Inductor

• 1. Introduction

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  An inductor is a passive two-terminal electrical component that stores energy in a magnetic field when an electric current flows through it. It is also called a coil, a choke, or a reactor. In its simplest form it is nothing more than an insulated wire wound into a coil. Yet that humble loop of wire sits beside the capacitor and the resistor as one of only three passive linear circuit elements that make up electronic circuits.

  The word itself carries a 19th century echo. It seems to come from Heinrich Daniel Ruhmkorff, who called the induction coil he invented in 1851 an inductorium. From that single Latinate flourish grew a component now wound onto doughnut-shaped ferrite cores, etched as spirals onto circuit boards, and increasingly faked entirely by clever active circuits.

  Why does a coil of wire fight any attempt to change the current passing through it? Why do radio engineers braid their wire into baskets and spiderwebs? And why, after more than a century, are real inductors quietly vanishing from the devices in your pocket? Those questions run through everything that follows.

• 2. Opposing The Change

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  When the current flowing through a coil changes, a time-varying magnetic field induces an electromotive force, or voltage, in the conductor. This is Faraday's law of induction at work, and it is the heart of why an inductor behaves the way it does. The induced voltage is the coil's reaction to being disturbed.

  Lenz's law sets the direction of that reaction. The induced voltage always opposes the change in current that created it. If the current through an inductor is rising, the induced potential difference is positive at the entrance point and negative at the exit, pushing back against the extra current. If the current falls, the polarity flips, and the coil tries to keep the current going. The component, in short, resists change in either direction.

  That resistance to change has a measure. An inductor is characterized by its inductance, the ratio of the voltage to the rate of change of current. The unit is the henry, named for the 19th century American scientist Joseph Henry. Real components span a wide range, from 1 microhenry, that is 10 to the minus 6 henries, up to around 20 henries.

• 3. Energy In The Field

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  Increasing the current does not come without a price. The magnetic field around the coil contains potential energy, and building a stronger field requires more energy to be stored in it. That energy is drawn from the electric current itself. The magnetic potential energy rises while the electric potential energy of the charges flowing through the windings drops, and that drop appears as a voltage across the windings for as long as the current keeps climbing.

  Hold the current steady and the bargain closes. Once the current is constant, the energy in the magnetic field is constant too, no further energy must be supplied, and the voltage drop across the windings disappears. Let the current fall instead, and the field gives its stored energy back to the circuit, raising the electrical potential energy of the moving charges and producing a voltage rise across the windings.

  The capacitor is the inductor's mirror image. The source calls it the dual of the inductor, a component that stores energy in an electric field rather than a magnetic one. Its current and voltage relationship simply swaps the roles that the inductor assigns to current and voltage.

• 4. The Magnetic Core

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  Geometry decides how much inductance a coil can muster. The inductance of a circuit depends on the geometry of the current path and on the magnetic permeability of nearby materials. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, and the more turns there are, the higher the inductance climbs. The shape of the coil and the separation of the turns matter too.

  Dropping a slug of iron inside the coil changes everything. By adding a magnetic core made of a ferromagnetic material like iron, the field from the coil induces magnetization in the material and increases the magnetic flux. The high permeability of such a core can multiply the inductance by a factor of several thousand over an empty coil.

  That power comes attached to penalties. Ferromagnetic cores bring extra energy losses from hysteresis and from eddy currents that circulate in the core, and both grow with frequency. At high currents the core can saturate, at which point the inductance itself begins to change with the current. One early solid-state switching and amplifying device, the saturable reactor, actually exploited that saturation to halt the inductive transfer of current through the core.

• 5. The Gap Between Ideal And Real

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  An ideal inductor has inductance and nothing else. No resistance, no capacitance, no energy dissipation. Real inductors refuse to cooperate. They carry a measurable resistance from the wire and from losses in the core, and they hold a parasitic capacitance between the turns of the wire.

  That stray capacitance turns the coil against itself at high frequency. A real inductor's capacitive reactance rises with frequency, and at one particular frequency the inductor behaves as a resonant circuit. Above this self-resonant frequency, capacitive reactance becomes the dominant part of its impedance, so the coil stops acting like a coil. Higher frequencies also drive up resistive losses in the windings through the skin effect and the proximity effect.

  Engineers grade this gap with a number called Q. The quality factor of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and it measures efficiency. The higher the Q, the closer the component comes to the ideal, and the narrower the bandwidth of any resonant circuit built from it. A well designed air core inductor may reach a Q of several hundred.

• 6. Wound For Radio

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  At radio frequencies the wire fights the current it carries. Because of the skin effect, radio frequency alternating current does not penetrate far into a conductor but travels along its surface. At 6 megahertz the skin depth of copper wire is about 0.001 inches, that is 25 micrometers, so the interior of a solid wire carries little current and its effective resistance rises. The proximity effect compounds this in parallel wires lying close together, displacing current away from the adjacent surfaces.

  To dodge these losses, RF coil builders turned ordinary winding into something closer to weaving. Multilayer coils are wound so that successive turns crisscross at an angle rather than running parallel, and these are called honeycomb or basket-weave coils. Flat spiral coils wound on a support with radial slots, with the wire weaving in and out, are called spiderweb coils. The form carries an odd number of slots so successive turns sit on opposite sides, widening the gaps between them.

  The wire itself can be reinvented. Litz wire replaces a single solid conductor with many smaller strands, each insulated from the others and twisted or braided together. The twist ensures every strand spends the same length on the outside of the bundle, so the skin effect spreads the current evenly across all of them. The result is a larger conducting cross-section than an equivalent single wire could offer.

• 7. Shapes And Variables

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  A straight rod core leaks. The magnetic field lines leaving one end of a rod-shaped core must travel through the air to re-enter at the other end, which weakens the field and throws off electromagnetic interference. Closing the loop fixes this. Forming the core into a toroidal, doughnut-shaped ring keeps the field lines circulating inside the core, and the symmetry lets very little flux escape, so toroids radiate less interference than other shapes.

  Many inductors are built to be tuned after the fact. The most common variable type today uses a movable ferrite core that slides or screws in and out of the coil; pushing it farther in raises the permeability and the inductance. Cores meant for frequencies above 100 megahertz are sometimes made instead from a conductive non-magnetic metal such as aluminium, which lowers the inductance because the field has to bypass it.

  The variometer offers continuous adjustment with no sliding contacts. It uses two series-connected coils of equal turns, one mounted on a shaft inside the other. When their axes line up and the fields point the same way, the inductance is maximum; turn the inner coil 180 degrees so the fields oppose, and they cancel, leaving the inductance very small. This continuous range made it useful in antenna tuners and matching circuits that link low frequency transmitters to their antennas.

• 8. Where Inductors Live And Why They Are Leaving

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  Inductors keep the power flowing when a switch turns off. In switched-mode power supplies they store energy and feed it back to the circuit during the off periods, which even allows designs where the output voltage exceeds the input. Larger inductors in power supplies team up with filter capacitors to strip away ripple at multiples of the mains or switching frequency, while a tiny ferrite bead around a cable blocks radio frequency interference from traveling down the wire.

  Put two coupled coils together and you have a transformer. Mutual inductance between adjacent inductors is the basis of transformer construction, and the transformer is a fundamental component of every electric utility power grid. Because eddy currents and skin effect erode efficiency as frequency rises, but smaller cores become possible too, aircraft run on 400 hertz alternating current instead of the usual 50 or 60, saving considerable weight through smaller transformers.

  For all that usefulness, the coil is in retreat. Inductors create and suffer from electromagnetic interference, and their physical size keeps them off semiconductor chips, so their use is declining in modern devices, especially compact portable ones. Real inductors are increasingly replaced by active circuits such as the gyrator, which synthesizes inductance using capacitors and active components instead of a winding at all.