An inductor is a passive electrical device that stores energy in a magnetic field, typically by combining the effects of many loops of electric current.

Physics

Overview

Inductance (measured in henrys) is an effect which results from the magnetic field that forms around a current carrying conductor. Energy stored in the magnetic field has two effects on the inductor, an electromotive force is generated which opposes the voltage applied to the inductor and current in the inductor tends to remain constant regardless of voltages applied to the inductor. Inductance can be increased by looping the conductor into a coil which causes magnetic flux from adjacent loops of the conductor to link.

Stored energy

The energy (measured in joules, in SI) stored by an inductor is equal to the amount of work required to establish the current flowing through the inductor, and therefore the magnetic field. This is given by:

where I is the current flowing through the inductor.

In electric circuits

An inductor only resists changes in current. An ideal inductor does not offer any resistance to direct current, except when the current is switched on and off, in which case it makes the change more gradual. However, all real-world inductors are constructed from material with non-zero electrical resistance, which opposes even direct current.

In general, the relationship between the time-varying voltage v(t) across an inductor with inductance L and the time-varying current i(t) passing through it is described by the differential equation

When a sinusoidal alternating current (AC) flows through an inductor, a sinusoidal alternating voltage (or electromotive force, abbr. emf) is induced. The amplitude of the emf is related to the amplitude of the current and to the frequency of the sinusoid by the following equation.

where ? is the angular frequency of the sinusoid defined in terms of the frequency f as

Inductive reactance is defined as:

where X_L is the inductive reactance, ? is the angular frequency, f is the frequency in hertz, and L is the inductance.

Inductive reactance is the positive imaginary component of impedance.

The complex impedance of an inductor is then given by:

where j is the imaginary unit.

When using the Laplace transform in circuit analysis, the inductive impedance is represented in the s domain by:

Inductor networks

Inductors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent inductance (L_eq):

The current through inductors in series stays the same, but the voltage across each inductor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total inductance:

These relationships hold true only in the limit that they are in magnetically decoupled environments.

Q Factor

The quality factor of an inductor can be found through this formula, where R is its internal electrical resistance

Inductor Construction

An inductor is usually constructed as a coil of conducting material, typically copper wire, wrapped around a core of ferrous material, which is highly permeable to magnetic flux and confines the magnetic field closely to the inductor, thereby increasing the inductance. Inductors come in many shapes. most are constructed as enamel coated wire wrapped around a ferrite bobbin with wire exposed on the outside, while some enclose the wire completely in ferrite and are called "shielded". Some inductors have an adjustable core, which enables changing of the inductance. Small inductors can be etched directly onto a printed circuit board by laying out the trace in a spiral pattern. Small value inductors can also be built on integrated circuits using the same processes that are used to make transistors. In these cases, aluminum interconnect is typically used as the conducting material. However, practical constraints make it far more common to use a circuit called a "gyrator" which uses a capacitor and active components to behave similarly to an inductor. Inductors used to block very high frequencies are sometimes made with a wire passing through a ferrite cylinder or bead.

Applications

Inductors are used extensively in analog circuits and signal processing, including tuned circuits used in radio reception and broadcasting. Inductors in conjunction with capacitors and other components form tuned circuits which filter out specific signal frequencies.

Two (or more) inductors which have coupled magnetic flux form a transformer, which is a fundamental component of every electric utility power grid.

An inductor is used as the energy storage device in a switched-mode power supply. The inductor is energized for a specific fraction of the regulator's switching frequency, and de-energized for the remainder of the cycle. This energy transfer ratio determines the input-voltage to output-voltage ratio.

Inductors are also employed in electrical transmission systems, where they are used to intentionally depress system voltages or limit fault current. In this field, they are more commonly referred to as reactors.

History

In 1831, Michael Faraday began his great series of experiments in which he discovered electromagnetic induction. He found that if he moved a magnet through a loop of wire, an electric current flowed in the wire. The current also flowed if the loop was moved over a stationary magnet.

See also

• Capacitor
• Resistor
• Electricity
• Electronics
• Gyrator
• Inductance (including mutual inductance)
• Induction loop
• Saturable reactor
• Transformer

Synonyms

• coil
• induction coil
• choke
• reactor

External Links

• Spiral inductor models. Good article on inductor characteristics and modeling.