Influence of a magnetic field on coil impedance

If you take a coil and make a current flow through it, the coil creates a magnetic field. This field induces a voltage into the coil that produces a counter current that weakens the primary current and voltage. If you then measure the voltage and current you can calculate the impedance of the coil.

My question now is, is the impedance higher before the self-inductance or lower ? In other words, how does a magnetic field influence the impedance of a coil ? The complex impedance Z equals u/i ( complex ) but does u and i decrease proportionally or does u or i get smaller faster and make the impedance increase/decrease ?

• You might be interested in reading up on how dc current clamps work Commented Jul 4, 2016 at 12:57

The answer to your question depends on the coil. Assuming the coil is operated at a frequency that is fixed and reasonable for its construction, and ignoring winding resistance, coils without magnetic cores ("air core inductors") have a constant impedance because the permeability of the core is unchanged regardless of the current and the resulting field strength.

Most inductors have ferromagnetic cores whose permeability varies with field strength, so your inductance will decrease as the current increases. If you look at the magnetization curve (B-H curve) for a core material you can see that the curve flattens out as core saturates. Coils are designed to operate in the area around the origin so that the saturation effect is not as pronounced, but there is some small effect even in this area.

In addition, losses for cores occur ("hysteresis losses") when the direction of magnetization is reversed. So, a well-designed ferromagnetic inductor has a small variance in inductance with current that is unavoidable, as you have suggested. The impedance will be lower (the inductance will drop) slightly as the current increases. If the core is saturated, the inductance will drop dramatically.

• Thank you for the detailed answer! One more question though, if a coil is used for non destructive eddy current testing, then the coils impedance is measured and the changes in impedance reflect the material under test. So if the impedance is mot changing alot , how can this work at all ?
– Tom
Commented Jul 4, 2016 at 16:11
• The test piece acts as a part of the magnetizable core. A crack or nonconformity on the test piece will cause a measureable change in the magnetic path and the inductance. Commented Jul 4, 2016 at 20:26
• Okay, so if the eddy currents decrease, the secondary magentic field decreases too, the primary field is less weakened, so the induced current is higher --> Impedance is lower ?
– Tom
Commented Jul 4, 2016 at 20:36