What Inductance Is
Inductance is the property of an electrical conductor that opposes changes in the current flowing through it. When current through a coil of wire increases, the magnetic field generated by that current also increases. This changing magnetic field induces a voltage in the coil that resists the change in current. When the current decreases, the collapsing field induces a voltage that tries to maintain the current. This behavior is described by Faraday's law of electromagnetic induction.
Think of inductance as electrical inertia. Just as a heavy flywheel resists changes in rotational speed, an inductor resists changes in current flow. The larger the inductance value, the more strongly the component resists current changes.
This property makes inductors essential in power supplies (where they smooth out current ripple), filters (where they block high-frequency noise while passing DC or low-frequency signals), and energy storage applications (where they temporarily store energy in their magnetic field).
Units of Inductance
The unit of inductance is the Henry (H), named after Joseph Henry, who discovered electromagnetic self-inductance independently of Michael Faraday in the 1830s. One Henry is the inductance that produces one volt of electromotive force when the current through the inductor changes at a rate of one ampere per second.
In practice, one Henry is a very large inductance. Most components used in electronics operate in the millihenry (mH) or microhenry (uH) range.
| Unit | Symbol | Value | Typical Applications |
|---|---|---|---|
| Henry | H | 1 H | Large power line chokes, utility transformers |
| Millihenry | mH | 0.001 H (10-3) | Power supply output filters, EMI chokes, current sensors |
| Microhenry | uH | 0.000001 H (10-6) | DC-DC converter inductors, RF circuits, switching regulators |
| Nanohenry | nH | 10-9 H | High-frequency RF, chip inductors, parasitic effects |
How Inductance Is Determined
The inductance of a wound component depends on several interrelated factors. Understanding these relationships is critical for both design engineers specifying inductors and manufacturing engineers building them.
The Core Formula
For a component wound on a magnetic core, inductance is calculated as:
L = N² x AL
Where L is inductance, N is the number of turns, and AL is the inductance factor of the core (provided by the core manufacturer, typically in nH per turn squared).
The key insight in this formula is that inductance is proportional to the square of the number of turns. Doubling the turns count quadruples the inductance. Tripling it produces nine times the inductance. This squared relationship has significant practical implications: small changes in turns count produce large changes in the inductance value.
What Determines AL
The AL value (also called the inductance factor or permeance) is a property of the specific core being used. It depends on the core material's permeability, the core geometry (cross-sectional area, magnetic path length), and whether an air gap is present. Core manufacturers publish AL values for each core part number, making it straightforward to calculate the expected inductance for a given turns count.
Factors Affecting Inductance
Core Material and Permeability
The magnetic permeability of the core material has the most dramatic effect on inductance. Permeability describes how easily a material can be magnetized. It is expressed as a relative value compared to free space (air), which has a permeability of 1.
| Core Material | Relative Permeability | Common Applications |
|---|---|---|
| Air (no core) | 1 | RF coils, high-frequency applications |
| Iron Powder | 10 to 100 | DC bias applications, power inductors |
| Ferrite (MnZn) | 2,000 to 15,000 | Switching transformers, EMI filters |
| Grain-Oriented Silicon-Iron | 30,000 to 50,000 | Power transformers, current transformers |
| Nickel-Iron (Permalloy/1J85) | 50,000 to 100,000+ | High-sensitivity current sensors, precision instruments |
A coil with 100 turns on a ferrite core (permeability of 5,000) will have thousands of times more inductance than the same 100 turns wound on an air core. This is why magnetic cores are used in the vast majority of practical inductors. They allow achieving useful inductance values with a manageable number of turns in a compact package.
Number of Turns
As noted above, inductance scales with the square of the turns count. This relationship gives designers a powerful tuning knob: adding or removing just a few turns can shift the inductance value significantly. In manufacturing, this is why turn count accuracy is critical. A specification calling for 750 turns at plus or minus zero tolerance means the inductance value depends on hitting that number exactly.
Core Geometry
The physical dimensions of the core influence inductance through two geometric factors: the cross-sectional area of the core (the area of the "slice" through the magnetic material) and the magnetic path length (the distance the magnetic flux travels around the core).
Larger cross-sectional area increases inductance because the magnetic field has more material to flow through. Longer magnetic path length decreases inductance because the field is spread over a greater distance. Toroidal cores are efficient because their circular geometry provides a short, closed magnetic path with minimal leakage flux.
Air Gaps
Introducing an air gap into the magnetic path dramatically reduces the effective permeability of the core, which reduces the inductance for a given turns count. This seems counterproductive, but air gaps serve an important purpose: they stabilize the inductance value against variations in core permeability and against changes caused by DC bias current flowing through the winding.
In power inductor applications, where a significant DC current flows through the winding along with the AC signal, the DC current tends to push the core toward magnetic saturation. An air gap prevents saturation by absorbing most of the DC magnetization, keeping the core operating in its linear region. The trade-off is lower inductance per turn, which means more turns (or a larger core) to achieve the same inductance value.
For a gapped core, the effective permeability is approximately equal to the magnetic path length divided by the gap length. A core with a 100 mm path length and a 1 mm gap will have an effective permeability of roughly 100, regardless of the core material's inherent permeability. The gap dominates.
Inductance and Impedance
Inductance creates impedance (opposition to current flow) that varies with frequency. The relationship is:
XL = 2 x pi x f x L
Where XL is inductive reactance in ohms, f is frequency in Hertz, and L is inductance in Henrys.
This frequency-dependent behavior is the basis for all inductor applications in filtering. At DC (f = 0), an ideal inductor has zero reactance and passes current freely. As frequency increases, the reactance increases proportionally, and the inductor progressively blocks higher-frequency signals.
Practical Implications
Consider a 10 mH inductor used in a power supply output filter.
- At DC (0 Hz): Reactance = 0 ohms. DC current flows through unimpeded.
- At 60 Hz (power line frequency): Reactance = 3.77 ohms. Some impedance, but most current still passes.
- At 100 kHz (switching frequency): Reactance = 6,283 ohms. Effectively blocks the switching ripple.
This is exactly the behavior a power supply designer wants: pass the DC output current while blocking the high-frequency switching noise. The inductance value is chosen so that the crossover between "passing" and "blocking" occurs at the right frequency for the application.
Inductance in the Context of Manufacturing
For design engineers specifying custom inductors, understanding these relationships helps communicate requirements effectively to the manufacturer. Here are the most important considerations.
Specifying by Inductance vs. by Construction
Some specifications define the required inductance value (e.g., "10 mH plus or minus 10% at 1 kHz"). Others define the construction (e.g., "750 turns of 34 AWG on core part number XYZ"). Construction-based specs are more common for custom wound components because they allow the customer to control exactly how the part is built. The inductance value is a result of the specified construction.
Temperature Effects
Core permeability changes with temperature, which means inductance changes with temperature. Ferrite cores are particularly sensitive, with permeability varying significantly across a wide temperature range. Silicon-iron and nickel-iron alloys are more stable. If your application requires tight inductance tolerance across temperature, specify the acceptable range and the temperature at which the nominal value applies.
DC Bias Effects
When DC current flows through the inductor, the core begins to saturate, and the effective permeability drops. This means the actual inductance under load can be significantly lower than the inductance measured with no DC bias. For power applications, always specify the inductance value at the operating DC bias current, and make sure the core material and geometry can handle the bias without excessive saturation.
Measurement Conditions
Inductance values depend on the test conditions: frequency, amplitude, and DC bias. Two identical inductors can measure differently if tested under different conditions. Always specify the measurement frequency (commonly 1 kHz or 100 kHz), the test signal level, and whether DC bias is applied. This ensures the manufacturer's test results correlate with your design expectations.
The more precisely you define the inductance requirement, the measurement conditions, and the operating environment, the more accurately the manufacturer can build and verify the component. Ambiguity in the specification leads to parts that measure correctly in the factory but perform unexpectedly in the application.