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EMC coupling: capacitive, inductive, radiated

Guide, EMC fundamentals

Interference has only four ways to get from a source to a victim, and each one responds to a different fix. Naming the mechanism is therefore most of the work: it decides whether the answer is a shield, a filter, a different return path, or a change in geometry. This page sets out all four, shows where the near field ends, and derives the result that explains most radiated emission failures.

Two circuits share a conductor, and the shared conductor is not zero impedance. The current of one develops a voltage across it, and the other circuit sees that voltage in series with its own signal.

The classic case is a ground trace shared by a noisy power stage and a sensitive analogue return. Nothing radiates, nothing crosses space, and no shield helps: the coupling is a circuit, not a field. The fix is topological, giving each circuit its own return to a common point rather than sharing a path.

This is the only one of the four that behaves as a conducted problem inside the product, and it is the one people reach for shields to solve.

Two conductors at different potentials, separated by a dielectric, form a capacitor whether anyone intended it or not. Current flows through it:

i = C dv/dt

Everything follows from that expression. The coupling is driven by voltage and by rate of change, not by current, so a fast-edged, high-swing net is an aggressor even when it carries almost no current. It worsens with frequency, since dv/dt does.

The remedies follow the same expression: reduce C by increasing separation, reduce dv/dt by slowing the edge, or interpose a grounded conductor so the field terminates on it instead of on the victim. That last is why a guard trace or a ground plane between layers works.

Two current loops sharing magnetic flux. Faraday's law gives the induced voltage:

v = M di/dt

Now the driver is current and its rate of change, and the mutual inductance M is set by geometry: the loop areas, their separation, and their relative orientation.

Because it depends on area and orientation, the remedies are geometric. Reduce the loop area on either side, increase separation, twist a pair so successive twists induce opposing voltages that cancel, or rotate one loop so the shared flux drops. A non-magnetic shield helps far less here than against electric fields, because it acts only through induced eddy currents.

The symmetry is worth stating plainly: capacitive coupling is a voltage problem cured by separation and screening, inductive coupling is a current problem cured by area and orientation.

Once a structure is an appreciable fraction of a wavelength, it stops being a parasitic component and starts being an antenna. The energy leaves as a propagating wave, and neither separation nor a guard trace helps in the way it did before.

The conventional boundary is:

r = lambda / 2pi

which is about a sixth of a wavelength. Inside it the electric and magnetic fields are semi-independent, and their ratio depends on the source: a high-voltage, low-current structure produces a high-impedance field dominated by E, a high-current, low-voltage loop produces a low-impedance field dominated by H. Outside it, the two lock together into a wave whose ratio is the impedance of free space, 376.73 ohms, universally quoted as 377.

The distances matter for interpreting a test:

FrequencyWavelengthNear/far boundary
30 MHz9.99 m1.59 m
100 MHz3.00 m0.48 m
1 GHz0.30 m4.8 cm

At 30 MHz a 3 m measurement is only just in the far field for a product of any size, while at 1 GHz it is comfortably far. This is one reason 3 m data does not scale perfectly to 10 m at the low end, as decibels for EMC notes when it derives the 10.46 dB scaling.

Two radiating structures matter in practice, and they are not equally efficient.

Differential mode is the intended signal: equal and opposite currents in a loop. Its far field is set by the enclosed area:

E = (Z0 pi / c squared) x f squared x A x I / r, giving a constant of 1.32e-14

Common mode is current flowing the same direction on every conductor of a cable, returning through the environment. The radiating structure is the cable itself:

E = (Z0 / c) x f x L x I / r, giving a constant of 1.26e-6

Both constants derive from the free-space impedance and the speed of light; neither is empirical.

Now put realistic numbers in, at 100 MHz measured at 3 m:

SourceCurrentField at 3 m
1 cm2 loop, differential20 mA87.8 uV/m, 38.9 dB(uV/m)
1 m cable, common mode5 uA209.4 uV/m, 46.4 dB(uV/m)

Equalising the two, 20 mA of differential-mode current in that loop radiates about as much as 2.1 uA of common-mode current on the cable. That is a ratio close to ten thousand to one.

This single result explains why cables dominate radiated emission results, why a board that looks clean on a bench probe fails in a chamber the moment its harness is attached, and why common-mode chokes and cable filtering earn their place. A common-mode current far too small to notice with ordinary instrumentation is an efficient antenna.

Change one variable and watch the level.

ObservationLikely mechanism
Moving or reorienting a cable changes the levelCommon-mode radiation
Tracks the aggressor's voltage; better with separation or a guardCapacitive
Tracks the aggressor's current; better with smaller loop or twistingInductive
Better when a shared return is split or a connection movedCommon impedance
Only appears above a frequency where the structure nears a tenth of a wavelengthRadiated

Frequency is a useful discriminator on its own. Capacitive and inductive coupling both worsen steadily with frequency, but radiated coupling switches on when the geometry becomes electrically large.

A shield addresses field coupling and radiation. It does nothing for common impedance coupling, which lives in a shared conductor inside the product, and which is why an enclosure sometimes changes nothing at all.

Two further limits are worth knowing before ordering one. A shield needs a deliberate return path, or it becomes a radiator itself. And against low-frequency magnetic fields a non-magnetic shield is weak, because it acts only through induced eddy currents. In practice apertures and cable entries set the achieved performance well below the material figure.

  • Four mechanisms: common impedance, capacitive, inductive, radiated. Naming the one you have is most of the fix.
  • Capacitive follows i = C dv/dt, driven by voltage. Inductive follows v = M di/dt, driven by current.
  • The near field ends at lambda / 2pi, and beyond it the wave impedance is 377 ohms.
  • Common mode radiates roughly ten thousand times more efficiently than differential mode for the same current, which is why cables dominate.
  • A shield does nothing for common impedance coupling, and little for low-frequency magnetic fields.

Sources & references

  1. Henry W. Ott, Electromagnetic Compatibility Engineering (2009), Wiley , Wiley onlinelibrary.wiley.com/doi/book/10.1002/9780470508510
  2. Signal Consulting, Howard W. Johnson and Martin Graham, High-Speed Digital Design (1993), Prentice Hall , Prentice Hall www.sigcon.com/
  3. CISPR 16-1-4, radio disturbance and immunity measuring apparatus, antennas and test sites , IEC webstore.iec.ch/en/iec-search/result?q=CISPR%2016-1-4
  4. IEC TR 61000-5-3, installation and mitigation guidelines, HEMP protection concepts , IEC webstore.iec.ch/publication/4235

Frequently asked questions

What are the four coupling mechanisms?
Conductive or common impedance coupling, where two circuits share a physical path and the current of one develops a voltage across the shared impedance that the other sees as signal. Capacitive or electric field coupling, where two conductors at different potentials pass current through the parasitic capacitance between them, following i = C dv/dt. Inductive or magnetic field coupling, where two current loops share flux and one induces a voltage in the other, following v = M di/dt. And radiated coupling, a genuine electromagnetic wave crossing open space, which takes over once the structure involved is an appreciable fraction of a wavelength. The first three are near-field effects and dominate at short range; the fourth is what a chamber measures.
Where is the boundary between near field and far field?
Conventionally at a distance of lambda over two pi from the source, which is about one sixth of a wavelength. Inside that radius the electric and magnetic fields behave semi-independently and their ratio depends on whether the source is a high-voltage, high- impedance structure or a high-current, low-impedance one. Outside it the two lock together as a propagating wave with a fixed ratio, the free-space impedance of 377 ohms. The practical consequence is about test distance: at 30 MHz the boundary sits at 1.59 m, so a 3 m measurement is only just far field, while at 1 GHz it is 4.8 cm and 3 m is comfortably far field. That is part of why low-frequency 3 m data does not scale cleanly to 10 m.
Why does common-mode current radiate so much more than differential?
Because of what each one is geometrically. A differential-mode pair carries equal and opposite currents a small distance apart, so their fields largely cancel and what escapes is set by the enclosed loop area, which is small by design. Common-mode current flows the same way on every conductor of a cable and returns through the environment, so the radiating structure is the whole cable length with no cancelling partner. Working the two far-field expressions through for a realistic case, a 1 square centimetre loop carrying 20 mA at 100 MHz produces about the same field at 3 m as roughly 2 uA of common-mode current on a one metre cable. That is a ratio near ten thousand to one, and it is why cables dominate radiated emission results.
How do I tell which mechanism is causing a problem?
Change one variable and watch. If moving or reorienting a cable shifts the level, the coupling involves that cable, which usually means common-mode radiation. If the level tracks the aggressor's voltage and improves when you increase separation or insert a grounded plane, it is capacitive. If it tracks the aggressor's current and improves when you reduce loop area or twist the pair, it is inductive. If it improves when you split a shared return path or move a connection point, it is common impedance. Frequency helps too: capacitive and inductive coupling both worsen with frequency, but radiated coupling only becomes efficient once the structure approaches a tenth of a wavelength.
Does shielding fix all four?
No, and assuming it does is a common and expensive mistake. A shield addresses field coupling and radiation, and does nothing at all for common impedance coupling, which lives in a shared conductor inside the product. A shield also has to be given a deliberate return path or it becomes a radiator itself, and its effectiveness against magnetic fields at low frequency is far worse than against electric fields, because a non-magnetic shield works on magnetic coupling only through induced eddy currents. Enclosure apertures and the way cables enter usually set the real performance well below the material's theoretical figure.