- Minntronix Technical Note - Effects of Air Gap Tolerance on Inductance Tolerance Dave LeVasseur VP of Research & Development Minntronix, Inc. 4-Mar-2016

Inductance Tolerance As transformer manufacturers we are sometimes asked to provide parts with inductance tolerances that are too narrow for reasonable manufacturing efficiency and production yield. The core’s air gap is the key to providing controlled inductance but its dimension is subject to the limits of mechanical tolerance control. This App Note describes how magnetic cores are typically gapped and the effects of gap tolerance on inductance tolerance.

Inductance Tolerance Video still image from YouTube: *Gapped core image courtesy of Encyclopedia Magnetica: The air gap is typically quite small when compared to the core’s entire magnetic path length. Gaps are typically 0.001” to 0.1” ( to 0.25cm) compared to typical path lengths of cm for parts up to the size of a human fist. Magnetic path length L M Air gaps can be ground into the center leg using a wet grinding technique. Large gaps may require several passes. Small gaps can be done in one pass but due to manufacturing tolerance may vary ± ” (6.4um) from part to part. air gap length L g

Air gap L g  RcRc RgRg  (t) Physical GeometryMagnetic Circuit Effects of Air Gap on Permeability Path length L M

Effects of Air Gap on Permeability Air gap L g  Core with magnetic path length L M Magnetic path length L M  Core with magnetic path length L M and air gap L g * For this example we’ll assume the permeability of the “air” gap to be 1

Materials having high permeability also have a broad tolerance on their permeability. Materials with permeability greater than 10,000 may specified as minimum-only. To make the effective permeability  e have a tighter tolerance we must introduce an air gap in the core. Rearranging the formula to solve for the ratio of L g to L M yields: Effects of Air Gap on Permeability * For this example we’ll assume the permeability of the “air” gap to be 1

Given that once it is set up a typical ferrite gapping machine will stay within 0.2 thousandth of an inch (about 5um). For sake of example assume a typical power ferrite of size EE20 has a material permeability of 2000 and that we need to determine if we can control the inductance of a 15T winding to 100uH ±5%. The EE20 core has a magnetic path length L M of 4.28cm and cross-sectional area of 0.312cm 2. How manufacturing tolerances affect inductance tolerance Rearranging this:to solve: for µ e : Plugging in the values:

Although the actual gap calculation is an iterative process we can start to determine the gap using the effective permeability obtained with the starting values: How manufacturing tolerances affect inductance tolerance Rearranging this to solve for L g : Plugging in the values: (For sake of simplicity we are ignoring effects of flux fringing which typically impacts results when Lg is > 1% of the path length, but core shape and aspect ratio also play roles in this: )

If our gapping tolerance is ” (0.0508cm) the range of air gap becomes How manufacturing tolerances affect inductance tolerance ± = to ” ( to cm = to 0.071mm) Putting this range back into the equation for effective permeability results in: Running these through this:

How manufacturing tolerances affect inductance tolerance