Mutual Inductance Calculator

About the Mutual Inductance Calculator

The Mutual Inductance Calculator computes the magnetic coupling between two coils — a fundamental concept in transformer design, wireless power transfer, and electromagnetic compatibility. When current changes in one coil, it induces a voltage in nearby coils through their shared magnetic flux.

Mutual inductance M relates the voltage induced in coil 2 to the rate of current change in coil 1: V₂ = -M × dI₁/dt. The coupling coefficient k = M/√(L₁L₂) ranges from 0 (no coupling) to 1 (perfect coupling). Power transformers achieve k > 0.95, while wireless chargers operate at k = 0.1-0.5.

Enter coil parameters — self-inductance, number of turns, dimensions, and separation — to calculate mutual inductance, coupling coefficient, induced voltage, and transformer performance metrics.

When This Page Helps

Use this calculator when you need to estimate how strongly two coils interact before building the circuit. It is useful for transformer design, wireless charging, sensor coupling, and checking induced voltage or leakage behavior. That helps you compare coupling assumptions before winding coils or laying out a magnetic path in a transformer or charger.

How to Use the Inputs

1. Enter the self-inductance of coil 1 (L₁) and coil 2 (L₂).
2. Enter the coupling coefficient k (0 to 1), or compute from geometry.
3. Enter the frequency and current amplitude for induced voltage calculation.
4. View mutual inductance M, induced voltage, and energy coupling.
5. Use presets for common configurations: transformers, wireless charging, sensors.
6. Compare coupling at different separations in the sweep table.
7. Check the transformer turns ratio and impedance transformation.

Example Calculation

Tips & Best Practices

• For power transformers, always design for k > 0.95 to minimize leakage and voltage drop.
• Wireless charging coils: larger diameter and ferrite backing improve k at distance.
• Leakage inductance = L(1-k²) — at k=0.95, only 9.75% is leakage; at k=0.5, 75% is leakage.
• The dot convention determines the polarity of induced voltage — always mark coil orientations.
• For EMI analysis, unwanted mutual inductance between PCB traces can be reduced by orthogonal routing.
• At high frequencies, parasitic capacitance between windings creates a self-resonance limiting bandwidth.

Transformer Theory

An ideal transformer converts voltage by the turns ratio: V₂/V₁ = N₂/N₁, while conserving power: V₁I₁ = V₂I₂. Real transformers have losses from leakage inductance, winding resistance, core losses (hysteresis and eddy currents), and magnetizing current. The coupling coefficient k determines how close to ideal the transformer behaves.

The equivalent circuit of a real transformer includes the magnetizing inductance (L_m = kL₁), leakage inductances on both sides, winding resistances, and core loss resistance. For power transformers, the magnetizing current is typically 1-5% of full-load current.

Wireless Power Transfer

Wireless power transfer (WPT) operates at coupling coefficients far below transformer levels (k = 0.1-0.5 typically). To transfer power efficiently at low k, resonant circuits are used — both transmitter and receiver coils are tuned to the same frequency, creating a resonant "channel" that efficiently transfers energy despite weak coupling.

Modern Qi wireless chargers use resonant inductive coupling at 100-200 kHz with close-range (< 10mm) coupling. Longer-range systems (like EV wireless charging) use lower frequencies (85 kHz) with larger coils.

Coupled Inductor Design

Coupled inductors are used in multi-output DC-DC converters, common-mode chokes, and coupled filter networks. The design challenge is achieving the desired coupling coefficient while meeting self-inductance, current capacity, and core saturation requirements. Simulation tools and empirical testing are typically needed for optimization.

Frequently Asked Questions

• What is mutual inductance?

  Mutual inductance M is the property by which a changing current in one coil induces a voltage in a nearby coil. M depends on the coils' self-inductances and their coupling coefficient: M = k√(L₁L₂). It's measured in Henries (H).

• What is the coupling coefficient?

  k ranges from 0 (no shared flux) to 1 (all flux links both coils). Iron-core transformers: k = 0.95-0.99. Air-core RF transformers: k = 0.1-0.5. Wireless chargers: k = 0.1-0.6. k depends on geometry, distance, and core material.

• How does distance affect coupling?

  For air-core coils, coupling falls off roughly as 1/d³ at distances much greater than the coil dimensions. This rapid falloff is why wireless charging requires close proximity and why transformer cores are used to channel flux efficiently.

• What is leakage inductance?

  Leakage inductance is the portion of a coil's self-inductance that doesn't couple to the other coil: L_leak = L(1-k²). It causes voltage drops and limits power transfer at high frequencies. Minimizing leakage is key in transformer design.

• How do transformers achieve near-perfect coupling?

  By using high-permeability magnetic cores (iron, ferrite) that channel virtually all flux through both coils. Interleaving windings, using toroidal cores, and minimizing air gaps all push k toward 1.0.

• What are the applications of mutual inductance?

  Power transformers, current transformers (CTs), wireless power transfer (Qi charging), RFID, inductive sensors (proximity, metal detection), coupled filters in RF circuits, and electromagnetic interference (EMI) — both intended coupling and unwanted crosstalk. The same idea shows up in both useful magnetic coupling and the unwanted pickup designers try to reduce.