
Cut
Core Design Manual
HANNA CURVE CALCULATIONS
EXAMPLE:
Required L = 10 henry in an MBH18 cut core Superperm 49 4 mil with I = .1
amperes dc. As calculated V = 71.02 cm^{3} and l = 17.62 cm.
Calculate LI^{2}/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.
