Inductance is the property of an electrical conductor that opposes a change in the electric current flowing through it, and its standard unit of measurement is the Henry (H). When you read a schematic or specify parts for a power supply, you will rarely encounter a full 1 Henry component; instead, you will work with millihenries (mH), microhenries (µH), and nanohenries (nH). Understanding these units in inductance calculations is critical for designing filters, switch-mode power supplies (SMPS), and motor drives, because misplacing a decimal prefix by a factor of 1,000 will either cause your switching regulator to overheat or allow high-frequency noise to pass straight through your filter.
The Henry and Its Sub-Units Breakdown
Named after Joseph Henry, one Henry is defined as the inductance that induces one volt of electromotive force when the current changes at one ampere per second (1 H = 1 V·s/A). Because a full Henry is a massive amount of inductance for modern electronics, we rely on metric prefixes. Choosing the right unit depends entirely on the frequency domain of your circuit.
| Unit Name | Symbol | Multiplier | Typical Application Domain | Common Component Example |
|---|---|---|---|---|
| Henry | H | 100 | Large line reactors, massive smoothing chokes, Tesla coils | Custom iron-core 5H ballast |
| Millihenry | mH | 10-3 | Audio crossovers, 50/60Hz EMI filters, low-frequency boost converters | Würth Elektronik 744774210 (1mH) |
| Microhenry | µH | 10-6 | Switch-mode power supplies (buck/boost), RF chokes, intermediate filtering | Coilcraft MSS1210-473 (47µH) |
| Nanohenry | nH | 10-9 | High-frequency RF matching, VHF/UHF circuits, PCB trace parasitics | Murata LQG15HS (10nH) |
Worked Example: Calculating Inductive Reactance in a Real Circuit
To see why these units in inuctance matter, we need to look at inductive reactance ($X_L$), which is the opposition an inductor presents to alternating current. The formula is:
$X_L = 2 \pi f L$
Where $f$ is frequency in Hertz and $L$ is inductance in Henries. Let us compare a 4.7 mH inductor and a 4.7 µH inductor across two different frequency domains: a 60 Hz mains line and a 100 kHz SMPS switching node.
Scenario A: The 4.7 mH Inductor
- At 60 Hz (Mains): $X_L = 2 \times 3.14159 \times 60 \times 0.0047 = \mathbf{1.77 \Omega}$. This provides a gentle filtering effect with minimal voltage drop, perfect for a line-frequency EMI choke.
- At 100 kHz (SMPS): $X_L = 2 \times 3.14159 \times 100,000 \times 0.0047 = \mathbf{2,953 \Omega}$. This massive reactance would completely choke a switching regulator, preventing current transfer and likely destroying the switching MOSFET due to flyback spikes.
Scenario B: The 4.7 µH Inductor
- At 100 kHz (SMPS): $X_L = 2 \times 3.14159 \times 100,000 \times 0.0000047 = \mathbf{2.95 \Omega}$. This is an ideal reactance for smoothing the ripple current in a buck converter output stage.
- At 60 Hz (Mains): $X_L = 2 \times 3.14159 \times 60 \times 0.0000047 = \mathbf{0.0017 \Omega}$. This is effectively a dead short at line frequency, offering zero filtering capability.
Where You Meet Inductance Units in Practice
Understanding the theory is useful, but recognizing how these units manifest on the bench and in the panel is what separates hobbyists from proficient designers.
What Inductance Actually Changes in a Circuit
Inductance does not resist current itself; it resists the change in current ($di/dt$). In a DC-DC buck converter, the inductor value (specified in µH) directly dictates your ripple current amplitude and determines the boundary between Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). In a heavy industrial installation, a line reactor (specified in mH or H) limits inrush current and mitigates harmonic distortion caused by variable frequency drives (VFDs). According to Texas Instruments application notes on power magnetics, selecting the correct µH value requires balancing core saturation current against physical footprint and DC resistance (DCR).
The Water Hammer Analogy
Think of inductance like the inertia of water flowing through a long, heavy pipe: it takes significant pressure (voltage) to get the water moving, but once it is flowing, shutting the valve instantly causes a massive, destructive pressure spike (water hammer). This is the mechanical equivalent of inductive flyback.
What People Commonly Confuse It With
The most frequent mistake beginners make is confusing inductance (the physical property of the coil, measured in Henries) with inductive reactance or impedance (the effective AC resistance at a specific frequency, measured in Ohms). An inductor's Henries remain constant (ignoring core saturation), but its Ohms change dynamically with the frequency of the signal passing through it.
The formula for inductive kickback is $V = -L(di/dt)$. If you open a relay contact breaking a 2A circuit powered by a 10 mH inductor, and the current drops to zero in 1 microsecond ($1 \mu s$), the voltage spike is: $0.01 \times (2 / 0.000001) = \mathbf{20,000 Volts}$. This will instantly arc across mechanical contacts, destroy semiconductor switches, and poses a lethal shock hazard. Always use flyback diodes or snubber networks across inductive loads.
Frequently Asked Questions About Inductance Units
How do you convert microhenries to millihenries in inductance calculations?
The metric prefix step between micro (µ) and milli (m) is a factor of 1,000. To convert microhenries (µH) to millihenries (mH), divide by 1,000. For example, a 4,700 µH choke is exactly 4.7 mH. Conversely, to convert nanohenries (nH) to microhenries (µH), you also divide by 1,000. A 470 nH RF coil is equivalent to 0.47 µH. Always convert your component value to base Henries (H) before plugging it into formulas like $X_L = 2 \pi f L$ to avoid decimal errors.
What is the difference between units of inductance and units of impedance?
Units of inductance (Henries) measure a component's inherent physical ability to store energy in a magnetic field, regardless of the circuit's operating frequency. Units of impedance (Ohms) measure the total opposition to alternating current flow at a specific frequency. As explained in the All About Circuits textbook, an inductor has a fixed inductance of 10 µH whether it sits on your desk or operates at 1 MHz, but its impedance will be 0 Ohms at DC and roughly 62.8 Ohms at 1 MHz.
Why are PCB trace inductance units usually in nanohenries?
Physical inductance is proportional to the loop area and length of the conductor. On a printed circuit board, copper traces are very short and flat, resulting in extremely small parasitic inductance—typically around 1 nH per millimeter of trace length. While 2 nH sounds negligible, in modern high-speed digital circuits or SiC/GaN power switching nodes where current changes at 50A in 5 nanoseconds ($di/dt = 10^9$ A/s), that 2 nH of trace inductance generates a 20V spike ($V = 2 \times 10^{-9} \times 10^9$). This is why high-frequency layout guidelines obsess over minimizing nanohenry-level parasitic loops.
Can a standard multimeter measure units in inductance directly?
No. A standard digital multimeter (DMM) applies a DC voltage to measure resistance or uses a fixed low-frequency AC signal for capacitance, but it cannot measure inductance. To measure Henries, you need a dedicated LCR meter (Inductance, Capacitance, Resistance). For hobbyists, the DER EE DE-5000 is a highly regarded bench tool capable of measuring down to 0.01 µH. For professional lab environments, a benchtop unit like the Keysight U1733C applies selectable test frequencies (e.g., 100 Hz, 1 kHz, 100 kHz) to accurately characterize the inductance, since core materials like ferrite or powdered iron exhibit different permeability—and therefore different inductance values—depending on the test frequency.
