Optimizing Target Responses

[andreapas79]

Hi everyone, thanks Carl to share your knowledge... it's the real gold for me.. I've a couple of questions:
- with the term "tank cap" you mean the big capacitor in parallel (usually 1000uF)?;
- what change increasing impulse width? because i tried to change it and this is the result. I think the reason is longer pulse, much eddy current stored in the targets... is it correct or I wrong? thanks a lot. I hope I'm not off topic with this last question.

In the picture comparison between pure copper, iron and no target curve with different pulse width, RDump. (NoTarget line in red, target curve in blue)

[Old cart]

Will this article continue?

[Hamid]

Thank you very much Carl

[bbsailor]

Carl-NC said: "In another thread Joe/bbsailor suggested you want the turn-off time to be at least 5x faster than the target tau you want to detect. That's pretty fair, as anything better than that is hard fightin' for minimal gain."

I saw an article on Eric Foster's forum about optimizing mine detectors. After World War 2 many mines were still in the ground and very dangerous. In an attempt to optimize the design of mine detectors, they electrically stimulated all the metal parts and tried to fine the optimal mine detector pulse and coil characteristics. One conclusion was that after trying multiple coil discharge TCs that 5 TCs was optimal and going any higher did not increase the target's detectability. I wish Eric Foster could find this article and post it as it would give a practical frame of reference for developing a good mental model about the search coil discharge TC relative to the targets potential detectability.

Here is another thought to add to a good mental model. The coil charge TC follows this current rise graph. Try to visualize how vertical or horizontal the current rise chart would be with the current turn off point at each time constant.
1TC - 63.2% of maximum current
2TC - 86.5%
3TC - 95.1%
4TC - 98.2%
5TC - 99.3%

Most rules of thumb that I have read said that the coil should reach about 3 TCs before the current turns off to not loose some current intensity efficiency. While you are at 3TCs, the current has stopped rising to a great extent and the curve is almost flat and horizontal. If, however you turned the current off at 1TC, the current curve would be more vertical and turning off the current while it is still rising would cancel some already invested current. This might be a good addition to Carl's graphs to make the mental model more complete.

Carl, thanks for the graphs. Good and accurate mental models helps us all to better understand how the many variable interact and ways to optimize a design for a particular range of target TCs.

Joseph J. Rogowski

[waltr]

Making this thread a sticky is a good idea.

Would also be great material to add to the next edition of ITMD book.
I bought the 2nd edition when first study how detectors worked and was a bit disappointed at how little PI info it contained.

[ZED]

Great thread Carl ! Thank you for spending the time to right it up,this sort of info is usually spread all over the place,it be nice if you could make a sticky out of it,hate to see it disappear into all the other threads.

[Searchy]

Maybe you could also explain the Minelab ZVT technology (https://patents.google.com/patent/US7791345) a bit at this point?

[Searchy]

Thank you very much for the introduction series and the very well explanation!
That's exactly what i was looking for.
Hope you go into details about ground balancing, EFE, integration etc. later on aswell.

[Carl-NC]

Part 4: Optimizing the Turn-Off

Now we see that the energizing "kick" that gives us the target response occurs at the pulse turn-off event. Specifically, it is the dI/dt of the pulse turn off that determines the amount of induced EMF, which in turn determines the strength of the eddy currents. If we want a stronger target response then we can either increase the coil current at turn-off or decrease the turn-off time. Or both. Increasing the coil current is a no-brainer; you can reduce the amount of parasitic series resistance or increase the drive voltage. Decreasing the resistance might mean a heavier coil wire gauge, a better MOSFET, or a low-ESR tank cap. Reducing turn-off time is a bit more difficult; maybe a faster MOSFET, faster MOSFET driver, or lower coil parasitic C. Note that changing the coil turns can reduce C and R but impacts other aspects of the design; it is worthy of its own discussion.

You might be tempted to reduce the turn-off time to as close to zero as possible but there is a point of diminishing return. Here are 3 turn-off slew rates:



All 3 cases have the same peak current (1A), and the turn-off time is progressively halved for the middle and right cases (t -> t/2 -> t/4). This progressively doubles the slew rate which progressively doubles the induced EMF (Vf -> 2Vf -> 4Vf). If the EMF doubles, then the maximum peak eddy will also double (Ip -> 2Ip -> 4Ip); this is shown by the heavy dashed lines. However, the time to reach that doubled peak current is halved, so the gain in actual peak eddy current is marginal. The bottom curves are simply the eddy curves expanded a bit so you can better see the improvement in eddy drive vs slew rate.

The amount of eddy drive depends on tau(tgt). If you imagine the first case (t) with a much faster tau(tgt) then you can imagine that the t/2 and t/4 cases provide a much higher drive improvement. You can calculate hard numbers for all this. Given a fixed peak coil current, the turn-off slew efficiency vs tau(tgt) is:

= 63.2%
/2 = 78.7%
/3 = 85.0%
/4 = 88.5%
/5 = 90.6%
/10 = 95.2%
/20 = 97.5%
/50 = 99.0%
/∞ = 100%

In another thread Joe/bbsailor suggested you want the turn-off time to be at least 5x faster than the target tau you want to detect. That's pretty fair, as anything better than that is hard fightin' for minimal gain.

[Qiaozhi]

Thank you Carl! This makes complete sense to me. There is so much false/misleading information buzzing around, that I hope this key information can help clear things up once and for all.

On a more mundane matter, is it possible to extend the amount of time in between having to keep re-logging in? It seems to last only about 10 minutes or so (at least it feels that short).

There is no time-out associated with the Geotech forum.
When you log in, click on the "Remember Me" button.

[Elliot]

Thank you Carl! This makes complete sense to me. There is so much false/misleading information buzzing around, that I hope this key information can help clear things up once and for all.

On a more mundane matter, is it possible to extend the amount of time in between having to keep re-logging in? It seems to last only about 10 minutes or so (at least it feels that short).

[Carl-NC]

Part 3: Exponential Response

Part 1 showed the responses to a stepped TX current. We don't normally do PI that way. Part 2 showed the responses to a ramped TX current. That's a little closer to standard PI. Now we'll look at what actually happens in std PI.

When we turn on the coil the current starts at zero and charges exponentially to a maximum current with a time constant of tau(on) = L/Rs, where L is the coil inductance and Rs is the total series resistance. If tau(on) is very large compared to the actual turn-on pulse width then the current begins to approximate the ramped current discussed in Part 2. If tau(on) is small compared to the actual turn-on pulse width then the current will completely flat-top before turn-off. Usually tau(on) is around 100-200us and the pulse width is maybe 100us, so it's somewhere in between the ramp case and flat-topping.

The TX coil current, induced target EMF, and target eddy waveforms look like this:



The exponential turn-on current is (a) which induces an exponentially decreasing stepped EMF (b) in the target. The target EMF has the exact same tau as the coil's tau(on) regardless of the target's own tau (tau(tgt)). The EMF, in turn, produces an eddy current (c) which has an odd waveform that is the difference of two exponentials and very much depends on the relationship between tau(on) and tau(tgt). The curvature of (c) as shown might represent a medium conductive target like a copper coin. Other target taus will have different curvatures. In all cases one thing is consistent: as the target EMF exponentially decays toward zero, the target eddies will also decay toward zero. Whether the eddies die out before the end of the TX pulse depends on the taus and the TX-on time.

At point (d) the TX turns off and the current ceases in a non-zero amount of time. The results are as before: an EMF step (e) is induced, which cause the eddy current to abruptly rise (f) and then decay back to zero (g).

The important thing to understand from all this is that, for the purpose of detecting the target, it is the driven eddy current (f) that creates the decaying eddy current (g) that we actually detect. The eddy currents at (c) play no role except to slightly hinder sensitivity. If you want to say we're "charging the target" (and I don't really care for that term) then it is (f) where the charging occurs. The turn-on response (c) is simply an artifact that is necessary to get the TX current up to a peak value for our turn-off event. Ideally, we would always stretch the TX pulse out to ensure all target eddies (c) have completely died out before turn-off but this is impractical for 2 reasons: 1) For high conductors it means the TX pulse width may have to be very large, maybe 300-500us, which severely eats into the timing budget; and 2) leaving the TX turned on for an extended time wastes a lot of power.

More later...

[Carl-NC]

Part 2: Ramp Response

In Part 1 the TX waveform was a fairly idealized pulsed current with equally fast rise & fall times. I call this "constant-current PI." Achieving a fast turn-off is easy, we do it all the time in std PI. But a fast turn-on is difficult, it requires a very high voltage; in fact, exactly as high as the flyback voltage you get at turn-off. That is, 100V-600V. It is possible to do that either by brute force or by a clever self-regenerating kick-start circuit. I believe the latter was covered by Deemon in a thread somewhere.

If we're lazy, then instead of a high-voltage kick-start to get that fast rising edge, we simply apply a low voltage and let the coil charge as it will. If the coil is ideal (no R) then a DC voltage applied produces a linear ramping current:



So we've applied a low voltage for, say, 100us and then suddenly turned it off. This is a bit closer to the standard PI most people are working with. The EMF induced in a target now looks like this:



The slow-ramping magnetic field induces a low EMF (-Vr), and the sudden turn-off induces a much higher EMF (+Vf). Because the turn-on magnetic field is a perfect linear ramp, the EMF is a perfect constant level. Since the target can be modeled as an RL circuit, this is akin to applying a stepped DC voltage to an RL circuit. From Circuits 101, the current will exponentially rise to a peak value and stay there. The target EMF for a 20us target looks like this:



Now during the turn-on period the eddy current exponentially increases to a maximum value and would remain at that value is we could sustain the ramping magnetic field. In this case, you could say that the target will reach "saturation" at 5*tau. However, this effect is undesirable. As with the square pulse, the turn-on residual eddy current subtracts from the turn-off eddy drive current to weaken the target response. That is to say, we don't want to saturate the target with turn-on eddy currents, we want them to be zero.

While the fast target can mostly overcome the turn-on eddy offset, a slow target has more trouble:



In this case a 100us target wastes about 2/3rds of its flyback drive just overcoming the turn-on eddy offset. You might be tempted to suggest that we just use a shorter turn-on ramp, so that we cut the turn-on eddy losses earlier in the exponential. But that also means the magnetic field peak is proportionately cut, and the flyback EMF drive as well. It's a losing proposition. You're better off going the other way: let the turn-on eddies reach their exponential peak before turning off the TX. This may be what people refer to when they talk about letting the target fully saturate. Problem is, this isn't what really happens in a real design. That will be Part 3.

While on the subject of ramps, they are also used in VLF designs, namely multifrequency. You can drive a coil with a square wave to produce a triangle wave current, which continuously ramps up & down. The result is a square wave EMF in the target, which then creates a periodic exponential eddy current:



In the receive coil this looks like exponential spikes:



You can either demodulate this with time domain methods much like a PI, or with frequency domain methods like a normal VLF. Although this is really a subject for a separate thread, I thought I would include it as another example of how all this stuff works.

[waltr]

Yes, I agree that multi-pulse widths would certainly offer an advantage, but I was trying to also explain that to maximise the number of pulses being sampled, you can squeeze in more by having a multi-frequency arrangement too. In essence, you'd have multi pulse width and multi frequency machine. The multi frequency part enables you to optimise the accumulated integrated voltage to be higher, due to more samples being taken for a given time period.

Depends on how the processing is done. Let's say you have a 100us pulse every millisecond. That's 1kHz. Now you add a 20us pulse in between each 100us pulse. Normally you would process those in independent RX channels, each running at 1kHz. So you are still effectively at 1kHz as the two processing channels are independent of each other. OTOH, you might also blend them right into the first demod and then have an effective 2kHz.

Like this?

[Carl-NC]

Yes, I agree that multi-pulse widths would certainly offer an advantage, but I was trying to also explain that to maximise the number of pulses being sampled, you can squeeze in more by having a multi-frequency arrangement too. In essence, you'd have multi pulse width and multi frequency machine. The multi frequency part enables you to optimise the accumulated integrated voltage to be higher, due to more samples being taken for a given time period.

Depends on how the processing is done. Let's say you have a 100us pulse every millisecond. That's 1kHz. Now you add a 20us pulse in between each 100us pulse. Normally you would process those in independent RX channels, each running at 1kHz. So you are still effectively at 1kHz as the two processing channels are independent of each other. OTOH, you might also blend them right into the first demod and then have an effective 2kHz.