Inductor - Wikiparency

# Inductor An **inductor** is a passive component that stores energy in the [[Magnetic_field|magnetic field]] produced by current flowing through it, usually a coil of wire, often wound on a magnetic core. Its defining property, [[Inductance|inductance]], is the ratio of the magnetic flux linked by the winding to the current producing it. Where a [[Capacitor|capacitor]] resists a change of voltage, an inductor resists a change of current, and the two are duals throughout circuit theory. The property that most distinguishes a real inductor from the ideal one is that its core will hold only so much magnetic flux. Past that point the inductance collapses, and because stored energy depends on both inductance and current, the energy a core can hold approaches a ceiling that no further current lifts. The microsim on this page is built around that collapse: it plots inductance and stored energy against current, and marks the point a datasheet would call the saturation current. ## Description Current through a conductor produces a magnetic field around it, and winding the conductor into a coil concentrates that field through the centre of the turns. Each turn links the flux produced by all the others, so inductance grows roughly with the square of the number of turns rather than in proportion to it. A change in current changes the flux, and by [[Faraday's_law_of_induction|Faraday's law]] a changing flux induces a voltage in the winding that opposes the change, a direction given by [[Lenz's_law|Lenz's law]]. The voltage across an inductor is therefore proportional to the rate of change of current, which is the dual of the capacitor relation. A steady current produces no voltage at all, so an ideal inductor is a short circuit to [[Direct_current|direct current]] and an increasing impedance to rising frequency. That impedance is [[Electrical_reactance|reactance]], rising in proportion to frequency, and it is what makes an inductor useful for separating signals by frequency. The energy stored in the field is proportional to the inductance and to the square of the current, and unlike a resistor an inductor returns that energy to the circuit rather than dissipating it — which is why the collapse of inductance under bias matters so much in power conversion, where the energy stored per cycle is the whole point. ## Applications The largest use is in power conversion. A [[Switched-mode_power_supply|switched-mode power supply]] works by storing energy in an inductor during one part of a switching cycle and releasing it during the next, so the inductor is the energy-transfer element rather than an incidental component. Here saturation is a hard design limit: an inductor driven into saturation loses control of its ripple current, and the switch that drives it sees a current that rises far faster than intended. Inductors also filter. In combination with capacitors they form the resonant circuits that select a frequency in radio, and the [[Electronic_filter|low-pass]] sections that smooth a rectified supply. A common-mode choke passes the wanted differential signal while presenting a high impedance to interference common to both conductors. A ferrite bead on a cable is the same idea in its simplest form. Where two windings share a core, the changing flux from one induces a voltage in the other, which is the [[Transformer|transformer]]: it transfers energy between circuits without a conductive path and scales voltage by the ratio of turns. Inductors further appear as sensors, since anything that alters the magnetic path alters the inductance, and as the coils of motors, [[Relay|relays]] and loudspeakers, where the stored field does mechanical work. ## Inductor construction An inductor is a winding and, usually, a core. The winding is chosen for the current it must carry and for its resistance, and at high frequency for the way current crowds into the outer part of a conductor — the [[Skin_effect|skin effect]] — and into the parts of a winding facing away from neighbouring turns, the proximity effect. Litz wire, many fine strands individually insulated and transposed, exists to defeat both. The core sets how much inductance a given winding achieves and how much flux it can carry before saturating. A high-[[Permeability_(electromagnetism)|permeability]] core multiplies inductance for the same turns, which is why cored inductors are far smaller than air-cored ones of the same value. Cutting a deliberate air gap in the magnetic path lowers the inductance but raises the current at which the core saturates and makes the saturation knee gentler and more predictable: the gap, rather than the core material, then dominates the magnetic behaviour. This trade is exactly what the hardness control in the microsim represents. ## Types Air-cored inductors have no magnetic material and so cannot saturate at all, which makes them suitable for radio frequency work where linearity matters and the required inductances are small. Ferrite-cored inductors use a sintered ceramic [[Ferrite_(magnet)|ferrite]], whose high resistivity suppresses eddy currents and makes it the standard choice from tens of kilohertz upward; ferrite saturates fairly sharply, so gapped ferrite cores are usual in power applications. Powdered-iron and other composite cores distribute a deliberate gap throughout the material, giving a soft, gradual saturation characteristic that is forgiving of current overload at the cost of higher core loss. Laminated iron cores, built from thin insulated sheets to interrupt eddy-current paths, serve at mains frequency where the flux is large and the frequency low. Toroidal cores confine the field almost entirely within the core, which reduces radiated interference and makes them common where electromagnetic compatibility matters. ## Circuit analysis In series, inductances add; in parallel, their reciprocals add — the opposite of capacitors and the same as resistors. Two inductors sharing flux add or subtract a mutual inductance term depending on their relative winding sense, which is why physically adjacent inductors in a filter are usually oriented at right angles. With a resistance in series, an inductor gives an exponential approach of current to its final value with a time constant equal to inductance divided by resistance. With a capacitor it forms a resonant circuit, treated at [[RLC_circuit|RLC circuit]]: at resonance the inductive and capacitive reactances cancel, and the sharpness of that resonance is the [[Q_factor|quality factor]], which for an inductor is its reactance divided by its loss resistance and is the usual single-number figure of merit. A practical consequence of the current-opposing behaviour is that interrupting the current in an inductor produces a large voltage spike, since the field must collapse into whatever path is available. Circuits switching inductive loads therefore need a path for that current — a flyback [[Diode|diode]] across a relay coil, or a snubber across a switch — or the switch will be destroyed by the voltage its own turn-off produces. ## Inductance formulas Closed-form inductance expressions exist for a few regular geometries. For a long solenoid the inductance rises with the square of the turn count and with the cross-sectional area, and falls with the length, multiplied by the permeability of the core. For a toroid the same dependence on turns and permeability appears with the mean magnetic path length in place of the solenoid length. Real cores are described instead by an inductance factor supplied by the manufacturer, the inductance per turn squared for that specific core and gap, which absorbs the geometry into one measured number. This is the practical route: the designer chooses a core for the energy it must store, reads its inductance factor, and computes the turns needed. Checking the result against the saturation current is the step the microsim is meant to make concrete, since a winding that gives the right inductance at zero current may give far less at the current it will actually carry. ## Microsim The microsim plots inductance and stored energy against DC bias current, with current expressed as a multiple of the saturation current so the shape of the curve is universal and the numbers appear as readouts. The reader sets the small-signal inductance, the saturation current, a hardness exponent standing for the core type and gap, the winding resistance and a frequency. Three things are worth trying. Raise the bias current past the saturation current and watch the inductance fall while the energy curve flattens: past the knee, inductance falls roughly as the inverse square of current, so the product that gives energy stops growing. Lower the hardness exponent towards one, which behaves like a powdered-iron core, and watch the knee soften and spread out. Then read the saturation-current figure at a thirty percent drop, which is the convention many datasheets use, and compare it with the current at which the inductance has genuinely halved: the datasheet number is a long way inside the real collapse.  **Microsim — three.js (Wikitube framework):** *The inductor: core saturation and the energy ceiling* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/electronics/Inductor.html" data-title="Inductor"></div> *Built from `MICROSIM_GUIDE/specs/sims/Inductor.json`; part of the [[Electronics]] set ([[PORTAL_Electronics]]).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Inductor) : [Wikitube](https://en.wikitube.io/wiki/Inductor) Skeleton mirrored at revision 1373727531. Prose, emphasis and the microsim are Wikitube's own. ## See also - [[Inductance]] - [[Capacitor]] - [[Resistor]] - [[Transformer]] - [[RLC_circuit]] - [[Q_factor]] ## Notes The microsim's saturation law is a smooth algebraic stand-in for a measured B-H curve. It shows the collapse of inductance and the energy ceiling, which are the design-limiting behaviours, but it does not represent hysteresis loss, eddy-current loss, or the frequency dependence of winding resistance. This is stated on the sim's own notes line. ## References The electromagnetism and circuit theory here — inductance as flux linkage per unit current, Faraday's and Lenz's laws, reactance rising with frequency, stored energy, series and parallel combination, the inductance-over-resistance time constant, resonance and the quality factor, and the solenoid and toroid inductance expressions — is standard textbook material and is not separately footnoted, per the Wikitube style guide §6.1. *Citation needed:* the core-material classes and their saturation behaviour, the frequency ranges quoted for ferrite and laminated iron, and the thirty-percent-drop datasheet convention for saturation current are stated as general engineering practice rather than from a pinned source. Pinning them to manufacturer core data and to the relevant standards is queued for the next pass; no source is asserted for them here. ## External links - Manufacturer core data and inductance-factor tables, to be pinned with the citations above.