# Skin effect reduce inductance

I have a question about the skin effect on inductors, I would like to know why the skin effect will reduce the inductance? You could see from the below figure, in the high frequency the inductance was reduced, but the resistance will be increased. Could someone give me some suggestions, thanks?

In addition to the field explanation, there's a very basic argument from just the fact that an inductor is a real 2-terminal element: as a consequence of the impedance being analytical, the real and complex elements obey Kramers-Kronig relations. Basically, a lossy inductance is necessarily a decreasing inductance; the impedance is still going up with frequency, but a little slower than proportionally so ($$\\left|Z\right| < j \omega L\$$). The amount by which it's slower, gives the resistance fraction. (For example, if R = X_L, the slope (on log-log plot) is half, or Z ~ sqrt(F), a diffusion element.)

If impedance is rising faster than proportional (or falling faster than inversely for capacitors), it can only happen within a narrow band (approaching a resonance), as is the case near SRF (self resonant frequency).

(This is not a complete description of what impedance can do as a function of frequency, but is sufficient for commercial inductors, which can be modeled as a lossy inductor with some capacitance to cover DC to a bit beyond SRF, or including other more complex behavior at high frequencies which may not be very important to model anyway.)

• Hi Tim, It is hard for me to understand your explanation. Do you have a figure to let me understand ,more easily. May 7 at 13:34
• @Jitter456 en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations gives the basics, but, kinda as usual, not very useful if you don't already know complex analysis. The hand-wave of it is: real (resistance) and complex (reactive, inductance or capacitance) elements are not independent, but deeply linked. Put another way: try to build an RLC network with arbitrary R and X vs. frequency; you can't! May 8 at 17:53

The phenomenon that causes skin effect forces the curent to flow in the outer layers of the conductor. Because the current is flowing in the outer layers (and not uniformly throughout the conductor cross-section), there is less internal flux coupling, and in fact less total magnetic flux is generated (in the limit none inside the conductor). This directly means there is less inductance.

• are you saying that the magnetic flux inside the wire contributes significantly to the overall inductance? I have always assumed that the only significant flux is in the core, which is inextricably linked to current-turns.
– Frog
May 7 at 1:25
• Skin effect doesn't affect the flux in the core, or the portions of the inductance that generates. A magnetic core will have other losses and effects that make its inductance (generally) fall with increasing frequency. Usually those are lossy also, but skin effect isn't necessarily lossy (the wire could be a superconductor). May 7 at 2:30