Electromagnetism Questions - LC Tank Circuit - Metal Detector Issues - Page 1
Forum section: electronics / beginners

author: Rigolon
author_rank: Regular Contributor
timestamp: August 27, 2019, 07:22:25 pm
content: Hey guys, not quite sure if this post belongs here. But since there are all kinds of experts on this forum someone might help me.Since electromagnetism is usually seen as complicated I will try to be concise, I could try to give more info if needed.So let's go to the problem in hand. I have a walk-through metal detector circuit and want to give it more sensitivity. (detect really small objects, eg. nails, pins).To do that I'm studying a lot of electromagnetism theory. So far I come up with the following points:- RX coil with larger area and more turns.EMF = NRX*dΦ/dt(where NRXis the number of turns of RX coil - Faraday's Law)Φ = ∫ B.dS, therefore bigger area bigger flux. Bigger flux, biggerdΦ/dtso bigger EMF.- I also read a lot that higher frequency gives more senstivity.Given that B is proportional with the current (Biot-Savart law) and i(t) = Imax*sin(2πf*t), when solving EMF =dΦ/dtwe get a component i(t) = Imax*2πf*cos(2πf*t). Therefore higher f = higher EMF.Believing that I got all this right I could increase the frequency on my TX... BUT:At resonance frequency parallel LC is seeing by the circuit as an Open-Circuit, which means no current from power supply and IL=-IC, so I could say IL= V/XL. And that it's what I get in my simulations (If needed more info on this ask me and I will post it in the replies).So higher XL= lower Imax= lower B (magnetic field) = lower EMF.Given that XL= 2πf*L it means that Imaxis 2πf lower. But considering the current equation afterdΦ/dtthat i(t) = Imax*2πf*cos(2πf*t) and changing Imaxfor V/XLwe get i(t) =V/2πf*L*2πf*cos(2πf*t). Simplifying i(t) =V/L*cos(2πf*t).And by that i get that changing the frequency means nothing. But from all I read about metal detecting, changing frequency means something. What am I missing here??- Also read that I could increase the turns (NTX) on my TX coil.By Biot-Savart (or Ampere's Law) we get that B is proportional to NTXby a factor of 1 (1 turn = B, 2 turns = 2B, 3 turns = 3B...). So I understand that more turns = more magnetic field. But again the inductance (L) is also proportional with NTXbut the factor is not linear, and from the coil calculations (rectangular coil) when I double N (25 to 50) i get L1= 3*L[sub0. So my Imaxwill be lower by a factor of 3. Then I have that B is 2 times higher because I doubled N but also 3 times lower because of the current. At the final B is actually lower than before.I really don't know what i'm getting wrong, because whenever I try to develop the equation I go against the theories. As seen with the frequency from before. As the ratio that L increases by N is not linear, not sure if the values I am using is the problem or perhaps this equations don't work on tank circuits. Because when I remove the circuit from the equation and consider current always the same, then I can see how increasing the number of turns or the frequency will give more sensitivity.Not sure what I am doing anymorePS: Can't really increase V over the tank circuit. Unfortunately.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 28, 2019, 01:14:33 am
content: You're resonating in circlesbecause 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 betoolarge, 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 sideanda 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

author: Rigolon
author_rank: Regular Contributor
timestamp: August 28, 2019, 03:03:19 pm
content: WowThank you so much for the reply.I really learned a lot already from you, and although there is a lot to fully comprehend from all that you said I will keep reading it (already read it a few times) until I understand every piece of information here.Perhaps I got a few things wrong for now, but here's a few points that i may be having trouble with:- The transient excitation you talked about looks a lot like from what I read about Pulse Induction Metal Detectors (didn't read much about it). Is that correct?But as I said, for now, I'm already working on a research using a commercial Walk-through metal detector circuit. Can't do much about the circuitry, and it works, from what I get as a BFO (Beat Frequency Oscillator) metal detector. The TX and RX coils are 70cm apart.They work really good detecting guns and medium to large blades. But the idea of the project is to make detect smaller objects.So a few things you said I won't be able to use for now, and don't actually have to (especially about the batteries). But soon in the future I will try to develop my own Metal Detector and thanks to you I have a great foundation.- I noticed that I'm having trouble understanding the Q factor part. The resonant circuit is something like a class C amplifier:_____ L _____+15V ------- R --------| |---- MosFET --- R ------- -15V¯¯¯¯¯ C ¯¯¯¯¯* MosFET is driven by a PWM to switch the resonant frequency.My problem with Q is that I read that:1) For a series RLC resonant circuit Q = R*XL(R being the resistor on the circuit and not the inductor resistance)2) But for a parallel RLC resonant circuit Q = R/XL3) Q factor of the coil alone is the same equation as (1), but R being the inductor resistance.So I am not really sure which one to use, because R is in series but LC in parallel.Should I just care about the Q factor of the coil alone and not consider the circuit. Or given this circuit that R is in series I should use equation (1)As you said I would want Q higher or lower depending if it is series or parallel. LC is parallel but there is an R in series, not sure what it is that I would want in here.Somethings you said are already on the circuit, such as the differential amplifier.Other things I have to study more, there a few things that I never even heard about (impedance bridge). So will first try to learn more about what I don't know.I'm trying to get some money so I can buy my own tools and materials. I hope until the end of the year I get all I need and will try to build my own using all the knowledge you shared with me. Hopefully I will share my adventure with you and people here when I get to that point.PS: Really cool about how MRI works. Also:QuoteThis made me laugh.EDIT: New questionI've been reading about commercial walk-through metal detectors, and all of them operates on more than one frequency (channel). The one i'm working with has 10 channels. From 3.9kHz to 4.450kHz.As Q = fr/BW this means that, using this frequency I'm not able to have a high Q given my bandwidth? Could I say that changing my coils and increasing the resonant frequency I would be able to have a higher Q? And that would be better, correct?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 29, 2019, 02:20:43 am
content: R needs to be inside the LC loop to count for Q, either series (ESR of the inductor, say) or parallel. An R outside that loop sets gain and Q of the filter (which is different from Q of the coil*), which is relevant if you're using it as a filter.As drawn, you'd just be exciting it with pulses and not really having any means of sensing subtle changes in the coil's parameters.*We can put together many combinations of R and X. When we do this for a single L-R or R-C component, we get the quality factor of the component itself. When we put that component into a circuit with a source and load, we can take the Q factor of X with R_S or R_L. A lowpass filter has a Q factor associated with each section, defined in this way; the Qs are designed so that the peak of one section just fills in the valley of the last, and so on, to get an overall response that is much flatter, and sharper, than you'd get by setting the values all equal.I wonder if that's a problem for those detectors as well, with the BFOs -- the problem with an oscillator is, it operates with an excess of gain, in order to ensure startup. It saturates to whatever maximum amplitude it can run at, and that's that. So, it is insensitive to changes in coil resistance -- the oscillator simply delivers a little more power to maintain the same amplitude. (This can be sensed as supply current, at least.) So a BFO type detector discards that information, taking only the frequency difference instead, and I wonder if that is a major weakness of the design.For two coils, RX and TX, you get sensitivity in the near field of each, assuming a similar bridge type circuit that can resolve small changes. That gives you greater depth of sensitivity, which I suppose will be good for relatively thin coils (those frames aren't all that wide) and human bodies walking through, shoulders parallel with the frame.At some point, you'll run into the problem that:- Bodies are conductive,- Bodies come in different sizes,- Metal objects of sufficient size and composition will look indistinguishable from the difference between bodies.Switched frequency bands (which would most likely be done by switching the capacitors, setting a new resonant frequency) can help with this, because a metal object may only be in this range of confusion for a few frequencies; though 3.9 to 4.45kHz doesn't seem like nearly wide enough of a range to be able to tell such a difference.Q does generally rise with frequency, approximately proportionally for low frequencies, and approximately as sqrt(f) for high frequencies; the crossover point being where skin effect takes over (where AC resistance is noticeably higher than DCR).Tim

author: Rigolon
author_rank: Regular Contributor
timestamp: August 30, 2019, 01:48:35 pm
content: Once again, Thank you so much for the reply.I see that I also need to understand more on how this circuit works. It looks like a BFO but has some characteristics that it seems different from that.I will have to study it more.Quote from: T3sl4co1l on August 29, 2019, 02:20:43 amFrom what I get, the receiver circuit detects the change in phase on the RX coil when a metal goes by. But the TX circuit is as drawn, there are two big electrolytic caps besides the Resistors (on both ends). But from what I test it out and simulated its function is only to slowly turn the tank circuit On. Removing it the circuit works the same, but shows a high peak when turning ON. Which makes me believe it could be harmful for the circuit and others equipment nearby.