Kuliah Rangkaian Magnet 270809 11

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RANGKAIAN MAGNETIK

A ma Den u ya

Jurusan Teknik Konversi Energi

Politeknik Negeri BandungBandung – September 2009



History Electricity



To be able to convert Energy,

we nee a oup ng e



MAGNETIC CIRCUITS

• Magnetic Fields

• Magnetic Circuits

• Magnetic Materials

• Inductance and Mutualnductance and MutualInductance



Magnetic Circuit

1. Understand magnetic fields and their interactions with moving

.

1. Use the right-hand rule to determine the direction of the magneticfield around a current-carrying wire or coil.

.

to magnetic fields.

4. Calculate the voltage induced in a coil by a changing magnetic fluxor in a conductor cuttin throu h a ma netic field.

5. Use Lenz’s law to determine the polarities of induced voltages.

6. Apply magnetic-circuit concepts to determine the magnetic fields in

practical devices.7. Determine the inductance and mutual inductance of coils given their

physical parameters.

8. Understand hysteresis, saturation, core loss, and eddy currents in

cores compose o magne cma er a s suc as ron.



Magnetic Fields

Konsep Induktansi

dS.BΨ = ∫

d

atauIL,I

λ

λλ =

=

dI=



Magnetic Fields



Illustrations of the ri ht-hand rule



Concentric magnetic flux around a

curren -carry ng con uc or.



-



Example of Ampére’s Law

Find the magnetic field along a circular path around an infinitely longConductor carrying ‘I’ ampere of current.

900

B,H

r

Since both→

dl

→

Hand are perpendicular to radius ‘r’ at any point ‘A’

on the circular path, the angle θ is zero between them at all points. Also since all

the points on the circular path are equidistant from the current carrying

conductor is constant at all points on the circle→

Ir 2HdlHdl.H =π==→→→→→

∫ ∫ or

r 2

IH

π=

→



Magnetic Field Intensity andagnetic Field Intensity and

Ampère’s Law

7−=

’µ µ =

r

=⋅ id lH



Magnetic Field Around a Longagnetic Field Around a Long

Straight Wire

I

H B µ == r π



Flux Density in a Toroidal Core

NI

B

µ

=



Flux Linkages and Faraday’s Law

AB d ⋅=φ φ λ N = A

Faraday’s law of magnetic induction:

d λ

dt =



close together where the field is strong and.

-

magnet and enter the south-seeking end.

When placed in a magnetic field, a compass

.



Magnetic Circuit



Magnetic Circuits

F =NI= Magneto Motive Force or MMF = # of turns * Current passing through it

F = NI = Hl (why!)

NI=µlor NI

A=

µlor

or

)A/(µ=Φl

ℜ=Φor

ℜ = Reluctance of magnetic path



Magnetic Circuits (1)

w

I

N

d

l= mean length



Magnetic Circuits (2)

F =NI= Magneto Motive Force or MMF = # of turns * Current passing

through it

F = NI = Hl (why!)

NIB

=

µ

lor NI

A

=

µ

Φlor

or

)A/(

NI

µ=Φl

ℜ=Φ

NIor

ℜ = Reluctance of magnetic path



Magnetic Equivalent Circuits



Analogy between Electric circuit

an agne c rcu



The magnetic circuit for the toriodal coil




Φ

ℜ

F =MMF is analogous to Electromotive force (EMF) =E

Φ = Flux is analogous to I = Current

= Reluctance is analo ous to R = Resistance

P = Permeanceℜ

=1

= Analogous to conductanceR

1G =



Analogy between 'magnetic circuits'

and electrical circuits




and Magnetic Circuit



Equivalent circuits for the electrical



Magnetization Curve



Basic magnetic circuit



Simple Magnetic Circuit



Magnetic Circuit with Air Gap



-



Fringing

We approximately account for fringing byaddin the len th of the a to the de th and

width in computing effective gap area.



• Ratio of iron vs. stack areas

• Lamination thickness 0.35 ...

0.65 mm <-> stacking factor . ... . .

• Amorphous steel

– 80% iron, 20% boron

– cheap (less than silicon steel),

– low losses (1/5’th of best

– hard to punch



Composite Magnetic Circuit with

r-gap

Magnetic Circuit



Magnetic Circuit



Flux linkage & generated voltage

Kuliah Rangkaian Magnet 270809 11

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