EI Core Geometry — Definitions

Every quantity on this site derives from two numbers you choose — the tongue and the stack — plus the fixed proportions of a scrapless EI lamination. This page fixes the names, because the same dimension gets called different things depending on which way the lamination is drawn.

Always drawn upright. Width and height only mean something once the orientation is fixed, so every diagram here has the legs vertical — the same way textbook formulas assume. Window width then runs across the legs and window height along them, and the height is three times the width. If you meet a drawing rotated a quarter turn, the two swap over.

A scrapless EI stamping wastes nothing: the I piece is cut from the two windows. That single requirement fixes every proportion. The windows total 2 × (T/2 × 3T/2) = 3T²/2 and the I piece is 3T × T/2 = 3T²/2 — exactly equal.

Dimension	Value	What it is
Tongue	T	Width of the centre leg. The one dimension everything else is stated in.
Stack	S	How thick the lamination pile is. Your choice, not a property of the lamination — a square stack means S = T.
Window height	3T/2	Along the legs. This is the winding traverse, so it sets turns per layer.
Window width	T/2	Across the legs. This is the radial direction, so it limits coil build. The height is exactly three times it.
Outer leg	T/2	Each outer leg carries half the flux, so it is half the tongue.
Yoke	T/2	Top and bottom, same reasoning.
Overall	3T × 5T/2	Width × height, upright.
Steel area	6T²	15T²/2 overall less 3T²/2 of window.

Dimension

Value

What it is

Tongue

Width of the centre leg. The one dimension everything else is stated in.

Stack

How thick the lamination pile is. Your choice, not a property of the lamination — a square stack means S = T.

Window height

3T/2

Along the legs. This is the winding traverse, so it sets turns per layer.

Window width

T/2

Across the legs. This is the radial direction, so it limits coil build. The height is exactly three times it.

Outer leg

T/2

Each outer leg carries half the flux, so it is half the tongue.

Yoke

T/2

Top and bottom, same reasoning.

Overall

3T × 5T/2

Width × height, upright.

Steel area

6T²

15T²/2 overall less 3T²/2 of window.

On an EI-75 — a 0.75″ tongue — that gives a window 0.375″ wide by 1.125″ tall, and an overall lamination of 2.25″ wide by 1.875″ tall.

Imperial and metric EI numbers mean different things. An imperial EI-100 has a one inch tongue. A metric EI-96 is 96 mm across overall, which is a 32 mm tongue, since overall width is 3T. Same naming scheme, different dimension being named.

Quantity	Formula	Notes
Effective core area	A_e = T × S × k	k is the stacking factor, around 0.95 — laminations have insulation and do not pack solid.
Magnetic path	l_c = 6T	The mean of the shortest flux loop (4T, hugging one window) and the longest (8T, round the outside). See the derivation.
Window area	3T²/4	Per window, width × height. Only part of it becomes copper.
Mean length of turn	MLT	Grows as the coil builds outward from the former. See the MLT note.
Apparent permeability	μ_e = μ_r / (1 + μ_r l_g / l_c)	The assembled stack’s permeability, not the steel’s. An EI loop crosses the joint plane twice, so a shim of t contributes 2t to l_g.

Quantity

Formula

Notes

Effective core area

A_e = T × S × k

k is the stacking factor, around 0.95 — laminations have insulation and do not pack solid.

Magnetic path

l_c = 6T

The mean of the shortest flux loop (4T, hugging one window) and the longest (8T, round the outside). See the derivation.

Window area

3T²/4

Per window, width × height. Only part of it becomes copper.

Mean length of turn

MLT

Grows as the coil builds outward from the former. See the MLT note.

Apparent permeability

μ_e = μ_r / (1 + μ_r l_g / l_c)

The assembled stack’s permeability, not the steel’s. An EI loop crosses the joint plane twice, so a shim of t contributes 2t to l_g.

Why l_c matters less than it looks. Every EI core is joint-limited, so μ_e tends towards l_c / l_g — which means l_c cancels out of both A_L and the saturation current, and it never enters flux density at all. Choosing 6T over the centreline 6.5T changes results by about 1.5 %, except where a measured permeability is entered directly and nothing compensates.