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Summary of the last lecture. Magnetic circuits. Compare this formula with Ohm’s law in electric circuits:. Another useful formula in a series situation. Problem 1-8. Assume 4% increase in effective Cross-sectional area for fringing effect. Calculate the flux density in each of the legs.

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Presentation Transcript
slide2

Magnetic circuits

Compare this formula with Ohm’s law in electric circuits:

problem 1 8
Problem 1-8

Assume 4% increase in effective

Cross-sectional area

for fringing effect

Calculate the flux density in each of the legs

magnetic behaviour of ferromagnetic materials
Magnetic Behaviour of Ferromagnetic Materials

We talked about Ferromagnetic materials, such as iron, steel, cobalt, nickel and some alloys. They have a high relative permeability (2000-6000).

In magnetic circuit theory we assumed:

where is a constant.

slide9

By this assumption we have assumed a linear relation, i.e.:

This means in a coil if I increase the current to twice as much, the flux will be twice as much as well. This is what we call linear relation.

slide13

Now, can we solve the problems knowing these curves ?

In some problems, instead of giving the relative permeability, they produce the B-H curve.

In these cases, the operating condition (Bo-Ho), should be known somehow. If it is known, there would be no problem.

slide14

Remember the example:

Given : i=1 A, N=100, lc=40 cm, A= 100 cm2 r =5000

Calculate : F, H, B, , and

slide15

Now consider this example:

Given : i=1 A, N=100, lc=40 cm, A= 100 cm2 given the above B-H curve

Calculate : F, H, B, , and

From the magnetizing curve:

hysteresis
Hysteresis

When we increased the current we observed, saturation.

What would happen if I decrease the current after saturation?

The flux for a given H is higher when decreasing

can we explain the hysteresis phenomena
Can we explain the hysteresis phenomena?

All materials consist of small magnetic domains.

When they are in a magnetic field the domains are intended to be in line with the field.

slide18

The domains

after applying

magnetic field

The domains

before applying

magnetic field

When the magnetic field is removed, not all domains

are randomized again

hysteresis loss
Hysteresis loss

Hysteresis is not a serious problem when we have DC excitation (the examples considered so far). It causes some loss when we have AC excitation, called hysteresis loss.

If we have AC excitation, e.g. the current i is sinusoid, the hysteresis happens at each cycle. The hysteresis loss is proportional to the frequency and also depends on the area of the hysteresis loop.

other losses
Other losses

- Copper loss:

- Eddy Current loss:

- Core losses:

eddy current
Eddy Current

Eddy current:

As we saw, a flux induces a voltage on a coil.

Q: Why not inducing a voltage on the core itself?

A: It actually does.

The result is eddy current. That is why the transformers core are laminated.