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I need an antenna that can generate a nonuniform magnetic field over a very tiny region at 5 GHz. (By nonuniform, I mean that the field vectors are diverging as much as possible. I will place this device right next to my 0.5 mm crystal, so near-field is fine.) I want it to be as nonuniform as possible.

More specifically, I want nonuniform radiation to be generated in a 1 mm sphere near the antenna, which I can place as close as possible.

For example, with a loop antenna:

enter image description here
(adapted from original image at HyperPhysics - Magnetic Field of Current Loop)

But to get a nonuniform field, then I'd need a loop that's tinier than 0.5 mm, which seems challenging to construct by hand. For example, just to visualize it:

enter image description here
(adapted from original image at HyperPhysics - Magnetic Field of Current Loop)

Is there a simple way that this can be done? (for example maybe little "microloop antenna" or some "microcoil" or some type of unusual antenna).

I want a nonuniform field to talk to different "modes" of a YIG crystal.

The explanation is unfortunately pretty technical, related to this paper. I want to excite some crystal that can only be excited if it experiences a nonuniform magnetic field.

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    \$\begingroup\$ until you added the wavelength, it really was unclear, because the key design aspect – size of wavelength compared to size of uniform region – was left unclear. Now, however, I'm a bit surprised: 5 GHz is surprisingly low for you to ask this question: The wavelength of 5 GHz in free space is 6cm, so 120 times the size of the region you need things to be uniform. So, any antenna that is not extremely directive will do, which means you must have specific requirements that wouldn't even be fulfilled by a simple dipole, or you would have used that. Can you please put numbers on the uniformity you \$\endgroup\$ Commented Jun 13 at 8:53
  • \$\begingroup\$ need? This seems to be the other core design spec you're missing. (please, you're the one obviously working with EM here, nobody else would have requirements for a uniform field strength at 5 GHz, so we must assume you're well-versed in at least the basics. I'm surprised I have to still ask you for key requirement specs, the second time! Please give us a somewhat complete description of your problem!) \$\endgroup\$ Commented Jun 13 at 8:54
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    \$\begingroup\$ Why magnetic field? Nonlinear in what way? In what respect will it "radiate"? (You seem to be asking about a near-field environment, which makes far-field radiation irrelevant. All the more reason we need to ask clarification.) What load will be placed within the active region? \$\endgroup\$ Commented Jun 13 at 9:11
  • \$\begingroup\$ Try looking up anti-Helmholtz coils. The anti bit is important. Then you don't need to create such small coils to get a localized non-uniformity. \$\endgroup\$
    – Andy aka
    Commented Jun 13 at 9:42
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    \$\begingroup\$ @MarcusMüller, my attempt to do this antenna thing is specifically to avoid putting anything in a cavity. And I'm honestly not so sure if the center needs to be zero. I think it might be fine without that, but I'm not confident. \$\endgroup\$ Commented Jun 13 at 13:12

2 Answers 2

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I believe that anti-Helmholtz coils will likely service your needs: -

enter image description here

The beauty of this type of coil is that you can make the coils bigger than the target (more practical) and still get a steep field gradient near the centre.

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  • \$\begingroup\$ Thanks for your answer. I can try to simulate it myself of course, but a discussion of what the field lines look in a tiny area for reasonably sized coils would be helpful. For example if I have 1cm coils, if I put my sphere in the middle of these field lines, I'll still get a reasonably sized magnetic field? or perhaps the value of the magnetic field near the turning point is approximately zero in a 1mm area. \$\endgroup\$ Commented Jun 13 at 13:20
  • \$\begingroup\$ @StevenSagona this is easily simulated in a 2D solver like QuickField. If you drew a vertical line in the centre of the anti-Helmholtz image, the B-field would be zero. Moving left or right of that line will have a steep gradient of B-field. The B-field is proportional to current so, if you can create one hundred amps there will be ten times more B-field than 10 amps. I don't know what is reasonable for you in this respect. \$\endgroup\$
    – Andy aka
    Commented Jun 13 at 13:49
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A, more of a comment than an answer, but you may find the perspective useful.

What you are doing, is coupling into various field modes of the crystal.

Magnetic or electric field intensity is irrelevant; the levels simply are whatever they are, and proportional to signal level, which you are in complete control of. The ratio is more important (impedance), though that's somewhat prescribed by the choice of coupling (inductive, low impedance perhaps).

The magnitude of coupling, may not matter very much either -- depends on the Q of the resonance itself (probably quite high), and the desired Q of the system.

Presumably you're coupling to this as a one-port, so you will measure some dip, with the depth of the notch determined by matching, and the width determined by Q and coupling. A nearby terminator, and return loss bridge, may prove helpful, viewing the notches as peaks instead.

The remaining question is: how much, and of what modes, can you couple to?

With a single coil around the crystal (equatorially), you couple to the dominant odd modes aligned to the coil axis. Likewise for a pair of coils in a balanced, same-polarity (Helmholtz) configuration.

With two balanced coils but opposing phase, you couple to the even modes.

With a single coil off-side, you couple to both, and will find a richer spectrum. It's not clear if this is any value to you, but, if you just want to see modes, perhaps it's the better plan?

Note that, particularly for a single-coil configuration, but also for balanced configurations that aren't perfectly mechanically balanced, including of any nearby geometry, there will be some nonuniformity that perturbs modes on other axes. These can couple strongly enough to cause pole splitting and thus the frequencies seem unexpected or multiplied, but more likely they will be shallow notches that vary in magnitude as you nudge the crystal around.

Note that, at these frequencies, 1/4 wavelength adds up very quickly, so you'll need to make these small loop-ended hairpins of very similar length, and wire them to the transmission line symmetrically (or anti-symmetrically, as the case may be). The spacing between leads should be minimal to reduce stray fields; a thin PCB with symmetrical microstrip might be feasible, with the ring(s) cut from a helix, formed to shape and soldered onto pads as butt joints.

You'll still have resonances due to the apparatus itself, as the hairpins act as resonant stubs, and imperfect balance couples into them. You might want to calibrate the fixture as-is, then introduce the crystal and see how it changes. Mind that presence of the crystal will subtly shift the fixture resonances.

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