In the previous tutorial, we discussed magnetism, electromagnetism, and inductance. Inductance can be useful in circuits. Electronic components designed to provide inductance in a circuit are called inductors.
Inductors
Most conductive materials (metals) are paramagnetic or ferromagnetic, while most non-conductive materials (non-metals) are diamagnetic. Any conductor shows some inductance in response to the change in magnitude or direction of current. Even a simple straight wire has some inductance, although it is small enough to be neglected in a circuit. If the same wire is wound into a loop, its inductance increases. The greater the number of turns for the same length of wire, the greater the inductance shown by it. The inductance of a loop or coil of wire can be multiplied many times by using a suitable ferromagnetic core.
The simplest inductors are air-cored coils. They are constructed by wrapping a coil of wire around plastic, wood, or any non-ferromagnetic core. The inductance of a coil depends on the number of turns, the radius of the coil, and the overall shape of the coil. The inductance is proportional to the number of turns and also to the diameter of the coil. It is inversely proportional to the length of the wire for a given diameter and number of coil turns. Therefore, the closer the turns are, the greater the inductance. The current carrying capacity of the inductor depends on the material and thickness of the wire. The operational losses (in the form of heat) of an inductor largely depend on the material used as the inductor core.
Example of an air core inductor (Image: Wurth Electronics)
Air core coils offer small inductances that can reach a maximum of 1 mH. Air core coils can be designed to have unlimited current carrying capacity using thick wire over a large radius. These inductors are almost lossless as the air does not dissipate much energy as heat. The higher the frequency of the AC current, the smaller the inductance required to produce significant effects. Therefore, air core inductors are quite suitable for high frequency AC circuits due to lossless operation, high current capacity and sufficient inductance values.
By using iron or ferrite powered cores, the inductance can be increased significantly. However, the powdered iron or ferrite core also has a significant loss of electrical energy in the form of heat. The use of ferromagnetic cores also limits the current-carrying capacity of the inductor. With ferromagnetic cores, the inductance is saturated at a critical current value. By increasing the current beyond the critical value, the inductance may instead begin to decrease. At high currents, ferromagnetic cores can become hot enough to fracture and permanently change the inductor's rated inductance.
Solenoid vs Inductors
Solenoids are often confused with inductors. Solenoids are coils of wire intended to be used as electromagnets. Many inductors are also coils of wire, but they are intended to provide inductance in a circuit. Inductors using cylindrical coils are also called solenoid coils just because of their solenoid-like construction. However, they are not intended to be used as an electromagnet in a circuit. Solenoids are used specifically as electromagnets and generally have a moving or static core. Typically, solenoids are used as electromagnets in electric buzzers, DC motors, and relays.
Solenoid coils as inductors
The simplest and most common inductors are solenoid coils. These inductors are cylindrical coils wound around an air core or ferromagnetic core. These inductors are easier to build.
A solenoidal or cylindrical coil can be easily designed to vary inductance by incorporating a mechanism to slide in and out of the coil's ferromagnetic core. By moving the core in and out of the coil, the effective permeability of the coil can be varied and therefore the inductance of the coil. This is called permeability adjustment. This is used to adjust frequencies in radio circuits.
The core can be moved by attaching it to a screw shaft and attaching a nut to the other end of the coil. When the screw shaft is turned clockwise, the core moves within the coil increasing the effective permeability and therefore the inductance. When the screw shaft is turned counterclockwise, the core moves outward, decreasing effective permeability and therefore inductance.
Toroids as inductors
Toroid is another most common form of inductors today. Toroids have a donut-shaped ferromagnetic core on which the coil is wound. Toroids need fewer turns and are physically smaller for the same inductance and current carrying capacity compared to solenoid coils. Another big advantage of toroids is that the flux is contained within the core, which avoids any unwanted mutual inductance.
High current toroidal conductors. (Image: Signal Transformer, from Grupo Bel)
However, it is difficult to wind the coil into a toroid. It is still very difficult to adjust the permeability of a toroid. Designing variable inductors in toroids involves complex and complicated construction. In circuits where mutual inductance is desired, the different coils need to be wound on the same core if the toroid is used as an inductor.
Pot cores as inductors
In typical inductors – solenoidal and toroid coils – the coil is wound around the ferromagnetic core. The pot core is another type of inductor in which the coil winding resides within the ferromagnetic core. In the core of the pot, the ferromagnetic core is in the shape of two halves. The coil is wound and wound on one of the halves. The two halves have holes between them, from which the coil wire is removed. The entire assembly is held together by a bolt and nut.
Potentiometer cores like toroids offer large inductance and current carrying capacity in small size with fewer number of turns. The flow, as in toroids, remains contained within the assembly. Therefore, there is no unwanted mutual inductance with potentiometer cores. Again, as with toroids, it is difficult to vary the inductance in the potentiometer cores. It is only possible to vary the inductance in the potentiometer cores by varying the number of turns and using taps at different points of the coil.
Transmission line as an inductor
Inductors are mainly useful in AC circuits. For DC, inductors behave almost like a conductive wire, offering negligible resistance and nothing more. In AC, inductors find their real applications. Audio frequency circuits often use toroids, pot cores, or audio transformers as inductors. Audio circuits typically use inductors of values ranging from a few Milli-Henrys to 1 Henry. Inductors along with capacitors have been used in audio circuits for tuning. Nowadays, active ICs have almost replaced inductors and capacitors in audio circuits and applications.
As the frequency increases, inductors with cores of lower permeability are used. At the low end of radio frequencies, the same inductors used in audio applications are used. At radio frequencies up to a few MHz, toroids are quite common. For radio frequencies from 30 to 100 MHz, air core coils are preferred.
For radio frequencies greater than 100 MHz, transmission line inductors are useful. Short-length transmission lines (a quarter wavelength or less of the signal wavelength) can be used as inductors to tune high-frequency radio signals. The transmission line used as an inductor is generally a coaxial cable.
Inductor in DC circuit
Practically, inductors are not useful in DC circuits, as they do not have inductance for constant currents. However, assuming an inductor connected in a DC circuit can be useful to understand its working principle and its behavior in the face of pulsating DC voltages. Suppose a pure inductor is connected to a voltage source through a switch. When the switch is closed, voltage is applied to the inductor, causing a rapid change in current through it. As the applied voltage increases from zero to a peak value (in a short time), the inductor opposes the flow of changing current through it, inducing a voltage of opposite polarity to the applied voltage. The voltage induced during energization of the inductor is called back EMF and is given by the following equation –
V i = – L*(di/dt)
Where,
V i is the voltage (back EMF) induced in the inductor.
L is the inductance offered by the inductor.
di/dt is the rate of change of current in relation to time.
A sudden change in current through the inductor produces an infinite voltage, which is not viable. Therefore, the current through the inductor cannot change abruptly. The current faces the effect of inductance for every small change in magnitude and slowly rises to its constant peak value. Thus, initially, the inductor acts as an open circuit when the switch is closed. The back EMF remains in the inductor until the current changes through it. The induced back-EMF always remains equal and opposite to the increase in applied voltage. As the source voltage and current approach a constant value, the back EMF drops to zero and the inductor acts as a short circuit, like a connecting wire. During energization, the power stored by the inductor is given by the following equation –
P = V * I = L*i*di/dt
Where,
P is the electrical energy stored by the inductor.
V is the peak voltage across the inductor.
I is the peak current through the inductor.
The energy stored by the inductor during energization is given by the following equation –
W = ∫P.dt = ∫L*i*(di/dt)dt = (1/2)LI 2
Where,
W is the electrical energy stored by the inductor in the form of a magnetic field.
I is the maximum current passing through it.
When the voltage source is removed (by opening the switch), the voltage across the inductor drops from the constant peak value to zero. Unlike capacitors, when removing the voltage source, the voltage in the inductor is not retained. In fact, it already dropped to zero when the current through it became constant. Now, as the applied voltage drops from the constant peak value to zero, the current through the inductor also drops from the constant peak value to zero. Now, the inductor opposes the drop in current by inducing a direct EMF in the direction of the applied voltage. Due to the induced forward EMF, the current through the inductor drops to zero at a slower rate. Once the current reduces to zero, the forward EMF also drops to zero.
Thus, during energization, electrical energy was converted into a magnetic field in the inductor, which was evident from the back EMF induced through it. During de-energization, the same electrical energy is returned by the inductor to the circuit in the form of direct EMF. Whenever the voltage across the inductor increases, back EMF is produced and whenever the voltage across the inductor decreases, forward EMF is produced.
Practically, the back EMF or forward EMF developed in an inductor is many times greater than the applied voltage. If only one inductor is connected to a voltage source or one inductor is connected in a DC circuit without any protection, the electrical energy returned when opening the switch is released in the form of a voltage spike or spark at the switch contact. If the inductance is large or the current in the circuit is high, the energy released in the form of an arc or spark at the switch contact can even burn or melt it. This can be avoided by using a network of resistors and capacitors (RC) in series with the switch contact. This RC network is called Damper Network . It lets the electrical energy released by the inductor charge and discharge the capacitor, without damaging any other component. In many circuits, protection diodes are used to save other circuit components from back or direct EMF from an inductor or solenoid.
Inductor in AC circuit
Because the inductor opposes any change in current, the AC current lags the AC voltage across the inductor by 90°. Initially, when voltage from a source is applied to an inductor, the current through the inductor is maximum and in the opposite direction. As voltage is applied, current flows through the inductor due to the induced EMF opposite the applied voltage. The voltage induced in the inductor is always equal and opposite to the applied voltage at all times. As the applied voltage increases from zero to the peak value, the opposing current through the inductor drops from maximum to zero.
When the applied voltage drops from the peak value to zero, forward EMF is induced through the inductor, causing the current through it to increase from zero to its peak value in the opposite direction. When the applied signal changes polarity and rises to the peak value in the opposite direction, again a back EMF is induced in the inductor, causing the opposite current to fall from the peak value to zero. As the applied voltage drops back to zero to reverse the direction, a forward EMF is induced in the inductor, causing the current to rise again from zero to its peak value in the opposite direction. This continues for each cycle of the AC signal.
Inductive reactance
The opposition to current due to inductance is indicated by inductive reactance. The amplitude of the current through the inductor is inversely proportional to the frequency of the applied voltage signal. As the voltage across the inductor (back EMF or forward EMF) is proportional to the inductance, the current amplitude is also inversely proportional to the inductance. Thus, the opposition to current due to inductance in the form of inductive reactance is given by the following equation:
X l = 2πfL
= ωI
Consequently, the peak amplitude of the current through the inductor is given by the following equation:
EU peak =V peak /X eu
=V peak /ωL
Where,
L peak is the peak value of the AC current through the inductor.
V peak is the peak value of AC voltage applied to the inductor.
X i is the inductive reactance.
Just like resistance and capacitive reactance, the unit of inductive reactance is also ohms. It should be noted that there is no loss of energy in a circuit due to capacitive or inductive reactance, unlike resistance. However, reactance can limit current levels through the capacitor or inductor.
Inductor applications
Inductors are used with AC circuits. They are commonly used in analog and signal processing circuits in telecommunications. They are also used along with capacitors to design filter circuits. In telecommunications, inductors are also used to lower system voltages or fault currents along transmission lines. By coupling inductors, transformers are designed which are used to increase or decrease AC voltages. Inductors are also used to temporarily store electrical energy in SMPS and UPS circuits. In power supply circuits, inductors (where they are called filter coils) are used to smooth pulsating currents.
The signal behavior of an inductor can be summarized as follows:
- Whenever the voltage applied to an inductor increases, back EMF is generated by the inductor, causing the current through it to drop from a maximum value to zero or lower level. Whenever the applied voltage decreases, forward EMF is produced by the inductor, causing the current through it to increase from zero or current level to a maximum value or higher level.
- The back EMF or forward EMF remains through the inductor until the applied voltage and therefore the current through it is changing. As the applied voltage saturates to a constant value, the back EMF or forward EMF drops to zero and a constant current flows through the inductor without any opposition, like in a connecting wire.
- Due to inductance, the rate of change of current is slowed down in the circuit. If the signal is AC, the current will always lag the voltage by 90° due to inductance.
- Due to inductive or capacitive reactance, there is no loss of energy. The energy stored by an inductor in the form of a magnetic field or by a capacitor in the form of an electrostatic field is returned to the circuit as the applied voltage drops or reverses direction. However, due to reactance, the peak current level (current signal amplitude) is limited.
In the next article, we will discuss several non-ideal characteristics and key performance indicators of inductors.