Mutual inductance, measured in Henrys (H), is the property where a changing current in one coil induces a proportional voltage in a nearby coil through a shared magnetic field. In a real circuit or installation, this value dictates the voltage transformation ratio in switchmode power supplies, the power transfer efficiency in wireless charging pads, and the severity of unwanted signal crosstalk on high-speed PCBs. Despite its importance, hobbyists and students frequently confuse mutual inductance (M) with self-inductance (L), or mistakenly mix up the Henry with units of magnetic flux density (Tesla) or total magnetic flux (Weber). Understanding the exact unit and its physical implications is the difference between a cleanly isolated gate-drive circuit and a blown MOSFET.
The Math in Action: Calculating Induced Voltage
To see how mutual inductance units translate to real-world voltages, we use Faraday’s law of induction adapted for coupled circuits. The induced voltage ($V_2$) in the secondary coil is the product of the mutual inductance ($M$) and the rate of change of current ($di/dt$) in the primary coil:
$V_2 = -M \frac{di_1}{dt}$
Let’s run a worked numeric example using a pulse transformer designed to drive a MOSFET gate in a high-side switch configuration.
Worked Numeric Example
- Mutual Inductance ($M$): 150 μH (which is $150 \times 10^{-6}$ H)
- Primary Current Change ($di$): The drive circuit ramps current from 0 A to 2.0 A.
- Time Interval ($dt$): The switching edge takes 5 μs ($5 \times 10^{-6}$ s).
First, calculate the rate of current change:
$\frac{di}{dt} = \frac{2.0 \text{ A}}{5 \times 10^{-6} \text{ s}} = 400,000 \text{ A/s}$
Now, apply the mutual inductance to find the induced secondary voltage:
$V_2 = (150 \times 10^{-6} \text{ H}) \times (400,000 \text{ A/s}) = \mathbf{60 \text{ V}}$
The Bench Reality: That 60V spike is exactly what turns on your high-side MOSFET. However, if the current is interrupted too abruptly (e.g., $dt$ drops to 0.5 μs), the induced voltage spikes to 600V. This is why mutual inductance calculations are critical for selecting snubber networks and clamping diodes; if you ignore the $di/dt$ limits of your core, the induced voltage will exceed the MOSFET’s avalanche rating and destroy the silicon.
Where You Meet Mutual Inductance Units in Practice
You rarely buy a component labeled with its mutual inductance. Instead, you buy components with specific self-inductances and coupling coefficients, and the mutual inductance emerges from the physical geometry. Here is where these units dictate performance in modern electronics.
Switchmode Power Supplies (SMPS) and Coupled Inductors
In topologies like SEPIC or flyback converters, engineers use coupled inductors wound on a single ferrite core. The mutual inductance (typically in the tens to hundreds of microhenries) determines how energy transfers from the input to the output during the switch-off cycle. If the physical gap between the windings is too large, $M$ drops, leakage inductance rises, and you lose efficiency to heat.
Wireless Power Transfer (Qi Standard)
In Qi-compliant wireless chargers, the transmitter and receiver coils are separated by an air gap. Here, mutual inductance is highly dynamic. As you move your phone 5mm further from the charging pad, $M$ can drop from 15 μH to under 3 μH. The transmitter’s control IC must constantly measure this drop in mutual inductance to adjust the primary drive frequency and maintain a stable 5V output at the receiver.
Signal Integrity and PCB Crosstalk
On high-speed digital boards (like DDR5 memory routing), mutual inductance is the enemy. When two parallel traces run close together, they share a magnetic field. In this domain, mutual inductance is measured in nanohenries (nH) or even picohenries (pH). Just 5 nH of mutual inductance between a clock line and a data line can induce enough voltage to cross the logic threshold, causing bit errors. PCB designers use ground shielding and orthogonal routing to drive $M$ as close to zero as possible.
Self-Inductance vs. Mutual Inductance: Clearing the Confusion
Because both properties share the same unit (the Henry), it is easy to conflate them on a schematic or a datasheet. Use this comparison matrix to keep them straight when designing or troubleshooting.
| Criteria | Self-Inductance ($L$) | Mutual Inductance ($M$) |
|---|---|---|
| Physical Meaning | A coil’s opposition to its own changing current. | A coil’s ability to induce voltage in a neighboring coil. |
| Standard Symbol | $L$ (or $L_1$, $L_2$) | $M$ (or $L_m$) |
| SI Unit | Henry (H) | Henry (H) |
| Depends On | Number of turns, core material, coil geometry. | All of the above, plus the physical distance and alignment between the two coils. |
| Coupling Limit | N/A | Cannot exceed the geometric mean of the self-inductances ($M \le \sqrt{L_1 L_2}$). |
| Bench Measurement | Directly measured with an LCR meter across two terminals. | Calculated indirectly via series-aiding/opposing tests (see FAQ). |
For a deeper dive into the foundational physics governing these relationships, the HyperPhysics project at Georgia State University provides excellent interactive derivations of how coil geometry limits maximum mutual inductance. Additionally, Electronics Tutorials offers practical circuit examples showing how dot notation dictates the polarity of the induced voltage.
Frequently Asked Questions About Mutual Inductance Units
What is the standard SI unit for mutual inductance, and what are the common sub-units?
The standard SI unit is the Henry (H), named after Joseph Henry. Because one Henry is a massive amount of inductance for typical electronics, you will almost always see mutual inductance specified in millihenries (mH, $10^{-3}$ H) for audio and mains transformers, microhenries (μH, $10^{-6}$ H) for switchmode power supplies and RF circuits, and nanohenries (nH, $10^{-9}$ H) for PCB trace coupling and high-frequency parasitics.
Can I measure mutual inductance directly with a standard multimeter or LCR meter?
No, standard LCR meters only measure self-inductance ($L$) across a single pair of terminals. To measure mutual inductance ($M$) on the bench, you use the series-aiding and series-opposing method. Connect the two coils in series and measure the total inductance ($L_{aiding}$). Then, reverse the connections on one coil and measure again ($L_{opposing}$). The mutual inductance is calculated as: $M = (L_{aiding} - L_{opposing}) / 4$. This is a standard technique for characterizing custom-wound flyback transformers.
How does the coupling coefficient (k) relate to mutual inductance units?
The coupling coefficient ($k$) is a dimensionless ratio between 0 and 1 that describes how much of the magnetic flux from the primary coil actually links the secondary coil. It bridges self-inductance and mutual inductance via the formula: $M = k \sqrt{L_1 \times L_2}$. If $k = 1$ (perfect coupling, impossible in reality but approached by toroidal cores), $M$ is at its theoretical maximum. In wireless charging, $k$ might be as low as 0.3, drastically reducing $M$.
Why do PCB designers care about mutual inductance in nanohenries?
At high frequencies (like a 2 GHz clock signal), the rate of current change ($di/dt$) is enormous. Even a tiny mutual inductance of 2 nH between adjacent traces can induce voltage spikes large enough to cause false logic triggering (crosstalk). Designers minimize this by increasing trace spacing, routing sensitive signals over solid ground planes to confine the magnetic return path, and using differential signaling to cancel out induced noise.
