Targets frequency response

[Qiaozhi]

To remove any confusion, here is a summary of the tests I have performed so far, and my conclusions following these experiments. Please refer to the diagram below.

Different colors have been used to denote different parts of the experiment, as follows:

• The coin is shown in "brown".
• The individual eddy currents (gross representation) are shown in "blue".
• The areas of maximum current density are shown in "red" and "green".

First - some explanation. When the coin is close to the search head, eddy currents are generated throughout the body of the coin. These eddy currents tend to overlap each other, and due to the principle of superposition they more or less cancel each other, except around the circumference of the coin. This is where the current density is highest, resulting in a current flow around the circumference. So there are two things happening here:

1. The current (shown in "red") generates a magnetic field that is detected by the RX coil.
2. The body of the coin absorbs some of the TX energy, but fails to produce any significant magnetic field. i.e. the body of the coin actually weakens the target response.

It should be noted that the restriction of the current to the coin circumference has nothing to do with skin effect. This phenomenon is only significant at frequencies above 100KHz, and not at the VLF frequencies we are talking about here. Anyway, the skin effect only limits the depth of penetration of the TX signal, and hence the creation of eddy currents. Therefore in these experiments the whole volume of the coin has an effect on detection, not just the surface.

Coin #2 is identical to coin #1 except for a small hole drilled in the center. By the same reasoning you can determine that there will be a current flowing around the inner circumference of the hole, but in the opposite direction. This current is too far from the outer current to cause any cancellation. The result is that coin #1 and coin #2 produce no measurable difference in detection distance.

Coin #3 has a larger hole in the center than coin #2. In this case there is still insufficient material removed from the coin to provide a detectable difference.

It is not until enough material is removed (coin #4) that the target response is improved. What seems to be happening here is that more of the TX electromagnetic field is concentrated in the ring, and less energy is being lost in the coin body, which has essentially been removed. There is still one more experiment to perform, and that is shown by coin #8. This represents a situation where the ring is now very narrow. The expectation here is that the inner and outer currents will start to interact and the target response will again be reduced.

The experiments performed with coins #5, #6 and #7 all confirm the assumption that a current path is established around the circumference. It is unlikely that the air gap is being bridged by displacement current as the gap is too wide. These three coins all give a target response that is indistinguishable from coin #1. The only conclusion is that the current follows the edge of the cut. If this was not the case then the cut coins would have a reduced target response, whereas they have neither an improved or a reduced response.

All of this, of course, assumes that the coin is lying flat in the same orientation as the search coil.

If the concentric ring theory was correct, the three cut coins would show a massive reduction in target response. Which reminds me that there is one experiment I forgot to show in the diagram. That is a ninth coin, identical to coin #4, with a cut through the ring. This particular coin has a very poor target response, but the concentric ring theory would predict that coin #7 and coin #9 (not shown) would both show the same reduction, which they do not.

It is this last experiment that is probably the most interesting. As we have seen, you can drill out material from the center of the coin and the response improves. But if you remove material by cutting in from the edge, the response will initially be the same as coin #1. However, removing more material by this method causes the response to be dramatically reduced. The cut ring is an extreme example.

[Aziz]

Hi Qiaozhi,

thanks for your excellent work.
Could you make a tenth coin?
Take coin #3 and make a cut version of this (open the ring).
Than compare #3 and #10 (new one).

Aziz

[Tinkerer]

Hi Qiaozhi,

thanks for posting this excellent work.

Now, how would it look for a sphere instead of a coil? My guess is, probably not much different, since the VLF runs at low frequency.

It does look different for a PI though.

The di/dt at switch off of the PI can be a 100 times higher, so we are definitely in the skin effect region.

Tinkerer

[Qiaozhi]

Hi Qiaozhi,

thanks for your excellent work.
Could you make a tenth coin?
Take coin #3 and make a cut version of this (open the ring).
Than compare #3 and #10 (new one).

Aziz

Unfortunately I do not have coin #3 anymore. During the first set of experiments with the steel-based coins I managed to blunt several drill bits. Therefore I filed out coin #3 to make coin #4. However, I still have coin #2, which I have cut down to the inner circle. The response of this new coin (coin #10) is identical to the original coin. This of course now means that coin #2 no longer exists.

[Aziz]

Hi Qiaozhi,

it doesn't matter. I just want you to discover your wrong assumptions.

Particularly in the coin #2, #3, #4 and #8, the green opposite current flow is wrong. As long as the ring is not open, the current direction must be the same as on the outer side. The current density is lower in the inner area (could be visualised in light red).

I am sorry, but the circular eddy currents theory is not busted yet.

Aziz

[mikebg]

"... the cutoff frequency of a coin..."

???
I think Qiaozhi is confused mostly with this statement. Me too.

Ivica,
the cutoff frequency "fc" of a conductive target is explained in many postings of this thread. This is the point M shown in the lesson of posting #8, Exercise 1 in the posting #18, the figure in posting #42 etc. The Bode diagram is shown in several postings and was explained why it is called "cutoff frequency". If needed, I can explain it again with this draft, which is more clear than in the present posting #42. Is there a need?

[Qiaozhi]

Hi Qiaozhi,

thanks for posting this excellent work.

Now, how would it look for a sphere instead of a coil? My guess is, probably not much different, since the VLF runs at low frequency.

It does look different for a PI though.

The di/dt at switch off of the PI can be a 100 times higher, so we are definitely in the skin effect region.

Tinkerer

The formation of eddy currents in the target is slightly more complicated than my simple diagrams suggest, as they assume a 2-dimensional shape. However, any currents that circulate across the top and bottom of the coin will be perpendicular to the the plane of the coil and will not contribute to the target response.

Therefore I agree that a sphere, with the same cross-section as the coin, will most likely give a similar response.

[Qiaozhi]

Hi Qiaozhi,

it doesn't matter. I just want you to discover your wrong assumptions.

Particularly in the coin #2, #3, #4 and #8, the green opposite current flow is wrong. As long as the ring is not open, the current direction must be the same as on the outer side. The current density is lower in the inner area (could be visualised in light red).

I am sorry, but the circular eddy currents theory is not busted yet.

Aziz

If the concentric ring theory was correct the original coin (#1) would give the best response, as all the "rings" would contribute to the RX signal. Likewise coins #4 and #7 would have the worst response, as a large number of the "rings" are missing. In reality coins #1 and #7 give the same response, and coin #4 gives the best.

[Aziz]

Hi Qiaozhi,

do you remember the compact coil and its inductivity?

The coin #1 is a coil with 1 winding and the winding is not densed. It will induce not much compared to a thin ring version.

Now let's think of again.
Aziz

[Qiaozhi]

The formation of eddy currents in the target is slightly more complicated than my simple diagrams suggest, as they assume a 2-dimensional shape. However, any currents that circulate across the top and bottom of the coin will be perpendicular to the the plane of the coil and will not contribute to the target response.

Therefore I agree that a sphere, with the same cross-section as the coin, will most likely give a similar response.

Before anyone points this out, I was talking cr*p in the above post. Of course there are no perpendicular eddy currents, as all they are all formed around the magnetic lines of flux created by the TX coil. When the coin is in the center of the coil these magnetic force lines will be perpendicular to the coin's surface, and hence the eddy currents will be created in the same plane as the coin. Which means the coin can be treated as a 2-dimensional object. Hope this makes sense.

[Qiaozhi]

Hi mikebg,

So far you have failed to convince me that the concentric ring theory is correct ... BUT, I may have just convinced myself that it could be so.

Read on ...

In order to disprove the concentric ring theory I constructed a number of rings using some tinned copper wire (22 SWG, 0.71mm) with diameters of 3.7cm, 3cm, 2.5cm and 1.5mm. Let's refer to these rings as A, B, C and D.

I then performed some measurements using these rings by monitoring the output of the metal detector's sample gate in the GEB channel. Combinations of rings were tried so as to duplicate sets of concentric rings. The results were as follows:

* A = 75.8 mV
* A+B = 81.3 mV
* A+B+C = 79.2 mV
* A+B+C+D = 78.8 mV

As you can see, the maximum response was achieved with A+B, whereas I would have expected the response to increase as each subsequent ring was added. After some further experimentation, using different combinations of the rings, I found that the combination with the highest response was in fact A+C (87.5 mV). Things initially appeared very strange until I realized this was actually a measurement error, as far as this test was concerned. Instead of monitoring the output of the GEB sample gate I should really be monitoring the output of the DISC channel. By monitoring the GEB channel I am seeing the amplitude change caused by phase-shifts in the RX signal. A more accurate result can be obtained by using the DISC channel and, although there is still some error introduced by phase-shifts, the measurements should be accurate enough for these tests. The results using the DISC channel were:

* A = 68.7 mV
* A+B = 100.4 mV
* A+B+C = 111.0 mV
* A+B+C+D = 112.9 mV

As you can see the target response increases as more rings are added. At this point I thought "OK, that's the concentric ring theory busted!". Because it is clear from real world tests that a drilled-out coin has a better response than the original, but the concentric ring theory indicates the reverse.

Then ..... I repeated the original coin tests while also monitoring the DISC channel:

1. Original 2p coin = 51.3 mV
2. 2p coin drilled/filed to a 5mm ring = 49.7 mV
3. 2p coin with 5mm cut in circumference = 48.0 mV
4. 2p coin cut through to center = 32.7 mV
5. 2p coin cut through to other side = 30.7 mV
6. 2p cut ring = 3.4 mV

By the way, the voltages shown represent only the change in voltage at the DISC output. There was a residual voltage of 72.3 mV that was subtracted from each of the measurements.

Now - what very strange result can you spot from these tests?

Test #2 (the ring) gives a lower amplitude change than the original coin, whereas we all know that the ring can actually be detected at greater depth. So what's going on? The conclusion is that the improved target response is down to phase-shift alone.

Also (now the measurement error has been eliminated) you can see from test #3 that the 5mm cut causes a reduction in amplitude. Dare I say it? ... as if some of the outer rings (of the concentric ring theory) have been cut.

I should probably repeat these experiments while monitoring both the GEB and DISC channels, then calculate the resultant amplitude vector. This would eliminate any errors due to phase-shift in the DISC channel. Stay tuned for more later.

The big question I have at this time is, "What could cause the eddy currents to flow in concentric rings?", if of course that is what's actually happening.

Most curious.

[Esteban]

Hi mikebg,

So far you have failed to convince me that the concentric ring theory is correct ... BUT, I may have just convinced myself that it could be so.

Read on ...

In order to disprove the concentric ring theory I constructed a number of rings using some tinned copper wire (22 SWG, 0.71mm) with diameters of 3.7cm, 3cm, 2.5cm and 1.5mm. Let's refer to these rings as A, B, C and D.

I then performed some measurements using these rings by monitoring the output of the metal detector's sample gate in the GEB channel. Combinations of rings were tried so as to duplicate sets of concentric rings. The results were as follows:

* A = 75.8 mV
* A+B = 81.3 mV
* A+B+C = 79.2 mV
* A+B+C+D = 78.8 mV

As you can see, the maximum response was achieved with A+B, whereas I would have expected the response to increase as each subsequent ring was added. After some further experimentation, using different combinations of the rings, I found that the combination with the highest response was in fact A+C (87.5 mV). Things initially appeared very strange until I realized this was actually a measurement error, as far as this test was concerned. Instead of monitoring the output of the GEB sample gate I should really be monitoring the output of the DISC channel. By monitoring the GEB channel I am seeing the amplitude change caused by phase-shifts in the RX signal. A more accurate result can be obtained by using the DISC channel and, although there is still some error introduced by phase-shifts, the measurements should be accurate enough for these tests. The results using the DISC channel were:

* A = 68.7 mV
* A+B = 100.4 mV
* A+B+C = 111.0 mV
* A+B+C+D = 112.9 mV

As you can see the target response increases as more rings are added. At this point I thought "OK, that's the concentric ring theory busted!". Because it is clear from real world tests that a drilled-out coin has a better response than the original, but the concentric ring theory indicates the reverse.

Then ..... I repeated the original coin tests while also monitoring the DISC channel:

1. Original 2p coin = 51.3 mV
2. 2p coin drilled/filed to a 5mm ring = 49.7 mV
3. 2p coin with 5mm cut in circumference = 48.0 mV
4. 2p coin cut through to center = 32.7 mV
5. 2p coin cut through to other side = 30.7 mV
6. 2p cut ring = 3.4 mV

By the way, the voltages shown represent only the change in voltage at the DISC output. There was a residual voltage of 72.3 mV that was subtracted from each of the measurements.

Now - what very strange result can you spot from these tests?

Test #2 (the ring) gives a lower amplitude change than the original coin, whereas we all know that the ring can actually be detected at greater depth. So what's going on? The conclusion is that the improved target response is down to phase-shift alone.

Also (now the measurement error has been eliminated) you can see from test #3 that the 5mm cut causes a reduction in amplitude. Dare I say it? ... as if some of the outer rings (of the concentric ring theory) have been cut.

I should probably repeat these experiments while monitoring both the GEB and DISC channels, then calculate the resultant amplitude vector. This would eliminate any errors due to phase-shift in the DISC channel. Stay tuned for more later.

The big question I have at this time is, "What could cause the eddy currents to flow in concentric rings?", if of course that is what's actually happening.

Most curious.

Hi Qiaozhi. Good work!

Do you think can be used technology of coil selector/rejector for this purpose? Read the text of this magazine on Google books. Year: 1955.

http://books.google.com.py/books?id=...age&q=&f=false

[Qiaozhi]

Hi Qiaozhi. Good work!

Do you think can be used technology of coil selector/rejector for this purpose? Read the text of this magazine on Google books. Year: 1955.

http://books.google.com.py/books?id=...age&q=&f=false

Coin selector/rejectors are using the same principle that you see when dropping a magnet down a copper pipe. They induce a magnetic field in the coin and measure how long it takes to slide down the incline. It's probably not that useful for these tests.

I am working on a full summary of my experiments, that I intend to post here. It's starting to get a little confusing for anyone reading this thread with all the different posts. I will try and make it clear and simple with lots of diagrams.

[mikebg]

Editor wanted

Qiaozhi and Ivica,
Look again at the right side of the figure in posting # 134. It represents cross section of a cylinder made of magnetic field. This is the shape of the magnetic field in the volume of the coin when a DC TX current suddenly stops. How should eddy currents flow in the coin to form such a cylinder? How eddy currents are needed and how should they be distributed in coin volume to form such a cylinder?
Fourier (1768-1830) has decided to heat a similar task in 1807, ie more than 200 years ago. REMI group has already given me almost all of the draft decision valid for eddy currents. It says rediscovering of EMI! They did not accidentally invented the name of the group to begin with "RE". Once rediscovered eddy currents, they will reinvent even metal detecting :-)
Now faced with the task before me to translate in English, mathematics text, explaining the decision of the differential equation given in posting # 149.
But I have so little linguistic knowledge in this area, it is necessary to seek help from the participants in this forum. The mistake I made with the spelling the name as Quiaozhi is nothing compared to the errors which I will do in a mathematical text.
Someone who is familiar with mathematical terminology in English, must edit my translation. Please, who wants to edit a text written in mathematical language Pseudoenglish (worse than Chinglish), he gave me his email.

[mikebg]

LF region

Using the Normalized Impedance plot
The advantage of Normalized Impedance plot is that its shape is almost identical for all forms of nonferrous targets and nonferrous halfspace (ground, salt water). There is a difference, which
is illustrated in the attached figure, but it is not essential for design purpose. We need to determine in what area of the spectrum can be increased phase difference between
signals in order to improve discrimination and to suppress the signal from the ground.
Disadvantage of Normalized Impedance is that it not shows the real value of the magnitude and
frequency, but only relative to the maximum magnitude and relative to own cutoff frequency. This
shortcoming creates discomfort when in common drawing two targets are presented.
I will explain this in the next posting as damaged a few coins, but only virtually. Who does not
believe the results of virtual coins can actually damage :-).
Now to explain what is shown in the figure below. It is a comparison between the shapes of the normalized
impedance at 4 nonferrous solids: bracelet (ring), cylinder (coin), sphere (gold nugget) and
halfspace. They are scaled so that to coincide its LF region (below cutoff frequency). You may know what is the curve of the bracelet (ring), because occurs Moreland's effect.