frequency depth relation diagram

[Funfinder]

They say higher frequency can't penetrate ground that good.

But what is the exact ratio-curve of this?

If a given coil at 10kHz will penetrate the ground 50cm
how much reaches the same coil if 100kHz is used?

Is this a linear or eliptical curve?

Is this compensatable by more current / voltage / windings / inductivity?


Is there another curve how much better small objects
get detected by higher frequency compared to lower one?


And finally: is there a special coil size limit for a certain frequency?

[Davor]

I'd say you asked the right questions that need to be tackled with. There are several effects in play so we may come to some analytical result only if we have all the data put right at the first place.

All MDs of the VLF or PI type tackle the eddy currents induced in various materials, including targets, ground, parts of equipment, and trash. Eddy currents are related to the material resistivity and the skin depth.
In case a target is thinner than the skin depth at the working frequency, it will produce a response which corresponds to a higher resistivity material e.g. gold flakes, tin foil etc. Standard household foil is typically 0.016 - 0.024 millimeters thick.
Skin depth for copper at 10kHz is ~0.65mm and for gold is ~0.8mm. Double the frequency and you have 0.46mm for copper and 0.55mm for gold etc. Only the skin depth works for target recognition. Skin depth is proportional to 1/sqrt(f)
With objects thick enough (thicker than the skin depth) we can discriminate various materials by their tau, or the eddy current decay characteristic. In simulations we can represent various objects by a parallel connection of a coil and a resistor, where L/R gives a time constant (tau) that corresponds to a respective material. We can find values close to these (my estimates for 1mm thick objects, please correct me if you know more accurate values):
Silver: 165μs
Copper: 135-155μs
Gold (bulk): 105μs
Aluminum: 90μs
Nickel, brass: 15μs
Bronze: 8μs
Aluminum foil 16μm @ 10kHz: 1.7μs
same foil @ 100kHz: 5.4μs
...
sea water: ~0.3μs (estimate for 25 cm thick layer)

It is quite interesting to see that the sea water (my idea of a mineralised ground stand-in) has this much of a tau, and it has ~5 million times resistivity of copper, but trouble is with skin depth that is almost 2 meters thick at 10kHz, so it builds up tau. At 100kHz skin depth of sea water would be ~0.5m and that may prove to be a practical limiting effect.

Ground represents a half space looking from a coil, so ground coupling is big, despite the low conductivity.

In case water/mineralisation skin depth is a major limiting factor, then you'll have a third of a depth per 10 times the frequency. And you'll be able to correctly detect 3 times thinner targets.

I so hope to have my estimates/hypotheses corrected.

[Funfinder]

Thank you for this great answer!

Would be fantastic if more such real technical informed persons could respond and a little bit faster.


Now let's see how we can work with this disc @ certain frequency info.

It indicates that the lower the used frequency, the less reliable discrimination is possible.

btw. that eddy current skin responding time also with P.I. is detectable. And the skin effect usually is a high-voltage or high-frequency phenomena where the main electrons use the metals or wires skin for moving forward, but not just there.

And not to forget: in high mineralized soil for detection possibility at all (especially at high depth) a high enough "contrast factor" is needed or has to created by enough transmission energy or stable and very sensitive detection circuits.

And the surface of the ground also has a skin effect, especially if high mineralized.



OK - we have 2 possibilities:

- going for highest depth without (reliable) discrimination

- using a frequency that already has good disc capability (6kHz upwards) even for thin targets


If nobody here has the slightest clue about how deep a 10Hz detector can penetrate compared with a 100kHz one perhaps anyone knows at what frequency ground penetration no longer is possible.


And I really hope someone here knows how much deeper a detector at say 10kHz will penetrate if 20 volts instead of 10 volts is used or the double amount of TX energy.


For the beginning all we need is just a circa curve, not extremly exact one.



As example:
max detection for 1x1m metal-plate in medium mineralized ground


100 Hz - 20 volt - 50mW TX (too high? ) - 30cm coil @ 100V (or nTesla equivalent):
2.5 meter

1 kHz: 2m

10kHz: 1.5m

100kHz: 1m

1MHz: 0.5m

[Davor]

There is a little SNAFU with more-juice-better-yield concept, and that one deals with imperfections in system that make raising the Tx power a diminishing returns game. Wether it is a Tx noise, Rx dynamic range, or some other effect, you'll hit the ceiling one way or another.
At best you can get more in case you improve your Rx dynamic range, otherwise you are just chasing your tail ... a bit faster than before.

[Funfinder]

> you'll hit the ceiling one way or another.

Can't imagine that multi-frequency already will be the absolute final solution.

Especially not with one and the same coil.


We have the huge volume of the ground or explained better:

The coils size penetration energy related to ground volume and object-find size.

That's why of course large coils with more windings and therefore higher magnetical impulse energy can penetrate much better huge volume of ground / create better contrast factor (on larger objects).

So the best solution would be using a big coil with low frequency to reach the deep targets and an up to 30cm coil with higher frequency for the "close" small stuff.


> Wether it is a Tx noise, Rx dynamic range, or some other effect, you'll hit the ceiling one way or another.

I think the most important question is the responding time. Creating high power VLF fields at low frequency may lead to slow responding time while at 100kHz the detection circuit needs to be much more stable and accurate.


But now it seems we still have no clue how much better a 100Hz penetrate compared with 100KHz. Guess my Garrett Pro Pointer uses 100kHz but still has very good penetration results if manually tuned to absolute border-sensitivity by little screw! It can detect a horseshoe in ground from ca. 25cm.

[Carl-NC]

If a given coil at 10kHz will penetrate the ground 50cm
how much reaches the same coil if 100kHz is used?

Is this compensatable by more current / voltage / windings / inductivity?

This would make for a good experiment. Keep in mind that the TX magnetic field is proportional to N*I which appears to be frequency independent, but I (current) is inversely proportional to wL, assuming a sinusoid. So to make a good experiment, you need to be very careful in order to maintain a fair comparison.

[HECTOR]

It seems to me that one could design a detector circuit on a coil or the other way around. Has it been determined which way is most efficient?
Does it make any sense to add more controls to "fine tune" the coil?
I'd like to see a detector that can spank out two separate signals and frequencies for two stacked coils like a concentric over a DD.
What a depth/disc/pinpointing monster that would be.
Just throwing out ideas.

[Sean_Goddard]

Don't forget the fact that the more Tx signal you pump out, the more likely you are to saturate the ground mineral matrix. What this means is that you reach the point where the return signal from the ground is so large it masks the target (which is already pretty damned small in relation). Couple the above with the additional fact that this level varies depending on the TYPE of soil, whether is has been recently cultivated (i.e. density) moisture content and you have a whole gamut of fun on the horizon.

I suspect that most commecial detectors are a compromise in the area of "Well it works, sell it" but the reason that machines like the Deus go deeper is that the designer has a better understanding of the above and so has software routines that compensate (it would be interesting to look at the real time Tx/Rx levels on the Deus - HINT...HINT)!!

[Tinkerer]

I'd say you asked the right questions that need to be tackled with. There are several effects in play so we may come to some analytical result only if we have all the data put right at the first place.

All MDs of the VLF or PI type tackle the eddy currents induced in various materials, including targets, ground, parts of equipment, and trash. Eddy currents are related to the material resistivity and the skin depth.
In case a target is thinner than the skin depth at the working frequency, it will produce a response which corresponds to a higher resistivity material e.g. gold flakes, tin foil etc. Standard household foil is typically 0.016 - 0.024 millimeters thick.
Skin depth for copper at 10kHz is ~0.65mm and for gold is ~0.8mm. Double the frequency and you have 0.46mm for copper and 0.55mm for gold etc. Only the skin depth works for target recognition. Skin depth is proportional to 1/sqrt(f)
With objects thick enough (thicker than the skin depth) we can discriminate various materials by their tau, or the eddy current decay characteristic. In simulations we can represent various objects by a parallel connection of a coil and a resistor, where L/R gives a time constant (tau) that corresponds to a respective material. We can find values close to these (my estimates for 1mm thick objects, please correct me if you know more accurate values):
Silver: 165μs
Copper: 135-155μs
Gold (bulk): 105μs
Aluminum: 90μs
Nickel, brass: 15μs
Bronze: 8μs
Aluminum foil 16μm @ 10kHz: 1.7μs
same foil @ 100kHz: 5.4μs
...
sea water: ~0.3μs (estimate for 25 cm thick layer)

It is quite interesting to see that the sea water (my idea of a mineralised ground stand-in) has this much of a tau, and it has ~5 million times resistivity of copper, but trouble is with skin depth that is almost 2 meters thick at 10kHz, so it builds up tau. At 100kHz skin depth of sea water would be ~0.5m and that may prove to be a practical limiting effect.

Ground represents a half space looking from a coil, so ground coupling is big, despite the low conductivity.

In case water/mineralisation skin depth is a major limiting factor, then you'll have a third of a depth per 10 times the frequency. And you'll be able to correctly detect 3 times thinner targets.

I so hope to have my estimates/hypotheses corrected.

"Only the skin depth works for target recognition. Skin depth is proportional to 1/sqrt(f)"

The skin depth is the major factor for target recognition, but certainly not the only one.

Some time ago, I posted the test results of about 6 different copper disk targets. (if only I could find the post) All targets had the same diameter, but different thickness.
The target thickness varied from a single sided copper PCB disk to about 1.5".
The target response, in mV, taken at the output of the front end, seemed to be proportional to the thickness.
If the only target response were from the skin effect, the thickness would have no bearing on the response amplitude.

I still have these targets in my sample target box, so I could repeat the test.

How should we set the test parameters to obtain more information?

Tinkerer

[Davor]

If the only target response were from the skin effect, the thickness would have no bearing on the response amplitude.

PCB copper thickness is much thinner than the skin depth on bulk copper, so in fact - we are talking about the same thing. Such thin targets are more resistive than the bulk targets, hence lower response.

[Tinkerer]

PCB copper thickness is much thinner than the skin depth on bulk copper, so in fact - we are talking about the same thing. Such thin targets are more resistive than the bulk targets, hence lower response.

I think we misunderstood.
The samples are of different thickness.
All samples have approximately the same diameter or surface area.
The thinnest copper sample is a PCB cutout.
The next one is 0.5mm thick.
etc.
The thickest is 40mm thick.

I will add a picture of the test targets.

I will re-do the test and add a disk of alu foil and a disk of lead, just for kicks.

The measurements are in mV.

It will be your job to calculate the difference in response amplitude due of the skin effect and the response due to thickness.

Everybody is invited to help making sense of it.

The results might be very interesting.

To make it still better, I am going to add the RX circuit so that you can see what the gain is and how much processing the signal underwent, since this may explain something.

Tinkerer

[Davor]

Please do, we'll all benefit from real data.

This topic is shaping into something very educational

[Tinkerer]

THICKNESS TEST

Please do, we'll all benefit from real data.

This topic is shaping into something very educational

OK, I am ready for testing.

For the coil I have a 45cm (18") diameter coil, not shielded.

The targets are placed on a plastic box, 25cm (10") above the coil. Static measurement.

For the RX, I use a non-motion setup, because it is easier to take the measurement on the scope. The Schematic is attached and the point of measurement is indicated.

The measurements are not high precision, about +/- 5% accuracy.

To make it a bit more interesting, let's see who can guess.

I have taken 2 measurements already.

One is 50mV

The other one is 200mV

To which targets do these measurements belong?

A picture of the targets is attached.

Tinkerer

[Tinkerer]

Uploading schematic

The picture and schematic did not upload, so here we try again.

Again it did not go, so I try one at the time.

Tinkerer

[Tinkerer]

Test samples

Here are the test samples.
Tinkerer