CHAPTER 5 MAGNETIC CHAPTER 5 MAGNETIC CIRCUIT CIRCUIT

OBJECTIVES OBJECTIVES Becomes aware of the similarities between the Becomes aware of the similarities between the

analysis of magnetic circuits and electric circuits.analysis of magnetic circuits and electric circuits. Develop a clear understanding of the important Develop a clear understanding of the important

parameters of a magnetic circuit and how to find parameters of a magnetic circuit and how to find each quantity for a variety of magnetic circuit each quantity for a variety of magnetic circuit configurations.configurations.

Begin to appreciate why a clear understanding Begin to appreciate why a clear understanding of magnetic circuit parameters is an important of magnetic circuit parameters is an important component in the design of electrical/electronic component in the design of electrical/electronic systems.systems.

MAGNETIC FIELDMAGNETIC FIELD -Magnet and electromagnetic used widely in: -Magnet and electromagnetic used widely in: Motors, generators, transformers, loudspeaker medical equipment, Motors, generators, transformers, loudspeaker medical equipment,

relays and etc.relays and etc.

FLUX DENSITYFLUX DENSITY A Flux density (b) – A measure of the flux per unit area A Flux density (b) – A measure of the flux per unit area

perpendicular to amagnetic flux path.It is measured in tesla(T) or perpendicular to amagnetic flux path.It is measured in tesla(T) or webers per square meter.(Wb/m2)webers per square meter.(Wb/m2)

B = B = /A /A B = Wb/m2 =tesla (T)B = Wb/m2 =tesla (T) = webers (Wb)= webers (Wb) A = m2A = m2 The pressure on the system to establish magnetic lines of force is The pressure on the system to establish magnetic lines of force is

determined by the applied magnetomotive force which is directly determined by the applied magnetomotive force which is directly related realated to the number of turns and current of the related realated to the number of turns and current of the magnetizing coil .magnetizing coil .

Magnetizing coil : Magnetizing coil : F F =NI =NI F F = ampere turns (At)= ampere turns (At) N= turns (t)N= turns (t) I= amperes (A)I= amperes (A) The level of magnetic flux established in a ferromagnetic core is a The level of magnetic flux established in a ferromagnetic core is a

direction of the permeability of the material. Ferromagnetic materials direction of the permeability of the material. Ferromagnetic materials have a very high level of permeability while non- magnetic materials have a very high level of permeability while non- magnetic materials such as air and wood have very low levels. The ration of the such as air and wood have very low levels. The ration of the permeability of the material to that of air is called relative permeability of the material to that of air is called relative permeability and is defined: permeability and is defined:

r = r = / /oo o = 4o = 4 x 10-7Wb/A .m x 10-7Wb/A .m

Change the magnetomotive force, and the relative permeability Change the magnetomotive force, and the relative permeability changes.changes.

The resistance of a material to the flow of charge (current) is determined for electric The resistance of a material to the flow of charge (current) is determined for electric circuits by the equation : circuits by the equation :

RR = = ( l / A) ( l / A) (ohms, (ohms, ) ) The reluctance of a material to the setting up magnetic flux lines in the material is The reluctance of a material to the setting up magnetic flux lines in the material is

determined by the following equation: determined by the following equation:

R = R = l / l / A (rels or At/Wb)A (rels or At/Wb) R = reluctance R = reluctance l =l = length of the magnetic path length of the magnetic path A the cross-sectional area.A the cross-sectional area. Notes that the resistance and reluctance are inversely proportional to the area, Notes that the resistance and reluctance are inversely proportional to the area,

indicating that an increase in area results in a reduction in each and an increase in indicating that an increase in area results in a reduction in each and an increase in the desired result, current and flux.the desired result, current and flux.

For an increase in length , the opposite is true, and the desired effect is reduced.For an increase in length , the opposite is true, and the desired effect is reduced. The larger the The larger the , or the smaller the , or the smaller the , , the smaller the reluctance and resistance .the smaller the reluctance and resistance .

RELUCTANCERELUCTANCE

For the magnetic circuits, the effect desired is the For the magnetic circuits, the effect desired is the flux flux ..

= F / = F / RR MAGNETIZING FORCE MAGNETIZING FORCE The magnetomotive force per unit length is called the The magnetomotive force per unit length is called the

magnetizing force (H) : -magnetizing force (H) : -

HH = = F / l F / l (At/m) ……(1)(At/m) ……(1)

H H == NI / lNI / l (At/m) ……(2)(At/m) ……(2) If ,If ,NI NI = 40 At and l = 0.2 m , then = 40 At and l = 0.2 m , then H =H = NI / lNI / l = = 40 At / l = 0.2 m40 At / l = 0.2 m = 200 At/m= 200 At/m

OHM’S LAW FOR MAGNETIC OHM’S LAW FOR MAGNETIC CIRCUITCIRCUIT

FIGURE 1: Defining the magnetizing FIGURE 1: Defining the magnetizing force of a magnetic circuitforce of a magnetic circuit

In words, the result indicates that there are 200At of pressure In words, the result indicates that there are 200At of pressure per meter to establish flux in the core.per meter to establish flux in the core.

The direction of the flux The direction of the flux can be determined by placing the can be determined by placing the fingers of your right hand in the direction of current around the fingers of your right hand in the direction of current around the core and noting the direction of the thumb.core and noting the direction of the thumb.

Realize that, the magnetizing force is dependent of the type of Realize that, the magnetizing force is dependent of the type of core material, it is determined solely by the number of turns, core material, it is determined solely by the number of turns, the current and the length of the core.the current and the length of the core.

The flux density and the magnetizing force are related by the The flux density and the magnetizing force are related by the following equation : following equation :

B =B =H H = henries (not the magnetizing force H H = henries (not the magnetizing force (H)(H) The greater the permeability, the greater the induced flux The greater the permeability, the greater the induced flux

density.density.

HYSTERESISHYSTERESIS

FIGURE 2 : Normal magnetization curve for three ferromagnetic materials.

Figure 2 is called the normal magnetization curve.an expanded view of one region appears in figure 3

This is for the higher .

Figure 3 Expanded view of figure 2 for the low Figure 3 Expanded view of figure 2 for the low magnetizing force regionmagnetizing force region

AMPERE’S CIRCUITAL LAWAMPERE’S CIRCUITAL LAW A law establishing the fact that the algebraic A law establishing the fact that the algebraic

sum of the rises and drops of the mmf around a sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero.closed loop of a magnetic circuit is equal to zero.

SERIES MAGNETIC CIRCUITS : SERIES MAGNETIC CIRCUITS : DETERMINING DETERMINING NINI

NI= HNI= Hll N = no. of turnsN = no. of turns I = H I = Hll / N / N I = Current I = Current

EXAMPLE 1 EXAMPLE 1 Find the value of I required to develop a magnetic flux of Find the value of I required to develop a magnetic flux of = 4 x 10-4 Wb = 4 x 10-4 Wb Determine μ and μr for the material under these condition.Determine μ and μr for the material under these condition. Flux density B ;Flux density B ; B = B = /A /A = 4 x 10-4Wb / 2 x 10-3 m2= 4 x 10-4Wb / 2 x 10-3 m2 = 2 x 10-1 T= 2 x 10-1 T = 0.2T = 0.2T using B-H curves :using B-H curves : H = (cast steel )H = (cast steel ) = 170 At/m= 170 At/m

(Plot in the graph)(Plot in the graph) Applying Ampere’s circuital law yields Applying Ampere’s circuital law yields NI= HNI= Hll I = HI = Hll / N / N = = (170 At/m) (0.16m)(170 At/m) (0.16m) 400400 = = 68 mA 68 mA

The permeability of the material ; The permeability of the material ; = B /H= B /H =0.2T /170 (At/m)=0.2T /170 (At/m) = = 1.176 x 10-3 Wb/A.m 1.176 x 10-3 Wb/A.m

Relative permeability ; Relative permeability ; rr = = //oo = = 1.176 x 10-31.176 x 10-3 44 x 10-7 x 10-7 = = 935.83935.83

AIR GAPSAIR GAPS

FIGURE 4 : Air FIGURE 4 : Air gaps : ( a) with gaps : ( a) with fringing; (b) idealfringing; (b) ideal

The flux density of the air gap: The flux density of the air gap:

Bg =Bg =g / Agg / Ag g = g = core core Ag = A coreAg = A core Magnetizing force of the air gap is determine ; Magnetizing force of the air gap is determine ;

Hg = Bg /Hg = Bg /00 Hg = Bg /Hg = Bg /0 0

=Bg / 4=Bg / 4 x 10-7 x 10-7 Hg = (7.96 x 105 ) Bg (At /m)Hg = (7.96 x 105 ) Bg (At /m)

EXAMPLE 2 EXAMPLE 2 Find the value of I required to establish a magnetic flux of Find the value of I required to establish a magnetic flux of = 0.75 x 10- = 0.75 x 10-

4 Wb in the series magnetic circuit in figure below.4 Wb in the series magnetic circuit in figure below.

Solution Solution The flux density for each section is The flux density for each section is B = B = /A /A = 0.75 x 10-4 Wb /1.5 x 10-4 Wb= 0.75 x 10-4 Wb /1.5 x 10-4 Wb = 0.5 T = 0.5 T From the B-H curves From the B-H curves H (steel ) = 2801 At/mH (steel ) = 2801 At/m From the equation From the equation Hg = (7.96 x 105 ) Bg (At /m)( 0.5 T )Hg = (7.96 x 105 ) Bg (At /m)( 0.5 T ) = (3.98 x 105 At/m)= (3.98 x 105 At/m) the mmf drops are the mmf drops are Hcore lcore = ( 280 At/m)(100 x 10-3m) Hcore lcore = ( 280 At/m)(100 x 10-3m) = 28 At= 28 At Hglg = (3.98 x 105 At/m)(2 x10 -3 m ) Hglg = (3.98 x 105 At/m)(2 x10 -3 m ) = 796 At.= 796 At. Applying ampere’s circuital law,Applying ampere’s circuital law, NI = Hcore lcore + HglgNI = Hcore lcore + Hglg = 28 At + 296 At= 28 At + 296 At (200t) I = 824 At (200t) I = 824 At I = 4.12 AI = 4.12 A

DETERMINING , DETERMINING ,

Example 3 : Example 3 : Calculate the Calculate the

magnetic flux magnetic flux for for the magnetic circuit in the magnetic circuit in fig.below.fig.below.

Solution ; Solution ; By ampere’s circuital law,By ampere’s circuital law, NI = Habcda l abcdaNI = Habcda l abcda Or Habcda = NI /l abcda = (60t)(5A) / 0.3 m Or Habcda = NI /l abcda = (60t)(5A) / 0.3 m = 300 At / 0.3 m= 300 At / 0.3 m = 1000 At / m= 1000 At / m Babcda = Babcda = 0.39T0.39T (based on figure (based on figure Normal magnetization curve for three Normal magnetization curve for three

ferromagnetic material )ferromagnetic material ) And since B = And since B = /A , we have /A , we have = BA = BA = (0.39 T) (2 x 10-4 m2) = (0.39 T) (2 x 10-4 m2) = 0.78 x= 0.78 x10-4 Wb.10-4 Wb.

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