## Cut Core Design Manual

HANNA CURVE CALCULATIONS

EXAMPLE:
Required L = 10 henry in an MBH-18 cut core Superperm 49 4 mil with I = .1 amperes dc. As calculated V = 71.02 cm3 and l = 17.62 cm. Calculate LI2/V = 14.08 x 10-4. For estimated B = 1000g., NI/l = 16, and a/l is approximately .00200. Substituting for I and l, N = 2837 turns. The total air gap is approximately .002 x 17.62 = .035 cm or .014 inches. A spacer .007 inch thick will establish this total air gap.

B = Incremental Induction in Gausses.
I = d.c. Current in Amperes.
L = a.c. Inductance in Henries.
V = Core Volume in Cubic Centimeters.
a = Total Air Gap length in Centimeters.
l = Magnetic Path length in Centimeters.

FIGURE 22 - SUPERPERM 49 .004" THICKNESS - 60/400 HZ

FIGURE 23 - SUPERPERM 80 .004" THICKNESS - 60/400 HZ

HANNA CURVES* provide a simplified method of calculating inductances with direct current, and for determining the optimum air gap. Where L is the a.c. inductance in henries, I is the d.c. current in amperes, and V is the core volume in cubic centimeters; calculate LI² /V and enter the left side of the chart at that ordinate. Extend to the right along this ordinate to the appropriate B, for a.c. induction in gausses, and select the indicated abcissa for NI/. Calculate required turns by substituting the centimeters of path length in the core material for , and for the d.c. amperes, I. The optimum ratio of air gap length to path length (a/) applies to the points indicated.

* "Design of Reactors and Transformers Which Carry Direct Current", C.R. Hanna, Journal AIEE, Vol. 46, February 1927.