PECC Coils Inductors Coils Short history Electrical Properties Constructive elements for coils Parameters Categories Transformers Coils Short history 1821 Michael Faraday reveals the magnetic field lines which occur around a conductive material through which an electr ID: 797043
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Slide1
Lecture 10
1
Passive Electronic Components and Circuits (PECC)
Coils (Inductors)
Slide2Coils Short history Electrical Properties
Constructive elements for coils
Parameters Categories Transformers Coils
Slide3Short history
1821 – Michael Faraday reveals the magnetic field lines which occur around a conductive material through which an electric current flows.
Afterwards, Faraday builds the first electrical engine, the first electrical generator and the first transformer.
Henry builds the first telegraph improved later by Morse.
1825 – William Sturgeon builds the very first electromagnet.
1831 – independently, Michael Faraday and Joseph Henry discover the magnetic induction law.
1876 – Bell invents the first telephone and the first electromagnetic phonograph.
Slide4Coils Short history Electrical Properties
Constructive elements for coils
Parameters Categories Transformers Coils
Slide5Electrical properties
The inductance of a coil is strongly dependent of the coil’s geometry and the magnetic properties of the environment in which it is placed.
Equation 1 is suitable for the case in which the length “l” of the coil is higher then its diameter “2r
c
”.
Equation 2 is suitable for the case in which the length “l” of the coil is lower then its diameter “2r
c
”. The “r
w
” quantity represents the winding wire’s diameter.
Slide6Electrical properties
The inductance is dependent of the coil’s geometry (l, d=2r, h in mm). All the above formulas are available when the environment in which the coil is placed is the air.
Slide7Electrical properties
The inductance is dependent of the distance between its turns.
The inductance is dependent of the magnetic properties of the environment in which the coil is placed – magnetic permeability,
μ
.
Air: 1.257x10
-6
H/m.
Ferrite U M33: 9.42x10
-4
H/m.
Nickel: 7.54x10
-4
H/m.
Iron: 6.28x10
-3
H/m.
Ferrite T38: 1.26x10
-2
H/m.
Orr: 5.03x10
-2
H/m.
Super Malloy: 1.26H/m.
Slide8Electrical properties
Equivalent circuit
Slide9Electrical properties
Frequency characteristic
Slide10Electrical properties
Dimensioning the inductance:
Slide11Electrical properties
The parasitic capacitance value calculus:
Slide12Electrical properties
Steps in designing a coil:
The procedure starts from the desired value for the inductance – “L”, its diameter “D” and the frequency domain in which it will work – “ω
0”.
From the last slide characteristic the maximum value of the parasitic capacitance is chosen.
The turns number can be calculated in respect with the coil’s geometrical dimensions by resolving the adjacent equation.
Calculate the length of a coil with a
2
cm
diameter and an inductance of
50
H
which is executed in a single layer and will have a desirable parasitic capacitance lower then 2pF.
Slide13Coils Short history
Electrical Properties Constructive elements for coils
Parameters Categories Transformers Coils
Slide14Constructive elements for coils
The winding (the turns).
The casing.
The impregnation (soak) material.
The core.
without a core
Iron core
Ferrite core
Slide15Constructive elements for coils
The coil’s winding
The most common used material for the conductive winding wire is the copper (due to its electrical and mechanical properties) and rarely aluminum.
The conductive wires are being insulated to avoid short-circuits between two adjacent turns. The materials used for the insulation are
enamels
(
ro
:
emailuri
) –
different composition varnishes,
textile fibers
(silk, cotton) or mineral fibers (glass fiber). The insulating material type is generally chosen in strong dependency with the conductive wire’s estimated maximum temperature. The most thermal resistant materials are the glass fibers, the most susceptible ones are the textile fibers.
Slide16Constructive elements for coils
The coil’s winding
The coil’s winding diameter can be estimated following 2 criteria:
The maximum estimated value of the current
that passes through the conductive materials is inferiorly limiting this parameter due to excessive heating possibility.
The parasitic resistance maximum value
introduces a supplementary limitation for the windings diameter.
At high frequencies, due to the
pellicle effect,
stranded (
ro
:
litat
)
wires are used (thin bundles of wires –
ro
:
manunchiuri
de fire
) or silvered copper wires.
The conductive winding wires are being delivered by the producers in a standardized fashion: 0.05 mm, 0.07 mm, 0.1 mm, … , 2 mm. The thickness of the insulating material is not included in the above values.
Slide17Constructive elements for coils
The coil’s casing
The materials used must have adequate electrical (dielectric rigidity, low dielectric losses) and mechanical properties (thermal and humidity stability).
The coil’s casing fulfill the role of keeping the stiffness of the winding.
Examples – ascending order of theirs performances: electro-insulating carton,
pertinax
, textolit, thermo-rigid materials (Bakelite), thermo-plastic materials (polystyrene, polyethylene, Teflon) or ceramic materials.
From the geometrically point of view the material can be of different cross-sections: circular, square, rectangular.
At very high frequencies, the coils can be made without a casing.
Slide18Constructive elements for coils
The coil’s impregnation (soak) material
The impregnation advantages:
The impregnation material has the role to protect the coil against humidity and also realizes a supplementary stiffness (especially for the cases when the coils are not using casings).
Winding stiffness.
Improves heat dissipation.
Improves dielectric properties of the turns insulation.
Avoids humidity penetration between turns.
The impregnation disadvantages: can concur to a higher parasitic capacitance (by growing the electrical permittivity of the insulating material between the turns).
Slide19Constructive elements for coils
The coil’s core
To increase the obtained inductance, magnetic cores are being displaced inside coil’s winding. So a magnetic circuit is created which has the major contribution in concentrating the magnetic field lines. In this way the magnetic flux increases, almost all the magnetic lines intersect the turns, in conclusion the coil’s inductance increases.
The magnetic materials have a non-linear behavior when are being placed in an exterior magnetic field. This non-linearity is related with the dependency of the magnetic induction “b” and the magnetic field intensity “H”. The ratio between the above two quantities is
the environment's magnetic permeability
:
Slide20Constructive elements for coils
The magnetic materials properties – Hysteresis phenomena
Br – residual magnetic induction.
H
c
– coercive field – cancels the magnetic induction.
H
s
– the magnetic field intensity at which saturation phenomena occurs.
B
s
– the magnetic induction at saturation point.
Slide21Constructive elements for coils
The magnetic materials properties – Hysteresis phenomena
The magnetic materials have atoms with an own magnetic moment, and the neighbor atomic moments are being orientated identically, so the material will have a residual magnetization
.
When applying an exterior magnetic field, a reorientation of the magnetic domains occurs. The exterior field intensity at which the magnetic induction is canceling is called
coercive field.
When “H” increases, the
saturation phenomena
occurs (“B” remains constant).
The phenomena are dependent with the direction on which the magnetic field changes (
hysteresis).
The residual magnetization exhibits until a certain temperature
(Curie temperature)
at which the thermal agitation destroys the well-ordered orientation domains
.
Slide22Constructive elements for coils
Magnetic materials applications
Soft magnetic materials – Hc<80A/m (narrow hysteresis)
Rough magnetic materials – H
c
>80A/m (wide hysteresis)
Soft magnetic materials with the ratio B
r
/B
m
(ratio which characterizes the hysteresis inclination) lower then 0.5 are used for constant inductances, the ones with
0.5<
B
r
/B
m
<0.8 for common used cores, the ones with B
r
/B
m
>0.8 (rectangular hysteresis) are used in switching and memorizing applications.
Rough magnetic materials with the ratio B
r
/B
m
<0.4 are used for magnetically recording the information and the ones
with Br
/Bm>0.4 for permanent magnets fabrication.
Slide23Constructive elements for coils
Core constructive types
Core-trays (
ro: tole), bands, columns, coatings
for transformers magnetic circuits.
Cylindrical bars
for high frequencies inductances (also for adjustable inductances).
Torus
(
ro
:
miezuri
toroidale
) and
pots
(
miezuri
tip “
oala
”)
for high frequency and pulses applications.
Different forms of
yokes
(
ro
:
miezuri tip “jug”)
For high frequency applications, the cores are being obtained by compressing magnetic powders. That results in obtaining magneto-electric cores (the magnetic powder is a ferromagnetic material) or magneto-ceramic cores (
ferrites).
Slide24Constructive elements for coils
Designing a core coil
If a coil without a core has the “L0” inductance, the core displacements inside its windings changes its inductance:
The effective magnetic permeability,
μ
eff
, is dependent with the material’s relative permeability, with its geometry and with the relative position in respect with the winding.
The ferrite producers indicate in the datasheets a so called
inductance factor,
A
L
, having the following meaning: the inductance factor is the obtain inductance if on the ferrite core is made only 1 turn (nH/turn or
μ
H/turn). Using this parameter , the total inductance can be obtained:
Slide25Coils Short history
Electrical Properties Constructive elements for coils
Parameters Categories Transformers Coils
Slide26Parameters
The inductance and its tolerance.
The coil’s own resistance.
The loss-angle tangent.
The quality factor.
The temperature coefficient.
Slide27Coils Short history
Electrical Properties Constructive elements for coils
Parameters Categories Transformers Coils
Slide28Categories
Constructive types
Toroidal (A).
Cylindrical (B).
Encapsulated (C).
Adjustable (D, E).
Slide29Categories
Spiral
circular plane coil
Slide30Categories
Spiral square plane
coil
c – trace width
Slide31Coils Short history
Electrical Properties Constructive elements for coils
Parameters Categories Transformers Coils
Slide32Transformers
A transformer is
an electrical component which consists on two coils mounted on the same magnetic core.The magnetic core links the magnetic flux,
ФB , from the two coils.
Taking into consideration the Faraday law:
The transformer’s equation
Voltage increasing transformers
Voltage decreasing transformers
Slide33Transformers
Ideal transformer
An ideal transformer doesn’t have losses, so:
Input Power = Output Power
Real transformers can reach an efficiency higher then 99%
A transformer makes its job
only if the voltage/current varies through one of its windings.
This variation will generate a variable flux which will lead to a variable voltage into the second winding.
Slide34Transformers
Mutual inductance
The time variation of the current from the primary winding determines the occurrence of a induced voltage in the secondary winding. Obviously, the current through the second winding appears only if at the second windings terminals, a load is connected.
Let us consider the coil 1 with N
1
– turns number and coil 2 with N
2
– turns number and
Ф
21
– the magnetic flux in the second coil occurred due to the current that flows through the first coil:
Unit – Henry
1H=Vs/A=
Ω
s
Mutual inductance
Slide35Transformers
Mutual inductance
The induced voltage in the second coil can be expressed:
Slide36Transformers
Mutual inductance
Similar, it can be shown that the induced voltage into the first coil by the second coil’s current variation is:
In conclusion:
But, generally M
21
=M
12
and can be written as follows, where k – coupling factor:
Slide37Transformers
The transformer – circuit analysis
The transformer has two coils (as the symbol from the circuit above). The one from the circuit where the Vo source is applied is called
primary coil and has the Lp inductance, and the one from the circuit where the Rl
– load resistance is , is called secondary coil and has the L
s
inductance.
Both inductances work on theirs designated circuit as was presented before, but supplementary the inductances are being magnetically coupled through the mutual inductance, M.
Slide38Transformers
The transformer – circuit analysis
The voltage across the primary coil will be:
The voltage across the
secondary
coil will be:
Slide39Transformers
The transformer – circuit analysis
Applying the KVL in the primary winding:
Applying the KVL in the
secondary
winding:
Slide40Transformers
The transformer – circuit analysis
Extracting, from the second equation, the is current dependent of the i
p current and introducing it in the first equation (KVL for the primary winding), and also taking into consideration that:
It can be obtained that:
Slide41Transformers
The transformer – constructive types
Cylindrical (solenoidal)
Torus
Yoke
Slide42Important formulas
Resistors
Coils
Capacitors
Cu
=5,344 x 10
-7
-cm
0
=8,8542
·
10
-12
F/m
0
=4
·
π
·
10
-7
H/m
Slide43Problem
Using a copper wire (
φCo = 5.344x10-7 Ωm) with 1 mm diameter, a winding of 40 turns is being executed on insulated cylindrical support with the diameter of 10 mm.
What is the modulus of the coil’s impedance at 50Hz? What is the modulus of the coil’s impedance at 500kHz?
Please determine the electrical parameters of the realized coil.