Transformer under an external magnetic field.

[carllacan]

What happens to the current through a transformer windings if the whole system is under a uniform magnetic field in the direction of the coils and with frequency equal to that of the AC in current?

I think the current induced in the primary solenoid should generate a field that would make up for the current induced in the other secondary, and my calculactions agree on this, but I'm not sure. Would the field alter in any way the relation between the in and out currents?

Thank you for your time.

 

[anorlunda]

Are you considering saturation of the core?

 

[carllacan]

Are you considering saturation of the core?

No, for the moment I'm working with a simple model with just two solenoids side by side. I guess you mean that even if it doesn't induce any currents it can still saturate the core and reduce the output current, correct?

That's an interesting possibility. However I am more interested in finding ways that the field could couple to the currents. This is a real-life problem, actually: I have a transformer that seems to be sensitive to 1 kHz magnetic fields (I said the field had the same frequency as the input, but that was a mistake). So I want to find out how this could be happening.

 

[anorlunda]

Your description reminded me of an old fashioned device called the magnetic amplifier. It used an external field to saturate the core and thus modulate the transfer function of a transformer. https://en.wikipedia.org/wiki/Magnetic_amplifier Typically the external field was DC, but it could be AC also.

Your revised description in #3 also sounds like a multi-winding transformer. Transformers are not limited to two windings.

If you are investigating a real life problem with a simplified model, and if the problem is because of an effect you simplified away, then the model approach will fail.

What experiments can you think of, other than modeling, that could illuminate the problem? Let's see if other PF members might suggest troubleshooting experiments. ping @berkeman , @jim hardy , @Baluncore , @CWatters

 

[carllacan]

I have run a number of experiments, but none has shed any light on the matter. I have this set of three 2-winding transformers side-by-side, and when I apply a 1 kHz field on them the current through their windings increases, independent of other currents.

The transformer directly under the antenna's center shows the strongest current, which discards the hypothesis that the field is getting coupled to something other than the transformers, like another loop in the circuit.

When I apply fields with frequencies a little different the currents are smaller, and if I graph current vs frequency I get a Lorentzian curve. This suggests there's a resonance in an RCL circuit somewhere, but I've taken away the decoupling caps and the effect persists. There are no other reactive components that can form a resonance together with the transformer's coils.

Applying the field sideways doesn't create any current. It's only when the field is entering in the direction of the coils. That's why I was asking if it is theoretically possible for an external field to induce currents in the same way the primary coil induces a current in the secondary coil, which according to my calculations it doesn't. This is how I got to that conclusion, parting from a basic 2-solenoid transformer like you see in high-school physics, like this:

plus a downward-pointing uniform AC magnetic field:

The external flux is going to induce a current in the primary equal to
$$ I = \frac{\Phi_E}{N_1} $$
and in a sense contrary to the incoming current I1 (assuming the first coil is winded clockwise as seen from above). The total current through the primary coil will therefore create a magnetic flux equal to:
$$ \Phi_1 = N_1 ( I_1 - \frac{\Phi_E}{N_1} ) = N_1 I_1 - \Phi_E $$
The flux going into the secondary coil is the flux generated by the primary coil plus the external flux, so
$$ \Phi_2 = N_1 I_1 - \Phi_E + \Phi_E = N_1 I_1 $$
And therefore the currents will get transformed as if the external field wasn't there, i.e. a current will appear in the secondary coil that will create the Φ_2L flux equal but opposite to Φ₂:
$$ I_2 N_2 = N_1 I_1$$
$$ I_2 = \frac{N_1}{N_2} I_1 $$

Of course I haven't put any thought into whether the external field might be saturating the core. Would this effect be frequency-dependent?

Thank you for your time. I understand if the rules mean you'll only be helping me with the theoretical question and not with the practical side of what to do from there.

 

[jim hardy]

Let's see if other PF members might suggest troubleshooting experiments. ping @berkeman , @jim hardy , @Baluncore , @CWatters

I think in pictures , and slowly.

Seems to me you're postulating this:

Without ascribing numbers,
your external 1khz flux will induce into each winding a 1khz voltage, NdΦ_1khz/dt, adding to the voltage already there from V1
and additional currents will result .
The additional current in left coil will be (NdΦ_1khz/dt) / (impedance of source V1) and remember voltage sources have low impedance.
The additional current in right coil will be (NdΦ_1khz/dt) / (impedance of load Z) .
I doubt the external 1khz flux would split evenly between left and right paths because of counter-mmf's from the unequal 1khz currents added to I1 and I2.
So you'll need to write simultaneous equations or spiral in on the numbers by iteration.

There's an approach ?

old jim

 

[jim hardy]

@ anorlunda asked about an experimental approach...:

1. Remove V1 and the load. Measure the voltages induced in each winding by external field..
2. Reconnect the load, and connect in place of V1 an impedance that approximates V1's thevenin resistance. Measure voltage and current in each winding.

By superposition principle do you now have a pretty good guess at the effect of your external field?

old jim

 

[256bits]

There are no other reactive components that can form a resonance together with the transformer's coils.

There is self resonance for coils.
But the 1kHz frequency seems to be quite a bit low for that effect to show up.

 

[anorlunda]

The transformer directly under the antenna's center

You use the word antenna. Do you mean that you have a RF antenna with a signal modulated at 1kHz?

 

[carllacan]

@jim hardy Thank you very much for your input. For the sake of simplicity I ignored Faraday's law and used the current equations. I hoped there would be a clear-cut answer for this problem, but I see I was being naive. In any case the question I was interested in was whether it is possible, in principle, for an external magnetic field to induce currents in the transformer's windings, and it looks like it's definitely possible. Specially in a real-world, non symmetrical situation.

I don't see how that experimental procedure would help, though, since I can already quantify the effect of the field by simply turning it on and off and comparing measures. Perhaps I've misunderstood something.

Again, thanks!

 

[carllacan]

You use the word antenna. Do you mean that you have a RF antenna with a signal modulated at 1kHz?

Yes. A function generator plus an audio amplifier plus an antenna. I made a sweep between 20 Hz and 200 kHz while I measured currents, and noticed a peak at around 1 kHz (1.2 kHz, actually).

 

[anorlunda]

Yes. A function generator plus an audio amplifier plus an antenna. I made a sweep between 20 Hz and 200 kHz while I measured currents, and noticed a peak at around 1 kHz (1.2 kHz, actually).

That is interesting. I can't imagine an antenna for such low frequencies, but radio is not my field. 1kHz is in the Ultra Low Frequency band. The wavelength is 300 km.

I suggest that your antenna can't effect the transformer unilaterally. The transformer must be effecting the antenna also. In effect, the antenna is becoming the third winding of a three-winding transformer. I also suggest that ordinary circuit analysis is inadequate. You need to solve Maxwells Equations to model what it going on.

But I'm sticking my neck out to comment at all because this stuff is far far away from my own specialty.

Ping @sophiecentaur

 

[jim hardy]

I can already quantify the effect of the field by simply turning it on and off

Sounds like an interesting apparatus. Maybe you'll post a photo ? And your measurements ?

Is your 'antenna' a coil ?
I'm guessing that 1.2khz is a frequency of interest to something connected to one of your windings. That's why i suggested disconnecting them.

 

[slow]

Hi. Without to specify the main conditions of the transformer's design is too difficult to achieve an approach. For example, is the transformer constructed with full symmetry, with both windings totally equal, and a core that it's shape give two symetric sides? In other words, a design where only we choose what will be primary and what secondary, because all is symetric. If this is the case, the resonance behavior depends on two instances. If not, the unique instance is the resonance of the whole transformer when the external field is present.

 

[slow]

Have you measured how much power you provide to the primary and how much you obtain on the secodary?

 

[carllacan]

Thank you all for your answers. I will try what you proposed as soon as I can.

 

[slow]

Hi. You have observed that the resonance frequency is independent of all, but the transformer. If you make mathematical develope using circuits theory, with complex variable (j=√-1) , you see easyly that between the two points where are connected the load, coupling capacitor and/or inductors, etc. , when resonance condition is stablished, the transformer exhibit between that points an impedance equal to zero. So, no element around the transformer can modify the self resonance frequency. If you are interested, I want propose a new experiment, at least to know if it have somethig in common with your arrange of transformer and "antenna". All we, the first time to see the Tesla's pankake coil, do not think on the trick for achieve a low self-resonance frequency. What if you use a copper tape replacing the copper wire? Let say, you buy a pretty roll of copper tape and, with it, you make a bifilar Tesla coil. See the famous picture where Nikola Tesla is reading a book while a lot af lightings fill the room. Behind Nikola you can see an enormous coil. The angle used to take the photo not allow to know if the coil was maked with a wire or with a copper tape. This second case allows to diminish enough the self resonance frequency, because increase the distributed own capacity of the coil. The bifilar spiral coil is the best to achieve a very low inductance. Low inductance means, in bad but few words, grand current in the coil and tiny value of the magnetic field produced by the coil. Allways works, in all circumstances, the electromagnetic reversibility? If the answer were yes, you can create near such a coil an alternating magnetic field, with frequency equal to the coil self-resonance frequency, and a tiny value (tiny amplitude). What is your expectation? Believe you that the coil will provide a big current to a load cnnected between the two extremes of the coil? Yes, this requires to explain how the system does not violate energy conservation. But this is a problem for theoreticians, and you are making experiments. If both experiments, the multiple-transformers arrange, and the roll-like bifilar coil excited by a alternating magnetic field with little value, have the same behavior, then you have solved a good part of the mistery.

 

[carllacan]

That is interesting. I can't imagine an antenna for such low frequencies, but radio is not my field. 1kHz is in the Ultra Low Frequency band. The wavelength is 300 km.

I suggest that your antenna can't effect the transformer unilaterally. The transformer must be effecting the antenna also. In effect, the antenna is becoming the third winding of a three-winding transformer. I also suggest that ordinary circuit analysis is inadequate. You need to solve Maxwells Equations to model what it going on.

But I'm sticking my neck out to comment at all because this stuff is far far away from my own specialty.

Ping @sophiecentaur

Reasonings that compare sizes of antennas and wavelengths always confuse me a little. I know wavelength is important in waveguide theory and diffraction, but I don't see how it relates to antennas (maybe it's very basic, but I haven't studied antenna theory yet). I mean, my antenna is a coil, and a current passing through it creates a magnetic field. If the frequency of the current is 1 kHz then the magnitude of the field will change with frequency 1 kHz. The current induced, which depends on the magnitude of the field, will also oscillate with frequency 1 kHz. The wavelength of this oscillating magnetic field will be huge, sure, but why would the emitting or receiving devices have to be of a certain size to interact with it?

 

[slow]

Hi. Take in account that for a wavelenght of 300 Km, a few meters between antenna and transformers means very near field, where the phenomena can include some longitudinal components. If this were the case, seems non relevant to think in terms of wavelenght.

 

[jim hardy]

Reasonings that compare sizes of antennas and wavelengths always confuse me a little. I know wavelength is important in waveguide theory and diffraction, but I don't see how it relates to antennas (maybe it's very basic, but I haven't studied antenna theory yet).

I think anorlunda's point was that a wire doesn't act like an antenna until it reaches a sizeable fraction of a wavelength, like one-quarter.
So for a tabletop sized experiment you probably should consider your coil an inductor not a traditional long wire or dipole antenna.

 

[carllacan]

Oh, I see. I was considering the coil as a coil, but I was using the word antenna because at the end of the day it is something that emits EM waves. I suppose they are actually different things, then.

 

[jim hardy]

Oh, I see. I was considering the coil as a coil, but I was using the word antenna because at the end of the day it is something that emits EM waves. I suppose they are actually different things, then.

I understood what you meant.
It's just a limitation of language , we use words to paint a picture of what's in our mind.
But we cannot know what picture our words painted in the listener's mind. His 'word processor' is programmed differently.

So we go back and forth, spiraling in on mutual understanding. Precise wording takes a lot of effort..