Mutual inductance is the physical property where a changing current in one coil induces an electromotive force (EMF) in an adjacent coil, and its standard mutual inductance unit is the Henry (H). In a real circuit or installation, this value dictates exactly how efficiently energy transfers across an isolation barrier—such as in a switched-mode power supply (SMPS) transformer—or how much destructive voltage noise parasitically couples between high-speed digital traces on a printed circuit board.
The Mutual Inductance Unit: Henrys and Sub-Units
Named after Joseph Henry, the Henry (H) is the SI derived unit for both self-inductance and mutual inductance. By definition, a mutual inductance of one Henry exists between two coils when a current changing at the rate of one ampere per second in the primary coil induces an electromotive force of one volt in the secondary coil. Because a full Henry is a massive amount of inductance for most modern electronics, we almost exclusively work with sub-units in practical circuit design.
The relationship between the mutual inductance unit and the physical geometry of the coils is defined by the formula M = k√(L₁L₂), where M is mutual inductance in Henrys, L₁ and L₂ are the self-inductances of the individual coils, and k is the dimensionless coupling coefficient (0 to 1) representing magnetic linkage efficiency.
| Unit Prefix | Symbol | Multiplier | Typical Application | Real-World Value Range |
|---|---|---|---|---|
| Henry | H | 10⁰ | Mains isolation transformers, heavy audio crossovers | 1.0 H – 500 H |
| Millihenry | mH | 10⁻³ | SMPS flyback transformers, induction heating coils | 0.1 mH – 100 mH |
| Microhenry | µH | 10⁻⁶ | Qi wireless charging pads, RF coupling transformers | 1.0 µH – 50 µH |
| Nanohenry | nH | 10⁻⁹ | PCB trace crosstalk, parasitic package inductance | 1.0 nH – 50 nH |
Worked Numeric Example: Calculating Induced Voltage
To understand how the mutual inductance unit translates to actual circuit behavior, let’s calculate the induced voltage in a real-world scenario. Consider the primary and secondary coils inside a standard 5W Qi wireless smartphone charger.
The Setup:
- Mutual Inductance (M): 15 µH (15 × 10⁻⁶ H), measured across the air gap between the charging pad and the phone.
- Primary Current Change (di₁): The H-bridge inverter ramps the primary current from 0 A to 2.0 A.
- Time Interval (dt): This current transition occurs in 5 microseconds (5 × 10⁻⁶ s).
The Formula:
Faraday’s law of induction states that the induced voltage (V₂) in the secondary coil is proportional to the mutual inductance and the rate of change of current in the primary coil:
V₂ = -M × (di₁ / dt)
The Calculation:
- First, find the rate of current change: di₁ / dt = 2.0 A / (5 × 10⁻⁶ s) = 400,000 A/s.
- Next, multiply by the mutual inductance: V₂ = (15 × 10⁻⁶ H) × 400,000 A/s.
- V₂ = 6.0 Volts.
The Result: The secondary coil experiences a 6.0V induced EMF spike. In the actual device, this high-frequency AC voltage is immediately routed through a Schottky diode bridge rectifier and a buck converter to safely charge the 3.7V lithium-ion cell. If you were to increase the physical distance between the coils, M would drop (perhaps to 4 µH), and your induced voltage would plummet to 1.6V, causing the phone's charging IC to throw an under-voltage fault.
Where You Meet This in Practice (and Common Confusions)
You interact with the mutual inductance unit constantly in electrical work, whether you are harnessing it intentionally or fighting it as a parasitic effect.
Intentional Applications:
- Transformers: Every mains isolation transformer, Ethernet magnetics module, and gate-drive transformer relies on a high M to transfer power or signals while maintaining galvanic isolation.
- Wireless Power Transfer (WPT): From inductive cooktops to EV wireless charging pads, maximizing M across an air gap is the primary engineering challenge, usually solved by adding ferrite shielding to direct the magnetic flux.
- Current Sensors: Rogowski coils and split-core current clamps use mutual inductance to measure AC line current without breaking the circuit.
Parasitic Applications (The Enemy):
- PCB Crosstalk: On high-speed digital boards (like DDR4 memory routing), parallel traces act as tiny, unwanted air-core transformers. A mutual inductance of just a few nanohenrys (nH) between a clock line and a data line can induce enough voltage to flip a logic bit, causing system crashes.
Beginners frequently confuse mutual inductance (M) with self-inductance (L) and the coupling coefficient (k).
- Self-inductance (L) is a single coil fighting its own current changes. It is measured in Henrys.
- Mutual inductance (M) is the interaction between two separate coils. It is also measured in Henrys.
- Coupling coefficient (k) is a unitless ratio (0.0 to 1.0) describing what percentage of the magnetic flux from coil 1 actually intersects coil 2. A tightly wound iron-core transformer might have a k of 0.98, while loosely coupled wireless charging coils might have a k of 0.3.
FAQ: Bench Measurement and Troubleshooting
How do I measure the mutual inductance unit on my bench if my LCR meter only has two probes?
You can calculate M using the series-aiding and series-opposing method. First, wire the two coils in series so their magnetic fields add together (series-aiding) and measure the total inductance (L_a). Next, reverse the physical connections of just one coil so their fields fight each other (series-opposing) and measure again (L_o). The mutual inductance is exactly one-quarter of the difference: M = (L_a - L_o) / 4. This is a standard bench technique for characterizing custom-wound SMPS transformers.
Does changing the core material change the mutual inductance unit?
No. The unit remains the Henry regardless of the core. However, inserting a high-permeability material (like an N87 ferrite core) between the coils drastically increases the value of M by concentrating the magnetic flux lines, thereby increasing the coupling coefficient k. Air has a relative permeability of 1; ferrites can range from 400 to over 10,000.
Why does my mutual inductance measurement drop when I increase the frequency on my LCR meter?
At higher frequencies, parasitic capacitance between the windings begins to resonate with the inductance, altering the impedance your meter reads. Additionally, if you are using a solid iron core rather than powdered iron or ferrite, eddy currents at high frequencies will effectively cancel out portions of the magnetic field, lowering the apparent mutual inductance.
