# How does coil inductance vary with core cross section?

Discussion in 'Mathematics and Physics' started by DaveC53, Mar 26, 2015.

1. ### DaveC53New Member

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I am designing an EMI filter to keep smart meter SMPS noise out of my house wiring, which requires coils wound from very stiff 1 guage wire. I can only get it down to about 2" in diameter, and toroid cores with that cross section pretty much don't exist. I may have to use a core that does not fill the coil.

My question is, does the inductance of a toroid change if the coil is wound larger than just fitting over the core? I'm going nuts searching inductor design docs, all of which seem to assume that the coil fits the core tightly. Is the inductance what is expected given the core's Al factor (inductance per turn squared), or less because it does not intersect the entire coil cross section?

2. ### RCinFLAWell-Known Member

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Not by much. Most of toroid field is carried within the core which is usually much greater permeability then air. You will increase leakage inductance which is usually a bad thing for most applications.

Your biggest problem with EMI application is making sure the core is large enough so it does not saturate with the amount of desired 50/60 Hz carrying current for the load. Once the core saturates it is not much better then air. You can put two cores together side by side and wind them as if they are one core.

3. ### MrAlWell-Known MemberMost Helpful Member

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Hi,

The inductance goes up by the ratio of the cross sectional area of the core, so that a core with 2 times the cross section means you get an inductance twice as high. But that assumes that the core is homogenous, which means in most cases it is made of a single material. For what you are talking about, there would be two core materials: one is the core material itself and the other is air. Since the relative permeability of air is 1 and the core material could be 500, that means for a construction with the wire wound around the core with twice as much area as the core material itself the inductance would go up by a factor of approximately:
501/500
which is 1.002, or 0.2 percent which in words is "two tenths of one percent".
As you can see, it isnt a heck of a lot, so it's a waste, especially since the resistance will at least double.

There are other problems too though, that you probably are not aware of yet. One is the skin effect. The wire size you want to use roughly comes in at just the right size that might be called the maximum size wire to use with a 50 or 60 Hertz line frequency. But there are still losses. A better choice, as well as being simpler to wire, would be two wire lengths of wire 3 wire sizes up from that, so we're talking AWG number 4 (assuming you are using the AWG sizes already). So two lengths of #4 wire would work better and also be a little easier to wind onto the core, but be aware that in the constructions of large transformers even this size wire is beat down with a soft hammer in order to fit the wire better onto the core, so it's still not super easy to wind, so you might even be better off going with #7 or 8 and using four lengths for each turn.

As the previous post points out, if you use two cores side by side you get about twice the inductance as with one core, and of course three cores three times the inductance, but the resistance goes up because of the extra long length on each side of the core. With two cores it's not that bad, but as you go up in the number of cores the loss gets worse so it's better to go to a larger core. Also, you can put two entirely different inductors in series to get more inductance, and two similar inductors together means you end up with twice the inductance too. This means if one isnt enough, you can add more as time and money permits.

The other issue is DC saturation, which might come into play if you have any equipment that uses a half wave rectification to turn the AC into DC. You probably dont have this situation though, but you could make some measurements if you wanted to be sure.

Another thing to consider is what happens when you have a sizable load device turned ON, and then you turn it OFF with the power switch. What this might mean is that the inductor goes from supply a large current to supplying a small current, and that means the voltage will surge up for a short time interval. This means that you should have some very good surge protectors on the line also, or perhaps some capacitance to absorb that surge. This is a somewhat difficult thing to calculate, because the load varies and we dont really know the final inductance unless you measure it.

This brings us to the inductance measurement. If you can measure the inductance we could do a simulation to find out how bad the surge would be and stuff like that. Depending on the lowest frequency of the interference noise though, you could use a lower value inductance which would be nice. The lower the inductance the safer it is for the other appliances connected to the line at the time one device is switched off.
Sometimes even an inductance of just 2uH (two microhenries) is enough to kill higher frequency noise), and this can be made with an air core (maybe two inch diameter) and several turns of wire. It does depend highly on the problem frequency though so we'd have to know that to be sure.

You could also look into ready made line filters, which act on both sides of the line. These are made just for the purpose you are talking about as well as helping to lower noise going from your appliance back into the line. If you have a particular device that has a problem right now, perhaps even one smaller unit would work on that one device saving you a lot of time and money.

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5. ### Tony StewartWell-Known MemberMost Helpful Member

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A good line filter consists of a two PI filter for common mode and differential noise with caps on either side. The http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html impedance ratios determine attenuation. This calc will assist with the torroid.
So you would need a CM choke and a DM choke.

http://www.mag-inc.com/File Library/Product Literature/Ferrite Literature/fc-s5.pdf