Optimizing Target Responses

[Carl-NC]

Works for me in Firefox, but not Edge.

[Qiaozhi]

Yes - Chrome and Edge on Windows (different PCs) and Kiwi on Android. All the same - just show a little icon as if there should be an image for all the equations.

If I 'inspect' the icon the page source shows an <image> tag with a source url that contains what I think is LaTex code. I guess there should be a server-side cgi plugin to convert the LaTex code into an image format?

paul

Have you tried Firefox?
I'm using Firefox on Linux, and it displays just fine.

[Repwoc]

Yes, better late than never!

Part 5: Real Responses

So far we've looked at different responses and applied piecewise-linear solutions to much of it. That is, the PI turn-off was a linear ramp that induced a step EMF in the target. This is a good first-order approximation and a good way to do quick-n-dirty comparisons, like what happens when you try to get a sharper & sharper turn-off slew rate (Part 4).

In reality, the PI coil is an RL circuit during turn-on and an RLC circuit during turn-off. Equations can be derived that accurately describe what they do. I won't derive them here but rather just toss them out. ITMD3 will have full derivations.

The turn-on equation is simple:



The turn-off equation is non-obvious but here it is:



where is the peak current at the turn-off event.

In the above quote I have removed the CR/LF after the opening latex and before the closing latex tags. This results in the formulae being displayed instead of the broken image link icons.

paul

[Repwoc]

So the formula rendering issue seems to be due to html <br /> tags that are embedded in the img tag src url, eg:

<img src="http://www.geotech1.com/cgi-bin/mimetex.cgi?<br />
v_{off}(t) = \frac{I_0}{C_L}\cdot t \cdot e^{-t/\tau_{RX}}<br />
">

If I remove these (in Chrome DevTools) then the formulae are displayed correctly.

[Repwoc]

Have you tried a different browser?

Yes - Chrome and Edge on Windows (different PCs) and Kiwi on Android. All the same - just show a little icon as if there should be an image for all the equations.

If I 'inspect' the icon the page source shows an <image> tag with a source url that contains what I think is LaTex code. I guess there should be a server-side cgi plugin to convert the LaTex code into an image format?

paul

[Altra]

Hello - really enjoying reading this thread but ... the equations are not rendering. Do I need some special plugin or something?

thanks
paul

On my android phone. The equations are missing for me also on part 5. In other posts, same thread they are okay. Maybe the part 5 attachments are corrupted?

[Qiaozhi]

Have you tried a different browser?

[Repwoc]

Yes, better late than never!

Part 5: Real Responses

So far we've looked at different responses and applied piecewise-linear solutions to much of it. That is, the PI turn-off was a linear ramp that induced a step EMF in the target. This is a good first-order approximation and a good way to do quick-n-dirty comparisons, like what happens when you try to get a sharper & sharper turn-off slew rate (Part 4).

In reality, the PI coil is an RL circuit during turn-on and an RLC circuit during turn-off. Equations can be derived that accurately describe what they do. I won't derive them here but rather just toss them out. ITMD3 will have full derivations.

The turn-on equation is simple:



The turn-off equation is non-obvious but here it is:



where is the peak current at the turn-off event.

Let's look at a realistic example...

Measured coil parameters:
L = 300uH
Rs = 5 ohms (total series R)
SRF = 500kHz (inc. cable etc)

VTX = 10V

The parasitic C for the coil is



The require damping resistor for critical damping is



Now calculate the taus:





VTX (10V) and Rs (5 ohms) tells us the max flat-top current will be 2A. The TX tau os 60us so we would need a TX pulse width of ~300us to reach the flat-top current. A more normal TX pulse width is 100us which makes the calculated peak current 1.62A at turn-off. This becomes the starting point for the turn-off equation.

Here are both equations plotted in Excel. Note that the turn-on curve spans 100us whereas the turn-off curve spans only 3us.



Also note that in the turn-off side the tau_RX is 318ns. If you are expecting the current to be substantially gone in 5*tau (1.59us) you can see it is not. The 0.67% mark occurs at about 2.25ns which is about 7*tau, about 40% more than the usual RL curve.

But that's not the worst part; let's also look at the flyback voltage. Its equation can also be derived:



We have all the variables from above; the curve looks like this:



This curve is also plotted to only 3us. The peak hits ~560v which can be calculated from the derivative of the above equation. Note that the peak occurs at exactly tau_RX. If you were to assume that any kind of 5*tau settling applies here, then you would take 0.67% of 560v (=3.8v) and see that it occurs at about 2.57us, which is about 8*tau.

But this is the raw coil voltage which is then applied to a preamp with a fairly hefty gain, perhaps 500. It's immediately obvious that 3.8v will seriously overload the preamp. To determine a realistic required settling we need to make an assumption: that the preamp must be, say, within 0.5v of settled for the demods to work well. For a gain of 500, this means the coil voltage must be within 0.5v/500 = 1mv of settled. In the curve above, this happens at about 5.42us, or 17*tau.

You might be thinking that 5.42us is pretty darned good. But this is strictly the coil settling; the diode clamps and the preamp overloading have not been accounted for. And everything above assumes the MOSFET never avalanches.

[ATTACH]54867[/ATTACH]
[ATTACH]54866[/ATTACH]

Hello - really enjoying reading this thread but ... the equations are not rendering. Do I need some special plugin or something?

thanks
paul

[ivconic]

[Carl-NC]

One of the problems with putting components down below is that now you have to provide power and clock over the cable. In a traditional mono coil PI, you have to put both the TX and preamp down below so you might have TX power, VCC & VEE for the preamp, ground, and TX clock. Plus the RX signal, so a minimum of 6 lines. The TX power will have large transient currents unless you also place the tank caps down below.

It becomes a logistical challenge which is probably why no one has done it. And the only reason for doing it is to squeeze out a lower sample delay. But then all that metal close to the coil becomes a problem. And it's not the absolute decay deflection that's a problem; that just becomes an offset that can be ignored. Rather, it's the motion over variable mineralized ground (esp hot rocks) that causes variations in the TX field which then induces a transient response in the circuit components that looks just like a good target. This doesn't show up in bench testing or even in the usual backyard testing. Only when you finally get to a real gold field.

[bbsailor]

Another way is to put the RX front end and the TX pulse transistor into the detector head right at the coil. Then the cable has no effect.

Yes, Here is where experimentation is very important. If the active components are inside the coil housing, might they be seen as targets at certain delays. However, if these active components were located at the end of the plastic coil stem, they might be far enough away and outside an area where these components are detected as targets.

These are just thoughts to eliminate or minimize coil seen capacitance to sample faster and better detect smaller targets. Good experiments can lead to better performance!

Joseph J. Rogowski

[waltr]

Another way is to put the RX front end and the TX pulse transistor into the detector head right at the coil. Then the cable has no effect.

[ivconic]

... One of the most impractical designs I've ever seen...

Wait a minute! The conductors can be "impregnated" into a strong plastic material, in the form of a rod that will go between the detector and the coil.
With a very simple connection system. It doesn't have to be impractical that much.


"...So 75Ω is better than 50Ω..."


And 300Ω is better than 75Ω !
So called "twin lead" (but not twisted) Tv antenna cable is practically a form of a Lecher line!
(i haven't read your post completely, haven't seen that you also mentioning it)
Wink! Wink! Wink!
Does it have to be shielded at all?
FelezJoo works better if not shielded. Much calmer and more accurate.
And yes it can be additionally shielded if needed.
"...The conductors can be "impregnated" into a strong plastic material..."
The very same material with conductive compound used in common search head shielding.
And if give more freedom to my imagination; the connecting system can be made with two small neodymium pairs, one pair also "impregnated" into rod and another pair into detector enclosure.
(Similar to Apple charging&data transfer connectors)
Give your imagination total freedom to figure out how actually easy it can be done!


"...So called "twin lead" (but not twisted) ..."
Yes there is also a twisted one version too.
Come to think... why they also made a twisted one?

Go figure...

[Carl-NC]

Ha, I haven't seen Lecher lines mentioned in over 35 years, back to my e-mag lab in college. I actually own a metal detector that almost uses that concept, a Roth BFO. The coil is connected to the control box by two regular 70s-style telescoping antennae, and each antenna is a conductor for the coil. One of the most impractical designs I've ever seen.

Back to practical matters, a higher impedance cable has lower capacitance. So 75Ω is better than 50Ω. I have seen stranded-core coax up to 125Ω but can't seem to find any for sale. And then there is 300Ω twin-lead which looks more like a Lesher line, but it's not shielded.

[ivconic]

Thoughts to consider when trying to reduce coil capacitance.

Sources of coil- seen capacitance.

1. The coil windings, turn to turn capacitance governed by the dielectric constant of the wire insulation and the insulation thickness and coil to shield capacitance.
2. MOSFET and other diode capacitance as seen by the coil.
3. COAX cable capacitance based on the length between the coil and the control box that is about 100pf.

We can reduce number 3 by being creative and building a remote circuit located at the end of the aluminum shaft, near the coil that puts the necessary circuits in the available space to reduce or eliminate the coil- seen coax capacitance.

The less capacitance that the coil sees, the higher value the damping resistor can be and the steeper the coil discharge sloop will be to better stimulate smaller targets. However, smaller targets may be parts of the coil that retain eddy currents such as coil wire, shield, or other metal parts that were not previously detected.

These thoughts are just to get the creative minds of this forum to push forward.

Thanks

Joseph J. Rogowski

Obviously the technology is having its limits.
Change the technology if possible.
If you can't squeeze more juice from a lemon: change a lemon... or take a orange!


Purely for the sake of theoretical discussion; how would it be if instead of a cable we connect the coil to the TX output with the Lecher line?