In this blog I show how Ampere's Law is applied to determine how much current a conductor enclosed by a magnetic core must carry to obtain the B value from a BH value operating point which corresponds to the max B value in the magnetic core material. I use two operating points on the BH curve, one in the linear region and the other in the saturation region.

AMPERE"S LAW

The H field is inversely proportional to the radial distance from the conductor. We can pick an operating point (H, B), and choose the inner core radius as the Amperian contour in applying Ampere's Law to compute the current enclosed (flowing through the conductor) since maximum H and B will occur over the surface of the core closest to the conductor. It is important for the inner core surface to have very high mesh density to accurately compute the distribution of the magnetic field strength and flux density.

BH CURVE

Here is the BH curve for AK Steel-H-0. Examples using operating points in the linear region and saturation region are given below.

LINEAR REGION

The operating point chosen in the linear region is shown below and the computed max B value is less than 3% different than the B value of the operating point. This magnetic core material is not saturated just as it should not be based on the BH curve and operating point chosen. In the properties of the winding I use Ampere's Law for the current carried by the conductor, where Hlin (10.0233 A/m) is the magnetic strength value of the operating point in the linear region.

SATURATION REGION

The operating point chosen in the saturation region is shown below and the computed max B value is less than 3% different than the B value of the operating point. This magnetic core material is saturated just as it should be based on the BH curve and operating point chosen. In the properties of the winding I use Ampere's Law for the current carried by the conductor, where Hsat (101500 A/m) is the magnetic strength value of the operating point in the saturation region.

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December 22, 2023