D10.1w MagneticCircuits&Transformers

7/26/2019 D10.1w MagneticCircuits&Transformers

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1

Magnetic Circuits

and Transformers

Discussion D10.1

Chapter 6


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2

Hans Christian Oersted (1777 1!1"

#ef$ http$%%chem.ch.hu&i.ac.i'%eugenii)%histor*%oersted.htm

122

+n 120 he sho,ed that a currentproduces a magnetic fie'd.

X
http://chem.ch.huji.ac.il/~eugeniik/history/oersted.htmhttp://chem.ch.huji.ac.il/~eugeniik/history/oersted.htm


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-

Andr-Marie Ampre (177! 1-6"

rench mathematics professor ,ho on'*a ,ee) after 'earning of Oersted/s

discoeries in ept. 120 demonstrated

that para''e' ,ires carr*ing currents

attract and repe' each other.

attract

repe'

moing charge of 1 coulomb

per second is a current of

1 ampere(amp".


4/16

3

Michae' arada* (1741 167"

e'f5taught ng'ish chemist and ph*sicistdiscoered e'ectromagnetic induction in

1-1 * ,hich a changingmagnetic fie'd

induces an e'ectric fie'd.

arada*/s e'ectromagnetic

induction ring

capacitance of 1 cou'om per o't

is ca''ed a farad("


5/16

!

8oseph Henr* (1747 17"

merican scientist9 :rinceton ;niersit*professor9 and first ecretar* of the

mithsonian +nstitution.

Discoered se'f5

induction


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6

Magnetic Fields and Circuits

current ithrough a coi' produces a

magnetic f'u@9 9 in ,eers9 A.

BA=A

d= B Ag

HB magnetic fie'd intensit* in %m.

BB magnetic f'u@ densit* in A%m2.

=B H

B magnetic permeai'it*

mperes =a,$ d i= H lgHl Ni=

Ni=FMagnetomotie force =F R

re'uctance


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Magnetic Flux

Magnetic f'u@9 9 in ,eers9 A.

11f'u@ in coi' 1 produced 7* current in coi' 1 =

12 f'u@ in coi' 1 produced * current in coi' 2 =

21 f'u@ in coi' 2 produced 7* current in coi' 1 =

22 f'u@ in coi' 2 produced 7* current in coi' 2 =

1 11 12tota' f'u@ in coi' 1 = = +

2 21 22tota' f'u@ in coi' 2 = = +

Current entering

dots produce

f'u@es that add.


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Faraday's Law

1 1 1N =

arada*s =a,$ induced o'tage in coi' 1 is

ign of induced o'tage v1is such that the current ithrough

an e@terna' resistor ,ou'd e opposite to the current i1that

produces the f'u@ 1.

Tota' f'u@ 'in)ing coi' 1$

1 11 1( "

d dv t N

dt dt

= =

i

@amp'e of =enEs 'a, *mo' Lof inductance from =enE


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4

Mutual Inductance

1 11 121 1 1 1( "

d d dv t N N N

dt dt dt

= = +

arada*s =a,

1 21 11 12( "

di div t L L

dt dt = +

+n 'inear range9 f'u@ is proportiona' to current

se'f5inductance mutua' inductance


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10

Mutual Inductance

1 21 11 12( "

di div t L L

dt dt = +

1 22 21 22( "

di div t L L

dt dt = +

12 21L L M= =

=inear media

1 21 1( "

di div t L M

dt dt = +

1 22 2( "

di div t M L

dt dt = +

2 22L L= 1 11L L==et


11/16

11

Ideal Trans!rmer - "!ltage

1 1( "

dv t N

dt

=

2 2( " d

v t Ndt

=

1 1 1

2 2 2

d

v N Ndtdv N N

dt

= = 22 1

1

Nv v

N=

11

1( "v t dt

N=

The input C o'tage9 v19

produces a f'u@

This changing f'u@ through

coi' 2 induces a o'tage9 v2

across coi' 2


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12

Ideal Trans!rmer - Current

12 1

2

Ni i

N=

The tota' mmf app'ied to core is

Ni=F

Magnetomotie force9 mmf

1 1 2 2N i N i = =F R

or idea' transformer9 the re'uctance R is Eero.

1 1 2 2N i N i=


13/16

1-

Ideal Trans!rmer - Impedance

11 2

2

NN=" "+nput impedance

2

2

L =

"#

I

21 2

1

N

N=I I

=oad impedance

1

1

i =

"#

I

2

1

2

i L

N

N

=

# #

2

Li

n=

## 2

1

Nn

N=Turns ratio


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13

Ideal Trans!rmer - $!wer

12 1

2

Ni iN

=

:o,er de'iered to primar*

P vi=

22 1

1

Nv v

N=

1 1 1P v i=

:o,er de'iered to 'oad

2 2 2P v i=

2 2 2 1 1 1P v i v i P= = =

:o,er de'iered to an idea' transformer * the source

is transferred to the 'oad.


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1!

=.F.D.T.

=inear Faria'e Differentia' Transformer

http$%%,,,.rdpe'ectronics.com%disp'acement%'dt%'dt5princip'es.htm

:osition transducer

http$%%,,,.efunda.com%Designtandards%sensors%'dt%'dtGtheor*.cfm
http://www.rdpelectronics.com/displacement/lvdt/lvdt-principles.htmhttp://www.efunda.com/DesignStandards/sensors/lvdt/lvdt_theory.cfmhttp://www.efunda.com/DesignStandards/sensors/lvdt/lvdt_theory.cfmhttp://www.rdpelectronics.com/displacement/lvdt/lvdt-principles.htm


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LVDT's are often used on clutch actuation

and for monitoring brake disc wear

LVDT's are also used for

sensors in an automotive

active suspension system

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