Basic Electronics On The Go - Applications of Inductor

From http://www.electronicshub.org/applications-of-inductor/

Like resistors and capacitors, inductors are also passive elements which are used to store the electric energy in the form of magnetic field. Simply an inductor is a wire or coil of a good electric conducting material with few turns (twists) in it.

They will produce the magnetic flux (field) around them by the flow of an alternating current through it. An ideal inductor has no inductive reactance, so it acts as short circuit. Practically, every inductor has some resistance internally which we call as ‘Inductive reactance’. It is measured in ohms. When the inductive reactance of a coil is very high then the circuit acts as an open circuit and allows maximum current through it. Inductance is the phenomenon of an inductor that opposes the flow of current in the circuit, by generating the back EMF. This inductance is measured in Henry.

Inductors are of many types like air cored, iron cored, coupled or differential type and many more. Based on the requirement, inductors have many applications in electrical transmission.

Inductors in Tuned Circuits

Inductors are used in tuning circuits which are used to select the desired frequency. In a tuned circuit, we have capacitor connected along with the inductor, either in parallel or series. The frequency of the tuning circuit at which the capacitive reactance is equal to the inductive reactance (XC = XL) is called ‘Resonant Frequency’.

The series resonance circuits are used in many electronic circuits like television , radio tuning circuits and filters to vary the frequency and selecting the various frequency channels.

Inductive sensors

Inductors are used in proximity sensors which work on the principle of inductance. We know that inductance is the phenomenon in which , the magnetic field produced in the coil , will oppose the flow of current in it. Thus the inductance will restrict the current flow and reduces the circuit performance.

For better performances, we need to amplify the current in a circuit. We use proximity sensors to find the level of amplification factor at which we need to amplify the current.

The manufacturers design the sensors by twisting the wire into a tight coil. There are 4 components in the inductive proximity sensor; they are an inductor or coil, an oscillator, a detection circuit and an output circuit.

In the inductive proximity sensor, a fluctuating magnetic field is generated by oscillator around the winding of coil, which locates in the sensing face of the device.

When an object moves in the field of inductive proximity area of detection, eddy currents starts building up in the metal object which will reduce the inductive sensor’s magnetic field.

Strength of the oscillator is monitored by the detection circuit and an output is triggered from the output circuitry , when the oscillations are below the sufficient level.

The inductive proximity sensor is a contactless sensor and is very reliable in operation. The inductive sensors are used at traffic lights to detect the traffic density.

Energy Storage Devices

We can store the energy in passive elements like capacitor and inductors. Inductors can store energy for a limited time. As the inductors store the energy in the form of magnetic field, it will collapse when we remove the power supply.

The inductors functions as energy storage devices in switch mode power supplies (generally we use in our computers). In these type of power supplies, the output voltage ratio depends upon the charging time of the inductor.

Induction Motors

The well known and wide range application of inductors is in  Induction motors. In these induction motors or asynchronous motors, the inductors are in a fixed position and they are not allowed to move in the  nearby magnetic field.

Induction motors converts the electrical energy into mechanical energy. The shaft in the motors will rotate because of the magnetic field produced by the alternating current.

The speed of the motor is fixed as it depends on the frequency of the power supplied from source. So we use inductors in these motors to control the speed by connecting them in series or parallel to the shaft. These induction motors are very reliable and robust.

Transformers

Transformer is another popular application of inductors. By combining the inductors of a shared magnetic field, we can design a transformer. Transformer is the basic and fundamental component of the power transmission system.

These are used to increase or decrease the power in transmission lines to required level, as step up and step down transformers respectively. In the transformers, the inductor (wire) is wounded to the core as primary and secondary windings.

The impedance of the inductor increases with increase in the frequency of supply. The impedance produced in the inductor will limit the effectiveness of transformer. In general, the inductance based transformers are limited to very low operational values.

Inductive Filters

Inductors and capacitors are combined to form filters. The filters are the electronic devices which are used to limit the frequency of the input signal entering to a circuit. There are many types of filters like low pass filter, high pass filter, band pass filter, notch filter etc which are designed by using inductors.

As the frequency increases, the impedance of the inductor also increases. Then the properties of the filter will change according to the impedance value. There are many number of filter topologies we can create by using inductors.

Chokes

Inductors are also used as chokes. We know that the inductors will create an opposite current flow, when the alternating current flows through it. This means the inductors will choke the AC current and allows DC current to pass. This property of inductors is used in power supply circuits, where AC supply need to be converted to DC supply.

Ferrite beds

Generally we see the ferrite beds in computer cables and mobile chargers etc. these ferrite beds use inductors to reduce the radio frequency interference created by the cables.

Relays

A relay is like an electrical switch. It uses an  inductor coil to control the current flow in it. When the AC current flows through the inductor of the relay, it produces a magnetic field which effects the switch contacts.

Basic Electronics On The Go - Inductors in Parallel

From http://www.electronicshub.org/inductors-in-parallel/
From   http://www.electronics-tutorials.ws/inductor/parallel-inductors.html

Inductors are said to be connected in parallel when two terminals of an inductor respectively connected to each terminal of other inductors or inductor. Similar to the parallel connection of resistors, the total inductance in parallel connection of inductors is somewhat lesser than smallest inductance of an inductor in that connection.

When the inductors are connected in parallel, the current flow through each inductor is not exactly equal to the total current, but the sum of each individual current through the  parallel inductors gives the total current (as it divides among parallel inductors).

If the current flow through the each inductor is less than the total current, the magnetic field generated by each inductor is also less than that of field generated by total current through it.

In case of resistors in parallel, most of the current flows through the smallest resistor as it offer the least opposition to the current flow than larger resistor.

Likewise, if the inductors are connected in parallel, the current chooses the least opposition path of the inductor when current in that circuit is decreased or increased while each inductor individually opposes that change (increase or decrease of current).

Inductors Connected in Parallel (Without Magnetic Coupling)

As we discussed above, one end of inductors is connected to a node and other ends of inductors are collectively connected to another node in parallel connection. The parallel connection of n inductors is shown in below figure.

Consider that there is no magnetic coupling between inductors and hence the total inductance equal to the sum of reciprocals of the individual inductances. Let us discuss how this statement can be obtained.

We know that, in a parallel network the voltage remains constant and the current divides at each parallel inductor. If IL1, IL2, IL3 and so on ILn are the individual currents flowing in the parallel connected inductors L1, L2 and so on Ln, respectively, then the total current in the parallel inductors is given by

ITotal = IL1 + IL2 + IL3 . . . . + In

If the individual voltage drops in the parallel connection are VL1, VL2, VL3 and so on VLn, then the total voltage drop between the two terminals VT is

VTotal = VL1 = VL2 = VL3 . . . . = Vn

The voltage drop in terms of self inductance can be expressed as V = L di/ dt. This implies total voltage drop,

VT = LT di/dt

⇒ LT  d/dt (IL1 + IL2 + IL3 . . . . + In)

⇒ LT ( (di1)/dt + (di2)/dt + (di3)/dt . . . .)

Substituting V / L in place of di/dt, the above equation becomes

VT = LT (V/L1+ V/L2 + V/L3 . . . .)

As the voltage drop is constant across the circuit, then v = VT. So we can write

1/LT = 1/L1 + 1/L2 + 1/L3 . . . . .

This means that the reciprocal of total inductance of the parallel connection is the sum of reciprocals of individual inductances of all inductors. The above equation is true when there is no mutual inductance between the parallel connected coils.

For avoiding complexity in dealing with fractions, we can use product over sum method to calculate the total inductance of two inductors. If two inductors are connected in parallel, and if there is no mutual inductance between them, then the total inductance is given as

LT = (L1× L2)/(L1+ L2)

Mutually Coupled Inductors in Parallel

When there exist magnetic coupling between the inductors, the above derived formula for total inductance must be modified because total inductance can be more or less depending on the magnetic field directions from each inductor. The magnetic flux produced by the parallel connected inductors will link with each other.

Mutually connected inductors in parallel can be classed as either “aiding” or “opposing” the total inductance with parallel aiding connected coils increasing the total equivalent inductance and parallel opposing coils decreasing the total equivalent inductance compared to coils that have zero mutual inductance.

Consider that two inductors are connected in parallel with self inductances L1 and L2, and which are mutually coupled with mutual inductance M as shown in the  figure.below

Parallel Aiding Inductors

Consider the figure (a), in which inductors L1 and L2 are connected in parallel with their magnetic fields aiding. The total current through the circuit is given as

i = i1 + i2

di/dt = (di1)/dt + (di2)/dt …………. (1)

The voltage across the inductor or parallel branch is given as

V = L1 (di1)/dt + M (di2)/dt or L2 (di2)/dt + M (di1)/dt

L1 (di1)/dt + M (di2)/dt = L2 (di2)/dt + M (di1)/dt

(di1)/dt (L1– M) = (di2)/dt (L2– M)

(di1)/dt = (di2)/dt ((L2 – M))/((L1 – M)) …………. (2)

Substituting equation 2 in equation 1, we get

di/dt = (di2)/dt ((L2– M))/((L1– M)) + (di2)/dt

di/dt = (di2)/dt { (L2– M))/((L1– M)) + 1} …………. (3)

If LT is the total inductance of the parallel inductor circuit , then voltage is given by

V = LT di/dt

LT di/dt = L1 (di1)/dt + M (di2)/dt

di/dt = 1/ LT { L1 (di1)/dt + M (di2)/dt }

Substituting equation 2 in above equation, we get

di/dt = 1/ LT { L1 (di2)/dt (L2– M))/((L1– M)) + M (di2)/dt }

di/dt = 1/ LT { L1 (L2– M))/((L1– M)) + M }(di2)/dt …………. (4)

Equating equations 3 and 4, and simplifying the results, we get

LT = (L1 L2– M2)/(L1+ L1 )-2M)

Here 2M represents the magnetic flux of L1 on L2 or L2 on L1.

Parallel Opposing Inductors

Similarly, if we consider the figure (b), in which inductors L1 & L2 are connected in parallel with their magnetic fields opposing, the total inductance is given as

LT = (L1 L2– M2)/(L1+ L2)+ 2M)

Summary

• When two terminals of the  inductor are connected respectively to other inductor or inductors terminals, then that connection is referred to as “a parallel connection of inductors”.
• When the fluxes produced by individual inductors are in the same direction, the mutual inductance will be increased; then these coils are called “Aiding” coils. Total inductance for aiding coils is LT = (L1 L2– M2)/(L1+ L2 )-2M).When the fluxes produced by individual inductors are in the opposite direction of magnetic flux, the mutual inductance will be decreased; then these coils are called “opposing” coils. Total inductance for aiding coils is LT = (L1 L2– M2)/(L1+ L2 )+2M)

Basic Electronics On The Go - Inductors in Series

From www.electronicshub.org/inductors-in-series/

An inductor is a passive element which is used in electronics circuits for temporary storage of electrical energy in the form of magnetic flux or simply magnetic field. Inductance is the property of any coil which can set up a magnetic flux when current passes through it.

Any device which has the property of inductance can be called an inductor. Usually inductor is built in the form of a coil with copper material around the core of a magnetic (iron) or nonmagnetic medium (like air).

Inductors may be connected in series or parallel configuration depending on the  performance required by the circuit. These combinations are used to design more complex networks. 

Inductors are arranged on the basis of their mutual inductance or magnetic coupling in series or parallel combinations.

Inductors Connected in Series

Assume that inductors connected in the circuit do not have any coupling between them. This implies that there are no flux lines from one inductor linking with another, and hence there will be no mutual flux between the coils.

The end to end connection of two or more inductors is called “series connection of inductors”. In this connection the inductors are connected in series so the effective turns of the inductor increases. 

The inductance of series connected inductors is calculated as the sum of the individual inductances of each coil since the current change through each coil is same.

This series connection is similar to that of the resistors connected in series, except the resistors are replaced by inductors. If the current I is flowing in the series connection and the coils are L1, L2, and so on, the common current in the series inductors is given by

ITotal = IL1 = IL2 = IL3. . . = In

If the individual voltage drops across each coil in this series connection are VL1, VL2, V¬L3, and so on, the total voltage drop between the two terminals VT is given by

VTotal = VL1 + VL2 + VL3…. + Vn

As we know that the voltage drop can be represented in terms of self inductance L, this implies

V = L di/ dt.

This can also be written as

L_T di/dt = L1 di/dt + L2 di/dt + L3 di/dt + . . . + Ln di/dt

Therefore the total inductance is

LTotal = L1 + L2 + L3 + ….. + Ln

Mutually Connected Inductors in Series

Now consider that inductors are connected such that magnetic field of one coil affects the other. When two or more inductors are connected in series, then the inductance of one inductor will be affected by the magnetic field produced by the other coil.

This is called mutual inductance and the coils are called “Mutually connected inductors”. This mutual inductance may increase or decrease the total inductance of the series circuit.

The factor that affects the mutual inductance of a series connected of inductors is the distance between the coils and their orientation.

The mutually connected inductors can be coupled in two ways

1) Cumulatively coupled or Series Aiding

2) Differentially coupled or Series opposing

Cumulatively Coupled Inductors in Series

If the magnetic fluxes produced by the inductors are in the same direction to the flow of current through them, then the coils are known as “Cumulatively coupled”.

In this series aiding or cumulative coupled circuit, the current  that enters or leaves the terminals of coils at any instant of time are in the same direction.

The figure below shows the connection of two inductors in a series aiding arrangement.

If we pass the current through the cumulatively coupled coils (between the nodes A & D) in the same direction, the voltage drop of each individual coil will affect the total inductance of the series.

Let self inductance of the coil-1 is L1, self inductance of the coil-2 is L2 and the mutual inductance is M between coil 1 and coil2.

Self induced emf in coil-1 is

e1 = – L1 di/ dt

Mutual induced emf in coil-1 due to change of current in coil-2 is

eM1 = – M di/ dt

Similarly, Self induced emf in coil-2 is

e2 = – L2 di/ dt

Mutual induced emf in coil-2 due to change of current in coil-1 is

eM2 = – M di/ dt

Therefore, total induced emf in the series aiding circuit is given as

e = – L1 di/ dt– L2 di/ dt– 2M di/ dt

= – (L1+ L2 + 2M) di/ dt

If LT is the total inductance of the circuit, the total induced emf will be equivalent to

e = – LT di/ dt

Substituting in the above equation, we get

– LT di/ dt = – (L1+ L2 + 2M) di/ dt

Therefore, LT = (L1 + L2 + 2M)

Differentially Coupled Inductors in Series

If the magnetic fluxes produced by the inductors are in the opposite direction to each other, then the coils are known as “Differentially coupled”.

In this differential coupled or series opposition connection, the current enters or leaves the terminals of coils at any instant of time are in the opposite direction.

The figure below shows the connection of two inductors in series opposition arrangement.

 total induced emf in the series opposing circuit is given as

e = – L1 di/ dt– L2 di/ dt + 2M di/ dt

= – (L1+ L2 – 2M) di/ dt

If LT is the total inductance of the circuit, the total induced emf will be equivalent to

e = – LT di/ dt

Substituting in the above equation, we get

– LT di/ dt = – (L1+ L2 – 2M) di/ dt

Therefore, LT = (L1 + L2 – 2M)

 Summary

• An inductor is a passive element which is used in electronics circuits for storing energy as magnetic flux. Inductance is measured in Henry.
• The dissipation amount of actual power with the current flow in the circuit is called “Inductive reactance”. It is measured in ohms. XL = 2  f L

• Self inductance is the property of an electric circuit or a loop in which its own magnetic field opposes any change in current
• Mutual inductance is the ability of an inductor that causes to induce emf in another inductor placed very close to it when current in first inductor changes.
• The end to end connection of two or more inductors is called “series connection of inductors”. The formula for total inductance in series is LT = L1 + L2
• The total inductance of the series connected inductors is always greater than the largest inductor in that series.
• If the magnetic fluxes produced by the inductors are in the same direction to the flow of current through them, then the coils are known as “Cumulatively coupled”. LT = L1 + L2 + 2M
• If the magnetic fluxes produced by the inductors are in the opposite direction to each other, then the coils are known as “Differentially coupled”. LT = L1 + L2 – 2M