Coil larger than wavelength

[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 wavelenght 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 wavelenght 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 wavelenght 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 wavelenght) 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 wavelenght 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 wavelenght 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.