Magnetism and Magnetic Circuits

1
Lecture 3

• Magnetism and Magnetic Circuits

2
The Nature of a Magnetic Field

• Magnetism refers to the force that acts between
  magnets and magnetic material.
• Flux lines show the direction and intensity of
  this field at all points.
• The field is strongest at the poles the
  direction is from N to S.
• Unlike poles attract, like poles repel.

3
Ferromagnetic Materials

• Materials that are attracted by magnets are
  called ferromagnetic materials.
• These materials provide an easy path for magnetic
  flux.
• Iron, nickel, cobalt, and their alloys are
  ferromagnetic.
• Nonmagnetic materials such as plastic, wood, and
  glass have no effect on the field.

4
Electromagnetism

• Many applications of magnetism involve magnetic
  effects due to electric currents.
• Place your right hand around the conductor with
  your thumb in the direction of the current. Your
  fingers then point in the direction of the field.

5
Flux and Flux Density

• Flux, ?, refers to the total number of lines.
• Flux density, B, refers to the number of lines
  per unit area.
• Flux density is found by dividing the total flux
  passing perpendicularly through an area by the
  area.
• B ?/A

6
Flux and Flux Density

• The units for flux are webers.
• Area is measured in square meters.
• The units for flux density are teslas.
• B may also be measured in gauss.
• 1 tesla 10 000 gauss
• We will work only with teslas.

7
Magnetic Circuits

• Most practical applications use structures to
  guide and shape magnetic flux. These are called
  magnetic circuits.
• A speaker uses a magnetic circuit to guide the
  flux to an air gap to provide the field for the
  voice coil.
• The playback heads on tape recorders, VCRs, and
  disk drives pick up the varying magnetic field
  and convert it to voltage.

8
Air Gaps, Fringing, and Laminated Cores

• For circuits with air gaps, fringing may occur.
• Correction may be made by increasing each
  cross-sectional dimension of the gap by the size
  of the gap.
• Many applications use laminated cores.
• In these cases, the effective area is not as
  large as the actual area.

9
Series Elements and Parallel Elements

• Magnetic circuits may have sections of different
  materials - for example, cast iron, sheet steel,
  and an air gap.
• For this circuit, flux is the same in all
  sections this circuit is a series magnetic
  circuit.
• A magnetic circuit may have elements in parallel
  the sum of fluxes entering a junction is equal to
  the sum leaving.

10
Magnetic Circuits with dc Excitation

• Current through a coil creates magnetic flux.
  Magnetomotive force ? NI.
• The opposition of the circuit is the reluctance ?
  l/µA.
• Ohms Law for magnetic circuits ? ?/?.
• This is a useful analogy but not a practical
  solution method.

11
Magnetic Field Intensity

• The magnetic field intensity, H, is the
  magnetomotive force (mmf) per unit length.
• H ?/? NI/?
• The units are Ampereturns/meter.
• NI H?

12
The Relationship between B and H

• B and H are related by the equation B µH, where
  µ is the permeability of the core.
• Permeability is the measure of how easy it is to
  establish flux in a material.
• The larger the value of µ, the larger flux
  density for a given H.
• H is proportional to I therefore the larger the
  value of µ, the larger the flux density for a
  given circuit.

13
Amperes Circuital Law

• The algebraic sum of mmfs around a closed loop in
  a magnetic circuit is zero ?? 0.
• Since ? NI, ?NI ?H?.
• NI - Hiron?iron - Hsteel?steel - Hg?g 0

14
Series Magnetic Circuits

• To solve a circuit where ? is known, first
  compute B using ?/A.
• Determine H for each magnetic section from B-H
  curves.
• Compute NI using Amperes circuital law.
• Use the computed NI to determine coil current or
  turns as required.

15
Series-Parallel Magnetic Circuits

• Series-parallel magnetic circuits are handled
  using the sum of fluxes principle and Amperes
  Law.
• For this circuit, find B and H for each section.
• Then use Amperes Law.

16
Series Magnetic Circuits

• If we are given NI and required to find ?, for
  circuits with one material, we can solve
  directly.
• For two or more substances, the problem is we can
  not calculate either ? or H without knowing the
  other.
• Trial and error is used by taking a guess at the
  flux to compute NI, then comparing this against
  the given NI.

17
Forces due to an Electromagnet

• Electromagnets are used in relays, doorbells,
  lifting magnets, etc.
• This force can be computed from the flux density,
  the gap area, and the permeability.

18
Properties of Magnetic Materials

• Atoms produce small, atomic-level magnetic
  fields.
• For nonmagnetic materials, these fields are
  randomly arranged.
• For ferromagnetic materials, the fields do not
  cancel, but instead form into domains.
• If the domain fields in a material line up, the
  material is magnetized.

19
Magnetizing a Specimen

• A specimen can become magnetized if a current
  passes through it and causes the domain fields to
  line up.
• If all of the fields line up, the material is
  saturated.
• If the current is tuned off, the material will
  retain some residual magnetism.
• Turning off the current does not demagnetize the
  material some other method must be used.

20
Measuring Magnetic Fields

• One way to measure magnetic field strength is to
  use the Hall effect.
• When a piece of metal is placed in a magnetic
  field, a small voltage develops across it.
• For a fixed current, the Hall voltage is
  proportional to the magnetic field strength B.
• The direction of the field may be determined by
  the right-hand rule.

21

• Inductance and Inductors

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Inductors

• A common form of an inductor is a coil of wire.
• They are used in radio tuning circuits.
• In fluorescent lights, they are part of the
  ballast circuit.
• On power systems, they are part of the protection
  circuitry used to control short-circuit currents
  during faults.

23
Electromagnetic Induction

• When a magnet moves through a coil of wire,
  voltage is induced.
• When a conductor moves through a magnetic field,
  voltage is induced.
• A change in current in one coil can induce a
  voltage in a second coil.
• A change in current in a coil can induce a
  voltage in that coil.

24
Electromagnetic Induction

• Faradays Law states that voltage is induced in a
  circuit whenever the flux linking the circuit is
  changing and that the magnitude of the voltage is
  proportional to the rate of change of the flux
  linkages.
• Lenzs Law states that the polarity of the
  induced voltage is such as to oppose the cause
  producing it.

25
Induced Voltage and Induction

• If a constant current is applied to an inductor,
  no voltage is induced.
• If the current is increased, the inductor will
  develop a voltage with a polarity to oppose the
  increase.
• If the current is decreased, a voltage is formed
  with a polarity that opposes the decrease.

26
Iron-Core Inductors

• Have their flux almost entirely confined to their
  cores.
• All flux lines pass through the windings.
• Flux linkage is the product of flux times number
  of turns.
• By Faradays law, the induced voltage is equal to
  the rate of change of N?.

27
Air-Core Inductors

• All of the flux lines do not pass through all of
  the windings.
• Flux is directly proportional to current.
• The induced voltage will be directly proportional
  to the rate of change of current.

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Self-Inductance

• The voltage induced in a coil is proportional to
  the rate of change of the current.
• The proportionality constant is L, the self-
  inductance of the coil.
• The inductance of a coil is one henry if the
  voltage created by its changing current is one
  volt when its current changes at the rate of one
  amp per second.

29
Inductance Formulas

• The inductance of a coil is given by
• ? is the length of the coil in meters.
• A is the cross-sectional area in square meters.
• N is the number of turns.
• µ is the permeability of the core.

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Inductance Formulas

• If an air gap is used, the formula for inductance
  is
• where µo is the permeability of air.
• Ag is the area of the air gap.
• ?g is the length of the gap.

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Computing Induced Voltage

• When using the equation
• If the current is increasing, the voltage is
  positive if the current is decreasing, the
  voltage is negative.
• ?i/?t is the slope for currents which can be
  described with straight lines.

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Inductances in Series

• For inductors in series, the total inductance is
  the sum of the individual inductors.

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Inductances in Parallel

• Inductors in parallel add as resistors do in
  parallel

34
Core Types

• The type of core depends on intended use and
  frequency range.
• For audio or power supply applications, inductors
  with iron cores are generally used.
• Iron-core inductors have large inductance values
  but have large power losses at high frequencies.
• For high-frequency applications, ferrite-core
  inductors are used.

35
Variable Inductors

• Used in tuning circuits.
• Inductance may be varied by changing the coil
  spacing.
• Inductance may also be changed by moving a core
  in or out.

36
Circuit Symbols
37
Stray Capacitance

• Because the turns of the inductors are separated
  by insulation, a stray or parasitic capacitance
  may develop.
• At low frequencies, it can be ignored at high
  frequencies, it must be taken into account.
• Some coils are wound in multiple sections to
  reduce stray capacitance.

38
Stray Inductance

• All current-carrying components have some stray
  inductance due to the magnetic effects of the
  current.
• The leads of resistors, capacitors, etc. have
  inductance.
• These leads are often cut short to reduce this
  stray inductance.

39
Inductance and Steady State DC

• The voltage across an inductance with constant dc
  current is zero.
• Since it has current but no voltage, it looks
  like a short circuit at steady state.
• For non-ideal inductors, the resistance of the
  windings must be taken into account.

40
Energy Stored by an Inductance

• When energy flows into an inductor, energy is
  stored in its magnetic field.
• When the field collapses, the energy returns to
  the circuit.
• No power is dissipated, so there is no power
  loss.
• The energy stored is given by

41
Troubleshooting Hints

• Check with an ohmmeter.
• An open coil will have infinite resistance.
• A coil can develop shorts between its windings
  causing excessive current. Checking with an
  ohmmeter may indicate lower resistance.

42

• Inductive Transients

43
Transients

• Voltages and currents during a transitional
  interval are called transients.
• In a capacitive circuit, voltages and currents go
  through a transitional phase while the capacitor
  charges and discharges.
• In an inductive circuit, a transitional phase
  occurs as the magnetic field builds and
  collapses.

44
Voltage across an Inductor

• The induced voltage across an inductor is
  proportional to the rate of change of current.
• If the inductor current could change
  instantaneously, its rate of change would be
  infinite. This would cause infinite voltage.

45
Continuity of Current

• Since infinite voltage is not possible, inductor
  current cannot change instantaneously.
• This means it cannot jump abruptly from one value
  to another, but must be continuous at all values
  of times.
• Use this observation when analyzing circuits.

46
Circuit and Waveforms for Current Build-up
47
Inductor Voltage

• Immediately after closing the switch on an RL
  circuit, the current is zero, so the voltage
  across the resistor is zero.
• Since the voltage across the resistor is zero,
  the voltage across the inductor is source
  voltage.
• The inductor voltage will then decay to zero.

48
Open-Circuit Equivalent

• Just after the switch is closed, the inductor has
  voltage across it and no current through it.
• An inductor with zero initial current looks like
  an open circuit at the instant of switching.
• This statement will later be applied to include
  inductors with nonzero initial currents.

49
Initial Condition Circuits

• Voltages and currents in circuits immediately
  after switching can be determined from the
  open-circuit equivalent.
• By replacing inductors with opens, we get the
  initial condition circuit.
• Initial condition networks yield voltages and
  currents only at the instant of switching.

50
Circuit Current

• Current in an RL circuit is an increasing
  function.
• The current begins at zero and rises to a maximum
  value.

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Circuit Voltages

• The voltage across the resistor is given by iR.
• The voltage across the resistor is an increasing
  function.

52
Circuit Voltages

• By KVL, the voltage across the inductor is
• E - vR.
• The voltage across the inductor is a decreasing
  function.

53
Time Constant

• ? L/R
• The units are seconds.
• The equations may now be written as

54
Time Constant

• The larger the inductance, the longer the
  transient.
• The larger the resistance, the shorter the
  transient.
• As R increases, the circuit looks more and more
  resistive if R is much greater than L, the
  circuit looks purely resistive.

55
Interrupting Current in an Inductive Circuit

• When the switch opens in an RL circuit, a great
  deal of energy is released in a short time.
• This may create large voltage.
• This induced voltage is called an inductive kick.
• The breaking of current may cause voltage spikes
  of thousands of volts.

56
Interrupting a Circuit

• Switch flashovers are generally undesirable, but
  they can be controlled with proper engineering
  design.
• These large voltages are sometimes useful, such
  as in automotive ignition systems.
• It is not possible to completely analyze such a
  circuit because the resistance across the arc
  changes as the switch opens.

57
Interrupting a Circuit

• In the circuit shown, we can see the changes as
  after the switch opens

58
Inductor Equivalent at Switching

• The current through an inductor is the same
  immediately after switching as before switching.
• An inductance with an initial current looks like
  a current source at the instant of switching.
• Its value is the value of the current at
  switching.

59
De-energizing Transients

• If an inductor has an initial current I0, the
  equation for the current becomes
• ? ' L/R. R equals total resistance in the
  discharge path.

60
De-energizing Transients

• The voltage across the inductor goes to zero as
  the circuit de-energizes.

61
De-energizing Circuits

• The voltage across any resistor is the product of
  the current and that resistor.
• The voltage across any of the resistors goes to
  zero.

62
More Complex Circuits

• For complex circuits, it is necessary to
  determine the Thévenin equivalent of the circuit
  with respect to the inductor.
• RTh is used to determine the time constant.
• ETh is used as the source voltage.