Post on 01-Mar-2018
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Magnetic Circuits
and Transformers
Discussion D10.1
Chapter 6
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Hans Christian Oersted (1777 1!1"
#ef$ http$%%chem.ch.hu&i.ac.i'%eugenii)%histor*%oersted.htm
122
+n 120 he sho,ed that a currentproduces a magnetic fie'd.
X
http://chem.ch.huji.ac.il/~eugeniik/history/oersted.htmhttp://chem.ch.huji.ac.il/~eugeniik/history/oersted.htm7/26/2019 D10.1w MagneticCircuits&Transformers
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Andr-Marie Ampre (177! 1-6"
rench mathematics professor ,ho on'*a ,ee) after 'earning of Oersted/s
discoeries in ept. 120 demonstrated
that para''e' ,ires carr*ing currents
attract and repe' each other.
attract
repe'
moing charge of 1 coulomb
per second is a current of
1 ampere(amp".
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Michae' arada* (1741 167"
e'f5taught ng'ish chemist and ph*sicistdiscoered e'ectromagnetic induction in
1-1 * ,hich a changingmagnetic fie'd
induces an e'ectric fie'd.
arada*/s e'ectromagnetic
induction ring
capacitance of 1 cou'om per o't
is ca''ed a farad("
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!
8oseph Henr* (1747 17"
merican scientist9 :rinceton ;niersit*professor9 and first ecretar* of the
mithsonian +nstitution.
Discoered se'f5
induction
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Magnetic Fields and Circuits
current ithrough a coi' produces a
magnetic f'u@9 9 in ,eers9 A.
BA=A
d= B Ag
HB magnetic fie'd intensit* in %m.
BB magnetic f'u@ densit* in A%m2.
=B H
B magnetic permeai'it*
mperes =a,$ 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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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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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
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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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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=
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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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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.htm7/26/2019 D10.1w MagneticCircuits&Transformers
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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