coil design for 1MHz Magnetic field

What capacitance are you using? Is the LC resonant such that:

Freq = 1/(2 pi sqrt(LC))

Are your impedences matched for max power transfer? (Zin=Zout )

Zc = 1 / 2 pi f C ZL = 2 pi f L

Zout will be the series or parallel combination of Zc and ZL depending on the circuit

better yet use the phasor notation:

Zin is the standard 50 ohm.

Because I need to ensure the magnetic field to be about 100 Oe, I wound the coil accordingly first, measured the inductance at a lower frequency (the equipment can't go up to 1 MHz) then drew the LC circuit diagram. Then determined C value according to impedance match. I actually also analized the transmission and reflection using a network analyzer. Is this the usual routine for designing stuff like that? If so, how would I be able to improve the performance and ultimately get the magnetic field required for further experimentation.

Perhaps it will help you to know that in a coil about 1cm ID and 1cm long at 1MHz, you should not expect to achieve a Q greater than about

1. Assume for a moment that you achieve Q = 30. That means that when you pump 5 watts into it, so the coil is actually dissipating 5 watts (almost all as heat), the energy stored in the coil will be 30 times the energy lost per radian. That, along with the coil's inductance, will let you find the RMS current in the coil. That, along with the number of turns, should let you find the magnetic field intensity. In addition, note that if the Q is indeed 30, and if you want to drive it through a capacitor at series resonance, the coil's reactance at 1MHz should be 30*50 ohms, or 1500 ohms. That implies a 239uH coil and a

106pF capacitor. That may be an inconveniently large inductance -- lots of turns. You can just as well use a much lower inductance coil with fewer turns, driven through a matching network. I would expect the field strength to be independent of the inductance of the coil, for a given energy stored in the coil tank circuit and a given coil geometry, since the energy is stored in the magnetic field. For example, a 23.9uH coil with 5 ohms RF resistance at 1MHz can be matched to 50 ohms using a series capacitance a bit less than 1.2nF, and a shunt capacitance across the source of a bit less than 10nF. Note that the tuning will be quite sharp! You need a way to know when you've properly adjusted the matching capacitors to present the proper load to your source.

Finally, note that 5 watts dissipated in such a small coil will make it get pretty hot! Be sure to provide a way to remove the heat, if you really need to drive it with such high power to achieve the desired field strength. (I leave all the field strength calcs to you...that's a domain I don't deal with if I don't have to, but the electrical part is easy.)

Cheers, Tom

At 1MHz the skin depth, 1/sqrt(omega*sigma*u/2), for Cu at 20 degree Celsius is 66u. So to get a high Q use a thin wire or a Litz-wire. And keep it cool. There is a free as in GPL computer program to optimize air coils at

You can find more on the skin effect at my page below.

--
Sven Wilhelmsson
http://home.swipnet.se/swi

Hello qiuie,

May not apply to what you are searching for, but there might be something in it you did not think of.

To small for what? Are we talking "Philadelphia Experiment" energy?

I show how to make an excellent #30 gauge wire coil 1" dia (2.5 cm), on my webpage to use in theremin design & research. With a 100 pf capacitor in parallel it tunes in at 1 mhz.

The design could be improved upon to better fit your needs and it would have good heat dissipation.

Less than one milli-amp drives my LC circuit and yet it can sense body proximity over six feet away. This shows how a magnetic field reaches out with very little power. Remarkable phenomena.

Just pump up the energy driving the LC, no telling what you would have. Your own neighborhood AM radio station or an out of the body experience.

Good Luck,

• * * Christopher

Temecula CA.USA

what happened to those charged capacitors, that you had floating around?

martin

Thanks, Sven, for the pointer to WCalc. It's one I hadn't run across before, and looks to be quite useful, especially in the variety of front ends to interface with other programs.

However, I don't understand your comment about "use thin wire." Surely for a single-layer solenoid, you can mitigate the proximity effect by using wire fine enough that you don't need to wind it close-spaced, but beyond that, for a given number of turns in a given length, finer wire increases the RF resistance and lowers the Q. And similarly, if you maintain a particular spacing in terms of the wire diameter, using thinner wire lets you get more turns, but the Q is practically unaffected. That's based on rules of thumb I've used for a long time, as well as on the results reported by WCalc and a couple other programs I trust for Q calculations.

I do agree that you can get higher Q by using Litz wire at frequencies between about 10kHz and 2MHz, for most practical coils. An engineer I used to work with managed by very careful design to make a 1MHz tank circuit with coils about 3cm diameter with a Q up around 300--higher than most experts would think possible, but I'm quite sure that was indeed the case.

Also, for the original poster, the coil Q I suggested in my earlier posting is slightly higher than what WCalc thinks you'll be able to do, but not too different. However, if you're using the coil to excite some material with a magnetic field, that material may lower the Q, and perhaps considerably. If it has high permeability, it will also increase the coil's inductance. Beware of those effects. You'd do well to use some equipment to make sure you have your matching network tuned properly, and the tuning will be rather sharp.

Cheers, Tom

They are still self-discharging, in a little cardboard box down in the basement. I haven't touched them for at least a couple years now. Perhaps it's time for another measurement?

Cheers, Tom

I agree, I've acheived Qs in the 300 region at 1MHz using litz wire.

I threw together (on paper) a small coil made with my largest litz, which is the size of #10 AWG, about 0.1" in diameter. I used 12 turns, five on the bottom layer with a 0.2" bore, then four on that and three on the third layer. Calculating the inductance for each layer and adding, I get 0.42uH. This has a reactance of 2.6 ohms at 1MHz, and resonates with 60nF (see below). The parallel L-C can be connected directly to the 50-ohm coax and if its Q is 50 or higher, its effective impedance will be higher than 50 ohms. Full matching at f_LC, if desired, can be had by adding some parallel resistance.

This 12-turn coil will yield 0.01T of field with 10A peak flowing, which corresponds to V = I sqrt L/C = 26V peak across the L-C. As it happens, that's just a tad higher than 5W at 50 ohms, but since the power loss is about 1.3W, qiuie yli can get his desired field with less than 5W by driving to a winding tap down on the coil.

0.42uH with #10 wire and 60nF aren't common values for RF work, most would start with smaller wire and more turns, N. While this is fine, it'll mean lower resonator currents and higher voltages. For a fixed magnetic field, current I goes by 1/N and hence by 1/L^2, and voltage V goes by N. And the resonate load impedance goes by N^2. One can use taps on the coil to match the 50-ohm source, or a coupling coil with fewer turns, or break the resonating capacitor into two series portions, with the larger one on the bottom.

Tuning a 1-MHz L-C resonator made with a low L and a high C can be a problem, because the capacitance values are so high. If the 1MHz 50-ohm source is below the center frequency the tuned resonator looks inductive, if above it looks capacitive. In either off-center case the current is not phase with the voltage. This may not be a very critical issue at low power levels and with a resonator loss that's much less than the power available. But for the HV RF systems I've made, which work to 10kV and use up to 250W, the tuning is critical. I use a simple current transformer and a capacitive voltage divider along with some circuits on a PCB to monitor the current and voltage magnitudes and the tuning phase on panel meters. A next step could be to use the phase voltage to make a servo-controlled tuner.

Back to qiuie yli's problem. The tuning issue could become a strong driving force pushing toward a many-turn coil with enough inductance to allow for small capacitors. But this might be an opportunity to explore variometer concepts for a simple inductance-tuning solution.

--
 Thanks,
    - Win

I like that program, so lets do what we can to make it perfect!

Your observation is certainly correct, however I had a multilayer coil in mind.

I guess a single layer coil would need some sophisticated cooling to reach

100 oe at 1MHz. (> 8 Ampere-Turns per mm coil length)

To make a high Q multilayer coil is an art in itself. I'm thinking of a multilayer coil where each layer is individually fed through an individual series capacitor in such a way that the current gets equally distributed among layers. In such a design a thin wire can be used. Using a Litz-wire is a related technique.

You can not just connect layers in series because the resonance frequency drops. I do not have to elaborate that one to experts :-)

--
Sven Wilhelmsson
http://home.swipnet.se/swi

Thanks to both Win and Sven for their comments.

Going further with Win's idea, there are practical ways to make a tuneable matching network. But you'll want to be sure to use a high Q capacitor for that 60nF part. I suspect that polypropylenes intended for use in switching power supplies will work well there, and it's also entirely possible to make up such a capacitance using C0G ceramics. Assuming the coil (with whatever it's exciting inside) provides a stable inductance, you won't need much tuning range, and a large compression mica cap might be just the ticket. I have some that have

If you know the coil's inductance and Q -- inductance pretty accurately, and Q at least in the ballpark -- you should be able to design a matching network that will not be difficult to tune, and if your RF generator can be tuned in frequency slightly, that may make the adjustment much easier. A couple ways to do it (there are many): you can parallel-resonate the coil with a capacitance and then feed that parallel-tuned tank with an "L" network consisting of a shunt capacitance at the coil and a series inductance to the RF generator. That series coil can be physically larger than the sample coil, so that its Q can be much higher and it won't waste too much RF power. That arrangement should be fairly easy to tune, and in fact the shunt capacitor can be partially absorbed into the fixed capacitance across the sample coil. -- A second way to do it that isn't as easily adjustable unless you have some pretty large variable capacitors is to tap the RF feed down on the resonating capacitance, so you have a capacitance in series between the coil and the RF generator, and another capacitor shunt across the RF generator output. That does have the advantage of not needing any other coil. -- A third way is to resonate the coil with a shunt capacitor that's a little too small, e.g. 59nF instead of 60. Then you can feed that with a series capacitance from the generator and a shunt capacitance across the generator, and the values for those caps are much smaller. They have limited ability to adjust the matching, but if the coil is stable, that should be OK.

Also, for tuning over a very limited range, akin to Win's variometer suggestion, you can just make the turns separation of your coil variable. This assumes that you've trimmed the capacitor(s) to very nearly the right value. But changing the frequency of the generator would have the same effect, and probably be much easier (if it's allowed).

Cheers, Tom

Thanks so much for all the suggestions and insights and education. I can't say enough thanks.

But it did take me quite a while to digest all the materials. And here are a few more questions?

As Sven has put it, I need to use thin wire considering the skin effect at 1MHz (66u for copper at 20 C) to get a high Q. But in Win's high-Q coil, he used a rather thick wire, (#10AWG). Although that was Litz wire. So is it safe to assume both cases are actually more or less similar?

Again in Win's post, I don't quite understand what is a winding tap?

thanks very much again

You're very welcome. What are you working on?

I'd say no, not at all. The skin-depth effect says conduction will be in the outer 0.0026" of a wire (#36) at 1MHz, and most of the current flows in the wire's circumference. However, you do still gain from using big wires with greater circumference. A small wire would make sense only if a number of them were used in parallel, all insulated from each other. But you'll still get into trouble from a related problem in coils, called proximity effect, which will mean the inner wires in a bundle won't carry much current. A good solution is to weave the small wires; but that's what litz wire does.

Since you don't need really high Qs (which requires careful tuning don't forget), you may get reasonable results with ordinary wire. You can also try hand weaving small wire (#26, etc) to get some quick improvement. I'd be pleased to give you some litz wire if you like. In addition to the big 0.10" stuff, I also have 0.039" dia litz, so you could try making small coils with more turns.

At high frequencies improvement comes from keeping turns apart, but this is usually not an issue at 1MHz. However, if you wind layers back and forth on top of each other, this is bad. Instead I use a method Terman called bank winding. This is a bit tricky to do when winding by hand, but you can manage or you can machine a small coil form to help hold the wire as you wind on the form.

One end of the coil is at ground, and the other is your output, with the parallel capacitor. The tap is a connection part way up the coil from the ground end, say 4 turns up, or whatever. Same idea when dividing the capacitance into two parts.

--
 Thanks,
    - Win

I'm working on some heating project. Basically, I have some magnetic particles, and they creat heat as their magnetization revolves around or follows the direction of the external AC magnetic field. It's heated more or less the same way as a ferrite core of a electro-magnet does, just the frequency is much higher, which is kinda necessary for small particles to generate sizable amount of heat. Also the heat generated by the small magnetic particles is proportional to the square of magnetic field strength, and that is why I need a high enough magnetic field, say 100 Oe. By the way, is there any apparatus that can measure magnetic field at such high frequency? I have a gaussmeter, which can only go up to 100 Hz or something.

I'm aiming at 1 MHz for the moment. But I might need to go for higher frequency in the future. I guess high-Q is not quite necessary for the moment, as long as the current flowing through the coil is large enough to give me the desired magnetic field. But I'm not sure if improving Q will improve the current level much more significantly than I guessed?

thanks so much. I really didn't expect so much help from so many experts.

just thought of another question.

as I mentioned in my last post, for the purpose of getting enough heat from magnetic particles, I need a high magnetic field strength as well as a uniform magnetic field throughout the space where the magnetic particles are placed. In that sense, is it better to have more turns? But then the inductance would get larger, then need more wire to wind the coil, then resistance of the coil getting larger, then the current running through the coil will decrease, then the magnetic field will decrease as well. Is there an easy way to find out the optimal conditions? It;s so over my head.

It's the area occupied by the turns that counts. In the old days physicists evaluated this as sheets of current flowing, without any regard to how many turns, etc., might be involved. More turns of less current, etc.,... Amp-turns.

What's the area over which you hope to have a constant field?

You may need a Helmholtz-coil configuration.

--
 Thanks,
    - Win

Depending on how large a sample you're inserting into the coil, your magnetic particles may significantly change both the inductance and the Q of the coil. You will need to allow for tuning of either the generator frequency or the matching network to allow for the resonant frequency shift, and if the Q changes enough, you may need to worry about adjusting the matching network to get maximum power transfer as well.

As Win noted, it's the number of ampere-turns that counts. Extending that thought a bit, a particular amount of energy stored in the tank circuit consisting of the coil and its resonating capacitor will yield a particular magnetic field strength, for a given overall coil geometry (diameter, length, ...). It does not matter what the coil inductance is--it does not matter how many turns it has. When the voltage across the resonating capacitor is zero, all the stored energy is in the inductor: in other words, in the magnetic field. And the stored energy at a particular frequency is proportional to the exciting power level and the Q of the tank circuit.

Continuing the power level though, assume you have a 5 watt source and you can get that 5 watts coupled into your tank circuit. Then if there is no sample inside the coil, and the capacitors have very low loss, practically all 5 watts will be dissipated in the wire of the coil. But if you put your magnetic sample in the coil and you expect it to heat up, if you would like to be dissipating 2 watts in your sample, then the coil will be dissipating only 3 watts. The power dissipated must add up to the power fed to the tank circuit. And that means that the Q will be lowered to 3/5 of what it originally was. So if you have an idea how much actual power your sample will be dissipating when you are getting the results you desire, you can estimate how much the Q will be lowered. How much power DO you expect the sample to dissipate?

As you move to higher frequencies, you'll find it easier to make the coil Q higher. The Q will go very nearly as the square root of frequency, so in your 1cm diameter coil (assuming about 1cm long), and assuming just solid copper wire, you'll go from a Q of maybe 35 at

1MHz (with no sample) to a Q of a little over 100 at 10MHz. That will make it easier to get to high field strengths, but harder to keep it tuned: a couple percent change in coil inductance as you introduce your sample will cause a signidicant change in tuning.

How big a sample do you have, relative to the coil size? How uniform do you need to keep the field? It may actually be easiest to go to a larger diameter coil and find a bit more power to excite it with, if you need to, though the larger diameter will also yield a higher Q, which will mitigate to some extent the need for more power.

Cheers, Tom

I'm not sure I understand the need for the COIL to have a high "unloaded" Q.

The specimen is going to absorb the energy and therefore lower the Q of the system which is what is desired. So getting a super high unloaded Q for the coil (without the speciem) doesn't really accomplish anything, does it?

I agree that a higher unloaded Q will provide a higher magnetic field strength WHEN THE SPECIMEN IS NOT IN PLACE....but as soon as you insert the specimen, the Q and therefore the field strength will go down.

So I think the OP has specified the problem incompletly... you need to provide a certain magnetic field strength INTO the SPECIMEN, not into empty space?

So I think more info is needed about the specimen...

Mark

Mark

It's not so bad, one merely wants to control the current in the coil, which corresponds to the field. I agree a high Q isn't very useful if the sample is highly lossy. It's only useful to reduce the required power, which doesn't look like it'll be very high anyway. I have found APEX PA09 amplifier ICs to be useful for this type of task.

--
 Thanks,
    - Win