Cable Radiated Emissions Calculator

Cable Radiated Emissions Calculator

The common-mode current an RE102 limit actually permits — usually a couple of microamps — and the field a measured common-mode current on a harness is expected to produce. The bridge between a current-probe reading and a radiated-emissions limit, with both of the model’s validity conditions worked out and printed.

Common-mode current against an RE102 limit

CM current, length, distance -> field and budget
The same nine curves as the margin page, read from MIL-STD-461G’s own figures. The last option takes a number from a copyrighted standard, from a programme specification, or from anywhere else. Figure RE102-3 is captioned for aircraft AND SPACE SYSTEMS, but all three of its curves are labelled in aircraft terms. Nothing on the figure and nothing in paragraph 5.18 says which one a spacecraft uses. Your programme’s EMC control plan or your contract decides that, and this page will not choose for you.
Only used when you have chosen to type the limit yourself. With one of the RE102 curves selected this box shows what that curve gives at your frequency, and is locked.
MEASURED, with a current probe clamped round the whole bundle — every conductor including the returns and the shields. This is not a number you can get from a circuit simulation, and the page says why below. If you have no measurement, use the headline figure instead: the current the limit permits does not depend on what you are actually producing.
The radiating length. MIL-STD-461G’s own setup exposes 2 metres of interconnecting and power leads along the front of the test setup boundary, which is why 2 m is this page’s default — but if your harness run is shorter or longer in the real installation, that is the number that matters.
RE102 places the antenna 1 metre from the front edge of the test setup boundary, so 1 m is the distance the limit refers to. Commercial standards use 3 m or 10 m. Note that at 1 m the far-field condition fails below about 48 MHz, which the page works out below.
The radiated field is proportional to frequency for a fixed current, so the common-mode current budget gets tighter at 20 dB per decade — while the RE102 limit is flat from 2 to 100 MHz. That squeeze is what makes the numbers on this page so small.
The mechanism, drawn as a geometry. A net common-mode current flows along the whole harness — every conductor including returns and shields — and returns through the ground plane, so the harness and its image act as a short radiator. The field at the measurement antenna is proportional to frequency, to that current and to the radiating length, and inversely to distance. The moving dots are the current you entered; the image current below the plane is what supplies the factor of two in the constant. The current the limit permits, the estimated field and the margin are live.
2.102µAExample

MIL-STD-461G RE102, Figure RE102-3, the “fixed wing internal, 25 m or more” curve, with 2 metres of harness measured at 1 metre and 5 µA of common-mode current at 30 MHz

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A harness over a ground plane is a short monopole

E = μ0 · f · Icm · L / r    V/m    μ0 = 1.2566 × 10−6
Icm,max = Elimit · r / (μ0 f L)
valid while   r > λ/2π   (far field)   AND   L < λ/4   (electrically short)
E(dBµV/m) = 20 log10(E × 106)
μ0
the permeability of free space, and the constant is exactly that — η0/2c doubled by the ground plane’s image gives η0/c, which is μ0. The 1.26 × 10⁻⁶ in the textbooks is this number
Icm
common-mode current: the net current on the whole bundle, measured with a current probe clamped round all of it. Not the signal current, not the differential current, and not anything a schematic can tell you
L
the radiating length. Proportional while the cable is electrically short; above a quarter wavelength the current distribution stops being uniform and the formula overstates
r
the distance to the measurement point. 1 metre for RE102, which is inside the far field below about 48 MHz — the page says so rather than pretending otherwise

Worked example

MIL-STD-461G RE102, Figure RE102-3, the "fixed wing internal, 25 m or more" curve, with 2 metres of harness measured at 1 metre and 5 µA of common-mode current at 30 MHz
At 30 MHz that curve is on its flat section at 44 dBµV/m, which is 158.5 µV/m
Turning the radiation formula round, the current that field corresponds to is E r / (μ₀ f L) = 158.5 µV/m × 1 m ÷ (1.2566 × 10⁻⁶ × 30 MHz × 2 m) = 2.102 µA, or 6.5 dBµA
That is the whole common-mode budget for the harness at that frequency. For scale: 10 pF of stray capacitance from a switching node to chassis, driven by 20 volts of common-mode at 30 MHz, passes 37.7 mA — three orders of magnitude more
Going the other way, the 5 µA entered gives E = 1.2566 × 10⁻⁶ × 30 × 10⁶ × 5 × 10⁻⁶ × 2 ÷ 1 = 377 µV/m, which is 51.53 dBµV/m
Against the 44 dBµV/m limit that is an estimated margin of -7.53 dB — above the line
Now the honesty. At 1 metre the far field starts at 47.71 MHz, and a 2 metre cable stops being electrically short above 37.47 MHz. The second is BELOW the first, so this geometry has no frequency at which both conditions hold
That is not a defect in the page: it is MIL-STD-461G's own test setup, 2 metres of exposed lead measured at 1 metre. The estimate is an order of magnitude, the headline budget is still the right thing to design to, and a current probe on the real harness is what settles it

What an RE102 limit permits, for 2 m of harness at 1 m

FrequencyLimit (fixed wing internal ≥ 25 m)Permitted common-mode current
2 MHz44.0 dBµV/m31.53 µA (30.0 dBµA)
10 MHz44.0 dBµV/m6.306 µA (16.0 dBµA)
30 MHz44.0 dBµV/m2.102 µA (6.5 dBµA)
100 MHz44.0 dBµV/m630.6 nA (-4.0 dBµA)
300 MHz53.5 dBµV/m629 nA (-4.0 dBµA)
1 GHz64.0 dBµV/m627.2 nA (-4.1 dBµA)
The limit is flat from 2 to 100 MHz while the radiated field rises with frequency, so the current budget falls at 20 dB per decade across that whole band — a factor of fifty between 2 and 100 MHz. Above 100 MHz the limit itself rises at very nearly the same rate, so the budget flattens out. Note that the electrically-short condition fails above 37.47 MHz for a 2 metre cable, so the last three rows are outside the model’s range and are shown for the shape of the curve, not as predictions.

Where the model is valid, and where it is not

ConditionWhyFails when
r > λ/2πBelow that distance the 1/r² and 1/r³ near-field terms dominate the radiation term, by tens of decibels at a tenth of the boundaryClose measurements at low frequency. At 1 m this fails below 47.71 MHz
L < λ/4The formula assumes a uniform current along the cable. A longer radiator has a standing-wave distribution with nulls, and the contributions stop adding in phaseLong harnesses at VHF. A 2 m cable fails above 37.47 MHz
The current is uniform along the cableEven when short, a standing-wave rather than uniform distribution reduces the effective lengthAlways, to some degree — worth 6.0 dB for a very short radiator and 3.9 dB at a half wavelength
A ground plane is present and the image is perfectThe factor of two in the constant comes from the image. A cable in free space, or over a lossy or distant plane, gets lessSpacecraft harnesses far from structure; any setup without a bonded plane
MIL-STD-461G’s own RE102 setup — 2 metres of exposed lead, antenna 1 metre from the test setup boundary — satisfies neither of the first two conditions at the same frequency. That is a real limitation of this class of estimate and not a reason to distrust the standard: the standard defines a measurement, and the measurement is the answer. What the estimate is for is knowing roughly what current budget you are working to before hardware exists.

Where the common-mode current comes from, and what moves it

MechanismTypical sizeWhat changes it
Stray capacitance from a switching node to chassis5 to 50 pF for a TO-247 on a heatsink; more with a thin insulatorInsulator thickness, a screened insulating pad, a smaller switching node, slower edges
Transformer interwinding capacitance10 to 200 pF across an unscreened flyback transformerA Faraday screen between the windings, brought out to the right node
Common-mode voltage on the harness from a poor chassis bondProportional to the bond’s inductance times dI/dtA bonded FACE rather than a wire; bonding straps are inductors
Imbalance between the two sides of a differential pairSmall but not zero, and it is what makes shielded twisted pair worth havingBalance, and a shield terminated through 360 degrees at both ends
Shield current from an unterminated or pigtailed shieldThe whole shield current appears as common mode on the bundleA 360-degree backshell. This is usually the largest single term
Every one of these depends on mechanical construction, and not one is on the circuit diagram. That is why this page takes the current as an input and why a current probe is the instrument for the job. The only route from a schematic to a common-mode current runs through a measured or estimated parasitic capacitance, and the estimate is the weak link.

Cables radiate; boxes mostly do not

A well-made enclosure is a good shield. The cables leaving it are not, and on most hardware they are what sets the radiated emissions. The mechanism is common-mode current: a net current flowing along the whole bundle, returning through structure, which makes the harness an antenna — a short monopole over a ground plane, radiating a field proportional to frequency, to the current, and to the radiating length.

The constant is exactly μ0. The far field of a short current element is η0fIL/2cr, and a ground plane’s image doubles it to η0fIL/cr. Since η0 = μ0c, that is simply μ0fIL/r. The 1.26 × 10−6 that appears in every EMC textbook is the permeability of free space, which is a satisfying thing to know and a useful check on any implementation.

The number worth designing to is the inverse. Turn the formula round and it gives the common-mode current a limit permits, and that is the figure this page leads with. For MIL-STD-461G’s aircraft and space limits in the VHF band, with the standard’s own 2 metres of exposed lead at its own 1 metre measurement distance, the answer is a couple of microamps. Microamps. For comparison, ten picofarads of stray capacitance from a switching node to chassis, driven by twenty volts at thirty megahertz, passes about 37.7 mA — three orders of magnitude more than the budget. That gap is the whole reason common-mode control is hard, and it is not a gap that component values close.

Common-mode current cannot be predicted from a schematic. It is set by the common-mode voltage driving the harness, by the harness’s own impedance to structure, and by parasitic capacitance from switching nodes to chassis — which depends on how the heatsink is mounted, how the transformer is wound, how the chassis is bonded and how the harness is routed. None of that is on the circuit diagram. It is measured, with a current probe clamped round the entire bundle including returns and shields, and this page takes it as an input and does not pretend otherwise. The headline figure does not need it: the current a limit permits depends only on the limit, the length and the distance.

Two validity conditions, and they may not overlap. The estimate is a far-field expression, so it needs the measurement point beyond λ/2π. It assumes a uniform current, so it needs the cable shorter than a quarter wavelength. For a 2 metre harness measured at 1 metre those two requirements are 37.47 MHz and 47.71 MHz — the wrong way round, with no window between them. That is MIL-STD-461G’s own geometry, and it is worth saying out loud: this class of estimate tells you the order of magnitude of the budget, not what the chamber will read. Both frequencies are printed on the page so you can see which one is biting.

What to do with the number. Use it as a budget. If the limit permits two microamps and you measure two hundred, you need 40 dB, and you now know where to look: the shield terminations first, then the chassis bond, then a common-mode choke on the harness, then the switching node capacitance. Once you have hardware, the RE102 margin page takes the measured field and the transfer impedance page says what your terminations are costing. For the conducted side of the same problem, the conducted emissions margin page works to CE102, and its measurement is at the power input rather than on the harness.

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Frequently asked questions

Why is the permitted common-mode current only a few microamps?

Because the radiated field is proportional to frequency, current and length, and the limit is flat. At 30 MHz with 2 metres of harness measured at 1 metre, 44 dBµV/m corresponds to about two microamps. It is not an error in the arithmetic — it is why common-mode control dominates military and space EMC work, and why a design that passes conducted emissions comfortably can fail radiated by 30 dB.

How do I measure common-mode current?

With a current probe clamped round the entire bundle — every conductor, including returns and shields. The net current is what radiates; the differential current cancels. Use a probe with enough bandwidth and check its transfer impedance at the frequency you care about. The same instrument used for CS114 bulk current injection will do it.

Can I calculate the common-mode current from my circuit?

No, and this page will not pretend you can. It depends on parasitic capacitance from switching nodes to chassis, on the harness’s impedance to structure, and on the common-mode voltage the layout creates — all of which are properties of the mechanical assembly rather than of the schematic. Estimates built on an assumed stray capacitance can be an order of magnitude out in either direction.

At what frequency does this model stop working?

Two frequencies, and the page prints both. Below the one where your measurement distance equals λ/2π you are in the near field and the estimate understates. Above the one where your cable reaches a quarter wavelength the uniform-current assumption fails and it overstates. For MIL-STD-461G’s own geometry — 2 m of lead at 1 m — those are the wrong way round and there is no valid window at all, which is a real limitation of the method and worth knowing.

Does a common-mode choke fix this?

It helps, in proportion to the impedance it adds compared with the harness’s own impedance to structure — which is usually a few hundred ohms at VHF, so a choke has to be worth more than that to matter. It is one of several levers, and rarely the largest. Shield terminations, chassis bonding and switching-node capacitance usually have more authority, and none of them costs a part.

Why does the ground plane double the field?

Because a current above a conducting plane has an image current below it, and at broadside the two add in phase. That is where the factor of two in the constant comes from, and it is why the same harness in free space — a spacecraft harness far from structure, say — radiates about 6 dB less. If your geometry has no plane, the estimate is pessimistic by that much.

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References

  1. Ott HW. Electromagnetic Compatibility Engineering. Wiley, 2009. Chapter 12 Digital Circuit Radiation, which develops the common-mode cable radiation model used here, and Chapter 2 Cabling for where the current comes from. Chapter titles verified against the author’s own published contents listing.
  2. MIL-STD-461G, paragraph 5.18 RE102, radiated emissions, electric field. The limit curves used here are read from Figures RE102-1 to RE102-4. Paragraph 5.18.3.3 sets the antenna 1 metre from the front edge of the test setup boundary at 120 cm above the floor, and paragraph 4.3.8.6 fixes the 2 metres of exposed interconnecting and power leads that give this page its default radiating length.
  3. MIL-STD-461G, paragraph 5.13 CS114, conducted susceptibility, bulk cable injection. The requirement that puts a current probe on the harness in the first place, and the instrument this page’s input comes from.
  4. Balanis CA. Antenna Theory: Analysis and Design. Wiley. The infinitesimal dipole fields, including the induction and electrostatic terms, from which the far-field expression used here is the leading term and against which this page’s validity boundaries are derived.