chapter 7

1. electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA chapter 7

2. Where lines are close together, the flux density is higher. Where lines are further apart, the flux density is lower. Magnetic Quantities Magnetic fields are described by drawing flux lines that represent the magnetic field.

3. The Magnetic Field Magnetic fields are composed of invisible lines of force that radiate from the north pole to the south pole of a magnetic material. Field lines can be visualized with the aid of iron filings sprinkled in a magnetic field.

4. The Magnetic Field The magnetic field lines surrounding a magnet actually radiate in three dimensions. These magnetic field lines are always associated with moving charge. In permanent magnets, the moving charge is due to the orbital motion of electrons. Ferromagnetic materials have minute magnetic domains in their structure.

5. Magnetic Materials In ferromagnetic materials such as iron, nickel, and cobalt, the magnetic domains are randomly oriented when unmagnetized. When placed in a magnetic field, the domains become aligned, thus they effectively become magnets.

6. Magnetic Quantities The unit of flux is the weber. The unit of flux density is the weber/square meter, which defines the unit tesla, (T), a very large unit. Flux density is given by the equation where B = flux density (T) j = flux (Wb) A = area (m2)

7. Magnetic Quantities To measure magnetic fields, an instrument called a gaussmeter is used. A typical gaussmeter is shown. The gauss, (G) is a unit of flux density and is a much smaller unit than the tesla (104 G = 1 T). Gaussmeters are commonly used for testing motors, classifying magnets, mapping magnetic fields, and quality control by manufacturers of motors, relays, solenoids, and other magnetic devices.

8. Solution: Magnetic Quantities Example: What is the flux density in a rectangular core that is 8.0 mm by 5.0 mm if the flux is 20 mWb? Follow up: Express this result in gauss.

9. Iron filings Current-carrying wire Magnetic Quantities • Magnetic flux lines surround a current carrying wire. • The field lines are concentric circles. • As in the case of bar magnets, the effects of electrical current can be visualized with iron filings around the wire – the current must be large to see this effect.

10. Magnetic Quantities • Permeability (m) defines the ease with which a magnetic field can be established in a given material. It is measured in units of the weber per ampere-turn meter. • The permeability of a vacuum (m0) is 4p x 10-7 weber per ampere-turn meter, which is used as a reference. • Relative Permeability (mr) is the ratio of the absolute permeability to the permeability of a vacuum.

11. Magnetic Quantities • Reluctance (R) is the opposition to the establishment of a magnetic field in a material. R= reluctance in A-t/Wb l = length of the path m = permeability (Wb/A-t m). A = area in m2

12. Fm = NI Magnetic Quantities • Recall that magnetic flux lines surround a current-carrying wire. A coil reinforces and intensifies these flux lines. • The cause of magnetic flux is called magnetomotive force (mmf), which is related to the current and number of turns of the coil. Fm = magnetomotive force (A-t) N = number of turns of wire in a coil I = current (A)

13. 2.0 mWb Magnetic Quantities • Ohm’s law for magnetic circuits is • flux (j) is analogous to current • magnetomotive force (Fm) is analogous to voltage • reluctance (R) is analogous to resistance. Problem: What flux is in a core that is wrapped with a 300 turn coil with a current of 100 mA if the reluctance of the core is 1.5 x 107 A-t/Wb?

14. 750 A-t Magnetic Quantities The magnetomotive force (mmf) is not a true force in the physics sense, but can be thought of as a cause of flux in a core or other material. Current in the coil causes flux in the iron core. Iron core What is the mmf if a 250 turn coil has 3 A of current?

15. The Hall Effect The Hall effect is occurrence of a very small voltage that is generated on opposite sides of a thin current-carrying conductor or semiconductor (the Hall element) that is in a magnetic field. The Hall effect is widely employed by various sensors for directly measuring position or motion and can be used indirectly for other measurements.

16. Sliding core (plunger) Stationary core Spring Solenoids A solenoid is a magnetic device that produces mechanical motion from an electrical signal. One application is valves that can remotely control a fluid in a pipe, such as in sprinkler systems.

17. Alternate schematic symbol Relays A relay is an electrically controlled switch; a small control voltage on the coil can control a large current through the contacts. Structure Schematic symbol

18. or Magnetic field intensity is the magnetomotive force per unit length of a magnetic path. H= Magnetic field intensity (Wb/A-t m) Fm = magnetomotive force (A-t) l = average length of the path (m) N = number of turns I = current (A) • Magnetic field intensity represents the effort that a given current must put into establishing a certain flux density in a material.

19. B = mH Magnetic Quantities If a material is permeable, then a greater flux density will occur for a given magnetic field intensity. The relation between B (flux density) and H (the effort to establish the field) is m = permeability (Wb/A-t m). H= Magnetic field intensity (Wb/A-t m) This relation between B and H is valid up to saturation, when further increase in H has no affect on B.

20. As the graph shows, the flux density depends on both the material and the magnetic field intensity.

21. As H is varied, the magnetic hysteresis curve is developed.

22. Annealed iron Magnetization Curve A B-H curve is referred to as a magnetization curve for the case where the material is initially unmagnetized. The B-H curve differs for different materials; magnetic materials have in common much larger flux density for a given magnetic field intensity, such as the annealed iron shown here.

23. Relative motion When a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field. When a magnetic field is moved past a stationary wire, there is also relative motion. In either case, the relative motion results in an induced voltage in the wire.

24. Induced voltage The induced voltage due to the relative motion between the conductor and the magnetic field when the motion is perpendicular to the field is dependent on three factors: • the relative velocity (motion is perpendicular) • the length of the conductor in the magnetic field • the flux density

25. The rate of change of the magnetic flux with respect to the coil. Faraday’s law Faraday experimented with generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors: Voltage is indicated only when magnet is moving.

26. The number of turns of wire in the coil. Faraday’s law Faraday also experimented generating current by relative motion between a magnet and a coil of wire. The amount of voltage induced across a coil is determined by two factors: • The rate of change of the magnetic flux with respect to the coil. Voltage is indicated only when magnet is moving.

27. Magnetic field around a coil Just as a moving magnetic field induces a voltage, current in a coil causes a magnetic field. The coil acts as an electromagnet, with a north and south pole as in the case of a permanent magnet.

28. Brushes Commutator To external circuit DC Generator Mechanical drive turns the shaft A dc generator includes a rotating coil, which is driven by an external mechanical force (the coil is shown as a loop in this simplified view). As the coil rotates in a magnetic field, a pulsating voltage is generated.

29. DC Motor A dc motor converts electrical energy to mechanical motion by action of a magnetic field set up by the rotor. The rotor field interacts with the stator field, producing torque, which Mechanical output causes the output shaft to rotate. The commutator serves as a mechanical switch to reverse the current to the rotor at just the right time to continue the rotation. Commutator Brushes

30. Brushless DC Motor A brushless dc motor has rotating field and a permanent magnet rotor. An electronic controller periodically reverses the current in the field coils. This causes the stator field to rotate, and the permanent magnet rotor moves to keep up with the rotating field. Hall sensor Permanent magnet rotor (Courtesy of Bodine Electric Company)

31. Brushless DC Motor Series wound dc motor • A series wound dc motor has the field coil(s) in series with the armature. • The series wound motor has very high starting torque. • It can run too fast if a load is not connected; therefore it is always used with a load.

32. Shunt wound dc motor • A shunt wound dc motor has the field coil(s) in parallel with the armature. • The magnetic flux is constant because of the parallel arrangement. • Unlike the series wound motor, torque tends to be nearly constant for different loads.

33. Magnetic units It is useful to review the key magnetic units from this chapter: Quantity SI Unit Symbol Magnetic flux density Tesla Weber Weber/ampere-turn-meter Ampere-turn/Weber Ampere-turn Ampere-turn/meter B f m R Fm H Flux Permeability Reluctance Magnetomotive force Magnetizing force

34. Selected Key Terms A force field radiating from the north pole to the south pole of a magnet. Magnetic field Magnetic flux Weber (Wb) Permeability Reluctance The lines of force between the north pole and south pole of a permanent magnet or an electromagnet. The SI unit of magnetic flux, which represents 108 lines. The measure of ease with which a magnetic field can be established in a material. The opposition to the establishment of a magnetic field in a material.

35. Selected Key Terms The cause of a magnetic field, measured in ampere-turns. Magnetomotive force (mmf) Solenoid Hysteresis Retentivity An electromagnetically controlled device in which the mechanical movement of a shaft or plunger is activated by a magnetizing current. A characteristic of a magnetic material whereby a change in magnetism lags the application of the magnetic field intensity. The ability of a material, once magnetized, to maintain a magnetized state without the presence of a magnetizing current.

36. Selected Key Terms Voltage produced as a result of a changing magnetic field. Induced voltage (vind) Faraday’s law Lenz’s law A law stating that the voltage induced across a coil of wire equals the number of turns in the coil times the rate of change of the magnetic flux. A law stating that when the current through a coil changes, the polarity of the induced voltage created by the changing magnetic field is such that it always opposes the change in the current that caused it. The current cannot change instantaneously.

37. Quiz 1. A unit of flux density that is the same as a Wb/m2 is the a. ampere-turn b. ampere-turn/weber c. ampere-turn/meter d. tesla

38. Quiz 2. If one magnetic circuit has a larger flux than a second magnetic circuit, then the first circuit has a. a higher flux density b. the same flux density c. a lower flux density d. answer depends on the particular circuit.

39. Quiz 3. The cause of magnetic flux is a. magnetomotive force b. induced voltage c. induced current d. hysteresis

40. Quiz 4. The measurement unit for permeability is a. weber/ampere-turn b. ampere-turn/weber c. weber/ampere-turn-meter d. dimensionless

41. Quiz 5. The measurement unit for relative permeability is a. weber/ampere-turn b. ampere-turn/weber c. weber/ampere-turn meter d. dimensionless

42. Quiz 6. The property of a magnetic material to behave as if it had a memory is called a. remembrance b. hysteresis c. reluctance d. permittivity

43. B = mH Fm = NI Quiz 7. Ohm’s law for a magnetic circuit is a. b. c. d.

44. Quiz 8. The control voltage for a relay is applied to the a. normally-open contacts b. normally-closed contacts c. coil d. armature

45. Quiz 9. A partial hysteresis curve is shown. At the point indicated, magnetic flux a. is zero b. exists with no magnetizing force c. is maximum d. is proportional to the current

46. Quiz 10. When the current through a coil changes, the induced voltage across the coil will a. oppose the change in the current that caused it b. add to the change in the current that caused it c. be zero d. be equal to the source voltage

47. Quiz Answers: 1. d 2. d 3. a 4. c 5. d 6. b 7. c 8. c 9. b 10. a