Dangerous EMF from coiled power cords?

[jaunty]

So - I'm finally getting the finishing touches set up on some rack mounted audio and electrical test equipment mounted in racks. I started trying to tidy up my IEC cables by 'coiling' them and putting a twist tie around them. I've recently had some tricky interference issues with some of the equipment necessitating moving a power supply transformer or two to another location inside a case - another i had to move outside a case... in another enclosure. Anyway- since i'm being so persnickety about trying to keep all my noise etc super low - i'm wondering if i'm not unintentionally creating undue magnetic fields due to the coiling of these cables (some are ending up right next to low voltage circuitry). Is it smarter just to let the cables hang? I'll assume that I'm increasing the local EMF of a given cable by some number like the root of the number of turns (probably not so far from the truth?) - any suggestions? or am I just going too far in worrying about it?

[AndyC_772]

Do you hear a hum?

If so, does it change or go away if you uncoil a cable?

If yes, then you may have an issue. If not, then enjoy the music and don't worry about it.

[jaunty]

thanks for the response but it's going to be about a hundred hours of cabling and putting in screws and whatnot until i can even TEST this rig... so i want to be as careful as possible beforehand and was looking for some kind of advice on 'best practices' - surely there are some EE's out there with experience setting up lab test gear with mains cabling etc who might have an opinion on this?

[T3sl4co1l]

No worry at all.  The + and - currents are perfectly paired (or at least, they damn well better be, else you have a fault somewhere).

Tim

[Zero999]

The only possible danger with coiling power cords is the heat, generated by the I²R can't be dissipated as easily, so the cable needs to be derated to less than half the current rating. This is unlikely to be an issue if the cable is only being used at a fraction of its current rating but could cause a fire if it's used for high powered appliances such as a toaster, fan heater, microwave etc.

[jaunty]

thanks but that's really not the kind of 'danger' i am referring to... the danger i am referring to is picking up the tiniest millihenry of inductance in low noise circuitry inside adjacent equipment cases. I guess the ideal would be altering power cords to EXACTLY the right length to hit the outlets on my mounted power strips

[salbayeng]

In general, as TeslaCoil says, the currents  will cancel , so zero amps x n turns = zero ampere turns.

In terms of interference, having coiled cable is generally helpful as it increases the common mode inductance, hence any induced voltage generates less current, and vice versa.
If you can't get enough inductance by coiling your cables, then slap a big ferrite core around the cable bunch, Viola! you have made a common-mode-transformer , one of the most effective EMI filters.

You always have to watch for ground loops / hum loops , so if you have mucked up there, coiling/uncoiling cables won't help much!

[salbayeng]

... the danger i am referring to is picking up the tiniest millihenry of inductance in low noise circuitry inside adjacent equipment cases....

You can't pick up  millihenries,  first off it would be micro-henries, and secondly they are not "picked up". Thirdly the inductance goes as turns squared. The current induced with noise voltage applied goes down as turns squared.

The issue you are grappling with is "mutual inductance"  , 
compared to "self inductance" which is where the voltage is induced proportionally to the current and frequency in a coil.
but with "mutual inductance" a voltage is induced in one coil proportional to the current and frequency in another coil.
 Note that both inductance have the same proportionality. So a loop of mains cable will couple the same noise signal across giving the same forcing voltage, irrespective of number of turns. In general the forcing voltage is created by ground loops, so longer cables have more resistance + inductance, hence create less current in the earth conductor.  Mutual inductance drops off incredibly quickly with distance.

If it really bothers you, wind the cable up in a figure 8 pattern, that will produce zero mutual inductance (in the far field), and alternate the figure8's when you strap the bundles together.

[snarkysparky]

I would try to avoid coiling near low voltage circuitry.  There is always some common mode current that will be concentrated by the coiling. It is unlikely to be a problem but still I would keep distance from sensitive circuits.  A serpentine pattern bound together will create much less magnetic field.

[PointyOintment]

A serpentine pattern bound together will create much less magnetic field.

Not necessary. It's already a bifilar winding as described here.

[jaunty]

... the danger i am referring to is picking up the tiniest millihenry of inductance in low noise circuitry inside adjacent equipment cases....

You can't pick up  millihenries,  first off it would be micro-henries, and secondly they are not "picked up". Thirdly the inductance goes as turns squared. The current induced with noise voltage applied goes down as turns squared.

The issue you are grappling with is "mutual inductance"  , 
compared to "self inductance" which is where the voltage is induced proportionally to the current and frequency in a coil.
but with "mutual inductance" a voltage is induced in one coil proportional to the current and frequency in another coil.
 Note that both inductance have the same proportionality. So a loop of mains cable will couple the same noise signal across giving the same forcing voltage, irrespective of number of turns. In general the forcing voltage is created by ground loops, so longer cables have more resistance + inductance, hence create less current in the earth conductor.  Mutual inductance drops off incredibly quickly with distance.

If it really bothers you, wind the cable up in a figure 8 pattern, that will produce zero mutual inductance (in the far field), and alternate the figure8's when you strap the bundles together.

 salbayeng- as for 'millihenries - i wasn't really expecting someone to take me too literally... but was trying to be a bit 'cute' hoping someone would get my gist. I'm not worried at all about the 'mutual inductance' between 'windings' in the power cable- but rather the effect it might have on adjacent transformers and other circuitry containing microvolt signals etc. if you see what i mean... a six turn coil containing household current next to a 200 turn transformer for a microphone preamplifier etc... hopefully you get the picture

[jaunty]

I would try to avoid coiling near low voltage circuitry.  There is always some common mode current that will be concentrated by the coiling. It is unlikely to be a problem but still I would keep distance from sensitive circuits.  A serpentine pattern bound together will create much less magnetic field.

yes - that's what i'm talking about. Someone's got the right idea. How do you distinguish 'serpentine' from 'coiled'? not sure i follow that part.

[jaunty]

In general, as TeslaCoil says, the currents  will cancel , so zero amps x n turns = zero ampere turns.

In terms of interference, having coiled cable is generally helpful as it increases the common mode inductance, hence any induced voltage generates less current, and vice versa.
If you can't get enough inductance by coiling your cables, then slap a big ferrite core around the cable bunch, Viola! you have made a common-mode-transformer , one of the most effective EMI filters.

You always have to watch for ground loops / hum loops , so if you have mucked up there, coiling/uncoiling cables won't help much!

and so therefore transformers can never induce current in other conductors - because their 'currents will cancel'...? that's really not making sense to me - in theory OR practice... sorry

[Zero999]

In general, as TeslaCoil says, the currents  will cancel , so zero amps x n turns = zero ampere turns.

In terms of interference, having coiled cable is generally helpful as it increases the common mode inductance, hence any induced voltage generates less current, and vice versa.
If you can't get enough inductance by coiling your cables, then slap a big ferrite core around the cable bunch, Viola! you have made a common-mode-transformer , one of the most effective EMI filters.

You always have to watch for ground loops / hum loops , so if you have mucked up there, coiling/uncoiling cables won't help much!

and so therefore transformers can never induce current in other conductors - because their 'currents will cancel'...? that's really not making sense to me - in theory OR practice... sorry

Magnetic fields in the same direction add together and magnetic fields in the opposite direction cancel one another.

In a transformer the turns on the primary coil are wound in one direction only, so the field generated by each turn adds to the neighbouring turns.

In a coiled piece of mains cable, for every turn on the live, there's another turn on the neutral which is carrying the same current but in the opposite direction, so the magnetic fields cancel one another out.

[T3sl4co1l]

Magnetic fields in the same direction add together and magnetic fields in the opposite direction cancel one another.

In a transformer the turns on the primary coil are wound in one direction only, so the field generated by each turn adds to the neighbouring turns.

Although, considering the transformer as a whole: the secondary current opposes the primary current, so that the total (external) magnetization is near zero.

Just in case you needed something to cook your noggin today.

Tim

[jaunty]

Magnetic fields in the same direction add together and magnetic fields in the opposite direction cancel one another.

In a transformer the turns on the primary coil are wound in one direction only, so the field generated by each turn adds to the neighbouring turns.

Although, considering the transformer as a whole: the secondary current opposes the primary current, so that the total (external) magnetization is near zero.

Just in case you needed something to cook your noggin today.

Tim

thanks Tim - i  think my noggin's already cooked... just from all the different interpretations of what i guess must have been a poorly worded question...

[salbayeng]

Let's try a different approach, to see if we can't added a splattered brain cell motif to your wallpaper.

First note that all this electromagnetic stuff is reversible, so "receiving" is the same as "transmitting" , so if you can find an explanation that works as a transmitter, it's the same for a receiver.

Consider your audio transformer, it has a bobbin onto which the primary and secondary windings are wound. This bobbin wraps around the magnetic yoke (or core) (or the core wraps around the yoke, whatever, they both interlink like two links on a chain).
In the transformer, consider just one winding, now let's pass an AC current into this winding, this winding creates a magnetic flux that flows around the core, (and a miniscule amount of that flux takes a shortcut through the air inside the transformer). There is a voltage induced in the winding ( a back emf) that is proportional to the rate of change of the current.  Inductance is defined by the ratio of the two variables v=L di/dt.  So (flipping this around so voltage > current) in order to apply say 1v rms at 1kHz, to a winding of that transformer a certain small current must flow to create magnetic field, this is the magnetising current, and the inductance represented by this is the magnetising inductance.

Now add a secondary to the transformer, when this is done the voltage on the secondary is turns_ratio x primary_voltage.
If we add a load to the secondary, then the current in the primary is now  turns_ratio x secondary_current + magnetising_current.
And of course secondary_voltage= turns_ratio x primary voltage.
If we short circuit the secondary, the primary_current is now approximately turns_ratio x secondary_current, but the primary_voltage is not zero, as some flux leaks out between the windings.  We define (when secondary=short-circuited) primary_current = leakage_inductance x rate_of_change of primary_current. It is this leakage flux that leaks out of the windings and permeates the air around the transformer.  Now a good quality transformer will have a thick copper strap wound around the outside of it, and be inside a steel can,  both of these serve to contain the leakage flux within the transformer., but some miniscule amount of flux will escape. Let's call it external_leakage_flux.  So the flux of a good transformer might have 98% magnetising , 1.9% internal_leakage, and 0.1% external_leakage.  For convenience we have a coupling factor k , so k=0.98 for primary to secondary coupling, k=0.019 for primary to internal air space, and k=0.001 for primary to external_flux.
So we have defined a "transmitter" so that primary_voltage > magnetising_flux > external_leakage flux.
So let's say we make a big solenoidal coil that completely surrounds the outside of the transformer, and we put say 1v across the primary, this makes say 1milli-tesla of flux in the core, and because k=0.001, we also get 1microTesla through that big coil we wrapped around it, and it might induce a  milliVolt of "signal". So it's another "secondary", but an incredibly inefficient one.
I said before everything was reversible , but the k factor applies both ways , Hence I can't apply 1uT around the transformer and expect 1mT in the core, and 1v output. I actually need to apply sufficient current in that big winding to generate 1Tesla of flux on the outside in order to get 0.001 x 1T =  1mT in the primary = 1volt.
I don't know whether you have been inside a MRI machine, that's 3Tesla, but you would be acutely aware of 1tesla due to all the steel flying through the air, not to mention the accidental orchidectomy due to your steel belt buckle.

We can then define mutual inductance between that big old coil, and the transformer primary as V_primary = Lmutual x rate_of_change of big_coil_current.  In essence the mutual inductance defines how many mV of noise injection we get per Amp  of current in the big old coil.
This for a coil wrapped tightly around the outside of the transformer,  if the coil was moved some distance away, the coupling would be even lower.

...... back shortly after dinner......
Some background reading:
http://www.electronics-tutorials.ws/inductor/mutual-inductance.html

[salbayeng]

An equivalent way of looking at loosely coupled coils is to consider the magnetic moment ,  this is a convenient measure of the "strength" of a magnet, and can be used with bar magnets and coils,  obviously more turns, more amps, or more area make a magnet "stronger" and magnetic  moment is a way of capturing that "strength".

For a coil of wire of n turns, carrying I amps, with an area of S sq metres, then the magnetic moment calculation is simply  \$\mu\$ = n I S  a nice easy representation!  The moment is a vector quantity, and it points along the centreline of a  circular coil (or in general is othogonal to the area, i.e. the "directed area").  The units are A·m² .

We can use magnetic moment , for example , to describe how strong a transmitter we can make with our mains cable.
First consider a single wire, make it 3.14m long, and let it carry 1 amp, if we wind this into a horizontal loop 100mm across, we have an area of 0.0078 and ten turns so \$\mu\$ = n I S = 10 x  1  x  0.0078 = 0.078 A·m² .
What if we only make 1 turn that is 1m diameter? then it is n I S = 1 x  1  x  0.78 = 0.78 A·m²
So winding a fixed length cable into many small loops is better (part of your original question)
What if we take the ten turn, 100mm loop , and flop half of it over, so it is two loops, side by side, each of 5 turns, so one loop has  \$\mu\$ = .0039 A·m²  pointing up , and the other half has 0.0039 pointing down, the net effect is zero in the far field.  So you should be able to work out what happens with figure-8 loops or serpentine loops yourself and drawing pictures to determine the effective directed area.

Let's now consider something approximating a power cable, say we have a 3.14m long cable where the active and neutral are spaced by 10mm and there is no twist (a bit like the old 300ohm TV cable), so the area is 3.14 x 0.01=.0314 and n I S = 1 x  1  x  0.0314 = 0.0314 A·m².  If the cable is laying flat, then the moment is directed upwards.
Lets twist this cable so its one twist per 400mm, i.e. one twist per 100mm,  So one 100mm segment has an average moment pointing up, the next segment points left, then down, then right, so in the far-field the net magnetic moment vanishes for each of the 31 100mm segments, so just the remainder of 40mm actually radiates, so an area of 0.01 x 0.04 =.0004 sqm or \$\mu\$ = .0004 A·m² .

--- let's get back to your case ----
Assume the power cable feeds a 240VA load from 240V, so the active carries one amp of load current and the neutral 1 amp. In actual practice you may have a line filter in your amplifier, the capacitors in this will carry say 1mA on the active to earth, and none on the neutral to earth, (they are the same potential) and 1mA flows back on the earth line, so if we consider the power cable is say 3.14m long in a straight line, and twisted, its much the same problem as above,  but you have 1.001A on A, 1.00A on N and 0.001. So the net magnetic moment in the far-field is miniscule as the directed areas cancel out.
Let's take this cable and make 10 loops 100mm across, we can calculate the moment again of this as  \$\mu\$ = n I S = 10 x  0  x  0.0078 = 0.0000000 A·m² .(That's because the net current is 0 = I_A + I_N +I_E = 1.001-1.000-0.001)

More realistically some of that 1mA of earth current might flow through the chassis, even if all of did divert through the chassis, the moment would then be \$\mu\$ = n I S = 10 x  0.001  x  0.0078 = 0.000078 A·m².

Once you've got the magnetic  moment calculated, i.e. your transmitter strength, you can determine the magnetic field applied outside your "leaky" transformer, numerically this will be a handful of nanotesla's for a magnetic moment of 1 A m² .
(See about the middle of this page: https://en.wikipedia.org/wiki/Magnetic_moment )

So the whole signal chain from mains current to your transformer  is milli x nano x micro  = vanishingly small.

Compare this to the earth leakage current of ~ 1mA due to filter caps , which if applied across a 1ohm resistance between various chassis parts yields a millivolt of noise , if you are real sloppy with earthing your mikes, and see even a tenth of this across your mike input it will be very loud!
So earth leakage is likely to be a stronger noise source, and this won't change if you cut the power cables shorter.

[salbayeng]

Want to know what a million ampere-turns.m² looks like, see figure 3 here http://csegrecorder.com/articles/view/the-megatem-fixed-wing-transient-em-system-applied-to-mineral-exploration .

It's on a dash7 (like the common dash8, but with two more engines!), The transmitter uses all the available electrical energy from the 4 engines for Megatem II to generate a whopping 2.2MAm².

Even in the middle of this magnetic field, it only presents as a background buzz on the audio systems in the aircraft.

[SL4P]

Small question.
If you're putting so much effort into building the rack, why not. it, terminate, cut and dress the cables to suit the installation?

Another technique is to cross power at 90-degrees to introduce induced interference.