Coils (Inductors)
An inductor is a coil of wire that stores energy in a magnetic field and, because of that field, resists any sudden change in the current through it. That property lets inductors tune radios, smooth power supplies, block noise, run efficient voltage converters and fire spark plugs. It also lets them deliver a nasty high-voltage kick when their current is switched off. This article covers how inductors work, their markings, types and circuits, and how to test and handle them safely. No background is assumed.
About the analogies. Everyday comparisons appear only in shaded "Analogy" boxes beside the real physics, and each box says where the comparison stops working.
1. A short recap: charge, current, copper, resistors and capacitors
- Current is the rate at which electric charge flows, in amperes (A). Voltage is the energy per unit of charge between two points, in volts (V). (Recap: the atom and charge; current, voltage and resistance.)
- Copper conducts well because each atom gives up one loosely held electron that can drift through the metal, which is why coils are wound from copper wire. (Recap: conductors.)
- A resistor obeys Ohm's law, V = I × R, and turns energy into heat at P = I2R. (Recap: resistors in circuits; power ratings.)
- A capacitor stores energy in an electric field and, with a resistor, charges with a time constant τ = RC. (Recap: how a capacitor works; RC circuits.) An inductor is its mirror image.
2. What an inductor is
An inductor is a component built to have a useful amount of inductance: the property of opposing any change in the current through it.[1] In practice it is almost always a coil, a length of insulated wire wound into loops, and "coil" is simply another name for an inductor.[1][2] The coil may be wound on air or on a core of magnetic material such as iron or ferrite, which greatly increases the inductance.[3][2] Inductance has the symbol L and is measured in henries (H).[3]
On a schematic, an inductor is drawn as a row of loops, a picture of the coil. Parallel lines drawn alongside the loops mean the coil has an iron core.[1] An inductor used to block alternating current or noise while passing steady current is often called a choke.[4][5]
3. How it works: from magnetic field to back-EMF
Current makes a magnetic field
A magnetic field is the region around a magnet or a current where a compass needle, a piece of iron or a moving charge feels a magnetic force. Its strength is measured in teslas (T).[8] In 1820 the Danish scientist Hans Christian Oersted found that a current in a wire deflects a nearby compass needle: electricity and magnetism are linked.[9][10]
The field around a straight wire forms closed circles centered on the wire. Its direction follows right-hand rule 2: point your right thumb along the current, and your fingers curl the way the field goes.[6] The field is proportional to the current and weakens with distance from the wire.[10]
Wind the wire into a long coil, a solenoid, and the turns' fields add up: strong, nearly uniform and proportional to the current inside, very weak just outside. The whole coil behaves like a bar magnet, with a north pole at one end and a south pole at the other (Figure 1).[6][7]
Magnetic flux
Magnetic flux, symbol Φ (Greek phi), measures how much magnetic field passes through an area such as the inside of a loop. For a uniform field at right angles to the loop, it is simply field times area, Φ = BA. Flux is measured in webers (Wb); one weber is one tesla across one square meter.[8]
Faraday's law: a changing flux makes a voltage
In 1831 Michael Faraday discovered the reverse of Oersted's effect: a changing magnetic flux through a loop of wire produces a voltage in that loop.[8] This voltage is called an induced EMF. EMF stands for electromotive force, an old name for a voltage produced by a source; despite the name, it is a voltage, not a force. Faraday's law says the induced EMF equals the number of turns N times the rate at which the flux changes.[8] A steady flux, however strong, induces nothing. Only change counts.
Lenz's law: the induced voltage opposes the change
Lenz's law gives the direction: the induced EMF always drives current that creates a magnetic field opposing the change in flux that caused it.[11] This is a direct consequence of conservation of energy. If the induced current aided the change, it would feed on itself and create energy from nothing.[11]
Self-induction and back-EMF
When the current through a coil changes, its own field and the flux through its own turns change, so Faraday's law induces an EMF in the coil itself. This is self-induction.[12][3] By Lenz's law, that EMF opposes the change in current (Figure 2).[12] A rising current is pushed back; a falling current is pushed onward.[12] This voltage is often called back-EMF or counter-EMF.[13]
VL = L × (rate of change of current) or VL = L ΔI/Δt
This defines inductance (textbooks add a minus sign to record Lenz's law).[3] It also defines the unit: a coil has an inductance of one henry if a current changing at one ampere per second induces one volt across it.[13] The unit is named after Joseph Henry, and one henry equals one ohm-second.[3] The key consequence is that the current through an inductor cannot change instantly. A sudden change would take an infinite voltage, and the field's energy cannot be built up instantly either.[3]
Analogy: a heavy flywheel. A flywheel is hard to spin up and hard to stop. An inductor treats current the same way, and the energy it holds while current flows is like the flywheel's energy of motion. NEETS uses a similar picture: the inertia of a boat.[13]
Where it breaks down: a flywheel's energy sits in its moving mass. An inductor's energy sits in the magnetic field around the coil, not in the electrons, which drift only slowly. And a flywheel that suddenly jams just stops, while an inductor whose current is suddenly interrupted produces a voltage high enough to jump the gap (see Safety).
Energy stored in a magnetic field
Pushing current into an inductor against its back-EMF takes work, and that energy is stored in the magnetic field:[14]
U = ½LI2
where U is the energy in joules (J), L the inductance in henries and I the current in amperes. Compare the capacitor's ½CV2 (Capacitors: how it works). Both components store energy, the capacitor in an electric field and the inductor in a magnetic field, and a circuit containing both can pass energy back and forth between them.[15] The difference matters for safety. A charged capacitor holds its energy as long as its charge stays put, even after it is disconnected. An inductor holds energy only while current flows through it. Open the circuit and the field collapses, and the energy has to go somewhere, usually into a spark.[3]
What sets the inductance
For a long air-filled solenoid, the inductance is:[3]
L = μ0N2A / ℓ
Here N is the number of turns, A the coil's cross-sectional area (m2), ℓ its length (m), and μ0 (mu-zero) the permeability of free space, a constant equal to 4π × 10−7 T·m/A.[3] Permeability describes how readily a material supports a magnetic field. In plain terms:[1]
- Turns squared. Double the turns and the inductance quadruples.
- Area. Double the radius and area and inductance quadruple.
- Length. Spread the same turns over twice the length and inductance halves.
- Core. A core with higher permeability raises the inductance.
OpenStax works an example: 200 turns, 2.00 cm radius and 10.0 cm long gives 0.632 mH. At 30.0 A, that coil stores 0.284 J, which OpenStax notes is enough to cause a spark.[3]
Iron, nickel and cobalt are ferromagnetic: tiny regions called domains line up with an applied field and add to it enormously, multiplying a filled solenoid's field by roughly a thousand to ten thousand.[9][16] The effect is not constant. In OpenStax's annealed-iron example, the multiplier falls from about 6,000 to about 2,500 as the applied field rises.[16] Once nearly all domains are aligned, the core can add little more. This is saturation, and it limits the current in every iron- or ferrite-cored inductor.
4. The numbers that describe an inductor
| Unit | Symbol | Value | Typical home |
|---|---|---|---|
| henry | H | 1 H | Large iron-core power-supply chokes; one henry is a large inductor[3][4] |
| millihenry | mH | 0.001 H | Audio-frequency filtering, as in OpenStax's 3.00 mH example[17] |
| microhenry | µH | 0.000 001 H | Power-converter inductors; the unit used in markings[18][2][19] |
| nanohenry | nH | 0.001 µH | Radio-frequency (RF) circuits[20] |
- Tolerance. How far the real value may stray, often as a letter: F = ±1%, G = ±2%, H = ±3%, J = ±5%, K = ±10%, L = ±15% and M = ±20%.[2] Power chokes are often loose; Hammond's filter chokes are ±15%.[4]
- Rated current (Irms). The steady current that heats the part by a set amount, typically 15 °C for chip inductors and 40 °C for power inductors at Coilcraft: a thermal limit, not a magnetic one.[21][2]
- Saturation current (Isat). The current at which saturation has cut the inductance by a stated amount, commonly 10% for ferrite or 20% for powdered iron (some makers use 30%).[2][22] Ferrite saturates abruptly at a sharp "knee"; powdered iron rolls off gradually.[22] A saturated inductor "no longer functions as an inductor".[18] Air does not saturate, so air-core coils have no Isat rating.[2] Hammond quotes its iron-core chokes' inductance at rated DC current, because it falls as current rises.[4]
- DC resistance (DCR). The winding wire's resistance, quoted as a maximum.[2] It wastes power as heat (I2R, called copper loss)[23] and rises with temperature by about 0.385% per °C.[21] At 85 °C that is about 23% more than at 25 °C. Cores also waste energy (core loss) as they are magnetized back and forth.[23][2]
- Q (quality factor). The ratio of an inductor's reactance (its opposition to alternating current, explained in section 7) to its loss resistance: Q = 2πfL/R.[2] A higher Q means lower losses. For example, a 10 µH coil at 1 MHz with 0.5 Ω of loss resistance has a reactance of 62.8 Ω and a Q of about 126. Q varies with frequency in a bell-shaped curve.[2]
- Self-resonant frequency (SRF). The tiny capacitance between turns resonates with the inductance; above this frequency the part acts like a capacitor.[2] Use inductors well below it.[18]
5. Reading inductor markings
Inductor values are marked in microhenries, using the same digit-and-multiplier schemes as resistors (Resistors: the color code).[2][19]
- EIA color bands. Digit, digit, multiplier, tolerance. A gold multiplier is ×0.1 and silver ×0.01; a gold tolerance band is ±5% and silver ±10%. So red-violet-brown-gold is 270 µH ±5%, and blue-gray-gold-silver is 6.8 µH ±10%.[24]
- Military-style bands. A double-width silver band first identifies an inductor, and gold in a digit position is a decimal point. Silver (wide), blue, gold, gray, silver reads as 6.8 µH ±10%.[24] Molded inductors can look exactly like resistors; a near-zero ohmmeter reading is a clue.
- Printed codes on surface-mount parts. Like resistor codes (Resistors: SMD codes): two digits and a multiplier, in µH, with R as the decimal point. "101" is 10 followed by one zero, or 100 µH; "100" is 10 µH; "4R7" is 4.7 µH; and "R47" is 0.47 µH.[19]
On a datasheet, look for the inductance and the test frequency it was measured at, the tolerance, the maximum DCR, Irms and Isat (and the percentage drop used to define Isat), SRF, Q for RF parts, and the operating temperature range.[18][22] Pick a part with Isat and Irms comfortably above the highest current it will carry.[18]
6. Kinds of inductor
| Type | Construction | Strengths | Typical use |
|---|---|---|---|
| Air core | Self-supporting coil, or wound on a nonmagnetic ceramic form | No saturation, very low core loss, very high Q, tight tolerance; low inductance (nH) | RF matching and tuning[20][2] |
| Ferrite rod (slug) or bobbin | Coil on a rod or spool of ferrite, a fired mixed oxide of iron with manganese-zinc or nickel-zinc | Simple, compact; the field spreads into the space around the part | General-purpose parts; a magnetic sleeve is needed to shield them[2] |
| Ferrite toroid | Coil on a doughnut-shaped ring | Closed magnetic path keeps most of the field inside (self-shielding); saturates early | Where stray fields would disturb neighbors[2] |
| Pot core | Coil enclosed in a two-part ferrite shell | Self-shielding | Where a contained field is needed[2] |
| Powdered iron | Insulated iron particles pressed into a core; the gaps between particles act as a built-in air gap | Lowest cost; soft (gradual) saturation | Carrying higher DC current before saturating[2][22] |
| Laminated iron | Stack of thin insulated steel sheets | Large inductance (henries) at low frequency; laminations cut eddy-current loss | Power-supply filter chokes; transformers[2][25][4] |
| SMD wirewound | Fine copper wire on a tiny core (alumina in Murata's RF parts) | Low DCR, very high Q, higher current | RF circuits[26][27] |
| SMD multilayer | Printed conductor layers stacked in ceramic, no wire | Very small, low cost; lower Q | Compact, low-cost RF circuits[26][2] |
| Shielded SMD power | Core shape or magnetic sleeve encloses the winding | Less stray field; shielding is a matter of degree | Crowded boards near sensitive circuits[2] |
| Variable (slug-tuned) | Threaded core screwed in or out of the coil | Adjustable inductance | Tuning radio circuits[28][29] |
| Ferrite bead | Ferrite sleeve or chip around a conductor | Lossy at noise frequencies, so it turns noise into heat; rated in ohms at 100 MHz | Suppressing interference on signal and power lines[30] |
| Common-mode choke | Two windings on one core | Blocks noise traveling the same way on both wires; passes the wanted signal | Differential signal lines such as USB[5] |
Why the special cores? A changing field induces swirling eddy currents in any conductive core, wasting energy as heat.[31] Eddy currents flow only if the core material conducts,[2] so iron cores are made of thin insulated laminations,[25] and powdered-iron particles are insulated from each other.[2] A ferrite bead's material is chosen to be lossy, turning noise into heat rather than storing it.[30] In a common-mode choke, the signal goes out on one wire and back on the other, so its fields cancel in the core; noise traveling the same way on both wires adds up and is blocked.[5] Slug-tuned coils such as Coilcraft's 148 series are lowest in inductance with the core half out and highest with it centered.[28]
7. Inductors in circuits
Switching on: the RL time constant
Connect an inductor in series with a resistor R and close a switch onto a DC supply V. At switch-on the current is zero, since it cannot jump, and the whole supply appears across the inductor. As current grows, more voltage drops across the resistor, less is left for the inductor, and the rise slows. The current approaches V/R along an exponential curve (Figure 4):[32][33]
I = (V/R)(1 − e−t/τ), τ = L/R
The time constant τ (tau) is in seconds when L is in henries and R in ohms. In one time constant the current reaches 63.2% of its final value.[32][33] After about five, it is within 1% and is considered settled. On switch-off through a resistor, the current decays to 36.8% in one time constant.[33] Compare the capacitor (Capacitors: RC circuits): there the voltage lags and τ = RC; here the current lags. A bigger resistor makes an RL circuit faster.
Worked example. A 12 V supply drives a 100 mH coil through a total resistance of 100 Ω, which includes the coil's own DCR.
- Time constant: τ = 0.100 H ÷ 100 Ω = 0.001 s = 1 ms.
- Final current: 12 V ÷ 100 Ω = 120 mA.
- After 1 ms: 63.2% of 120 mA ≈ 75.9 mA, and the coil's voltage has fallen from 12 V to about 4.4 V. After 2 ms: 103.8 mA. After 5 ms: 119.2 mA, essentially there.
- Stored energy at full current: ½ × 0.100 × 0.1202 = 0.72 mJ. That is small, but see Safety for what happens if this current is cut suddenly.
Passing DC, opposing AC: inductive reactance
Once a steady DC current settles, a coil induces no voltage and is just its winding resistance; at low frequencies, inductors look like shorts.[34] Alternating current (AC) changes constantly, so the inductor keeps opposing it. That opposition is the inductive reactance, measured in ohms:[17][35]
XL = 2πfL
where f is the frequency in hertz (Hz, cycles per second). Reactance rises in direct proportion to frequency.[35] A capacitor does the opposite: it blocks DC, and its reactance falls as frequency rises (Capacitors: reactance).[17] OpenStax's example is a 3.00 mH coil, which has a reactance of 1.13 Ω at 60 Hz but 188 Ω at 10 kHz.[17] For a 1 mH coil:
| Frequency | 60 Hz | 1 kHz | 100 kHz | 1 MHz |
|---|---|---|---|---|
| XL | 0.377 Ω | 6.28 Ω | 628 Ω | 6.28 kΩ |
Series and parallel
Inductors whose fields do not interact combine like resistors.[36] In series, the inductances add: L = L1 + L2 + …. In parallel, the reciprocals add: 1/L = 1/L1 + 1/L2 + …. This is the reverse of capacitors. If one coil's field passes through the other, an extra term, set by how strongly they are coupled, is added or subtracted.[36][23] That coupling, called mutual inductance, is the principle behind transformers, the subject of article 8 in this series.
Resonance: tuning a radio
Connect a charged capacitor across an inductor and the energy passes back and forth between the capacitor's electric field and the coil's magnetic field. This is an LC circuit (L for inductor, C for capacitor), and it oscillates at a natural frequency.[15] Equivalently, that is the frequency at which the inductor's rising reactance equals the capacitor's falling reactance (Figure 5):[37]
f0 = 1 / (2π√(LC))
A radio's LC circuit picks one station: adjusting the capacitor or coil moves f0, and the circuit responds strongly only near it.[38][37] Higher Q narrows that window.[38] The U.S. AM broadcast band runs from 535 to 1705 kHz.[39] Worked example (calculated): with a 240 µH coil, a variable capacitor of about 362 pF tunes 540 kHz, about 105.5 pF tunes 1,000 kHz, and about 36.5 pF tunes 1,700 kHz. Because of the square root, a 10-to-1 capacitance range covers only about 3.2-to-1 in frequency.
Filters and chokes
An inductor in series with a load filters out high frequencies;[17] a capacitor across the load shunts away what gets through. Power supplies can use henry-sized iron-core filter chokes to smooth DC, such as Hammond's 193H: 5 H at 200 mA.[4] Speaker systems use a crossover network to route bass to the woofer and treble to the tweeter,[40] and OpenStax notes that a large inductor in series with a sound system reduces its high-frequency output.[17] Ferrite beads and common-mode chokes do the same kind of job against radio-frequency noise.[30][5]
Switching power supplies
Storing energy and releasing it as current is the heart of switching regulators. A buck converter lowers a DC voltage: a switch chops the input into rapid pulses, and an inductor and capacitor average them into a smooth, lower output (Figure 6).[2] While the switch is on, current builds in the inductor; while it is off, the inductor keeps current flowing through a diode, giving up its energy. The output is set by the duty cycle D, the fraction of time the switch is on. Texas Instruments gives D = Vout/(Vin × η), where η (eta) is the efficiency.[41] For 12 V to 5 V, D is about 0.42 ideally, or 0.46 at 90% efficiency (calculated).
A boost converter raises a voltage by storing energy in the inductor through a switch across the supply, then releasing it on top of the input.[2] TI gives D = 1 − (Vin × η/Vout);[42] 3.3 V to 5 V takes about 0.34 ideally, or 0.47 at 80% efficiency (calculated). The inductor's Isat must exceed the peak current.[18] The switch is a transistor (article 7); diodes are article 6.
8. Testing an inductor
Work only on de-energized equipment.[43] If the circuit has large capacitors, discharge them first (Capacitors: safety). To avoid measuring parallel paths through other parts, lift at least one lead of the inductor out of the circuit.[43]
- Continuity and DCR with a multimeter. A good coil beeps or reads a low resistance. An "OL" reading, the same as with the probes apart, means the winding is open (broken).[43] Compare with the datasheet DCR. This does not measure inductance: to DC, an inductor looks like a short.[34]
- Inductance with an LCR meter. An LCR meter is an instrument that measures inductance (L), capacitance (C) and resistance (R) at a chosen test frequency, and usually Q as well.[34] Run its open/short calibration first and note the test frequency, often 1 kHz.[34]
- Shorted turns. If the insulation between turns fails, from hot spots, physical damage or a manufacturing defect, a shorted turn lowers the inductance.[34] The DCR may barely change, so an ohmmeter alone can miss this fault. B&K suggests recording inductances when equipment is new, or comparing matched windings.[34]
- Look and smell. Winding insulation is rated for limited temperatures, commonly 130 °C or 150 °C for power inductors and 105 °C for Hammond's chokes.[18][4] Darkened insulation, a cracked core or a burned smell are signs of overheating or damage.
9. Everyday uses
- Radio tuning: LC circuits select stations (above).[38]
- Switching power supplies: buck and boost converters that change one DC voltage to another.[2][41]
- Filters: power-supply chokes, beads and common-mode chokes on cables.[4][5]
- Ignition coils: an iron core carries a 150-to-300-turn primary and a 15,000-to-30,000-turn secondary. Interrupting the primary current induces about 200 V in the primary and about 20,000 V in the secondary.[44] HELLA cites 300 to 400 V and up to 40 kV.[45]
- Relays: a small coil current makes an electromagnet that pulls an armature to switch a larger load.[46] Solenoids pull an iron plunger; a spring returns it.[47]
- Loudspeakers: a voice coil sits in a permanent magnet's field, and the audio current through it pushes the cone back and forth.[40]
- Wireless charging: AC in a transmitter coil induces a voltage in a receiver coil in the phone. Efficiency depends on how closely the coils are coupled and on their Q.[48][49]
- Induction cooktops: a coil under the glass induces eddy currents that heat the base of a ferromagnetic pan.[50]
- Metal detectors: an AC coil induces eddy currents in buried metal, whose own fields are picked up by a second coil.[31][50]
- Traffic-signal loops: a vehicle over a wire loop in the road induces eddy currents that lower the loop's inductance, which the detector senses.[51]
10. Safety: inductive kickback, heat and strong fields
Warning. Interrupting the current in an inductor can produce hundreds or thousands of volts across the break, even from a 12 V supply. This can arc across switch contacts and destroy semiconductors,[3][52] and HELLA warns that touching live parts of an ignition system, primary as well as secondary, can cause potentially fatal injuries.[45] Never open a circuit carrying current through a large coil with your fingers in the path, and never work on ignition systems while they are running.
Why the voltage spikes
Recall VL = L × (rate of change of current). Opening a switch tries to drop the current to zero almost instantly, so the rate of change is huge. The coil responds with whatever voltage it takes to keep the current flowing, until something breaks down and conducts: the air across the switch contacts, or a transistor junction. This voltage spike is called inductive kickback. OpenStax calculates that a 1 H coil carrying 10 A, switched off in 1 ms, produces 10,000 V, and warns that such voltages "can cause arcs, damaging switching equipment."[3] TE Connectivity notes that an unsuppressed 12 V DC relay coil "may generate a voltage of 1,000 to 1,500 volts during turn-off", causing interference, semiconductor breakdown and contact wear.[52] Ignition coils use the same effect deliberately, to reach tens of kilovolts at the spark plug.[44][45] For our worked example (120 mA in 100 mH), cutting the current in 1 µs would in theory demand about 12,000 V (calculated); in practice the voltage stops rising when something arcs or breaks down.
The flyback diode
The standard fix is a flyback diode connected across the coil. A diode is a component that lets current flow in only one direction. It is fitted so that it carries nothing while the coil is powered. When the switch opens, the coil's current turns through the diode instead and dies away harmlessly in the loop's resistance (Figure 7). TE notes that a diode alone "fully eliminates the transient voltage", but the slowly decaying current also slows the relay's armature, which can cause random "tack welding" (sticking) of its contacts. TE's suggested method is a diode in series with a Zener diode, which limits the spike with minimal effect on the relay's release.[52] If you drive relays or motors from boards like those in the Microcontrollers section, the switching transistor is exactly the kind of semiconductor this spike destroys. Diodes, including flyback diodes, are the subject of article 6 in this series.
Hot chokes
Power inductors are allowed to run warm: Coilcraft defines their rated current by a 40 °C temperature rise above the surroundings, and core losses add more heat at high frequency.[21][2] A choke in a 50 °C enclosure can therefore reach 90 °C or more, hot enough to burn. Let equipment cool before touching it, and never run an inductor beyond its Irms. The insulation will degrade, which can lead to shorted turns.[18][34]
Strong magnetic fields and implanted devices
Strong magnets and magnetic fields can switch a pacemaker into a fixed-rate "magnet mode" or suspend an implanted defibrillator's (ICD's) treatment.[53][54] The FDA and the American Heart Association advise keeping phones, smartwatches and other magnet-containing items at least 6 inches (15 cm) from an implanted device.[54][55] The AHA advises people with an ICD to stay at least 12 inches from the ignition system of a vehicle or other gas-powered equipment, and anyone with either device to stay, in general, at least 2 feet from power-generating equipment, arc welders and jumper cables.[55] Harvard Health advises 12 to 24 inches from induction cooktops, whether on or off.[53] Anyone with an implant should follow the device maker's guidance and their clinician's advice over any general list.
Coming up in this section: 6 Diodes (including the flyback diode), 7 Transistors, and 8 Transformers (mutual inductance put to work).
The whole story in brief
- Current makes a magnetic field; a changing field induces a voltage that opposes the change (Oersted, Faraday, Lenz).
- An inductor applies this to itself: V = L ΔI/Δt. Its current cannot jump, and it stores ½LI2 in a magnetic field, where a capacitor stores ½CV2 in an electric one.
- Inductance grows with turns squared, area and core permeability. Cores saturate above Isat; Irms is a heating limit. "101" means 100 µH.
- RL circuits settle with τ = L/R; XL = 2πfL; with a capacitor, resonance is at 1/(2π√LC).
- Cutting an inductor's current makes a high-voltage spike: fit flyback diodes, respect hot chokes, and keep strong fields away from heart implants.
Sources
- U.S. Navy, NEETS (Navy Electricity and Electronics Training Series) Module 2, chapter 2 "Inductance", "Characteristics of inductance" and "Factors affecting coil inductance" (public-domain text, reprinted by Integrated Publishing): https://tpub.com/neets/book2/2b.htm
- Vishay Dale, "Inductor and Magnetic Product Terminology" (document 34053; PDF): https://www.vishay.com/docs/34053/definit.pdf
- OpenStax, College Physics 2e, section 23.9 "Inductance": https://openstax.org/books/college-physics-2e/pages/23-9-inductance
- Hammond Manufacturing, 193 Series filter chokes product page and specifications: https://www.hammfg.com/electronics/transformers/choke/193
- Murata, Guidelines for EMI Suppression, "Noise Suppression in Differential Transmission" (common-mode choke coils): https://www.murata.com/en-us/products/emc/emifil/library/knowhow/basic/s2-chapter03-p1
- OpenStax, College Physics 2e, section 22.9 "Magnetic Fields Produced by Currents: Ampere's Law": https://openstax.org/books/college-physics-2e/pages/22-9-magnetic-fields-produced-by-currents-amperes-law
- OpenStax, University Physics Volume 2, section 12.6 "Solenoids and Toroids": https://openstax.org/books/university-physics-volume-2/pages/12-6-solenoids-and-toroids
- OpenStax, University Physics Volume 2, section 13.1 "Faraday's Law": https://openstax.org/books/university-physics-volume-2/pages/13-1-faradays-law
- OpenStax, College Physics 2e, section 22.2 "Ferromagnets and Electromagnets": https://openstax.org/books/college-physics-2e/pages/22-2-ferromagnets-and-electromagnets
- OpenStax, University Physics Volume 2, section 12.2 "Magnetic Field Due to a Thin Straight Wire": https://openstax.org/books/university-physics-volume-2/pages/12-2-magnetic-field-due-to-a-thin-straight-wire
- OpenStax, University Physics Volume 2, section 13.2 "Lenz's Law": https://openstax.org/books/university-physics-volume-2/pages/13-2-lenzs-law
- OpenStax, University Physics Volume 2, section 14.2 "Self-Inductance and Inductors": https://openstax.org/books/university-physics-volume-2/pages/14-2-self-inductance-and-inductors
- U.S. Navy, NEETS (Navy Electricity and Electronics Training Series) Module 2, chapter 2 "Inductance", "Unit of inductance" and "Growth and decay of current in an LR series circuit" (reprinted by Integrated Publishing): https://tpub.com/neets/book2/2c.htm
- OpenStax, University Physics Volume 2, section 14.3 "Energy in a Magnetic Field": https://openstax.org/books/university-physics-volume-2/pages/14-3-energy-in-a-magnetic-field
- OpenStax, University Physics Volume 2, section 14.5 "Oscillations in an LC Circuit": https://openstax.org/books/university-physics-volume-2/pages/14-5-oscillations-in-an-lc-circuit
- OpenStax, University Physics Volume 2, section 12.7 "Magnetism in Matter": https://openstax.org/books/university-physics-volume-2/pages/12-7-magnetism-in-matter
- OpenStax, College Physics 2e, section 23.11 "Reactance, Inductive and Capacitive": https://openstax.org/books/college-physics-2e/pages/23-11-reactance-inductive-and-capacitive
- Coilcraft, Document 469, "Selecting the Best Inductor for Your DC-DC Converter" (PDF): https://www.coilcraft.com/getattachment/31fff647-10ae-4cef-aae1-463f41af851e/Doc469_selecting_inductors.pdf?lang=en-US
- TDK Product Center, Inductors FAQ, "Why are the characters such as '4R7' or '100' printed on some products?": https://product.tdk.com/en/contact/faq/inductors-0032.html
- Coilcraft, "Air Core Inductors" product family page: https://www.coilcraft.com/en-us/products/rf/air-core-inductors/
- Coilcraft, Document 361, "Current and Temperature Ratings" (PDF): https://www.coilcraft.com/getmedia/42878a08-a05a-4640-9c6d-f2eb5152046c/doc361_current_temp.pdf
- Coilcraft, Document 1287, "Getting Started: An Introduction to Inductor Specifications" (PDF): https://www.coilcraft.com/getmedia/ac56eabb-8678-4ca2-9604-c609886d68c1/doc1287_inductor_specifications.pdf
- U.S. Navy, NEETS (Navy Electricity and Electronics Training Series) Module 2, chapter 2 "Inductance", "Power loss in an inductor" and "Mutual inductance" (reprinted by Integrated Publishing): https://tpub.com/neets/book2/2e.htm
- Bourns, "Color Code Markings" for molded inductors, MIL and EIA standards (PDF): https://www.bourns.com/docs/technical-documents/technical-library/inductive-components/publications/ColorCodeMarkings.pdf
- OpenStax, College Physics 2e, section 23.7 "Transformers": https://openstax.org/books/college-physics-2e/pages/23-7-transformers
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- Coilcraft, 148 Series tunable inductors datasheet (PDF): https://www.coilcraft.com/getmedia/9df6a31b-338d-429f-a669-de9fbb91659d/148.pdf
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- Murata, Guidelines for EMI Suppression, "Proper Use of Noise Suppression Products for Digital Circuits" (ferrite beads): https://www.murata.com/en-sg/products/emc/emifil/library/knowhow/basic/s2-chapter01-p1
- OpenStax, University Physics Volume 2, section 13.5 "Eddy Currents": https://openstax.org/books/university-physics-volume-2/pages/13-5-eddy-currents
- OpenStax, University Physics Volume 2, section 14.4 "RL Circuits": https://openstax.org/books/university-physics-volume-2/pages/14-4-rl-circuits
- OpenStax, College Physics 2e, section 23.10 "RL Circuits": https://openstax.org/books/college-physics-2e/pages/23-10-rl-circuits
- B&K Precision, "LCR Meter Guide" (PDF): https://bkpmedia.s3.amazonaws.com/downloads/guides/en-us/lcr_meter_guide.pdf
- OpenStax, University Physics Volume 2, section 15.2 "Simple AC Circuits" (inductive reactance): https://openstax.org/books/university-physics-volume-2/pages/15-2-simple-ac-circuits
- U.S. Navy, NEETS (Navy Electricity and Electronics Training Series) Module 2, chapter 2 "Inductance", "Series and parallel inductors" (reprinted by Integrated Publishing): https://tpub.com/neets/book2/2f.htm
- OpenStax, College Physics 2e, section 23.12 "RLC Series AC Circuits": https://openstax.org/books/college-physics-2e/pages/23-12-rlc-series-ac-circuits
- OpenStax, University Physics Volume 2, section 15.5 "Resonance in an AC Circuit": https://openstax.org/books/university-physics-volume-2/pages/15-5-resonance-in-an-ac-circuit
- U.S. Code of Federal Regulations, 47 CFR 73.14, "AM broadcast definitions" (eCFR): https://www.ecfr.gov/current/title-47/chapter-I/subchapter-C/part-73/subpart-A/section-73.14
- HyperPhysics (Georgia State University), "Loudspeakers": http://hyperphysics.phy-astr.gsu.edu/hbase/Audio/spk.html
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- Texas Instruments, SLVA372D, "Basic Calculation of a Boost Converter's Power Stage" (PDF): https://www.ti.com/lit/an/slva372d/slva372d.pdf
- Fluke, "A Guide to Continuity Testing with a Multimeter": https://www.fluke.com/en/learn/blog/digital-multimeters/how-to-test-for-continuity
- DENSO Aftermarket Europe, "Back to basics: How an ignition coil works": https://www.denso-am.eu/news/deneur21_04_ignition-coil-basic-principles
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- ARATAS Americas (formerly Omron Components), "What are the basics of an electrical relay?": https://components.omron.com/us-en/products/basic-knowledge/relays/basics
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- Wireless Power Consortium, "How Qi Works": https://www.wirelesspowerconsortium.com/knowledge-base/magnetic-induction/how-qi-works/
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- OpenStax, College Physics 2e, section 23.4 "Eddy Currents and Magnetic Damping": https://openstax.org/books/college-physics-2e/pages/23-4-eddy-currents-and-magnetic-damping
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- Harvard Health Publishing, "Pacemaker precautions in the age of electrification" (May 1, 2023): https://www.health.harvard.edu/heart-health/pacemaker-precautions-in-the-age-of-electrification
- U.S. Food and Drug Administration, "Magnets in Cell Phones and Smart Watches May Affect Pacemakers and Other Implanted Medical Devices": https://www.fda.gov/radiation-emitting-products/cell-phones/magnets-cell-phones-and-smart-watches-may-affect-pacemakers-and-other-implanted-medical-devices
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