Chapter 8

Magnetism and Magnetic Circuits

The Nature of a Magnetic Field

• Magnetic field– Force field

• Magnetic flux– Flux lines (lines of

force)• Show direction and

intensity of the field

The Nature of a Magnetic Field (cont’d.)

• Unlike poles attract• Like poles repel

Ferromagnetic Materials

• Magnetic materials– Materials attracted by

magnets– Iron, nickel, cobalt, and

their alloys– Provide an easy path for

magnetic flux

Ferromagnetic Materials (cont’d.)

• Nonmagnetic materials– Have no effect on a magnetic field– Ex: copper, aluminium, gold, etc

• Application: loudspeaker

Figure 12-4

Electromagnetism

• Right hand rule for a uniform length conductor– Used to indicate field direction– Place right hand around conductor– Thumb points in direction of current– Fingers point in direction of the field

Electromagnetism (cont’d.)

• Rule for coils– Curl fingers of right hand around coil in

direction of the current– Thumb will point in direction of the field

Magnetic Flux and Flux Density

• Weber– Unit of flux

• Tesla– Unit of flux density

Equation 12-1

Magnetic Flux and Flux Density (cont’d.)

• Example: • For the magnetic core

shown, the flux density at cross section 1 is B1 = 0.4T

• Determine B2

Magnetic Flux and Flux Density (cont’d.)

Magnetic Circuits

• Found in motors, generators, speakers, transformers

• Magnetic fields can be created by electric currents– Or electric currents and permanent magnets

• Example: speaker application in Figure 12-4

Magnetic Circuits (cont’d.)

Figure 12-10 Audio speaker, conceptual representation

Magnetic Circuits (cont’d.)

• Magnetic stripe containing information – Used in bank ATM cards, library cards, etc.– Magnetic patterns encode information– Reader sees varying magnetic field

• Induces a voltage in the pickup winding• Voltage is amplified and sent to decoding circuitry

• MRI machine uses superconductor coils– Create intense magnetic field

Magnetic Circuits (cont’d.)

Air Gaps, Fringing, and Laminated Cores

• Most practical magnetic circuits:– Have air gaps essential to their operation

• Fringing occurs at air gaps

• Fringing occurs at air gaps– Results in slight weakening of the field in the

gap• In a gapped inductor, airgap fringing flux induces

eddy currents in coil conductors in the vicinity of the airgap, producing unwanted power loss and heat in the coil.

• Can be neglected for short gaps• Or estimate the effect by increasing each cross-

sectional dimension of the core by gap length

Air Gaps, Fringing, and Laminated Cores (cont’d.)

• Lamination– Core is created with thin sheets of stacked

iron or steel• Stacking factor

– Ratio of actual area of ferrous material to physical area of the core

– Use to determine core’s effective area

Series Elements and Parallel Elements

• Series magnetic circuit

Series Elements and Parallel Elements (cont’d.)

• Parallel elements

Magnetic Circuits with DC Excitation

• Two basic problems– Determine current required to produce a given

flux– Compute flux produced by a given current

MMF: The Source of Magnetic Flux

• Current through a coil creates magnetic flux– The greater the current or number of turns,

the greater the flux• Magnetomotive force (mmf)

– Measured in ampere-turns– Denoted by the symbol

MMF: The Source of Magnetic Flux (cont’d.)

• Equation defining mmf

Equation 12-2

Reluctance : Opposition to Magnetic Flux

• Opposition that circuit presents to flux

Where µ=material permeability

Equation 12-3

Reluctance : Opposition to Magnetic Flux (cont’d.)

• Permeability measures ease of establishing magnetic flux in a material– Ferromagnetic materials have high

permeability– Nonmagnetic materials have low permeability

Ohm’s Law for Magnetic Circuits

• Flux does not flow like current

Equation 12-4

Magnetic Field Intensity and Magnetization Curves

• Magnetic field intensity, H– Also called magnetizing force– Measures mmf per unit length of a circuit

Equation 12-5

Equation 12-6

Magnetic Field Intensity and Magnetization Curves (cont’d.)

• Electric circuit analogy– NI is an mmf source– Hl is an mmf drop

The Relationship Between B and H

• For air gaps:

Equation 12-7

Equation 12-9

B-H Curves

• Curves obtained experimentally– Available in

handbooks

Force Due to an Electromagnet

• Electromagnets– Used in relays, doorbells, lifting magnets

• Where Bg is the flux density in the gap in teslas

Ag is gap area in square meters

F is force in Newtons

Equation 12-13

Properties of Magnetic Materials

Magnetizing a Specimen

Magnetizing a Specimen (cont’d.)

• Saturation– All domain fields line up– Cannot magnetize it much further

Measuring Magnetic Fields

• Hall effect– Voltage proportional to field strength B

Measuring Magnetic Fields

• Hall effect– The Hall effect is the production of a voltage

difference (the Hall voltage) across an electrical conductor when the current flows through the conductor in a magnetic field.

Measuring Magnetic Fields (cont’d.)

• Hall effect gaussmeters use this principle

Transformer

• A transformer is a device that changes ac electric power at one voltage level to ac electric power at another voltage level through the action of a magnetic field.

• There are two or more stationary electric circuits that are coupled magnetically.

• It involves interchange of electric energy between two or more electric systems

• Transformers provide much needed capability of changing the voltage and current levels easily.– They are used to step-up generator voltage to an appropriate

voltage level for power transfer.– Stepping down the transmission voltage at various levels for

distribution and power utilization.

Transformer Classification

• In terms of number of windings– Conventional transformer: two windings– Autotransformer: one winding– Others: more than two windings

• In terms of number of phases– Single-phase transformer– Three-phase transformer

• Depending on the voltage level at which the winding is operated– Step-up transformer: primary winding is a low voltage (LV)

winding– Step-down transformer : primary winding is a high voltage (HV)

winding

Primary and Secondary Windings A two-winding transformer consists of two windings interlinked by a mutual magnetic field.– Primary winding – energized by connecting it to an input

source– Secondary winding – winding to which an electrical load is

connected and from which output energy is drawn.

Primary winding Secondary winding

Ideal Transformers

• No iron and copper losses• No leakage fluxes• A core of infinite magnetic permeability and of infinite

electrical resistivity• Flux is confined to the core and winding resistances are

negligible

An ideal transformer is a lossless device with an input winding and an output winding. It has the following properties:

Ideal Transformers An ideal transformer is a lossless device with an input winding and an output winding.

The relationships between the input voltage and the output voltage, and between the input current and the output current, are given by the following equations.

ati

ti

tv

tv

p

s

s

p In instantaneous quantities

fM

Ideal Transformers

Np: Number of turns on the primary winding

Ns: Number of turns on the secondary winding

vp(t): voltage applied to the primary side

vs(t): voltage at the secondary side

a: turns ratioip(t): current flowing into the primary side

is(t): current flowing into the secondary side

a

N

N

ti

ti

tv

tv

s

p

p

s

s

p

aI

I

V

V

p

s

s

p In rms quantities

Thank you