1. 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

2. Hysteresis Losses Figure shows the effect within ferromagnetic materials known as hysteresis. ferromagnetic We start with an unmagnetized sample at the origin (P1) where both field strength and flux density are zero. The field strength is increased in the positive direction and the flux begins to grow along the dotted path until we reach P2. This is called the initial magnetization curve.field strengthflux densityinitial magnetization curve.

3. Hysteresis Losses….contd If the field strength is now relaxed then some curious behavior occurs. Instead of retracing the initial magnetization curve the flux falls more slowly. In fact, even when the applied field is returned to zero there will still be a remaining (remnant or remanent) flux density at P3. It is this phenomenon which makes permanent magnets possible.remnant or remanent

4. 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.

5. The domains before applying magnetic field The domains after applying magnetic field When the magnetic field is removed, not all domains are randomized again

7. 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.

8. Other losses - Copper loss: - Eddy Current loss: - Core losses:

9. 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.

12. Eddy current losses

13. How do we reduce Eddy current losses LAMINATED SOLID

14. Eddy current losses

15. Eddy current losses in windings Can be a problem with thick wires - Low voltage machines - High speed machines