Chapter 11 Magnetic Circuits

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Chapter 11 Magnetic Circuits

• Introductory Circuit Analysis
• Robert L. Boylestad

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11.1 - Introduction

• Magnetism is an integral part of almost every
  electrical device used today in industry,
  research, or the home
• Generators, motors, transformers, circuit
  breakers, televisions, computers, tape recorders
  and telephones all employ magnetic effects to
  perform a variety of important tasks
• Chinese sailors used compasses, as early as the
  second century A.D., that relied on a permanent
  magnet
• In 1820, the Danish physicist Hans Christian
  Oersted discovered that a needle of a compass
  would deflect if brought near a current-carrying
  conductor

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11.2 - Magnetic Fields

• In the region surrounding a permanent magnet
  there exists a magnetic field, which can be
  represented by magnetic flux lines similar to
  electric flux lines
• Magnetic flux lines differ from electric flux
  lines in that they dont have an origin or
  termination point
• Magnetic flux lines radiate from the north pole
  to the south pole through the magnetic bar

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Magnetic Fields

• Continuous magnetic flux lines will strive to
  occupy as small an area as possible
• The strength of a magnetic field in a given
  region is directly related to the density of flux
  lines in that region
• If unlike poles of two permanent magnets are
  brought together the magnets will attract, and
  the flux distribution will be as shown below

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Magnetic Fields

• If like poles are brought together, the magnets
  will repel, and the flux distribution will be as
  shown
• If a nonmagnetic material, such as glass or
  copper, is placed in the flux paths surrounding a
  permanent magnet, there will be an almost
  unnoticeable change in the flux distribution

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Magnetic Fields

• If a magnetic material, such as soft iron, is
  placed in the flux path, the flux lines will pass
  through the soft iron rather than the surrounding
  air because the flux lines pass with greater ease
  through magnetic materials than through air
• This principle is put to use in the shielding of
  sensitive electrical elements and instruments
  that can be affected by stray magnetic fields

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Magnetic Fields

• The direction of the magnetic flux lines can be
  found by placing the thumb of the right hand in
  the direction of conventional current flow and
  noting the direction of the fingers (commonly
  called the right hand rule)

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11.3 - Flux Density

• In the SI system of units, magnetic flux is
  measured in webers and has the symbol ?
• The number of flex lines per unit area is called
  the flux density, is denoted by B, and is
  measured in teslas
• Its magnitude is determined by the following
  equation

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11.4 - Permeability

• If cores of different materials with the same
  physical dimensions are used in the
  electromagnet, the strength of the magnet will
  vary in accordance with the core used
• The variation in strength is due to the number of
  flux lines passing through the core
• Magnetic material is material in which flux lines
  can readily be created and is said to have high
  permeability
• Permeability (?)is a measure of the ease with
  which magnetic flux lines can be established in
  the material

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Permeability

• Permeability of free space ?0 (vacuum) is
• Materials that have permeability slightly less
  than that of free space are said to be
  diamagnetic and those with permeability slightly
  greater than that of free space are said to be
  paramagnetic

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Permeability

• Magnetic materials, such as iron, nickel, steel
  and alloys of these materials, have permeability
  hundreds and even thousands of times that of free
  space and are referred to as ferromagnetic
• The ratio of the permeability of a material to
  that of free space is called relative permeability

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11.5 - Reluctance

• The resistance of a material to the flow of
  charge (current) is determined for electric
  circuits by the equation
• The reluctance of a material to the setting up of
  magnetic flux lines in a material is determined
  by the following equation

l
R ?
A
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11.6 - Ohms Law For Magnetic Circuits

• Ohms law
• For magnetic circuits, the effect is the flux ?
• The cause is the magnetomotive force (mmf) F,
  which is the external force (or pressure)
  required to set up the magnetic flux lines within
  the magnetic material
• The opposition to the setting up of the flux ? is
  the reluctance R

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Ohms Law For Magnetic Circuits

• Substituting
• The magnetomotive force F is proportional to the
  product of the number of turns around the core
  (in which the flux is to be established) and the
  current through the turns of wire

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11.7 - Magnetizing Force

• The magnetomotive force per unit length is called
  the magnetizing force (H)
• Magnetizing force is independent of the type of
  core material
• Magnetizing force is determined solely by the
  number of turns, the current and the length of
  the core

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11.8 - Hysteresis

• Hysteresis curve is named from the Greek
  hysterein, meaning to lag behind
• To an engineer it is important to know the curve
  of the flux density of B versus the magnetic
  force H of a material

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Hysteresis

• The entire curve represented by bcdefb is called
  the hysteresis curve
• The flux density B lagged behind the magnetizing
  force H during the entire plotting of the curve.
  When H was zero at c, B was not zero but had only
  begun to decline. Long after H had passed
  through zero and had equaled to Hd did the flux
  density B finally become equal to zero

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11.9 - Ampères Circuital Law

• Ampères circuital law The algebraic sum of the
  rises and drops of the mmf around a closed loop
  of a magnetic circuit is equal to zero that is,
  the sum of the rises in mmf equals the sum drops
  in mmf around a closed loop

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11.10 - The Flux ?

• The sum of the fluxes entering a junction is
  equal to the sum of the fluxes leaving a
  junction.
• ?a ?b ?c
• ?b ?c ?a
• both of which are equivalent

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11.11 - Series Magnetic Circuits Determining NI

• Two types of problems
• ? is given, and the impressed mmf NI must be
  computed design of motors, generators and
  transformers
• NI is given, and the flux ? of the magnetic
  circuit must be found design of magnetic
  amplifiers
• Table method
• A table is prepared listing in the extreme
  left-hand column the various sections of the
  magnetic circuit. The columns on the right are
  reserved for the quantities to be found for each
  section

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11.12 - Air Gaps

• Effects of air gaps on a magnetic circuit
• The flux density of the air gap is given by
• Where
• ?g ?core
• Ag Acore
• The permeability of air is taken to be equal to
  that of free space. The magnetizing force of the
  air gap is then determined by
• And the mmf drop across the air gap is equal to
  Hg Ig

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11.13 - Series-Parallel Magnetic Circuits

• Close analogies between electric and magnetic
  circuits will eventually lead to series-parallel
  magnetic circuits similar in many respects to
  electric circuits encountered previously (in
  Chapter 7)

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11.14 - Determining ?

• When determining magnetic circuits with more than
  one section, there is no set order of steps that
  will lead to an exact solution for every problem
  on the first attempt
• Find the impressed mmf for a calculated guess of
  the flux ? and then compare this with the
  specified value of mmf
• Make adjustments to the guess to bring it closer
  to the actual value
• For most applications, a value within ?5 of the
  actual ? or specified NI is acceptable

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11.15 - Applications

• Recording systems
• Speaker and microphones
• Computer hard disks
• Hall effect sensor
• Magnetic reed switch
• Magnetic resonance imaging