Ground Loop Coupling Calculator
Ground Loop Coupling Calculator
Two mechanisms that get called the same thing and are not. Common-impedance coupling, where a noisy circuit’s return current develops a voltage across a shared conductor that appears as a series source in the quiet one — and magnetic loop pickup, where a changing field through a loop induces a voltage round it. Both against a noise budget you set, and both with the inverse: the impedance, or the loop area, the budget allows.
Coupled noise against your budget, and the layout rule that follows
two circuits sharing 300 mm of 1.0 mm copper wire as a return, with 200 mA of noisy current at 100 kHz in it, against a 50 mV budget in the quiet circuit
Two laws, and neither of them is about ground
R = ρl ÷ A, L = (µ₀ ÷ 2π)·l·[ln(4l ÷ d) − 0.75] for a round wire
Magnetic pickup: V = −dΦ/dt, Φ = B·A·cos θ, |V| = 2πf·B·A·cos θ
and the inverse: Amax = Vbudget ÷ (2πf·B·cos θ)
- l shared
- the length both circuits’ return currents flow along together. Not the length of the wire — the length that is shared. Make it zero and the mechanism disappears
- L
- Rosa’s round-wire formula, or Terman’s flat-conductor formula for a strip. Note what is not in either of them: the resistivity. Above the crossover a stainless steel return is as good as a copper one, which is to say as bad
- A
- the area the signal conductor and its return enclose, projected perpendicular to the field. It is almost always larger than the drawing suggests, because the return is not where the drawing says
- peak or rms
- the relation is linear, so the voltage comes back in whatever convention the field went in. There is no factor of root two anywhere in it
Worked example
two circuits sharing 300 mm of 1.0 mm copper wire as a return, with 200 mA of noisy current at 100 kHz in it, against a 50 mV budget in the quiet circuit
The shared conductor's resistance is ρl ÷ A = 6.585 mΩ, and its inductance from Rosa's formula is 380.4 nH — which is 239 mΩ of reactance at 100 kHz, 36 times the resistance
So the shared impedance is 239.1 mΩ and 200 mA through it develops 47.82 mV in series with the quiet circuit — 95.6% of the 50 mV allowed. Of that, 1.317 mV comes from the resistance and 47.8 mV from the inductance
The crossover is at 2.755 kHz: below it a thicker wire helps, above it nothing about the material or the cross-section matters much and only the length and the shape do. Resistivity does not appear in the inductance formula at all.
Turned around, the budget permits a shared impedance of 250 mΩ at this current, or 209.1 mA of noisy current through this conductor. Neither is reachable by making the wire thicker; both are reachable by not sharing the conductor
For comparison, the other mechanism at the same frequency: a 2,000 mm² loop in a 10 µT field picks up 2π × 100 kHz × 10 µT × 2 mm² = 12.57 mV, and the budget would permit a loop of 7,957.7 mm² — about 89.2 mm square. Switch modes above to work that case properly
Telling the two apart, and what each responds to
| Common-impedance coupling | Magnetic loop pickup | |
|---|---|---|
| The mechanism | one circuit’s return current in a conductor the other also uses | a changing external field through an enclosed area |
| Needs a loop? | no — it happens with a single shared conductor | yes, by definition |
| Needs a shared conductor? | yes, by definition | no — it happens to a perfectly isolated pair |
| Scales with | the noisy current and the shared impedance | frequency, field, area and cos θ, all directly |
| A thicker conductor | helps below the crossover, does almost nothing above it | does nothing at all |
| A shorter shared length | helps in direct proportion, at every frequency | not applicable |
| Bringing the return next to the signal | helps if it also removes the sharing | the single most effective fix there is |
| Adding another ground connection | can help if it truly separates the returns; usually it just adds a second shared path | makes it worse, by creating a loop where there was none |
| A twisted pair | does nothing — the sharing is not about geometry | very effective: each twist reverses the enclosed area and the contributions largely cancel |
| A shield | does nothing unless it carries the return current | little at low frequency for a magnetic field; a shield works on electric fields and on magnetic fields only once eddy currents can flow in it |
Two different things, both called a ground loop
The phrase is used for both of these and they are not the same, do not respond to the same fixes, and are told apart by a single question: does it need a shared conductor, or does it need an enclosed area?
Common-impedance coupling needs a shared conductor and no loop at all. Two circuits return their currents along the same piece of metal. The noisy one’s current develops a voltage across that metal’s impedance, and because the quiet circuit measures its own signal with respect to that same metal, the voltage appears in series with the quiet signal. It is Ohm’s law applied to a conductor that the schematic drew as one node. It happens in a single wire, on a single plane strip, in a shared connector pin. The only complete fix is to stop sharing: bring each return separately to the point where they have to meet, so the shared length is zero. That is what a single-point return is, and it is why it is drawn as a star rather than as a bus.
And the impedance is mostly inductance. This is the part that surprises people and it is the reason the obvious fix fails. 300 mm of 1 mm copper wire is about 6.6 mΩ and about 380 nH, and the reactance of 380 nH passes 6.6 mΩ at about 2.8 kHz. Above that, the coupled voltage is set by the inductance — and resistivity does not appear in the inductance formula at all. A thicker wire, a better alloy, a second wire in parallel a few millimetres away: none of them changes the answer much. What does change it is the length, which is directly proportional, and the shape, because a flat conductor of the same cross-section has less inductance than a round one. That is the real argument for a ground plane, and it is a different argument from the one about loop area.
Magnetic loop pickup needs an area and no sharing. A changing field through a loop induces a voltage round it, V = −dΦ/dt, which for a sinusoid is 2πf·B·A·cos θ. It happens to a perfectly isolated, perfectly balanced pair of conductors if they enclose an area. Every term is first order: double the frequency, double the field, or double the area and you double the voltage. Which means the inverse is the useful form — the loop area a noise budget permits — and that is a layout rule you can hand to whoever is routing the board or making the harness. The page computes it, and also the square loop that area corresponds to, because that is the form a layout engineer can check with a ruler.
The conclusion both mechanisms share. The fix is reducing the area and separating the returns. It is not adding more ground. A second connection between two sub-systems does not lower an impedance in any useful way and it definitely creates a loop, which is the area in the second calculation. The productive moves are the same in both cases and they are geometric: put the return immediately beside the signal — a trace over an unbroken plane, a twisted pair, a tightly routed differential pair — and give each circuit its own return to the point where they have to join. Everything else is argument.
What this page is not. It is not about earth electrodes in soil, which is a different problem entirely — the earthing resistance calculator does that. It is not about how much current a capacitor to chassis injects or what isolation a platform requires — the Y capacitor limit calculator does that. It does not do the skin-effect arithmetic on the shared conductor, which barely matters here because the reactance dominates where skin effect starts; the bonding strap impedance calculator does it properly for a bond. And it cannot tell you the noisy current or the field: both have to be measured or estimated with a stated method. Above roughly 10 to 30 MHz the answer stops being component values and becomes layout: the loop a part is mounted in, where the chassis is bonded, how the harness is routed. A component-value prediction carried to 100 MHz without that caveat is wrong.
Frequently asked questions
What is the difference between a ground loop and common-impedance coupling?
A ground loop, strictly, is an enclosed area that a magnetic field can drive a voltage around. Common-impedance coupling is one circuit’s return current developing a voltage across a conductor a second circuit also uses, and it needs no loop whatsoever. They get the same name and they have different fixes: reduce the area for the first, stop sharing the conductor for the second.
Will a thicker ground wire fix it?
Only below the crossover frequency, which for a typical wire is a couple of kilohertz. Above it the shared impedance is inductive, and inductance depends on the conductor’s length and shape and not at all on its resistivity or much on its diameter — the diameter is inside a logarithm. That is why audio-frequency hum sometimes responds to a heavier ground wire and switching noise never does.
Should I add another ground connection to lower the impedance?
Almost never, and this is the single most common unhelpful instinct in the subject. A second connection between two sub-systems creates an enclosed area where there was none, which is exactly the thing the second calculation on this page is about, and it rarely reduces the shared impedance by enough to matter because the shared segment is usually still shared. Separate the returns instead.
How do I work out the loop area?
Trace where the current actually returns, not where the schematic says the ground is. Over an unbroken plane the return runs directly beneath the trace and the area is the trace length times the dielectric height, which is tiny. Over a split or a slot it detours round the gap and the area can be a hundred times larger for the same schematic. In a harness it is the separation between the signal wire and its return times the run length.
Does a twisted pair help?
A great deal against magnetic pickup and not at all against common-impedance coupling. Each twist reverses the sense of the enclosed area, so the contributions from a uniform field alternate in sign and largely cancel; what is left is the pitch’s own small loop plus whatever imbalance the pair has. It does nothing about a shared return conductor, because that problem is not geometric.
Do I enter a peak or an rms field?
Either, and the answer comes back in the same convention — the relation between field and induced voltage is linear, so there is no factor of root two hiding in it. Just be consistent, and note that a switching converter’s field is not a sinusoid, so its rms and its peak are related by something other than root two and the harmonics matter more than the fundamental.
Related calculators
References
- Ott HW. Electromagnetic Compatibility Engineering. Wiley, 2009. The standard treatment of common-impedance coupling, of the distinction between it and magnetic loop pickup, and of why single-point and multi-point grounding schemes each work over a limited frequency range. The crossover argument used here — that a conductor’s shared impedance is resistive below R/2πL and inductive above it — is developed there.
- Paul CR. Introduction to Electromagnetic Compatibility, 2nd ed. Wiley, 2006. Conducted and radiated coupling, including the derivation of the induced voltage in a loop from Faraday’s law and the treatment of twisted-pair rejection as a sequence of alternating enclosed areas.
- Rosa EB. The self and mutual inductances of linear conductors. Bulletin of the Bureau of Standards, vol. 4 no. 2, 1908, pp. 301–344. A US Government work. The round-wire formula used here, L = (µ₀/2π)·l·[ln(4l/d) − 0.75], whose −0.75 includes the internal inductance term µ_r/4 that vanishes at high frequency once the current is confined to the surface. Verified in this page’s build script against the exact partial self-inductance of a cylindrical conductor, computed as the four-dimensional average of the exact two-filament mutual inductance over both cross sections: agreement better than 0.2% for length-to-diameter ratios of 50 and above. The same computation shows that the plus-0.75 form printed in NASA’s 1998 electrical bonding survey is wrong by 20 to 33%.
- Terman FE. Radio Engineers’ Handbook. McGraw-Hill, 1943. The flat-conductor inductance formula used for the flat-conductor case, L = (µ₀/2π)·l·[ln(2l/(w+t)) + 0.5 + 0.2235(w+t)/l].
- MIL-STD-461G, Requirements for the Control of Electromagnetic Interference Characteristics of Subsystems and Equipment, 11 December 2015. A US Department of Defense standard, approved for public release. RS101 is the magnetic field radiated susceptibility requirement — the test in which a radiating loop is driven close to the equipment and the equipment must not misbehave — and it is the reason a flight or vehicle design has to know the loop areas inside it. The limit curves and test distances are in the standard.
- The free-space impedance µ₀c = 376.730313412 Ω, from which the far-field relation B = µ₀H = µ₀E/Z₀ = E/c used for the electric-field input follows exactly.