Copper Wires and Magnetic Core Characteristics

8/7/2019 Copper Wires and Magnetic Core Characteristics

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Coils andCoils and MagneticMagnetic CoresCoresCharacteristicsCharacteristics



I. CoilsI. Coils

y COPPER:

y Because of its ductility, it is used to make

wires of varying diameters, and it is very

strong

y Has the second lowest resistivity, behind

silver, which is much more expensive

making copper the best choice.



ResistivityResistivity

y It is the opposition to the flow of

electrical current

y The SI unit for electrical resistivity is the

ohm meter.



y Copper like most metals, as the

temperature goes up, so does the

resistivity.



Skin effectSkin effect

y Skin effect is an effect that the electricity

in high frequencies does not use the

whole conductor area

y High frequencies tend to use only the

outer parts of the conductor.

y The higher the frequency, the less of the

wire diameter is used and higher thelosses.



y

Copper wires are given gauge numbersthat indicates its diameter



y Assuming wires are same material and

same length then a thinner wire will have

a higher resistance than a thick wire



Here is a small current and AWG table taken from the Amateur Radio Relay Handbook, 1985.

The inductance increases directly as

the cross-sectional area of the coilincreases.



yWhen the length of the coil is increased

while keeping the number of turns the

same, the turn-spacing is increased. This

decreases the inductance of the coil.

y An increase in an electrical current will

cause magnetism to increase.



II. Magnetic coreII. Magnetic core

y A magnetic core is a piece of magnetic

material with a high permeability used to

confine and guide magnetic fields in

electrical devices such as electromagnets,transformers, electric motors, and

inductors. It is made of ferromagnetic

metal such as iron, or ferromagneticcompounds.



y The use of a magnetic core can

enormously concentrate the strength and

increase the effect of magnetic fields

produced by electric currents andpermanent magnets.



The properties of a device will depend

critically on the following factors:

y The geometry of the magnetic core.

y The amount of air gap in the magnetic

circuit.

y The properties of the core material(especially permeability and hysteresis).

y The operating temperature of the core.

yWhether the core is laminated to reduceeddy currents.



Air coreAir core

y Air core coils have lower inductance than

similarly sized ferromagnetic core coils,

but are used in radio frequency circuits to

prevent energy losses called core lossesthat occur in magnetic cores.



y U and C-shaped cores are used with I oranother C or U' core to make a square

closed core, the simplest closed core

shape.



y Sheets of suitable iron stamped out in

shapes like the letters "E" and "I", are

stacked with the "I" against the open endof the "E" to form a 3-legged structure.

Coils can be wound around any leg, but

usually the center leg is used. This type of

core is much used for powertransformers, autotransformers, and

inductors.



y Pair of ́ Eµ cores is used for iron cores.

Similar to using an "E" and "I" together, a

pair of "E" cores will accommodate alarger coil former and can produce a

larger inductor or transformer. If an air

gap is required, the centre leg of the "E" is

shortened so that the air gap sits in themiddle of the coil to minimize fringing and

reduce electromagnetic interference.



Magnetic core materialsMagnetic core materials

y Soft iron:

y "Soft" iron is used in electromagnets and in someelectric motors; and it can create a field as much as50,000 times more intense than with an air core.

y It is also used because, unlike "hard" iron, it does notremain magnetized when the field is removed, whichis often important in applications where the magneticfield is required to be repeatedly switched.

y Unfortunately due to the simplicity of its design, abulk block or rod of soft iron suffers from large eddycurrents circulating within it that waste energy andcause undesirable heating of the iron.



y Because iron is a relatively good conductor,it cannot be used in bulk form with a rapidly

changing field, such as in a transformer, asintense eddy currents would appear due tothe magnetic field, resulting in huge losses.

y Two techniques are commonly used

together to increase the resistivity of iron:lamination and alloying of the iron withsilicon.



y Laminated magnetic cores are made of thin,insulated iron sheets.Using this technique,the magnetic core is equivalent to many

individual magnetic circuits, each onereceiving only a small fraction of themagnetic flux.

y Furthermore, these circuits have a resistance

that is higher than that of a non-laminatedcore, also because of their reduced section.From this, it can be seen that the thinner thelaminations, the lower the eddy currents.



y A small addition of silicon to iron (around

3%) results in a dramatic increase of the

resistivity, up to four times higher. Further

increase in silicon concentration impairsthe steel's mechanical properties, causing

difficulties for rolling due to brittleness.



DesignDesign



The window utilization factorThe window utilization factor KuKu

also called the ́ fill factorµalso called the ́ fill factorµy Ku is the fraction of the core window area that is filled by copper Mechanisms that cause Ku to be less than one:

Round wire does not pack perfectly, which reduces Ku by afactor of 0.7 to 0.55 depending on winding technique

y Insulation reduces Ku by a factor of 0.95 to 0.65, depending on

wire size and type of insulationy Bobbin uses some window area

y Additional insulation may be required between windings

y Typical values of Ku :

0.5 for simple low-voltage inductor

0.25 to 0.3 for off-line transformer0.05 to 0.2 for high-voltage transformer (multiple kV)

0.65 for low-voltage foil-winding inductor



Core geometrical constantCore geometrical constant Kg Kg

y The core geometrical constant Kg is

defined as:

y Kg is a figure-of-merit that describes the

effective electrical size of magnetic cores, in

applications where the following

quantities are specified:y Copper loss

y Maximum flux density



DiscussionDiscussion

y How specifications affect the core size:y A smaller core can be used by increasing1-Bmax : use core material having higher Bsat2-R :allow more copper loss

y How the core geometry affects electricalcapabilities:

y Alarger Kg can be obtained by increase of

1-Ac : more iron core material, or

2-WA : larger window and more copper



StepStep--byby--step design procedure:step design procedure:

Coupled inductorCoupled inductor



1.Determine core size1.Determine core size

y Choose a core that satisfies this inequality.

Note the values of Ac, WA , and MLT for

this core.

y The resistivity of copper wire is 1.724 ·

10²6 cm at room temperature.



y Allocation of window area:

y Copper loss



22--Determine air gap lengthDetermine air gap length

y The air gap length is given in meters.

y The value expressed above is

approximate, and neglects fringing flux

and other non idealities.



A ALL



33-- Determine number of turnsDetermine number of turns nn



Evaluate wire sizeEvaluate wire size

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Copper Wires and Magnetic Core Characteristics