8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 1/43

RANGKAIAN MAGNETIK

  A ma Den u ya  

Jurusan Teknik Konversi Energi

Politeknik Negeri BandungBandung – September 2009

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 2/43

History Electricity

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 3/43

To be able to convert Energy,

 we nee a oup ng e

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 4/43

MAGNETIC CIRCUITS

• Magnetic Fields

• Magnetic Circuits

• Magnetic Materials

• Inductance and Mutualnductance and MutualInductance

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 5/43

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.

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 6/43

Magnetic Fields

Konsep Induktansi

dS.BΨ = ∫

d

atauIL,I

λ

λλ =

=

dI=

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 7/43

 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 8/43

Magnetic Fields

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 9/43

Illustrations of the ri ht-hand rule

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 10/43

Concentric magnetic flux around a

curren -carry ng con uc or.

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 11/43

-

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 12/43

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=

→

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 13/43

Magnetic Field Intensity andagnetic Field Intensity and

Ampère’s Law

7−=

’µ µ  =

r 

 

=⋅ id lH

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 14/43

Magnetic Field Around a Longagnetic Field Around a Long

Straight Wire

 I 

 H  B µ == r π 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 15/43

Flux Density in a Toroidal Core

 NI 

 B

µ 

=

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 16/43

Flux Linkages and Faraday’s Law

AB d ⋅=φ  φ λ  N = A

Faraday’s law of magnetic induction:

d λ 

dt =

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 17/43

 

close together where the field is strong and.

-  

magnet and enter the south-seeking end.

When placed in a magnetic field, a compass

.

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 18/43

Magnetic Circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 19/43

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

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 20/43

Magnetic Circuits (1)

w

I

N

d

l= mean length

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 21/43

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

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 22/43

Magnetic Equivalent Circuits

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 23/43

Analogy between Electric circuit 

an agne c rcu

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 24/43

The magnetic circuit for the toriodal coil

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 25/43

Analogy between Electric circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 26/43

Analogy between Electric circuit 

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 =

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 27/43

Analogy between 'magnetic circuits'

and electrical circuits

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 28/43

Analogy between Electric circuit 

and Magnetic Circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 29/43

Equivalent circuits for the electrical

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 30/43

Magnetization Curve

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 31/43

 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 32/43

Basic magnetic circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 33/43

Simple Magnetic Circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 34/43

 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 35/43

Magnetic Circuit with Air Gap

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 36/43

 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 37/43

- 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 38/43

Fringing

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

width in computing effective gap area.

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 39/43

• 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

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 40/43

Composite Magnetic Circuit with

r-gap

Magnetic Circuit

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 41/43

Magnetic Circuit 

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 42/43

Flux linkage & generated voltage

8/3/2019 Kuliah Rangkaian Magnet 270809 11

http://slidepdf.com/reader/full/kuliah-rangkaian-magnet-270809-11 43/43

Flux linkage & generated voltage