Near-Field Electromagnetic Coupling Analysis
Theory: treat electric and magnetic fields separately up close
Overview
On our board, a sensor signal running near the switching-supply wiring picks up noise. Is it being radiated as a radio wave?
Probably not. At a few centimetres, most frequencies are in the near field, where electric and magnetic fields haven't yet formed a propagating wave. Voltage changes couple through capacitance and current changes through mutual inductance, straight into the neighbouring trace. Think of it as a circuit-parasitics problem, not a radio problem. Which coupling dominates depends on whether the source has large voltage swings or large current swings.
Near/far-field boundary
| Frequency | Boundary |
|---|---|
| 1 MHz | 48 m |
| 10 MHz | 4.8 m |
| 100 MHz | 48 cm |
| 1 GHz | 4.8 cm |
Inductive coupling (magnetic)
Mutual inductance per length $l$ between two traces at height $h$ above a ground plane, spaced $d$ apart. Return current in the plane cancels the field, so the closer the traces are to the plane, the weaker the coupling. An approximation valid when $h$ and $d$ are well above trace width.
Capacitive coupling (electric)
$C_m$ is inter-trace mutual capacitance. Current flows from nodes with fast, large voltage swings (switching nodes, clocks) into high-impedance victims (sensor inputs, reset lines). The higher the victim impedance, the larger the voltage for the same current.
Crosstalk began with telephone lines
In the late 19th century, telephone lines strung side by side on poles suffered from “crosstalk” — hearing conversations from neighbouring circuits. The cause was exactly near-field coupling via inter-line capacitance and mutual inductance, and the remedies were twisted pairs and transposition (swapping line positions at intervals). Twisted pairs are still used in LAN cables, and today's high-speed boards and cables rest on the same basic ideas.
Worked examples
Example 1: trace spacing
Two traces 0.2 mm above a ground plane running side by side for 50 mm, with 1 A rising in 10 ns on one (di/dt = 10⁸ A/s):
| Spacing | Mutual inductance | Induced voltage |
|---|---|---|
| 0.2 mm | 8.1 nH | 805 mV |
| 0.5 mm | 2.5 nH | 247 mV |
| 1.0 mm | 0.74 nH | 74 mV |
| 3.0 mm | 0.09 nH | 9 mV |
Fifteen times the spacing gives a ninetieth of the voltage.
With a ground plane, coupling falls roughly as the inverse square of spacing. 805 mV at 0.2 mm can upset 3.3 V logic or badly corrupt analog signals — so a little extra spacing goes a long way. But the formula assumes an unbroken ground plane; a slot that forces the return current to detour multiplies the coupling.
Example 2: height above the plane
| Height | Mutual inductance (1 mm spacing) | Induced voltage |
|---|---|---|
| 0.1 mm | 0.20 nH | 20 mV |
| 0.2 mm | 0.74 nH | 74 mV |
| 0.8 mm | 6.4 nH | 635 mV |
At the same spacing, being far from the ground plane (as on a thick two-layer board with ground on the back) increases coupling more than thirtyfold. That is why multilayer boards put a ground layer directly beneath signal layers.
Example 3: distance from a magnetic source
Near a small current loop (inductor, transformer, switching loop) the magnetic field falls with the cube of distance: about 18 dB weaker at twice the distance, 29 dB at three times and 60 dB at ten times. Moving a sensitive circuit slightly away helps greatly — and moving it closer hurts quickly.
Analysis and mitigation
Analysis approach
- Classify the source as voltage-type (large dV/dt) or current-type (large di/dt).
- Extract parasitic capacitance and mutual inductance with 2D cross-section analysis and add them to circuit simulation.
- Where 3D effects matter — plane slots, component placement — confirm with 3D electromagnetic analysis.
- Measure near fields on hardware with probes and compare with analysis.
Mitigation
- Shrink loops: route switching currents' go and return paths close together.
- Spacing and ground: route sensitive traces away from sources over unbroken ground.
- Guard traces: grounded traces between conductors reduce capacitive coupling.
“A ground slot made it ten times worse”
A familiar story: in a board revision, a thin slot was cut in the ground plane to route another supply, and noise on signals crossing it jumped. Return current wants to flow in the plane directly under the signal; a slot forces it around, forming a large loop that raises both mutual inductance and radiation. Treating the ground as an ideal uniform plane hides this, so model the slots as they really are.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Treating in-box coupling as far-field | Wrong diagnosis | Compare distance with λ/2π |
| Idealising the ground plane | Slot effects missed | Model the slots |
| Confusing voltage- and current-type sources | Ineffective fixes | Check dV/dt and di/dt |
| Ignoring victim impedance | Impact underestimated | Evaluate through the victim circuit |
| Leaving loop area large | Strong magnetic coupling | Route go and return together |
I'd like to try coupling calculations myself.
Try the coupled-line crosstalk tool for crosstalk and the magnetic induction simulator and Faraday's law tool for induction. Mitigation details are in cable crosstalk, PCB EMC layout, shielding effectiveness and grounding and bonding.
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