THE COIL - INDUCTANCES

They are passive two-terminal components that generate a magnetic flux when they are made
to pass an electric current through them.
They are made by winding a conductive wire around a core of ferromagnetic material or in the air.
Its unit of measurement is the Henry (H) in the International System, but they are often used the
submultiples:

mH – milli Henry uH – micro Henri nH – nano Henry

It is equal to one thousandth of a henry.
It is equal to one millionth of It is equal to one billionth of
Henrio. Henrio

Symbols:

Bobbin Inductance Coil with fixed terminals

Core coil Reel with core of

Armored coil
ferromagnetic ferroxcube

Electromagnetic coil Adjustable coil Variable bobbin

There are various types of coils depending on their core and the type of winding. We find coils in
filters, tuned circuits and impedance adapters, transformers, etc.
CHARACTERISTICS
Magnetic permeability (µ) :

It is a characteristic that has a great influence on the core of the coils regarding the value.
of their inductance. Ferromagnetic materials are very sensitive to fields
magnetic materials and produce high values of inductance, however other materials show less
sensitivity to magnetic fields. The factor that determines the greater or lesser sensitivity to them
Magnetic fields are called magnetic permeability. When this factor is large, the value of the
inductance is also.

2. Quality factor (Q):

Relate inductance with the resistive value of the coil wire. The coil will be good if the
Inductance is greater than the ohmic value due to the wire itself.

TYPES OF COILS

FIXED

With air core:

The conductor rolls over a hollow support and subsequently this is removed, leaving it with a
looks similar to a spring. It is used at high frequencies. A variant of the previous coil is
it is called solenoid and differs in the insulation of the coils and the presence of a support that does not
it necessarily has to be cylindrical. It is used when many turns are required. These coils
They can have intermediate windings, in this case they can be considered as 2 or more coils wound.
on the same support and connected in series. They are also used for high frequencies.

With a solid core:

They have higher inductance values than the previous ones due to their elevated level of
magnetic permeability. The core is usually made of a ferromagnetic material. The most commonly used are the
ferrite and the ferroxcube. When handling considerable powers and the frequencies that are desired
eliminating are low, cores similar to those of transformers are used (in power supplies
above all). Thus we will encounter the configurations specific to the latter. The sections of
The cores can have shapes of EI, M, UI, and L.
 Ferrite core nest Ferrite coils for Coils with core
Ferrite core of bee SMD toroidal

Honeycomb coils are used in the tuning circuits of radio devices in

the medium and long wave ranges. Thanks to the winding shape, high inductive values are achieved.
in a minimum volume.
Toroidal core coils are characterized by the fact that the generated flux does not disperse towards the
exterior because its shape creates a closed magnetic flow, giving them a high performance and
precision.
Ferrite coils wound on ferrite cores, usually cylindrical, with applications
on the radio it is very interesting from a practical point of view as it allows to use the set as
antenna placing it directly on the receiver.

The coils etched onto the copper, in a printed circuit, have the advantage of their low cost.
but they are hardly adjustable through the core.

2. VARIABLES

Adjustable coils are also manufactured. Usually, the variation in inductance occurs due to
nucleus displacement.
The shielded coils can be variable or fixed, consisting of enclosing the coil within a cover.
cylindrical or square metal, whose mission is to limit the electromagnetic flow created by the coil itself
and that can negatively affect nearby components.

IDENTIFICATION OF THE COILS

The coils can be identified by a color code similar to that of resistors or
by direct screen printing.
The coils that can be identified by color code have an appearance similar to the
resistances.
 Color 1st Digit and 2nd Digit Multiplier Tolerance
Black 0 1 -
Brown 1 10 -
Red 2 100 -
Orange 3 1000 +/-3%
Yellow 4 - -
Green 5 - -
Blue 6 - -
Violet 7 - -
Gray 8 - -
White 9 - -
Gold - 0.1 +/- 5%
Silver - 0.01 ±10%

- - +/-20%
None

The nominal value of the coils is marked in microhenries µH.

 Inductances
Content:

1. Inductances.
2. Inductance Calculations.

3. Permeability of coils with iron core.

4. Foucault Currents and Hysteresis.

Inductances

It is possible to demonstrate that the flow of current through a conductor is accompanied by magnetic effects; the
A compass needle placed near a conductor, for example, will deviate from its normal position.
north-south. The current creates a magnetic field.

The transfer of energy to the magnetic field represents work performed by the source of EMF. It
it requires power to do work, and since power is equal to current multiplied by the
voltage, there must be a drop in voltage in the circuit during the time that the energy is
storing in the field.

This voltage drop has nothing to do with the voltage drop of any resistance of the
circuit is the result of an opposing voltage induced in the circuit as the field grows to its
final value. When the field becomes constant,

The induced EMF or counter-electromotive force disappears, as no more is being stored.

energy. Since the induced EMF opposes the EMF of the source, it tends to prevent the current
increase rapidly when the circuit is closed.

The amplitude of the induced EMF is proportional to the rate at which the current varies and to a constant.
associated with the circuit, called the inductance of the circuit.

Inductance depends on the physical characteristics of the conductor. For example, if a coil is wound around a
conductor, the inductance increases. A winding with many turns will have more inductance than one
of a few turns. Additionally, if a winding is placed around an iron core, its
inductance will be greater than it was without the magnetic core.

The polarity of an induced EMF always acts in the direction of opposing any change in the
circuit current. This means that when the current in the circuit increases, work is done
against the induced EMF by storing energy in the magnetic field. If the current in the circuit tends to
Descender, the energy stored in the field returns to the circuit, and therefore adds to the energy.
supplied by the source of FEM. This tends to keep the current flowing even when the
FEM applied can descend or be removed. The energy stored in the magnetic field of a
the inductor is given by:

W = I² L / 2

where:

W = energy in joules
I = current in amperes
L = inductance in henries
 The unit of inductance is the henry. The values of inductance used in radio equipment vary in
a wide margin. In radio frequency circuits, the values of inductance used will be measured in
millihenries (1 mH is one thousandth of a henry) at low frequencies, and in microhenries (millionth of
henrio) in the medium and high frequencies. Although coils for radio frequency can be wound
about special iron cores (common iron is not suitable), many of the coils used
The fans are of the air core type, meaning they are wound on a support material that is not
magnetic.

Any conductor has inductance, even when the conductor does not form a coil. Inductance
of a small length of straight wire is small, but not negligible if the current through it
It changes quickly, the induced tension can be appreciable. This can be the case of even a few
few inches of wire when a current of 100 MHz or more flows. However, at frequencies
much lower the inductance of the same wire can be negligible, since the induced tension will be
despicably small.

Inductance calculations

The approximate inductance of a single-layer air-wound coil can be calculated with the
simplified formula:

L (microH) = d².n² / (18d + 40l)

Where:

L = inductance in microhenries
d = diameter of the coil in inches
l = length of the coil in inches
n = number of turns

The notation is explained in figure 1.

In order to use this formula with measurements in centimeters, it must be multiplied by the
second member by the factor 0.394. Thus

L (microH) = 0.394.(d².n²/18d + 40 l)

This formula is a good approximation for coils that have a length equal to or greater than 0.4 d.

Example: Suppose a coil that has 48 turns wound at a rate of 32 turns per inch and a
diameter of 314 inches. Therefore, d = 0.75 l = 48/32 = 1.5 and n = 48. Substituting:

L = 0.75² x 48² / (18 x 0.75) + (40 x 1.5) = 1.296 / 73.5 = 17.6 microH

To calculate the number of turns required in a single-layer coil to obtain a

determined inductance:

n = square root of ( L ( 18d + 40l ) / d

Example: Suppose that an inductance of 10 microH is required.

The way the coil will be wound has a diameter of 1 inch and enough length to
to accommodate a coil of 1-1/4 inches long.

Therefore:

d=1

l = 1.25

L = 10 microH.

Substituting:

n = square root of ( 10. ( (18x1) + (40 x 1.25) ) ) / 1

n=square root of 680= 26.1 turns

A coil of 26 turns would be close enough for practical purposes. Since the coil
It will be 1.25 inches in length, the number of turns per inch will be 26.1/1.25 = 20.9.
Consulting the thread table, we found that a thread number 17 enameled (or any lower) is
valid. The appropriate inductance is obtained by winding the required number of turns around the shape and
adjusting the spacing between turns until a uniform spacing with a length of
1.25 inches.

Permeability of coils with a iron core

Suppose that the coil in Figure 2 is wound on an iron core that has a section of
2 square inches.

When a certain current is sent through the coil, it is found that there are 80,000 lines of force.
in the core. Since the area is 2 square inches, the magnetic flux density is 40,000.
lines per square inch. Now suppose that the core is removed and the same current is maintained
in the core. Also suppose that the flux density without the core is 50 lines per inch.
square. The relationship between these two flow densities, iron to air, is 40,000/50 = 800. This is
calls permeability of the nucleus.

The inductance of the coil has increased 800 times by inserting the iron core, since the inductance
it will be proportional to the magnetic flux through the coils, if the other parameters remain the same.

The permeability of a magnetic material varies with the flux density.

For low flow densities (or with an air core), the increase in current through the coil
it will produce a proportional increase in the flow. But with very high flow densities, increasing the
current will not cause a noticeable change in the flow.
When this is the case, it is said that the iron is saturated. Saturation causes a rapid decrease in the
permeability since the ratio of flow lines decreases in relation to the same current and
air core. Obviously, the inductance of a coil with a iron core is largely,
dependent on the current flowing in the coil. In a coil with an air core, the inductance is
independent of the current because the air does not saturate.

Iron core coils like the one shown in Figure 2 are mainly used in power supplies.
feeding. Usually, direct current circulates through the flux density which is controlled by the
separation instead of by iron.

This reduces the inductance, keeping it practically constant regardless of the value of the
current.

For radiofrequency, the losses in the iron cores can be reduced to acceptable values.
pulverizing the iron and mixing the powder with a "binder" of insulating material so that the
iron particles are isolated from each other. By this system, cores can be built that
They will work satisfactorily even in the VHF range.

Since a large part of the magnetic path occurs through non-magnetic material (the
(binder), the permeability of iron is low compared to the values obtained at the frequencies
of the power supplies. The core generally has the shape of a rod or cylinder that
put inside the insulating shape on which the coil is wound. Although with this
construction, most of the magnetic flow path is through the air, the bar is quite effective
to increase the inductance of the coil. Pushing the rod in and out of the coil, you
Inductance can vary over a considerable range.

Foucault currents and hysteresis

When alternating current flows through a coil wound around an iron core, it will induce.
an FEM as indicated above. And, since iron is a conductor, a current will flow in
the core. Such currents are called eddy currents and represent a loss of power.
since they circulate through the resistance of iron and therefore produce heating. Such
losses can be reduced by laminating the core (cutting it into thin strips). These strips or sheets
They must be isolated from each other by painting them with some insulating material such as varnish or shellac.

There is another type of energy loss in inductors. The iron tends to oppose any change in
its magnetic state, therefore a current that changes rapidly, such as AC, must supply
continuously energy to iron to overcome that "inertia." Losses of this type are called losses
by hysteresis.

Losses due to eddy currents and hysteresis increase rapidly as the frequency of
the alternating current. For this reason, normal iron cores can only be used at frequencies
from the domestic low voltage line and in audio frequencies -up to about 15,000 Hz-. Despite everything, it
needs iron or very good quality steel if the core is to operate efficiently in the
higher audio frequencies. The iron cores of this type are completely useless in