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Cut
Core Design Manual
DESIGN GUIDE
The power
handling capacity VA, in Volt Amperes, of a transformer at
a given
current density s, flux density B and frequency f is:
VA= 4.55 x s x
DE x FG x B x f x 10-8 Eq.1
Where:
s = Current density (A/in²)
FG = Window area (in²)
DE = Core cross section (in²)
B = Flux density (Gauss)
f = Frequency (Hz)
The flux and current densities to be used in the design depend on the allowable
regulation and temperature rise. It is best to stay close to the test points
given in Table III on page 9. It is sometimes possible to use 5% to 10% higher
flux densities than those listed.
Equation (1) determines the required DE x FG dimensions for a specific power
rating (VA) and this leads to the selection of the proper core size for the
application. For example, the power handling capacity (VA) of a C-Core operating
at 18 Kilogauss
and a current density of 1500 A/in² is
computed by:
VA = 74 DE FG for 60 Hz Eq.2a
VA = 491 DE FG for 400 Hz Eq.2b
To design cores of the size determined by Equations 1 and 2 use strip widths
(dimension D), which are listed in Table II (Material Standard Stripwidth).
The maximum loss P, in Watts, of a core can be calculated as:
P = Weight x W/lb. Eq.3
The maximum exciting current I, in Amperes, of a core can be calculated as:
I = Wt x VA/lb / Volts + 1.43 x B x a x S / N Eq.4
The turns/Volt can be calculated as:
Turns/Volt = N/V = 3.5 x 106 / f x B x DE x S Eq.5
Where:
Wt = lb = y x DE x S x (2F + 2G + 2.9E)
W = Watts γ = Spec. Weight, lb/in²
V = Volt S = Stacking Factor
B = Gauss a = airgap in inches
N = turns a = .001" for DE <2.25 in² or E <1
A = Amps a = .002" for DE >2.25 in² or E <1
For transformers of 500 watts and greater, the current density of the coils
should be 1,500 A/in² to 1,700 A/in²; for smaller transformers
1,800 A/in² to 2,000 A/in². Higher flux and current densities are
possible when forced air cooling is applied.
PULSE PERMEABILITY
Typical pulse permeability using DC-reset and a flux change δB
= 22 Kilogauss for 2 mil material and δB = 28 Kilogauss for 4 mil
material are shown in Figure 1. These curves can also be used for pulse
cores having an airgap reset.
In this case the pulse permeability is 60% of the value
shown for a flux change δB = 10 Kilogauss for 2 mil and δB
= 15 Kilogauss for the 4 mil material.
Pulse permeability: μp = 2.54 x δB x ι / .4 x ¶ x n
x lm Eq.6
Peak Pulse voltage during pulse duration td = 6.45 x
N x DE x δ B x S x 10-8 Eq.7
Where:
ι = mean path length (2F + 2G + 2.9E)
lm = peak exciting current in Amperes
td = seconds
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