18007983-Transformer-Core-Design-Consider-At

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TRANSFORMER LAMINATIONS,

DESIGN CONSIDERATIONS

Guenter B. Finke, Ph.D. Magnetic Metals Corporation Camden, New Jersey 08101

Engineers inductors will the following netic materials applications. Why Magnetic

and designers of transformers and find the information presented in helpful in the selection of magand core shapes for specific

sinusoidal Ei= 4.44

flux, nfB

we find AC . 10s4 volts, with i,

in which AC is in square cm multiplying we find for the power VA Materials VA= 4.44 n f B AC i 9 lo-4 (4),

Magnetic materials are useful for the generation and distribution of electrical power because these materials allow to transmit large power densities at low losses. In addition, voltage and impedance can be easily changed from one level to another, since changes in the flux density of materials induce voltages in copper coils surrounding the magnetic cores (Faraday's law). The energy E= HB ($&2 density 1 or (s in a magnetic 1 (1) material is

since ni= S . Aw * K, we can substitute in equation 4 and transform into in2, so that VA= 4.55 S B . f AC Aw . lo-4,(5)= (3) in volt amperes.

H is the magnetic field, B the magnetic induction (1 Vs./cm2= log Gauss= lo4 Tesla). In a field of 500 A turns/cm and an induction of 2 Tesla, an energy density of 5 * 10-2 W/cm3 can be stored, which is as high as in the best capacitors. By multiplying equation (1) with core volume Vc= A, . lm, where A, is the core cross section and lm the mean path length and assuming a sinusoidal change of B at the frequency f, it can be rewritten as follows. The power handling capacity in VA is VA= 4.44 lm AC f B H 10v8 (2)

Fig.

1

Transformer

Core of core

AC= ED= cross section Aw= Gf= window area

Since H= ni/lm, the turns and ni the copper wire, factor (.35% for the power handling derived from the VA= 4.55

n number of turns, i current in= S Aw K, S current density in Aw core window, 2K copper fill primary and secondary turns), capacity of a transformer as energy storage equation is (3) Tesla,

S B f AC Aw * 10-4

in which AC and Aw are in in2, B in S in A/in2 and f is the frequency.

The same result is, of course, obtained if we multiply Faraday's law for induction with the current i. Ei= -n AC dB/dt, where Ei is a voltage induced in n turns by a flux change dB/dt. Solving this equation for

Metallic magnetic materials can be used from low frequencies of a few Hz to high frequencies of few hundred kHz, ferrites and iron powder cores can be used up into the MHz range. With above equations, the designer can select suitable dimensions for the copper coil and the magnetic core cross section at the given frequency which meets the loss requirement. Most manufacturers of core components list in their catalogs the Aw AC products for available shapes of core structures. Transformers and inductors can be reduced in weight and volume by operating at higher frequency or by selecting materials which can work at a higher flux density.

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Magnetic

Materials

and Their

Properties

nickel and their alloys cobalt, Iron, have atomic spacings in various crystalline or amorphous structures which produce an interchange of some spins of their 3-D shell so that these spins align in domain electrons, patterns and cause a strong magnetism called The magnetic material proferromagnetism. perties like saturation flux density, the ease of magnetization, permeability, the the changes of these properties core loss, with temperature are therefore influenced by the atomic structure, the anisotropies its impurity levels and of this structure, Imthe stress patterns in the material. provements in the magnetic properties of materials can be made by controlling the purity or adding certain impurities for grain refinement, by adding alloying elements to increase the resistivity, by influencing size and grain orientation, by reducgrain ing the thickness of materials and influencing domain wall spacing through stress coatings, laser scratching and crystal orientation. Figure 2 shows the hysteresis loop of a few commercial grade magnetic materials, low carbon steel, grain oriented 3% Si-Fe and 2V cobalt iron, which in 1984 cost in dollar per pound .30, .75 and .35. The area inside the loop is the core loss per For motor cycle at the measured frequency. and low cost transformer laminations, which are not continuously on-line, the low carbon steel is a suitable material. Low carbon a relatively high core steel has, however, For continuous on-line loss (wider loop). transformers grain oriented steel, with its narrower loop and higher flux density, is the optimum choice and for airborne application, where weight reduction is the main consideration, the 2V cobalt iron is the proper material, since it has the highest saturation flux density. Figure 3 gives the magnetization curves for these and some other alloys. Table 1 lists W/lb., VA/lb. and permeability at 1.5 Tesla (15,000 Gauss) for typical cowercial steels.At Thickness Inches .014, N.O. si N.O. si G.O. si G.O. si 5-l% Steel 2-2.52 Steel 3.2% Steel 3.2% Steel .014, .018, .018, .m,025 W/l 4 3 1.5 T, 60 Hz” 2.600 3,000

Fig.

2

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