Can Coax-Wound Coils Prevent Radiation in Ferrite Core Magnetic Circuits?

[FusionJim]

Assume i want to create a magnetic circuit within a ferrite core with airgap (i need the B field in airgap). The ferite core would have a coil on it. Problem is if i want my core airgap area and magnetic path length longer than wavelength of current through the coil i would have high losses as it would radiate. Can i solve this issue with using coax to wind the coil? Is the coil the main problem that radiates or is it also the B field in the core? I guess i'm asking does the core also have to conform to wavelength constraints or just the coil?

Ps. Also what happens in the simpler case without a core, just a coax wrapped to form an air core coil, can such coax coil size be greater than wavelength and still result in homogenous B field in the coil inner volume?

 

[Baluncore]

Your reference to a coil that is larger than the wavelength suggests an antenna. A large coil becomes a lossy transmission line at shorter wavelengths. The winding of the coil acts like a rolled-up dipole antenna embedded in its insulation. It will have resonances due to that wire length.

You can make an inductance without winding a coil by cutting a transmission line to a short length. An inductor is a positive reactance, and appears λ/8 along a line from the open end, or 3λ/8 from a shorted end line.
https://en.wikipedia.org/wiki/Smith_chart

A ferrite core has fine magnetic particles held in a non-magnetic ceramic insulator. The magnetic particles must be smaller than the skin depth at the frequency of operation. A ferrite core would need to be smaller than the wavelength of operation, or it would need to be analysed as a cavity or part of a transmission line.

Since you only need the field in the air gap, I would suggest you excite a waveguide or cavity with RF from an oscillator.

There are also transmission line transformers, wound with short lengths of coaxial line on ferrite cores. But I don't think they are what you want.

Maybe if you tell us why, and what field you want in the air gap, we can work out if it is possible, and how to do it with the minimum effort.

 

[FusionJim]

Since you only need the field in the air gap, I would suggest you excite a waveguide or cavity with RF from an oscillator.

You think like make a small vertical opening within a waveguide at a place where the magnetic field is parallel to the lenght of the waveguide?

If I do away with ferrite altogether, leaving an air core then i guess i could also wind myself a pair of helmholtz coils. But if the diameter becomes large (compared to wavelength) the long coils, many turns might pose a problem of high inductance. Can i say take many loop antennas put them all in parallel together with one another and achieve the same result, given their all driven together? I assume a loop antenna can be larger than the wavelength of current driving it and the near field (the B field in the center area enclosed by the loop) should still be homogenous and in the same direction at all points within the loop, is that true?

For example imagine a loop of 30cm diameter driven by 10cm wavelength current, which is IIRC, 3Ghz

 

[Baluncore]

You need to describe what you are trying to do, not how you think you might do it. You will not get a good answer by trying all combinations of guesses. Hypotheticals are a waste of our time because the critical real design criteria are missing.

Be specific, and explain precisely why you need to do this thing.
Put real numbers, or ranges, on the things that you know.

 

[FusionJim]

Hey @Baluncore , so I am toying around with a faraday generator. Sure enough the solid copper disc rotating in a static magnetic field produces pure DC. I decided to see how the Lorentz force can also produce AC by having a AC magnetic flux. To stop eddy currents from forming the disc is cut up into thin strips only connected at the center. This is the easy part. The hard part is to get a homogeneous axial and symmetric B field within an airgap.
I could use something like helmholtz coils that is an aircore coil/inductor, but as we know air is a bad magnetic conductor therefore the currents needed for usable magnetic flux densities would be huge, this is practically impossible.

So I was looking at magnetic materials like ferrites. But I recalled that the typical silicon steel lamination within a 50 Hz transformer is about 0.8mm thick because that is the skin depth to which the 50 Hz magnetic field can penetrate a silicon steel permeability material , so making them thicker would result in wasted unused material. To my surprise I calculated that even at 3 Mhz which arguably is a low frequency in terms of radio frequencies , the skin depth for a 1000u permeability ferrite is roughly just 100 microns, if that is correct. Either way it seems that even for Ni-Zn ferrites that have properties suitable for use with high frequency RF , even into the Ghz range, skin depth is very shallow. Does this mean that such ferrite core , most material inside it never sees a magnetic field rendering it useless/wasted material/space?

I understand that main advantage for ferrite VS silicon steel or amorphous steel cores, is that ferrite has much higher electrical resistance therefore eddy currents are minimized. But the skin depth issue is still there.

Does this mean that to make a practical Mhz range ferrite core that is of larger size in order to have a wide airgap, one would need to make "ferrite laminations" ? Like I imagine taking a very thin plastic tape and rolling ferrite powder on it to create a ferrite strip , well you get the idea.

Does this also mean that practical size monolithic ferrite cores cannot work much past the hundreds of Khz range of frequencies due to skin depth limitations?

 

[Baluncore]

Does this mean that such ferrite core , most material inside it never sees a magnetic field rendering it useless/wasted material/space?

No. Only the size of the ferrite powder is critical. The ceramic or polymer binder provides access to the magnetic material at about half the speed of light.

The separation between magnetic particles can be 10% of the grain size, just like how the oxide insulation between transformer laminations can be thinner than the laminations.

 

[FusionJim]

Ok , so for the sake of education, in order for me to get this right. Say we have a coil around a ferrite core, The coil is within the size of the wavelength, I drive the coil with say 1 Ghz current, there is a skin depth to the magnetic field at any frequency right? So say the skin depth (just a random number for example) is 100 microns, but my core is a cylinder of 20mm diameter, how deep will the field get and what will be the "wasted" area/radius where there will be almost no field ?


I ask this also because , again numbers just for example, say I want to create a axially symmetrical airgap that has a diameter of 200mm , I take two ferrite toroids, and add "U" shaped ferrite cores around the toroid circumference with regular intervals, my excitation coils are located on the "U" shaped cores, the field is closed through the U shape cores in through the toroid discs that spread out the field s that the airgap between the two toroid discs has a roughly homogeneous field.
Now , let's say I drive the coils around the circumference U shaped cores with 1 Ghz, each coil is smaller than the wavelength so the field in the U core center is homogeneous and , now does the magnetic path length for a magnetic field within a core also has the same wavelength limit that a current within a coil, where if the coil gets large enough in length and diameter over the wavelength that current within the coils starts to experience cancellation from place to place?
In other words , antennas and coils have this "electrical length" , does it also apply to a magnetic field guided by a core on which the coil sits?

 

[Baluncore]

So say the skin depth (just a random number for example) is 100 microns, but my core is a cylinder of 20mm diameter, how deep will the field get and what will be the "wasted" area/radius where there will be almost no field ?

The field will pass through the entire 20 mm core, propagating through the ceramic binder, between the ferrite particles.
If the ferrite particles are smaller than 200 um, then no ferrite will be wasted as inaccessible.
There may be more binder than is required, so it might have been made as a more compact core, with the same magnetic material and properties. That would need less wire for the coil.

 

[Baluncore]

Now , let's say I drive the coils around the circumference U shaped cores with 1 Ghz, each coil is smaller than the wavelength ...

I would expect a coil driven at 1 GHz, to be only one turn, of less than 10 mm diameter. If the coil had more turns, or was bigger than that, the inductance would be so high, that the coil current would be limited, to the point where there was less magnetic field.

 

[FusionJim]

I would expect a coil driven at 1 GHz, to be only one turn, of less than 10 mm diameter. If the coil had more turns, or was bigger than that, the inductance would be so high, that the coil current would be limited, to the point where there was less magnetic field.

Well, the 1Ghz was just an example, given this is a shed hobby project i'd be happy to see it work with something like 500Khz - 3Mhz. Would work like a crude high frequency generator.

As for the 1 Ghz example, sure 1 turn would probably be enough, but wouldnt making multiple turns all in parallel decrease inductance? Inductors in parallel roughly halve inductance, i would suppose that still holds true in RF range of frequencies, does it not?

 

[Baluncore]

Inductors in parallel roughly halve inductance, i would suppose that still holds true in RF range of frequencies, does it not?

Inductors in parallel or series have a reduced or increased inductance respectively, but that assumes there is no coupling of their magnetic fields.

An n turn coil that couples the magnetic field n*n ways, has the inductance increased by n².

 

[FusionJim]

Inductors in parallel or series have a reduced or increased inductance respectively, but that assumes there is no coupling of their magnetic fields.

An n turn coil that couples the magnetic field n*n ways, has the inductance increased by n².

So are you saying that if the different coils share the same core then creating say 5 turns in series would have the same inductance as having 5 individual 1turn loops all in parallel?

 

[Baluncore]

So are you saying that if the different coils share the same core then creating say 5 turns in series would have the same inductance as having 5 individual 1turn loops all in parallel?

No.
5 turns in series on one core will have 25 times the inductance of one turn.

 

[FusionJim]

No.
5 turns in series on one core will have 25 times the inductance of one turn.

No, i was comparing 5 turns in series with 5x1 individual turns, both cases coils on same core, the 5 parallel single turn coils should have lower inductance than 5 series turn coil?

 

[berkeman]

No, i was comparing 5 turns in series with 5x1 individual turns, both cases coils on same core, the 5 parallel single turn coils should have lower inductance than 5 series turn coil?

If you connect 5 turns in parallel, that will just be like a single turn but with a lower resistance (the wire resistances are in parallel, so it's like a thicker single wire). 5 turns in series will have 25x the inductance of that single turn (or 5 in parallel), since as @Baluncore says the inductance scales with the number of turns squared.

 

[Baluncore]

A picture is worth one thousand words.
It is difficult to describe circuits precisely, in text, but I will give it a try.

Five turns, in electrical parallel, all on the same core, is the same as one turn on that core, but wound with a thicker wire.

5 turns, in electrical parallel, on separated cores, without inter-coupling, is equivalent to 1/5 of the inductance of one turn, because the voltage is the same across all, but the current will flow along five separate paths without cross-coupling.

5 turns, wound in electrical series, all on the same core, will have 5 times the wire resistance, and 25 times the inductance.

5 turns, in electrical series, but on separated cores, without inter-coupling, is equivalent to 5 times the inductance of one turn, because the current is the same, but the same voltage will appear across each of the 5 turns, without self coupling.

 

[FusionJim]

I got bit confused, but you explained it well, thanks @Baluncore i understood everything. The best way to decrease inductance then is to have a large cross sectional wire spread out across non coupled parallel inductors

 

[FusionJim]

@Baluncore two more questions, imagine you have two rectangular cores each having one turn coil on them, as long as the cores are physically separated there is no mutual inductance and if both coils are connected in parallel the inductance should be halved. What happens if the two cores are physically connected through the opposite "leg" of the core, the one that is directly opposite to the one on which the coil is located? Technically each coil still closes it's magnetic flux through the closest path and the two paths should not intersect much?
I myself would think there might be some complex interaction where the total inductance would be less than halved compared to the completely physically separated cores, correct?


The other question is about wavelength and core/coil size, now imagine that I have two toroids separated by an airgap, the toroids have equally spaced U shaped cores on their outer periphery , the U shaped cores have coils on them and the coils are electrically short compared to the wavelength of current through them. But the total magnetic path that goes through each U core then through the toroid across the airgap through the second toroid and back into the U core is larger than the wavelength of current through the coil, would this result in the magnetic flux not being homogeneous and equal across the airgap between the toroids? Or does it only depends on the coil/current and not the magnetic flux through a core?
because if a conductor rotates in the airgap , the conductor electrons should feel a VxB force aka Lorentz force, what if this rotating conductor rotates in a magnetic flux with frequency shorter than the electrical length of the rotating conductor, does the conductor in this case still produce a current that is coherent in one direction?

 

[Baluncore]

Technically each coil still closes it's magnetic flux through the closest path and the two paths should not intersect much?

The intersection of the two inductor's fields, is a coupling coefficient. The inductors are not isolated, they are no longer discrete. You will need to analyse and model that situation numerically.

Or does it only depends on the coil/current and not the magnetic flux through a core?

If the size of the core is anywhere near the wavelength, then, when it comes to discrete components, all bets are off. If the components are no longer discrete, a postmodernist essay will not suffice to describe the situation.

No matter how simple or complex a system you can imagine, you will have to go all the way back to first principles to analyse the situation. That requires drawings and documentation. Keep it simple.

 

[FusionJim]

If the size of the core is anywhere near the wavelength, then, when it comes to discrete components, all bets are off. If the components are no longer discrete, a postmodernist essay will not suffice to describe the situation.

No matter how simple or complex a system you can imagine, you will have to go all the way back to first principles to analyse the situation. That requires drawings and documentation. Keep it simple.

Let me see if I got your message. So your saying the core magnetic flux path lenght is not as easily describable as the coil current behavior when it comes to both of the reaching the wavelength or beyond?

 

[Baluncore]

When objects reach about λ/10 of the operating wavelength, they begin to do weird things. For example, a grounded post λ/4 long, looks like an insulator, while an open-stub at λ/4, looks like a ground. If you cannot analyse that, or explain it using a Smith Chart, you should not be coming up with these hypothetical scenarios, that are more like minefields.

There is no way I can be sure I understand what you are thinking.
I am saying that without a diagram, you don't stand a chance.

 

[FusionJim]

When objects reach about λ/10 of the operating wavelength, they begin to do weird things. For example, a grounded post λ/4 long, looks like an insulator, while an open-stub at λ/4, looks like a ground. If you cannot analyse that, or explain it using a Smith Chart, you should not be coming up with these hypothetical scenarios, that are more like minefields.

There is no way I can be sure I understand what you are thinking.
I am saying that without a diagram, you don't stand a chance.

Well my example in its simplest form is a rectangular core where there is a coil on one leg of the core and the coil is electrically short meanwhile the core aka the magnetic flux path approaches the wavelength. My question then is, does magnetic flux within a high permeability guiding medium like a core also experiences phase shifts and flux reversals like current does within an electrically long conductor or are there other phenomena that determine flux density and direction that are different from those that determine current in conductors/antennas that are electrically long?

 

[Baluncore]

If I understand correctly, a shorted secondary turn is a fault condition. The core becomes two shorted transmission lines in parallel, each with length λ/2, which will then appear to be short at the primary, in the steady state. Throw away the shorted turn, and the core-line. You are left with a shorted primary. Cost is lowest if you replace the primary with a short to ground.

If I did not understand, draw the diagram.

Edited to fix the core t'line length transformation.