You're resonating in circles
because while your magnetism is accurate,
it's too simple -- you need to include the Q factor of the coil itself (which draws finite power at parallel or series resonance, whatever the case may be), the coupling factor to the load, and its Q.
Load being the remotely sensed object.
This also works for induction heating (where you're not just sensing the load, but heating the shit out of it!), and for the electrostatic case (where the sensor is a Theremin, and the industrial process is dielectric heating). Any RLC circuit can be transformed L <--> C so these cases are equivalent.
Power, of course, factors out, because you're looking for a change in the coil impedance -- all that matters is that power is nonzero, otherwise there's no signal whatsoever, of course.
It doesn't quite, though, because "nonzero" is actually a quantity, not just a condition -- all circuits have a noise floor, so this determines your dynamic range, or what minimum excitation level you need for a given range. (There's good reason, after all, why RADAR transmitters have peak power in the 100s of kW!)
And noise depends on resistance, but it actually doesn't, in that, you're always looking at a signal that has some amount of resistance, and you always transform that resistance to match your sense amplifier's resistance; so again, it kind of factors out. This comes from a pair of facts: the amplifier has the least noise overall when it's connected to a source of matching impedance; and, the coil's impedance can be varied by the number of turns and size of wire (while coupling to the same magnetic field geometry).
But you do want the load resistance to be as large of a part of that signal as possible, and this means the coil Q should be high, so its resistance can be a smaller fraction of the total. (In practice, that fraction is going to be 0.9992 or something like that, but that's better than 0.99998 of the total, right?
)
There's also the matter of technique. You're considering the AC, single frequency, steady-state case. You can do transient excitation instead, in which case you're subtracting the fuckoff huge pulse from the coil's self-induction, and looking at the residual "drool", and if that is varying in subtle ways (amplitude and time constants) -- which depend upon the size, magnetism and conductivity of the load, just as the phase and amplitude varies for the steady-state case.
I guess the advantage is, you can get more information out this way. The single-frequency case has two parameters: amplitude and phase. (Or in-phase and cross-phase, or anything else equivalent; it's just polar vs. rectangular coordinates.) The information however is equivalent to sampling at multiple frequencies. If you're using an impedance bridge, then the bridge either needs to be nulled separately for each frequency, or the arms of the bridge need to be carefully matched to begin with. Once that's done though, it's the same (down to a Fourier transform, and the number of sample points feeding it) as a pulse metal detector.
Aside: chemists do this to atoms. NMR (nuclear magnetic resonance, also known as MRI when used for imaging) uses a burst of RF to excite atoms in a magnetic field, then watches them relax. Certain atoms ring down at a certain rate, so their concentration can be measured this way (with some other key facts, this is in a nutshell how MRI works). Even better, there are subtle differences in the magnetic fields around each atom, due to neighboring atoms in a given molecule; NMR analyzes the frequency response, allowing some molecular structure to be read out. Cool, huh?
So, that's very high level, but what you need to know is:
- You'll have a coil. It should be high Q at the operating frequency. The number of turns and wire gauge doesn't much matter, but this "turns ratio" can be matched to your receiver for best noise floor.
- The coil should be large, of course, so that you have good sensing depth. (There is no way to extend the sensing depth, or make it more than moderately directional, in the near field. An ordinary loop antenna is fine. To do better, you'd be looking at ground-penetrating RADAR, I guess.) I guess it also shouldn't be
too large, so you aren't picking up super deep objects that you may not be interested in, and so you have some resolution in terms of where the object might be.
- The load appears as a small change in coil impedance. This is hard to sense directly, so you want to subtract out the unloaded coil's response if possible. The usual way to do this is an impedance bridge.
- Using a differential amplifier, sense the bridge's balance; adjust phase and amplitude of the reference leg to match the coil leg, zeroing the output. Now, any imbalance should be due to signal. And you can see which phase and amplitude it has, relative to the excitation: if it's leading, the load is probably low resistance (copper, silver, gold?); lagging, magnetic (steel, rust, rocks?); amplitude falling, probably moderately resistive (stainless, titanium, graphite (charcoal?), or thin/weak shapes?). The amount of change corresponds to the size/distance ratio.
You don't really need an LC resonant circuit here; the bridge can be, like, L-R impedances instead. But going back to excitation level: you'll get a larger signal for less drive power when the reactance is resonated out, and that's good for battery life, which is probably advantageous here.
On the subject of battery life, you might even consider pulsing the network, so you apply excitation and let it ring up and stabilize (which might only take hundreds of microseconds), then sample the output, then turn it off; repeat this once every, say, 10ms or so. This is faster than the human will notice (and probably faster than they are swinging the sense area over a given volume of dirt), so can save a considerable amount of battery life! Of course, you don't need to do this for a proof of concept, CW is fine.
Putting some numbers to these steps:
- You might consider an op-amp with a ~1kohm noise match. This is pretty typical for bipolar types. I suppose lower might be preferable, and can be done with a CFB (current feedback) type amp, or a discrete circuit.
- Also, if you need better differencing / isolation than an amp can provide, consider an isolation transformer. This should be carefully designed to preserve balance and minimize loading on the bridge -- good luck finding one adequately designed, or specified for that matter, off the shelf -- but will allow you to use a bridge that's ground-referenced on one side
and a ground-referenced amp without any worry about common mode range. And you can use even more excitation level, if needed.
- Then, the bridge's impedance should be around 1kohm, which is 500 ohms per leg, so the equivalent resistance should be around there. Now, this sucks, because the resonant tank reactance needs to be either Q times larger than this (series resonant), or smaller (parallel). A Q of 200+ is reasonable, so that would be, at 100kHz, either 160mH (ridiculously huge) or 4uH (hm, quite reasonable actually). Well; it still sucks, because parallel resonant, you have all that voltage you need to isolate, which would pretty much require the transformer. Series resonant has less voltage at the feedpoint.
- So, we can transform the bridge itself; we can make one leg be a pair of voltage sources (+/- V_excitation), and the other leg be the pair of resonant tanks, which are parallel resonant. Now we have a ground referenced null, which is handy. The tanks act in parallel, so they should actually be 2kohms each, for 1k equivalent total, and so 16uH (which is still reasonable).
- One more remark about coil design: because the coil voltage is unbalanced, it will be sensitive to nearby electric fields (i.e., you'll have a combo Theremin and metal detector, and that's no good!). Wrap the coil in a foil shield, slitted to allow magnetic field through. (Imagine a hollow torus with the coil inside, but the torus is slitted like a split washer so it doesn't make a full shorted turn.) Ground the shield, and use coax cable to connect to the coil.
- Now we need a symmetrical excitation source, which isn't hard. We can use off-the-shelf transformers to do this, or wind our own. A Hartley oscillator is probably quite reasonable here, or you might use a crystal oscillator for stable reference (with a frequency divider if necessary to reach lower frequencies; e.g. a 4MHz crystal on a CD4060) and an amplifier/filter.
- This leaves one remaining question: what of the reference inductor? It should be made of the same materials, and same general geometry (but can be scaled down) as the sense coil. This should give a similar tempco, but will give a lower Q (needs more turns of finer wire). A ferrite core may be acceptable, but will affect the tempco; a low-tempco ferrite should at least be used (e.g., #31 rods?).
- Alternately, we can use the insight that the sense coil is resistive at resonance, to replace its balancing arm with just a resistor. This resistor should be adjusted to match amplitude; the resonant cap will need to be tuned to match phase. Alternately the excitation supply balance can be adjusted, but that may be more awkward, depends.
- Finally, the sense amp, has to be an amplifier to turn the ~mV of difference into a sensible ~V scale that can be read out; but preserving the phase information is a very cool perk of this architecture, so we might want to do that. We can do that by taking quadrature from the excitation oscillator -- this is fairly easy if we started with a frequency divider, because we can take 2*F_excitation and combine it with F_excitation with a few logic gates to get F_excitation(0°) and F_excitation(90°). Then we chop the amplified signal with an analog switch or mixer, and filter the results: this gets the in-phase and quadrature components. To read that out in polar form, eh, just read them into an MCU and compute it that way, I guess.
Tim
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