Presentation on magnetic ciruits

1. Magnetics: Principles and
Applications
Prof. Prashant Jamwal
SCHOOL OF ENGINEERING

2. magckt
2
Magnetic and Electromagnetic Fields

3. magckt
3
Electric Current and Magnetic Field

4. Electromagnetism
 A wire carrying a current I causes a
magnetomotive force (m.m.f) F
Which produces a magnetic field
 F has units of Amperes
 for a single wire F is equal to I

5. Magnetic Circuits
Complete path followed by the lines of flux is called
magnetic circuit.
Magnetomotive force (m.m.f.) is created by a current
flowing through one or more turns.
mmf (F) = NI (ampere turns)

6.  The magnitude of the field is defined by the magnetic field
strength, H , where
where N is for turns and l is the length of the magnetic circuit
 Example –
A straight wire carries a current of 5 A. What is the magnetic
field strength H at a distance of 100mm from the wire?
Magnetic circuit is circular. r = 100mm, so path = 2r =
0.628m
l
NI
=
H
A /m
96
.
7
628
.
0
5
=
=
=
l
I
H
Magnetic Circuits

7. ➢ When a current-carrying wire is formed into a coil
the magnetic field is concentrated
➢ As said before, for a coil of N turns, the m.m.f. (F) is
given by
and the field strength is
N
F I
=
l
IN
H =
Magnetic Circuits

8.  The magnetic field produces a magnetic flux, 
 This flux has units of weber (Wb)
 Density of the flux at a particular location is measured in
term of the magnetic flux density, B
 flux density (B) has units of tesla (T) (equivalent to one
Wb/m2)
 Flux density at a point is determined by the field strength
and the material present
or
where  is the permeability of the material,
r is the relative permeability and
0 is the permeability of free space
μH
B = H
μ
μ
B r
0
=
Magnetic Circuits
µ0 = 4π×10−7 H·m−1

9.  Adding a ferromagnetic ring around a wire will increase
the flux by several orders of magnitude
 since r for ferromagnetic materials is 1000 or more
Magnetic Circuits
H
μ
μ
B r
0
=

10.  Therefore the magnetic flux produced is determined by the
permeability of the material present
Magnetic Circuits

11. Reluctance
 In a resistive circuit, the resistance is a measure of how
the circuit opposes the flow of electricity
 In a magnetic circuit, the reluctance, Rl is a measure of
how the circuit opposes the flow of magnetic flux
 In a resistive circuit R = V/I
 In a magnetic circuit
 the units of reluctance are amperes per weber (A/ Wb)
A
l
F
l
R


=
=
F=NI; = BA = HA; H=NI/l;
 

12. Magnetic Circuits (Recap…)
Magnetic Field Intensity (H): Magnetomotive force per unit
length of the magnetic circuit.
H = NI/l (ampere turns/meter)
Permeability of free space (µ0): Ratio of flux density and
magnetic field intensity: µ0=B/H and for vacuum and air
its value is µ0=4π X 10
-7
heneries per meter
Reluctance (Rl): Opposition offered to the magnetic flux,
which is analogous to the resistance in electric circuits.
Rl=l/µA AT/Wb
Permeance (Л): Analogous to the conductance in El. Ckts.
Л = µA/l
Magnetic Flux (φ) =(mmf/reluctance) Wb OR φ=NI. µA/l
Flux density (B): B= Φ/A = µNI/l

13.  When a circuit forms a single loop, the e.m.f. induced is given by
the negative rate of change of the flux.
 When a circuit contains many loops the resulting e.m.f. is the
sum of those produced by each loop.
 Therefore, if a coil contains N loops, the induced voltage V is
given by
where d/dt is the rate of change of flux in Wb/s
 This property, whereby an e.m.f. is induced as a result of
changes in magnetic flux, is known as inductance
t
Φ
N
V
d
d
−
=
Inductance
A changing magnetic flux induces an e.m.f. in conductors:

14. Self-inductance
 A changing current in a wire causes a changing magnetic field
around, that induces an e.m.f. within the wire
 When a current in a coil changes, it induces an e.m.f. in the
coil and this process is known as self-inductance
where L is the inductance of the coil (unit is the Henry)
t
L
V
d
dI
=
 The inductance of a coil depends on its dimensions and the
materials around which it is formed
l
2
0AN
μ
L =

15.  The inductance is greatly increased using a
ferromagnetic core, for example
l
AN
r
μ
μ
L
2
0
=

16. Mutual Inductance
 When two coils are linked magnetically then a changing
current in one will produce a changing magnetic field
which will induce a voltage in the other.
 When a current I1 in one circuit, induces a voltage V2 in
another circuit, then
where M is the mutual inductance between the circuits.
The unit of mutual inductance is also Henry (as for self-
inductance)
t
I
M
V
d
d
1
2
=

17. Mutual Inductance
 The coupling between the coils can be increased by
wrapping the two coils around a core
 the fraction of the magnetic field that is coupled is
referred to as the coupling coefficient

18. Mutual Inductance
 Coupling is particularly important in transformers
 the arrangements below give a coupling coefficient that is
very close to 1

19. Magnetic vs Electric circuits
φ
Rl
E
I
R F=NI
Ф

20. Magnetic vs Electric circuits
Electric Circuit Magnetic Circuit
EMF (Volts) MMF (Amp Turns) IN
Resistance (R=ρl/A) Reluctance (Rl=l/µA) AT/Wb
Current (i=E/R) A Flux φ=(mmf/Rl) Wb
Electric field intensity
=V/m
Magnetic field intensity
H=IN/l (V/m)

21. Magnetic Circuits
pr
Series Magnetic Circuit
Parallel Magnetic Circuit

22. Series Magnetic circuits
Total Reluctance 𝑅𝐿 =
𝑙1
𝜇0𝜇𝑟1𝐴1
+
𝑙2
𝜇0𝜇𝑟2𝐴2
+
𝑙3
𝜇0𝜇𝑟3𝐴3
+
𝑙𝑔
𝜇0𝐴𝑔
Note that 𝜇𝑟 for air is one.
𝑇𝑜𝑡𝑎𝑙 𝑚. 𝑚. 𝑓.
= 𝑓𝑙𝑢𝑥 × 𝑡𝑜𝑡𝑎𝑙 𝑟𝑒𝑙𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑟𝑖𝑒𝑠 𝑐𝑖𝑟𝑐𝑢𝑖𝑡
𝑇𝑜𝑡𝑎𝑙 𝑚. 𝑚. 𝑓. = 𝜑
𝑙1
𝜇0𝜇𝑟1𝐴1
+
𝑙2
𝜇0𝜇𝑟2𝐴2
+
𝑙3
𝜇0𝜇𝑟3𝐴3
+
𝑙𝑔
𝜇0𝐴𝑔
=
𝜑
𝐴1
𝑙1
𝜇0𝜇𝑟1
+
𝜑
𝐴2
𝑙2
𝜇0𝜇𝑟2
+
𝜑
𝐴3
𝑙3
𝜇0𝜇𝑟3
+
𝜑
𝐴𝑔
𝑙𝑔
𝜇0
=
𝐵1
𝜇0𝜇𝑟1
𝑙1 +
𝐵2
𝜇0𝜇𝑟2
𝑙2 +
𝐵3
𝜇0𝜇𝑟3
𝑙3 +
𝐵𝑔
𝜇0
𝑙𝑔
𝐼𝑁 = 𝐻1𝑙1 + 𝐻2𝑙2 + 𝐻3𝑙3 + 𝐻𝑔𝑙𝑔
OR
𝑰𝑵 − 𝑯𝟏𝒍𝟏 + 𝑯𝟐𝒍𝟐 + 𝑯𝟑𝒍𝟑 + 𝑯𝒈𝒍𝒈 = 𝟎

23. A wrought iron bar 30 cm long and 2 cm in diameter is bent into a circular shape as shown.
It is then wound with 600 turns of wire. Calculate the current required to produce a flux of
0.5 mWb in the magnetic circuit, when (i) there is no air gap; (ii) there’s air gap of 1 mm;
Assume µr for iron as 4000 and H is 3000AT/m for B=1.59T (data taken from the
magnetization curve)
(i)
(ii)

24. Parallel Magnetic circuits
BE
F
F
can be

25. Leakage Flux and Fringing
➢Stray flux or the Leakage flux: The flux which does not follow the
intended path in a magnetic circuit.
➢Flux fringing is more if the air gap is longer.

26. Leakage Flux and Fringing
 Magnetic circuit with a ferromagnetic core:
 Paths a, b,& c are called leakage flux
(flux which does not follow the intended path)
 Value of leakage factor in electrical machinery is in the range of
1.15 to 1.25.
 At the air gap the flux lines bulge out which is termed as fringing
and longer the gap, more will be the fringing.
 Fringing is compensated by correcting the area (a X b) as
flux
Useful
winding
exciting
the
by
handled
flux
Total
factor
Leakage =
)]
(
)
[( g
g l
b
l
a
A +

+
=

27. Domain theory of magnetization
(a) Magnetic material in demagnetized condition,Atomic magnets in alignment
inside domains but domain magnetic axes are in random directions
(b) Magnetized state
Atomic magnets (not domains) turn
to bring domain magnetic axes in
the direction of magnetizing field.

28. Magnetic Materials and their Properties
 Materials classified based on their relative permeability (𝜇𝑟)
 All nonmagnetic materials are called paramagnetic (𝜇𝑟 ~>1) and
diamagnetic (𝜇𝑟~<1) similar to the free space
 Ferro-magnetic: Hard Ferromagnetic (permanent magnets, chrome
steels or Cu-Ni alloys); or Soft Ferromagnetic (iron alloyed with Ni,
Co, Al etc)
 Ferri-magnetic: Ferrites such as Fe2O3, Soft ferrites are used for
high frequency applications; hard ferrites used as permanent
magnets.
 Super-paramagnetic: made of iron powder and other magnetic
materials, it is used in electronics specially in hard disk drive
technology etc.

29. SATURATION
 B-H CURVE (Magnetization curve)
 B-H curve is linear for non-magnetic
materials and free space (since 𝜇0 is
constant) but is non-linear for
ferromagnetic (since 𝜇𝑟 is not constant).
 Relative permeability of ferro-magnetic
materials changes with the field strength
H. As the magnetizing field increases, the
relative permeability increases, reaches a
maximum, and then decreases.
 Electrical machines and transformers are
designed based on a flux density close to
the saturation zone and so B-H curve is
required to be used while designing.
H
μ
μ
B r
0
=

30. B-H curve or Magnetization curve

31. SATURATION AND HYSTERESIS
Figure: Hysteresis loop and family of hysteresis loops for different
peak values of excitation.
When AC is used for magnetization, B lags behind H,
A coercive field Hc is required to bring B to zero. However further increasing Hc
causes reverse magnetization (opposite polarity) which also has a saturation
value and residual values of B.
Family of loops can be drawn for different peak values of ac magnetization
field intensity cycle.
Magnetically soft materials are preferred for machines and transformers.
Higher the frequency of Hc broader the curve.

32. Eddy Currents and Loses
➢ Eddy currents (also called Foucault's currents) are
loops of electrical current induced within conductors by
a changing magnetic field in the conductor according
to Faraday's law of induction.
➢ Eddy currents flow in closed loops within conductors, in
planes perpendicular to the magnetic field.

34. 34
Iron Losses in Magnetic Circuit
There are two types of iron/core losses
a) Hysteresis losses; b) Eddy Current Losses
Total loss is the sum total of the two
Energy required for the reversal of magnetic domain alignments in the
magnetic core is termed as hysteresis loss.
Area of the hysteresis loop represents the energy loss during one cycle in a
unit cube of the core material. A Steinmetz’s empirical relation is:
Here is the proportionality constant for core material (for soft iron it is
0.025); v is volume and Bm is the max flux density; n is Steinmetz
exponent and for core material is taken as 1.6 to 2 generally.
Eddy-Current Loss: Induced eddy currents circulates within iron core due
to time varying magnetic flux and are large due to low core resistance. These
cause power loss from heating and demagnetization.
Due to these, the flux distribution become non-uniform. (Mag. Flux is pushed
outward). To increase resistance to eddy currents, insulated laminates are
stacked for core.
W
B
k
f
v
P n
m
h
h )
( 


=
h
k
W
B
t
f
v
k
Pe m
l
h
2
)
( 


=
tℓ is the lamination thickness

35. Example: Total core loss of a specimen is found to be 1500 W at 50
Hz. Keeping the flux density constant, the loss becomes 3000 W
when the frequency is raised to 75 Hz. Find the hysteresis and eddy
current losses at both the frequencies.
W
B
k
f
v
P n
m
h
h )
( 


= W
B
t
f
v
k
Pe m
l
h
2
)
( 


=

36. 36
Permanent Magnets
Looking at the second quadrant of
the curve, we notice that for H = 0,
(i.e. no current in windings) there
will be some nonzero flux density, Br.
▪ In addition, current (negative current) in the opposite
direction will be required in the winding for pushing flux in
order to make the flux zero.
▪ The iron core has become a permanent magnet.
▪ Value of field intensity for complete demagnetization is Hc.

37. Permanent Magnets
Suitable materials for permanent magnets are magnetically hard
materials which are difficult to magnetize and have high residual flux
density or coercive force.
Categories of permanent magnets:
1. Ductile metallic magnets, e.g. Cunife
2. Ceramic magnets, e.g. Indox (Indox V is a highly oriented barium ferrite material)
3. Brittle metallic magnets, Alnico
4. Rare-earth cobalt magnets, e.g. samarium-cobalt
Applications:
1. Loudspeakers
2. small generators
3. magnetic clutches and couplings
4. measuring instruments
5. video recording
6. information storage on computers
In magnet design, the shape affects amount of flux produced. Equal
volumes of magnetic cores will produce different amount of flux as
a function of their shapes.

38. Magnet Characteristics
Property of Alliance LLC
Materials Typical Shapes Pro Con
Cast Alnico
AlNiCo
Rods, Bars, U shape
and other cast type
High Br
High working T
Good T coef.
Very Low Hc
High cost
High L/D
Requires Cast
Sintered Alnico
AlNiCo
Powder pressed to shape
Complex shapes
High Br, T
Requires Tool
High cost
Low market
Ceramic/Ferrite
SrFe2O3
Blocks, Rings, Arcs, Discs
Most flux for $
High usage
Low corrosion
Low Br
Requires tool
Simple shapes
Samarium
Cobalt
SmCo
Blocks, Rings, Discs
Arcs, Segments
No corrosion
Very low T coef
Stable, No tool
Very expensive
Simple shapes
High Co content
Neodymium
NdFeB
Blocks, Rings, Discs
Arcs, Segments
Highest magnetic
properties
No tooling
Corrodes
Low working T
Difficult to Mag
Bonded Grades
All materials
Difficult geometries
Can be insert molded
or over-molded
Complex shapes
Various resins
High tooling
Low magnetics
High volumes

39. In practice a permanent magnet is operating not at the second
quadrant of the hysteresis loop, but rather on a minor loop,
that can be approximated with a straight line.
Bm
Hc
Hm
Br
B
H
Finding the flux density in a permanent magnet:

40. In a magnetic circuit shown, lm=1cm, lg=1mm and li=20cm. For the
magnet Br=1.1 T, Hc=750kA/m. Find the flux density in the air gap if
the iron has infinite permeability, and the cross section is uniform?
Since the cross section is uniform:
𝐻𝑖 × 0.2 + 𝐻𝑔 × 𝑙𝑔 + 𝐻𝑚 × 𝑙𝑚 = 0
𝜇𝑖 is given to be infinite and therefore 𝐻𝑖 =
0, Further,
𝐵𝑎𝑖𝑟
𝜇0
× 𝑙𝑔 +
𝐵𝑚𝐻𝑐
𝐵𝑟
− 𝐻𝑐 𝑙𝑚 = 0 OR
𝐵𝑎𝑖𝑟 × 796 + 𝐻𝑐
𝐵𝑚
𝐵𝑟
− 1 𝑙𝑚 = 0
𝐵𝑎𝑖𝑟 × 796 + 𝐻𝑐
𝐵𝑚−𝐵𝑟
𝐵𝑟
𝑙𝑚 = 0
Since the cross section is uniform 𝐵𝑎𝑖𝑟 = 𝐵𝑚
𝐵𝑎𝑖𝑟 × 796 + 6818 × 𝐵𝑎𝑖𝑟 − 1 = 0 Or
𝐵𝑎𝑖𝑟 = 0.985 𝑇𝑒𝑠𝑙𝑎