PI time constants and coil dynamics

[Noemio]

Hy all,

Is there somebody who can, kindly, explain me the last part of footnote n.2 in HH article: “…which can degrade performance if it is not settled out.”.
In particular “settled out” talking about the field.

Thank you in advance.

p.s.: I apologize for my “Tarzan style” English.

[Reg]

Hi,

Your question was quite clear, but I had to read Carl's article a couple of times before it soaked in what he was saying. (My problem in thinking and not his is in what he wrote)

Ok, Ideally, when a FET is turned on and current flows in the coil, as it rises in value, an opposing signal will be generated in any target nearby. This opposing signal will be there until the target is basically saturated and no more opposing signal will be generated.

This means you have reached the maximum signal that is needed into the target for the maximum return signal. Once this maximum is reached and the FET turned off, the target will now generate its maximum signal because of the collapsing field.

Now, if you turn off the FET before that maximum signal is reached, then some of the rising signal in the target will try to oppose the discharge signal resulting in a reduction of the signal from the target from what would be the maximum.

You can think of it this way in the most basic terms to try to get a mental picture of what I mean. Think of the target as a spring. If you push on that spring to compress it but only push half way, then release it so it is free to spring back, it will have a certain amount of oomph or energy response. If you push the spring farther to its maximum capacity, and then let go, it will have a much stronger push back energy response or simply stated a stronger oomph. Once the spring is full compressed, that is all you can go and get the maximum spring back out of it.

So, the ideal amount of coil current is that which is needed to saturate the target to its maximum amount. This would be equivalent to compressing that spring to is maximum amount.

I hope this makes sense.

Reg

[Noemio]

Thank you

Hi Geo,

THANK YOU SO MUCH for your exhausting explanation!!!

But now… could you tell me if there’s any coincidence between the trend of the current (and so the field) flowing through the coil and the signal into the target?
I mean: should I think that the current needed to saturate the target is approximately equal to the value of current reached in the almost flat-top part of the charge curve of the coil? Or the saturation of the target could be reached even in the ramp stage of the curve?

If the second hypothesis is correct, there should be a transmit pulse duration beyond which the current into the coil could be still rising fast when the target is already saturated; beyond this point any further energy (pulse length) used to drive the coil should be simply wasted.

If instead the first hypothesis is correct, I can’t understand why most of the PI MD I’ve seen use relatively short transmit pulse durations (100 – 150 – 200 µSec).

Let’s suppose to use a 350µH coil with 0,8 ohm (let’s say 1,5 ohm with coax cable and series resistance of mosfet); TX pulse should never be less than 700 µS (to reach about 7,5 A at shut-down point) to see a “settled out” coil current.

Where’s my mistake?


As much as you like, a few punctuation all around….. be patient.


Thank you again

[Reg]

The target saturation current is not obvious on a mono coil, nor is it dependent upon the flat top. If there is no series resistance, and the pulse length is long enough then a target could be saturated before maximum current is reached. Once saturation is reached, then any extra current is wasted on that particular target.

Now, a different target may take a much longer time to saturate, so such a target could be saturated, but if its time constant is longer than the pulse length, then it will not be saturate.

Most PI's are set up for a 100 usec to 300 usec pulse simply because it will provide a decent signal from most targets people search for. I have used pulses as short as 30 usec and get decent signals from various sizes of gold nuggets. So, one can use a very wide range and still have a detector work.

I personally have not done that much experimenting with pulse lengths and depth of detection. So, I can't tell you just how much of a benefit you will obtain by extending the pulse for a much longer period of time.

I suspect there will not be a tremendous depth increase on most targets when going from 200 usec to 1000 usec. The logical objects that would benefit would be large silver and copper objects, so those are what I would test.

Running your suggested coil and internal resistance, my spice program indicates about 650 usec to reach 7.5A current if a 12V battery is used. So, your calculations are very close.

In trying to answer your question, the target could be saturated early.

Now, most PI's use smaller batteries that don't do well when excessive current is needed. So, the logical solution is to find a decent current draw that provides good depth which is what most manufacturers do

Reg

[Carl-NC]

But now… could you tell me if there’s any coincidence between the trend of the current (and so the field) flowing through the coil and the signal into the target?

I mean: should I think that the current needed to saturate the target is approximately equal to the value of current reached in the almost flat-top part of the charge curve of the coil? Or the saturation of the target could be reached even in the ramp stage of the curve?

Target eddy currents are only generated when there is a changing magnetic field. So when you turn on the coil and the coil field is exponentially building up, eddies are generated. More eddies are generated at the very beginning of the coil turn-on, and as the coil field rises exponentially and settles out to a maximum value, the target eddies decay exponentially and settle out to zero.

A DC magnetic field does not cause induction, so when the coil is completely turned on and the magnetic field has stabilized to its peak value, there will be no eddy currents in the target. Therefore, there is no "saturation" of the target.

Again, eddy currents are generated only when the magnetic field is changing. So when we turn off the coil and the magnetic field collapses, we get eddy currents, and those are the ones we try to detect. So we have two cases of eddies: one when the coil is turned on and the magnetic field is building up, and another when the coil is turned off and the magnetic field collapses. In both case, eddies start out at a maximum and decay to zero.

OK, so let's finally get to the question... how does turn-on affect turn-off? The direction the target eddies flow depends on polarity of the magnetic field and whether its rising or falling. Well, it's the same field, so only the rising/falling matters, and these are opposite events. So the eddies from a rising field will be opposite in polarity from the eddies of a falling field. If the eddies from the turn-on portion have not completely decayed to zero, they will subtract from the eddies from the turn-off portion. That will decrease the target response.

That's why you generally want the turn-on pulse width to be just long enough to ensure the magnetic field has stabilized. I think you used 3 time constants in your example, which should suffice.

Now here's the Big Question: What is the real impact of not settling out during turn-on? To answer this, we need a little better understanding of induction. Magnetic flux is denoted with the letter B, and eddies are proportional to time-varying flux. So i(t) ~ dB/dt. Turn-on is a relatively slow event so the dB/dt is fairly weak at any point during that time. Turn-off is a very fast event; in fact, target eddies are proportional to the starting value of the magnetic field (B) and the speed at which you turn it off (1/dt). The stronger the better, the faster the better.

From this we can see another effect: if the turn-on hasn't settled out, the the starting value of the magnetic field at turn-off will be weaker. So with an unsettled turn-on, we have a both a weaker B-field and we have opposing eddies. Which is the bigger problem? It's the weaker B-field, and here's why.

In both turn-on and turn-off we're dealing with the exact same B-field. A weaker B-field at the turn-off point results in a directly proportional decrease in eddy currents. That is, if you turn off the coil after only one time constant of turn-on, the B-field will be at 63% of its peak, and the resulting turn-off eddies will start out at 63% as well.

But the opposing residual turn-on eddies are a result of not only the B-field, but also of the turn-on time constant. This happens to be much slower than the turn-off time constant, so the turn-on eddies will start out proportionally weaker by the ratio of the time constants. Add to that the fact that the residual eddies are in the process of decaying, so they not only start out weaker, but by the time turn-off occurs, they are even less.

So, if I'm not mistaken, in most PI designs the residual turn-on eddies really don't matter, they're "in the mud" compared to the weaker B-field.

- Carl

[Carl-NC]

Here is a graphical representation of what happens with premature coil turn-off.

The first plot is simply the coil switch. The second plot shows the coil current (the magnetic field is proportional to this). The rise time of the current, tau1, is determined by the L of the coil and the series resistance of the coil, cable, switch, and battery (or tank). The resistance is a few ohms typically. The fall time of the current is set by a different tau... same coil L, but the R is now mostly the damping resistor, which is a few hundred ohms. Since tau = L/R, the higher R makes tau2 much faster. Let's say for example that R2 = 100*R1, so tau2 is 100 times faster. This is pretty typical in a PI.

The third plot shows the waveform of the target's eddy response. Eddies are proportional to dB/dt (and therefore dI/dt), so if tau2 is 100 times faster than tau1, A2 will be 100 times larger than A1. Note that A1 is negative; that part of the waveform represents the residual eddy currents in the target.

The fourth plot shows coil turn-off after 1*tau1. The current in the coil (and therefore the B-field) has reach 63% of it's peak value. The final plot is the resulting eddies... the 37% reduction in B-field directly impacts eddy amplitude by 37%. But the residual eddies started out at 1% (A1), and have reduced by 63% at turn-off, so their impact is 1%*37% = 0.37%.

So, in this example, B-field reduction impacts target signals 100 times more than residual eddies. In general, the ratio is tau2/tau1, or Rdamping/Rseries.

- Carl

[bugwhiskers]

Hi Carl,

Given the demonstrable improvement in detection signal with early sampling do you consider that the signal strength has the same exponent as the decay curve ?

If the above is true then some considerable gains could be acheived by finding a method to get rid of the back EMF quicker.

regards
bugwhiskers

[Carl-NC]

Actually, I thought about this a little more on the ride home today. My analysis assumed the tau of the target's eddy response was the same as that of the coil, and obviously it's not, or we would never be able to detect anything. The target decay will be slower, which will slightly increase the impact of the residual eddies, but not by much. I'll post modified plots tomorrow.

So I guess that answers your question, the target always has to have a slower exponential. Early sampling helps because you're looking at an earlier part of the exponential, while it is stronger. This would be true for any target. Getting rid of the back EMF quicker is the goal of some of the fast-coil techniques that have been discussed, notably the article by bbsailor.

- Carl

[Reg]

Hi Carl,

How do you interpret the eddy current of the target only given your two different on times in your eddy 1 graphs, if the shorter pulse on time is 5 time constants of the target.

In other words, lets say we ignore the spike and can get rid of that immediately so we are just left with the target response. Now, if the shorter time on is long enough that it is 5 time constants of the target, what difference would there be in the target response between the shorter and the longer pulse on time.

As I understand it, there wouldn't be any target signal difference but I could be wrong.

I agree the spike would be different, but not the target response.

Am I looking at this wrong?

Reg

[Reg]

Hi Carl,

Changing the subject for a minute, the 15 minute time limit to make changes sucks. It takes a while for me to think about the subject more once I write something to see if I have expressed myself the way I want.

Now, my train of thought usually extends longer than 15 minutes, but once I post something, that train gets derailed and ends off track when I get the 15 minute notice. At least it happened again this time.

Ok, lets see if I can remember what else I wanted to say.

Now, my interpretation is the target response is limited by the target TC so once this target is saturated, then no further increase will occur in the target signal decay once that happens. Thus, the target decay time has reached its maximum.

Also, the target TC has to be longer than the effective coil TC to be seen, where the word effective is the key. The effective coil discharge TC is a function of the current and time applied as well as the fundamental TC components. So, the coil discharge signal can vary and extend longer as the current is increased if the coil tc is long.

However, the signal from a target does not extend the same as the result of an increased current once maximum is reached. If it did, then we could see even the smallest gold at extended delays if enough current is applied.

So, increasing the current into the coil will cause a the coil to take longer to decay, which then will simply generate longer decay signals than those from small gold that have quit extending once saturation is reached.

At least, that is what I think I observe as well as how I interpret what is happening.

Part of what is happening is not really thought of and that is the charge TC of the coil is different than the discharge. This shouldn't be the case for a target. Now, this brings up something else and that is if the TC of a target is critical as to how much effective current can be applied, then is it better to have a faster TC on the charge current in the coil for targets having a shorter time constant? Doesn't this allow for a shorter pulse time to get the same results?

Needless to say, this subject does get confusing.

Reg

[J_Player]

Now, my train of thought usually extends longer than 15 minutes, but once I post something, that train gets derailed and ends off track when I get the 15 minute notice. At least it happened again this time.

Hi Reg,
You can evade the 15 minute time limit by opening a new text file on your desktop to write your reply. By the time you have finished your reply, you may want to make changes, but no problem since you are working with a text file on your local computer that has no time limit. When the reply is done, then make sure the file is in the non-word wrap mode, and copy/paste it into the Geotech reply screen. Now you still have 15 minutes longer for last minute changes to your reply, and you also have a record of your reply on your PC in case you want to save the text file.

Also, your discussions about what happens during the PI pulse switching cycles is very interesting. From what I am reading, it appears to me that there may be some target identifying information in the receive signals if the pulse is modified for early switch-off, and if the received signal is monitored through the entire pulsing cycle to watch the rising eddy currents as well as the decaying signals under non-saturated conditions of differing strengths. To start with, we could experiment with watching the target saturation times and decay times as well as the eddy strengths at various times after the turn-on signal and turn-off signal. Maybe more important is to watch the eddy rise curves and decay curves with different PI on/off signal timings. These could be compared to curves of tested and known specimens. Things like the slope of the rising eddy curve at various time delays after turn-on, and the time to saturation could be important in revealing information about the target. The difficulties in measuring these properties of a target while the TX coil is pulsed on can maybe be overcome by making the search coil to transmit a train of pulses of graduated pulse widths to show a series of RX signals for a given target that include turn-off at very short durations expected to be in the non-saturated region of all targets. Then the following pulses in the train could be gradually increased until they reach a relatively long pulse duration, with maybe a total of 20 or 30 pulses in each pulse train packet. The objective of this pulse train packet would be to generate a set of data points of the target response from very early switch-off times through very long switch-off times, and use that collection of data points to assemble a response curve for the sample being tested. The response curve would show information not normally found on a simple adjustable PI detector.

This is only a speculative idea, but for experimenting purposes, it would be interesting to build a small database of known responses of different targets and see if there are any eddy response characteristics that are helpful in discriminating targets using the graduated width pulse train technique.

Best wishes,
J_P

[Reg]

Hi J_P,

You are right about just writing on my own computer and then entering it, but I normally don't do that. Also, sometimes I find it takes hours before I come up with a different idea I feel needs to be addressed in the same post.

Oh well, I will live.

Now, as for your idea, you will need to use a DD or a concentric coil to look at the target signal during the on time and that is what the PD does. So, yes, you can use that information to determine a lot about the target.

Using a mono coil makes it a little more difficult and trying to analyze a target by looking at the general curve becomes a little more complex because time constants are just part of the equation.

Early switch off of the pulse current in a mono coil is the only way to really sample to look for very small gold. Ideally, one needs an extremely fast coil and even then, the pulse current should be relatively short to assure the decay curve of the coil itself doesn't mask any gold signal. It is best if one can sample at 10 usec or less when trying to find the real small gold.

cheers,

Reg

[Carl-NC]

Hi Reg,

I'm glad you followed up the other post, because I didn't quite understand it.

Changing the subject for a minute, the 15 minute time limit to make changes sucks. It takes a while for me to think about the subject more once I write something to see if I have expressed myself the way I want.

Now, my train of thought usually extends longer than 15 minutes, but once I post something, that train gets derailed and ends off track when I get the 15 minute notice. At least it happened again this time.

I put a time limit on edits so people wouldn't go back some time later and change or delete posts, which can mess up the "conversation". I thought 15 minutes was plenty, mostly to allow for a post-submit review and edit. But I can increase it if you think I need to, I just don't want it open-ended.

Now, my interpretation is the target response is limited by the target TC so once this target is saturated, then no further increase will occur in the target signal decay once that happens. Thus, the target decay time has reached its maximum.

Yes, target response is limited by the target TC, which I failed to account for in the plots. But for the issue of residual eddies at turn-off, it doesn't matter a whole lot.

Fundamentally, I guess I don't understand the term "saturated". What do you mean by this?

Also, the target TC has to be longer than the effective coil TC to be seen, where the word effective is the key. The effective coil discharge TC is a function of the current and time applied as well as the fundamental TC components. So, the coil discharge signal can vary and extend longer as the current is increased if the coil tc is long.

The only mechanism I can see for current level affecting coil TC is that it would affect the dynamics of the MOSFET turn-off. If we have an ideal switch, then coil TC is set by the coil L and the parallel R, regardless of current.

However, the signal from a target does not extend the same as the result of an increased current once maximum is reached. If it did, then we could see even the smallest gold at extended delays if enough current is applied.

No, I would not expect the amount of coil current to have any effect on target TC.

So, increasing the current into the coil will cause a the coil to take longer to decay, which then will simply generate longer decay signals than those from small gold that have quit extending once saturation is reached.

OK, I agree that if increasing the coil current causes a longer turn-off TC, then it will degrade sensitivity to fast TC targets. But I still don't understand the saturation part.

Part of what is happening is not really thought of and that is the charge TC of the coil is different than the discharge.

Right, that's what I was trying to get across in the plots.

This shouldn't be the case for a target.

True again.

Now, this brings up something else and that is if the TC of a target is critical as to how much effective current can be applied, then is it better to have a faster TC on the charge current in the coil for targets having a shorter time constant? Doesn't this allow for a shorter pulse time to get the same results?

Yes, but only because you've reached the peak current faster. It should have no effect on target response.

My analysis was a reply to the question about overly short turn-on times, and the comment I made in the HH article about the turn-on state not being "settled out" (steady-state). There are two components to this. One is that the current is still increasing and has not reached its peak value. This results in a weaker peak B-field. The other is that, as long as the current (and hence the B-field) is on the rise, the target has reverse eddies flowing in it. They will directly subtract from the desired eddies at turn-off.

I used to think that the second component was at least significant, but upon further thought, I believe it is in the mud, at least for the typical mono coil PI front-end design. The only component that matters is the B-field strength. As you leave the coil turned on for longer and longer, the B-field peaks out, and the target reverse eddies decay to zero, so leaving the coil on any longer has no benefit, but no detriment either.

As far as the effects of current strength, I'll have to think about that some more, and look on the bench. Perhaps the reason early turn-off helps you with gold is that the higher current affects the switch dynamics... you could probably get the same results by current-limiting the switch, then turn-on time wouldn't matter. I designed a security wand with a 50mA coil current, and a lowly 2N3904 for the coil switch, and was very pleased with the results. I could use this to test current-vs-TC.

If I've missed something along the way, I hope you'll correct me.

- Carl

[Carl-NC]

Here's corrected plots with target TC added. Premature turn-off still will be dominated by B-field reduction, not residual eddies.

[bugwhiskers]

Target saturation

Many years ago a friend of mine showed me an Ultrasonic bath he had aquired. The cover was off and there was a large coil about 10 inches in diameter and about the same in length. The friend fired it up and put a metal bar in the middle of the coil, it started to glow red.... I guess this would mean that the target was saturated.

I believe Induction is often used to heat metals in foundries etc.

regards
bugwhiskers