Electronics Guide

Inductance and Energy Storage

Inductance measures how much magnetic flux linkage a component produces per unit of current, and therefore how much energy it stores in its magnetic field at a given current. The inductance L, measured in henries (H), relates the voltage v across the component to the rate of change of the current i through it:

v = L di/dt

This relationship explains why inductors oppose rapid current changes: driving the current through a 10 µH inductor up by 1 A in 1 µs takes 10 V. Under steady-state DC, where di/dt is zero, an ideal inductor drops no voltage, and a real one presents only its winding resistance. Conversely, interrupting an inductor's current abruptly makes di/dt very large, and the inductor develops whatever voltage is needed to keep the current flowing, which is why relay coils and other switched inductive loads need a flyback diode or a snubber.

The energy stored in an inductor carrying current I is

W = ½LI²

so a 10 µH inductor carrying 3 A holds 45 µJ. This stored energy is released when the current decreases, which is how switching power supplies move energy from input to output. In a cored inductor, the maximum energy storage is limited by core saturation, which caps the peak current regardless of the inductance value; an air-core inductor cannot saturate and is limited instead by the heating of its winding.

Magnetic Flux and Flux Linkage

Magnetic flux represents the total magnetic field passing through a surface. In an inductor coil, the flux links multiple turns, multiplying the effective flux linkage. Inductance is flux linkage per unit current:

L = NΦ/I

where N is the number of turns and Φ is the magnetic flux through each turn. The relation defines the inductance of a linear inductor; as a core approaches saturation, the flux no longer rises in proportion to the current, and the inductance falls.

Flux density B, measured in tesla (T), is the flux per unit area and indicates the intensity of the magnetic field. Each core material has a saturation flux density beyond which additional field produces almost no additional flux density: roughly 0.3 to 0.5 tesla for manganese-zinc power ferrites, about 0.75 to 1.6 tesla for powder cores depending on the alloy, and 1.5 to 2 tesla for silicon steel. Operating near saturation reduces effective inductance and can cause circuit malfunction.

Inductance from Geometry

For a long, single-layer air-core solenoid of N turns, cross-sectional area A, and length l, the inductance is approximately

L = μ₀N²A / l

where μ₀ ≈ 4π × 10⁻⁷ H/m is the magnetic constant. For N turns on a closed, ungapped core of relative permeability μ_r, effective cross-sectional area A_e, and effective magnetic path length l_e, the relative permeability multiplies the result:

L = μ₀μ_rN²A_e / l_e

Both expressions show the defining scaling of inductance: it rises with the square of the turns, so doubling the turns quadruples the inductance. Core manufacturers fold the geometry and the material into a single inductance factor A_L, usually quoted in nanohenries per turn squared, so that L = A_LN². A core with A_L = 250 nH needs 20 turns for 100 µH. An air gap in the core lowers A_L but makes it far less sensitive to the tolerance and temperature drift of the core material.

Inductive Reactance

Carrying a sinusoidal current at frequency f, an ideal inductor presents a reactance

X_L = 2πfL

which rises in proportion to frequency: a 10 µH inductor presents about 6.3 Ω at 100 kHz and about 628 Ω at 10 MHz, and the voltage across it leads the current by 90 degrees. This behavior, the opposite of a capacitor's, lets an inductor pass DC while blocking high-frequency noise and lets it form resonant circuits with capacitors. In a series circuit of inductance L and resistance R, the current responds to a voltage step with the time constant τ = L/R.

Inductors that share no flux combine like resistors: in series the inductances add, L = L₁ + L₂, and in parallel their reciprocals add, 1/L = 1/L₁ + 1/L₂. Mutual inductance M between the windings changes both results; two coupled windings connected in series aiding give L₁ + L₂ + 2M.

Air Core Inductors

Air core inductors use no magnetic material, relying solely on coil geometry for inductance. Without a magnetic core, they cannot saturate, and their inductance does not change with current. However, achieving substantial inductance requires many turns and significant physical size. Air core inductors excel in high-frequency applications where core losses would be excessive and in precision circuits requiring linear behavior.

Typical air core applications include RF tank circuits, antenna matching networks, and air-cored current sensors such as Rogowski coils. The inductance can be calculated accurately from coil dimensions, making custom design straightforward. The long-solenoid formula overestimates short coils because it ignores the weaker field near the ends. Harold Wheeler's 1928 approximation for single-layer coils is equivalent to replacing l with l + 0.9r, where r is the coil radius, and is accurate to about 1 percent for coils longer than 0.8r. For 20 turns on a 5 mm radius over a 20 mm length, the long-solenoid formula gives 1.97 µH and the corrected one 1.61 µH.

Ferrite Core Inductors

Ferrite cores dramatically increase inductance for a given size by providing a high-permeability path for magnetic flux. These ceramic materials combine iron oxide with zinc, manganese, or nickel to create soft magnetic materials with specific frequency characteristics. Different ferrite grades optimize for power applications, broadband transformers, or EMI suppression.

Manganese-zinc (MnZn) ferrites suit frequencies up to a few megahertz, offering high permeability (typically several hundred to over ten thousand) and relatively high saturation flux density. Nickel-zinc (NiZn) ferrites have lower permeability (roughly 10 to 2,000) but much higher resistivity, which suppresses eddy-current losses and extends usable operation from a few megahertz to several hundred megahertz. Core selection requires matching material properties to application frequency and power level.

Because ferrite saturates at a comparatively low flux density and saturates abruptly, ferrite power inductors usually include a discrete air gap. The gap stores most of the energy and holds the inductance steady under DC bias, at the cost of fringing flux near the gap that can heat nearby turns.

Powdered Iron Cores

Powdered iron cores consist of iron particles insulated from each other and pressed into shape. The distributed air gaps between particles provide soft saturation characteristics and inherent gapping, making these cores well suited to DC bias applications in switching power supplies. Various powder mixes optimize for different frequencies and permeabilities, and alloy powders such as molypermalloy (MPP), sendust, and high-flux nickel-iron offer lower core loss than plain iron powder at higher cost.

Unlike ferrites that saturate abruptly, powdered iron cores lose inductance gradually with increasing current. This soft saturation allows continued operation under overload conditions, though with reduced filtering effectiveness. The distributed gap also makes inductance relatively insensitive to temperature and manufacturing variations. Iron powder cores made with organic binders can age thermally, their core loss rising irreversibly after prolonged operation at high temperature, so designs that run hot should be checked against the manufacturer's aging data.

Molded Power Inductors

Molded, or composite, power inductors press a metal-alloy powder around a preformed winding, so the core material surrounds the coil completely. The result is magnetically shielded, soft-saturating like other powder cores, mechanically robust, and low in profile, which has made the construction common in point-of-load converters for processors and other high-current, low-voltage loads. Its core loss is generally higher than that of a gapped ferrite, which matters at high switching frequencies and large ripple currents.

Laminated Steel Cores

For low-frequency, high-power applications, laminated silicon steel cores provide a saturation flux density of roughly 1.5 to 2 tesla, the highest of the common core materials, together with high permeability. Thin laminations minimize eddy current losses at power line frequencies. EI, EE, and toroidal configurations address different mounting and winding requirements.

Steel core inductors dominate in line-frequency chokes and reactors, passive power factor correction, and audio-frequency chokes. Their high saturation flux density enables smaller size for given energy storage, but losses increase rapidly with frequency, limiting use above a few kilohertz. Amorphous and nanocrystalline tape-wound cores extend the metallic-core approach to tens of kilohertz with much lower loss.

Core Geometries

Toroidal cores confine nearly all magnetic flux within the core, minimizing external field and EMI. However, winding toroids requires special equipment or hand labor. Pot cores and shielded drum cores also provide low external fields with easier winding. E cores and similar gapped geometries allow simple bobbin winding while providing controlled inductance and saturation characteristics through air gap adjustment.

Surface-mount power inductors come in three broad forms: unshielded drum cores, which are cheapest but leak the most field; semi-shielded parts, in which a magnetic resin fills the space around the drum winding; and fully shielded parts with a ferrite sleeve or a molded body. Shielding reduces stray field and coupling to nearby circuits; unshielded parts remain common where cost matters and nothing sensitive sits nearby.

Inductance Value and Tolerance

Nominal inductance specifies the design value, typically at a specific frequency, current, and temperature. Standard tolerances range from ±5% to ±20%, with tighter tolerances available at premium cost. Applications like filters may require tight tolerance, while energy storage applications often tolerate wider variation.

Inductance varies with frequency due to core permeability changes, parasitic capacitance effects, and skin effect in windings. Datasheets specify measurement conditions, and inductance at operating frequency may differ significantly from the nominal value measured at 1 kHz or 100 kHz.

Saturation Current

Saturation current indicates when inductance drops significantly due to core saturation. Manufacturers typically specify the current causing 10%, 20%, or 30% inductance reduction, so ratings from different suppliers can be compared only when their definitions match. Operating beyond saturation current causes ripple current to increase, potentially damaging other circuit components or causing malfunction.

Saturation current decreases with temperature as core saturation flux density falls. The effect is strongest in ferrite: manganese-zinc power grades lose roughly a fifth of their room-temperature saturation flux density by 100 degrees Celsius. Designs should account for worst-case operating temperature. Soft saturation materials provide additional margin by maintaining some inductance even when heavily saturated.

Temperature Rise Current

Temperature rise current, often labeled I_rms, is the DC current that raises the part's temperature by a specified amount above a 25 degrees Celsius ambient through winding resistance losses, measured in still air without heat sinking. Coilcraft, for example, typically rates its power inductors for a rise of 40 degrees Celsius and its chip inductors for a rise of 15 degrees Celsius. This rating may be higher or lower than saturation current depending on inductor design. The two ratings limit different quantities: the peak current must stay below the saturation rating, and the RMS current below the temperature-rise rating.

Thermal design must consider ambient temperature, airflow, proximity to other heat sources, and duty cycle. The rated rise adds to the ambient temperature, and it grows in a hot ambient because copper resistance, and with it the winding loss, rises by about 0.4 percent per degree Celsius: a part rated for a 40 degree rise above a 25 degree ambient, run at its rated current in an 85 degree ambient, reaches roughly 135 degrees Celsius rather than 125. Inductors in enclosed spaces or near hot components may require derating from datasheet current ratings.

Winding Resistance

DC resistance (DCR) dissipates power I_rms²R_DC in the winding. Lower DCR improves efficiency in power applications but typically requires more copper, increasing size and cost. High-efficiency designs minimize DCR while meeting inductance and saturation requirements. DCR increases with temperature, approximately 0.4%/°C for copper windings.

At high frequency, the effective winding resistance rises above the DC value because of skin effect, which pushes current toward the conductor surface, and proximity effect, which crowds current where the magnetic fields of adjacent turns overlap. This AC resistance can reach several times the DCR in high-frequency power and RF inductors, increasing copper losses and lowering the quality factor. Litz wire, built from many thin, individually insulated strands twisted or woven so that each strand occupies every position in the bundle in turn, reduces skin and proximity losses, while foil or flat-wire windings help in some high-current designs.

Self-Resonant Frequency

Every inductor has parasitic capacitance between windings. This capacitance C_p resonates with the inductance at the self-resonant frequency (SRF),

f_SRF = 1 / (2π√(LC_p))

above which the component behaves as a capacitor rather than an inductor. A 10 µH inductor with 5 pF of winding capacitance, for example, resonates at about 22.5 MHz. Because larger inductances need more turns and accumulate more winding capacitance, SRF falls as the inductance value rises within a product family. For proper function, operating frequency must remain well below SRF. Datasheets give a minimum or typical SRF; applications should maintain adequate margin.

Quality Factor

Quality factor Q equals the ratio of inductive reactance to resistance at a given frequency. Higher Q indicates lower losses, important for filters and resonant circuits. Q varies with frequency: it rises at first, because the reactance grows while the resistance stays near its DC value, then peaks and falls as skin effect, proximity effect, core loss, and the approach to self-resonance raise the effective resistance faster than the reactance grows.

Power Inductors

Switch-mode power supply inductors store energy during switch-on time and release it during switch-off time. They must handle DC bias current while maintaining adequate inductance for proper converter operation. Key parameters include saturation current, DCR, and inductance under DC bias conditions. Various core materials and constructions address frequencies from tens of kilohertz to several megahertz. A common starting point in converter design guidance is to choose the inductance so that the peak-to-peak ripple current is 20 to 40 percent of the maximum load current.

Coupled inductors carry two or more windings on a shared core. A flyback converter's magnetic component is itself a coupled inductor, storing energy during the on-time and delivering it during the off-time, and SEPIC converters often use a two-winding coupled inductor in place of two separate parts. In multiphase buck converters, inverse coupling between phases reduces the ripple current in each phase while keeping a low leakage inductance for fast transient response; the coupling coefficient sets the balance between the two.

RF Inductors

Radio frequency inductors require high Q and stable inductance at operating frequency, with values typically ranging from a fraction of a nanohenry to a few microhenries. Air core and specialized ferrite designs minimize losses. Tight tolerance ensures predictable filter and matching network performance. Shielded designs prevent coupling to adjacent circuits.

Chip inductors in miniature packages suit wireless applications demanding small size. Wire-wound designs offer highest Q when space permits. Multilayer construction provides compact, inexpensive low-inductance values for high-frequency circuits, and thin-film chip inductors, patterned photolithographically, offer tight tolerances at small values.

EMI Suppression Inductors

Ferrite beads and common-mode chokes suppress electromagnetic interference. Unlike energy-storage inductors, ferrite beads are designed to dissipate noise energy as heat: above a crossover frequency their impedance becomes predominantly resistive. Impedance versus frequency characteristics, rather than inductance alone, determine effectiveness, and bead datasheets conventionally specify impedance at 100 MHz. A bead's impedance falls when it carries DC current, sometimes substantially, so the curve at the actual bias is the one that matters.

Common-mode chokes present high impedance to common-mode noise while passing differential signals. Because the flux of the differential load current cancels in the core, they can use high-permeability materials that would saturate immediately if the full load current produced net flux. They are essential in power supplies, data communication lines, and motor drives to meet EMC requirements.

Filter Chokes

Filter chokes carry a power current while blocking an unwanted alternating component, and they must withstand line voltage and handle load current while providing adequate inductance at the frequencies they filter. At line frequency and its low harmonics, smoothing chokes in rectifier filters and line reactors at the input of motor drives use laminated steel cores, which handle large currents economically. In the conducted-emissions band that commercial EMC standards regulate, roughly 150 kHz to 30 MHz, the differential-mode chokes of a power line filter usually use powder cores, which keep their inductance under the full line current, alongside a common-mode choke on a high-permeability ferrite or nanocrystalline core.

Determine Requirements

Begin by establishing inductance value, operating frequency, DC current, AC ripple current, and acceptable losses. Consider temperature range, vibration and shock requirements, and available board space. Power supply design tools and application notes from controller IC manufacturers often specify inductor requirements for their topologies.

Calculate Ratings

The peak current is the DC current plus half the peak-to-peak ripple current. Verify that it is below saturation current with margin for temperature effects. Calculate RMS current (considering AC waveform shape) and resulting power loss in DCR, and ensure temperature rise remains acceptable in the application environment. For a buck converter with duty cycle D = V_out/V_in and switching frequency f_sw, the peak-to-peak ripple current is

ΔI_L = V_out(1 − D)/(Lf_sw)

and, for the triangular ripple of a converter in continuous conduction, the RMS current is

I_rms = √(I_DC² + ΔI_L²/12)

As an example, a converter stepping 12 V down to 3.3 V at 3 A and 500 kHz with a 4.7 µH inductor has D = 0.275 and ΔI_L = (3.3 V × 0.725)/(4.7 µH × 500 kHz) ≈ 1.02 A, about a third of the load current. The peak current is 3 A plus 0.51 A, about 3.5 A; the RMS current is only 3.01 A, barely above the DC value; and an inductor with 20 mΩ of DCR dissipates about 0.18 W in its winding before core and AC winding losses are added. A suitable part needs a saturation rating comfortably above 3.5 A at the hottest expected temperature and a temperature-rise rating above 3 A.

Verify Performance

Check that inductance under actual DC bias meets requirements. Confirm SRF exceeds operating frequency by appropriate margin. For EMI-sensitive applications, consider shielded versus unshielded designs. Review available package options against PCB footprint constraints.

Prototype and Test

Actual circuit performance may differ from datasheet predictions due to layout parasitics, thermal interactions, and component variations. Prototype testing under worst-case conditions validates the design. Measure inductor temperature, ripple current, and converter efficiency to verify adequate margins.

Saturation

When current exceeds saturation rating, inductance drops and ripple current increases dramatically. In switching converters, this causes excessive switch current, EMI, and potential component damage. Symptoms include overheating, audible noise, and increased output ripple. Solutions include selecting higher saturation current inductors, reducing peak current, or using soft-saturation core materials.

Overheating

Excessive temperature indicates losses exceeding thermal dissipation capability. Causes include high RMS current, core losses at high frequency, and inadequate cooling. Verify current ratings under actual operating conditions. Consider inductors with lower DCR, better core material for operating frequency, or improved thermal management.

Audible Noise

Magnetostriction causes core dimensions to change with flux density. Because the strain does not depend on the direction of the flux, an alternating flux makes the core vibrate at twice its frequency, the familiar 100 Hz or 120 Hz hum of line-frequency magnetics. Switching converters operate above the audible range, but burst or pulse-skipping modes at light load and periodic load changes can modulate the inductor current at audible rates, and loose windings can also vibrate mechanically. Solutions include potting or varnish impregnation, low-magnetostriction core materials, or keeping the operating and modulation frequencies outside the audible range.

EMI

Inductors with open magnetic structures produce stray magnetic fields that couple into adjacent circuits. Symptoms include noise on sensitive signal lines and EMC test failures. Shielded inductors, toroidal cores, or improved layout and shielding address EMI problems.