement, positions and orientations of the atoms inside; so, heating up material actively works against its ability to store energy in a magnetic field.
This, however, doesn't explain the opposite observation you have. To clear things up a little, I'd like to preserve the comment discussion below here, credits to @jonk there:
Domain walls are like soap bubble surfaces arranged to minimize energy. At low currents, the applied field mostly goes into modifying the walls so that the volume of bubbles that line up with the magnetic field grow much larger than the volume within the oppositely aligned bubbles. This is a smooth effect. But there is also a number of complications lumped together as Barkhausen and magnetostriction effects. Higher temperatures, at low magnetization currents, allow the bubble walls to snap more easily over these Barkhausen effect barriers.
So the remaining vacuum path length (the physical path length minus the net bubble path lengths) is a little bit shorter resulting in a slightly higher inductance. At higher currents, most of the bubble walls have done all the moving they can do, as well as all of the lumped Barkhausen and magnetostriction effects, and now the effect of temperature is to reduce the net aligned bubble volume because of all the excess continual jostling (unsettling of existing aligned bubble volumes.) These two extreme ends explain the opposing behaviors.
@Tobalt argues
At high temperatures, both magnetic exchange and magnetic anisotropy decrease. This leads to: a) reduced domain wall energy and b) increased domain wall width. Both lead to lower domain wall pinning, which in turn c) decreases coercivity d) increases the dM/dH, i.e. permeability
Helpfully, @jonk also links to the Feynman lectures chapter on magnetic materials. I'd like to cite one thing from that:
At high temperatures, the thermal energy of the system is greater than the magnetic energy, EmJ. The Curie Temperature where the different magnetic domains cancel, and the relative permeability drops towards zero. and the energy stored cannot be increased so L collapse to zero, 0 not the magnetic flux. There is a thermal-magnetic equilibrium at this temperature. Heating up magnets to this temperature also demagnetizes.
In between absolute 0'K and the Curie Temp.,there exists a rate of change to temperature for any molecular magnetic domain structure that controls permeability \$\dfrac{\Delta M}{M}=k~ T^{\frac{3}2}~~~~~~~~~~\$ ref (31)
Magnetic qualities of charged particles have a complex interaction of forces that are maximized at absolute zero, 0'K and have zero magnetism at the Curie Temperature.
Air does not Saturate (yet)
This does not occur in vacuum of material excited by a wire loop, and we can neglect air as well for this application.
Transformer steels (Cold-rolled-grain-oriented-steel CRGOS) are usually 1.2 T up to exotic 1.9T (Est) while an air gap in 7 Tesla MRI can suck a metal folding chair across a cafeteria room at speeds up 60 MPH.
Anecdote from head of NRC (National Research Council of Canada) who reported to me in Winnipeg, on the capability of the world 1st non-magnetic (hydraulic) MRI for use in operating rooms
Take-a deep breath
An electron moving around a fixed point has an angular momentum. \$L=m_erv\$ which is also defined by the area and around a wire is excited by current per unit length.
The charged particles have a nuclear spin, like a spinning top that has a precessed orbit at a slower rate. This magnetic dipole moment produces magnetic flux and the magnetic force along the wire created by the electric charge flow rate or current. The energy of each spinning top is also an absolute permeability, and the sum of all tops is the net permeability of the material. The moments have distinct spin angles, discovered by Stern and Gerlach in 1922.
The rate of change of \$\mu_r\$ with temperature depends on the material type and gaps between magnetic particles and the ratio of insulation and conductive to the magnetic particles. Microwave has a higher ratio conductive/insulator material that creates the necessary equal gaps in ferrite magnetic particles. \$\mu/\epsilon\$.
The result is the knee of the curve where \$\mu_r\$ drops 10% is often used for the inductance at rated current. Above this in power ferrite, the margin to critical thermal runaway is the key figure of merit allowing aging of materials. This is where the rate of change of temperature rises above steady-state with a rapid loss of inductance and impedance as heat cannot be removed fast enough. This is because inductors are usually drive by switched voltage sources and cannot be switched with current sources unless actively sensed and limited.
Other Henries
Another odd fact is the domain walls of Quartz crystal (XTAL's as in oscillators) can have the equivalent inductance of more than 1 Henry, but the excellent insulation of Quartz creates a piezo effect, electromagnetic resonant vibrations with a tiny femptofarad "motional" capacitance. It cannot be saturated with current because between the domain walls values “Henry and fF” exists several kV, for a Xtal power with 10 uW that cannot be tapped. This is why Xtal powers are minuscule, as there is a breakdown voltage or flashover inside the crystal from molecular impurities.
If you notice for temperatures above room the Tempco is very small PTC then switches to NTC (bad) above 350mA yet saturates -10% around 450 mA . This means if your RMS current exceeds this a bit, you will run up to 100'C and close to runaway failure. A feature I added to a Lambda 1U 180W supply for my design for reliability was to epoxy a thermistor to the Ferrite XFMR to drive a small transistor to a LM317 to regulate the current in 2 fans in series off 48V, when it reached 50'C the fans started. At 60'C it would run at full RPM which would only happen in a 40'C ambient with my spoiler and plenum turbulent design so it never exceeds or even comes close to critical temperature.
**So for added reliability, include thermal ferrite sensing ** for current limiting or voltage regulation or temp controlled fans that normally don't need to run.
Question:
Why does inductor core saturation depend on the temperature?
Answer in 5 words:
In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the applied magnetic field, humidity, temperature, and other parameters.
Temperature Coefficient Of Magnetic Permeability from: NIST Research Library archive
Corelation of magnetic field and current, Ampere's law: B = f(u * I)
