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8/17/2019 El g 2336 Magnetic Circuits
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ELG2336: Magnetic Circuits
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Magnetic Circuit Definitions
• Magnetomotive Force
– The “driving force” that causes a magnetic
field
– Symbol, F
– Definition, F = NI
– Units, Ampere-turns, (A-t)
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Magnetic Circuit Definitions
• Magnetic Field Intensity
– mmf gradient, or mmf per unit length
– Symbol, H
– Definition, H = F/l = NI/l
– Units, (A-t/m)
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Magnetic Circuit Definitions
• Flux Density
– he concentration of the lines of force in a
magnetic circuit
– Symbol, B
– Definition, B = Φ /A
– Units, (Wb/m2), or T (Tesla)
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Magnetic Circuit Definitions
• Reluctance
– The measure of “opposition” the magnetic
circuit offers to the flux
– The analog of Resistance in an electrical
circuit
– Symbol, R – Definition, R = F/ Φ
– Units, (A-t/Wb)
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ECE 441 6
Magnetic Circuit Definitions
• Permeability
– Relates flux density and field intensity
– Symbol, μ
– Definition, μ = B/H
– Units, (Wb/A-t-m)
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Magnetic Circuit Definitions
• Permeability of free space (air)
– Symbol, μ 0
– μ 0 = 4πx10-7 Wb/A-t-m
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Definitions Combined
(Unit is Weber (Wb)) = Magnetic Flux Crossing a Surface of Area ‘A’ in m2.
B (Unit is Tesla (T)) = Magnetic Flux Density = /A
H (Unit is Amp/m) = Magnetic Field Intensity =
B
= permeability = o r
o = 4*10-7 H/m (H Henry) = Permeability of free space (air)
r = Relative Permeability
r >> 1 for Magnetic Material
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Magnetic Circuit
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Air Gaps, Fringing, and Laminated Cores
• Circuits with air gaps maycause fringing
• Correction
– Increase each cross-sectional
dimension of gap by the size of
the gap
• Many applications use
laminated cores• Effective area is not as large
as actual area
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18_18.jpg
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Electric and Magnetic Circuits
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Magnetization Circuits with Air-Gap
N
i
d
wlc
lg
cc
c
c A
l
g g
g
g A
l
g c
Ni
g g cc l H l H Ni )( fringing Neglecting wd A A g c
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Inductance(L)
Definition: Flux Linkage() per unit of current(I) in a magnetic circuit
I
N
IL
NI
2 N
L
Thus inductance depends on the geometry of construction
I N
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Series Magnetic Circuits
• Solve a circuit where is known
– First compute B using / A
– Determine H for each magnetic section from
B-H curves
– Compute NI using Ampere’s circuital law
– Use computed NI to determine coil current or
turns as required
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Series-Parallel Magnetic Circuits
• Use sum of fluxes
principle and Ampere’s
Law• Find B and H for each
section
• Then use Ampere’s
Law
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Structure of Transformer
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18_35.jpg
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Electromechanical Energy Conversion
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Reading
• Example 18.2
• Example 18.3
• Example 18.3• Example 18.7
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