Targets frequency response

[mikebg]

Eddy Diameter

Though experiment - Mentally damaged coins.
In the attached figure using a single term "eddy diameter" of the target. This is the largest recorded
diameter circle in the outlines of the target when it is viewed in the direction of the magnetic field.
The eddy diameter of halfspace is equal to diameter of TX loop. The fundamental time constant,
respectively, the fundamental cutoff frequency, depend on the square of the eddy diameter.
What happens with cutoff frequency when we cut the coin?
In frequency domain, if we reduce twice eddy diameter, the cutoff freqency will increase 4 times. This
is done by cut coin in half, as shown in case 2.
Let's see how this looks on Normalized Impedance plot and on a not normalized Impedance plot.
To be continued.
normalized.

[Tinkerer]

Though experiment - Mentally damaged coins.
In the attached figure using a single term "eddy diameter" of the target. This is the largest recorded
diameter circle in the outlines of the target when it is viewed in the direction of the magnetic field.
The eddy diameter of halfspace is equal to diameter of TX loop. The fundamental time constant,
respectively, the fundamental cutoff frequency, depend on the square of the eddy diameter.
What happens with cutoff frequency when we cut the coin?
In frequency domain, if we reduce twice eddy diameter, the cutoff freqency will increase 4 times. This
is done by cut coin in half, as shown in case 2.
Let's see how this looks on Normalized Impedance plot and on a not normalized Impedance plot.
To be continued.
normalized.

Hi Mikebg,

I understand the following sentence:"The fundamental time constant,
respectively, the fundamental cutoff frequency, depend on the square of the eddy diameter. "

In the time domain, like PI, we have a few test targets for testing the TIME CONSTANTS (TC) and the detector's ability to detect targets with these time constants.
A square of 1" of Aluminium foil, of the thin household kind, has a TC or time constant of about 10us. If we cut this square in half, the time constant is reduced to 5us.
The time constants are affected by the conductivity of the target. An example is nickel that is often used in alloys for modern coins and stainless steel, that shortens the TC.
High conductivity = long time constant, but the thickness of the target also affects the TC.
Targets with less that 0.5mm thickness show a short time constant. Example is an Aluminium soda can. It gives a high amplitude response because of it's large surface area, but the TC is very short compared to a Aluminium block of the same volume.
Magnetic targets have a longer TC. Some types of detector use this feature to differentiate or discriminate FE targets. However, thin rusty pieces of steel sheet, have short TC's, so this type of discrimination is not very good for these targets.
With the TINKERERS_V1 the TC of a target behaves much like a cutoff frequency in the frequency domain. This is why some degree of target identification can be gleaned.

Tinkerer

[bbsailor]

Though experiment - Mentally damaged coins.
In the attached figure using a single term "eddy diameter" of the target. This is the largest recorded
diameter circle in the outlines of the target when it is viewed in the direction of the magnetic field.
The eddy diameter of halfspace is equal to diameter of TX loop. The fundamental time constant,
respectively, the fundamental cutoff frequency, depend on the square of the eddy diameter.
What happens with cutoff frequency when we cut the coin?
In frequency domain, if we reduce twice eddy diameter, the cutoff freqency will increase 4 times. This
is done by cut coin in half, as shown in case 2.
Let's see how this looks on Normalized Impedance plot and on a not normalized Impedance plot.
To be continued.
normalized.

Mikebg, Tinkerer and other Gurus

The purpose of this thread is to try to identify an unknown target by some response properties that may help deduce an unknown target's identity. Because targets may lay in the ground in many different orientations, it is possible that some target responses may be ambigious requiring the target to be dug up to actually see its identity.

I am mostly a beach hunter as I live near the New Jersey Shore. I want to share some experiences and ask the active members of this discussion thread to comment and independently verify by doing a few quick tests.

I have experienced the following. When I locate a target on the beach, I visually pinpoint the target location, then move the coil about 2 inches off to the side and sweep the coil slowly over the target listening for the sound level in my headphones. I increase the sweeep speed about 3 times faster than the slowest sweep speed and listen for an increase in signal level. Most of the time the increase in signal level indicates a ferrous target like a washer.

If this technique could be verified, it may provide another tool in using coil sweep speed changes to help better deduce the identity of an unknown ferrous target. This should be tried with and without Ground Balance methods being activated.

Thanks for the interesting discussion.

bbsailor

[Qiaozhi]

Eddy Current Experiments

The following information is provided as a summary of the recent experiments on eddy current generation in a coin used as a metal detector target.

This exercise was started when mikebg posted a claim that Carl's article on "Induction Basics" contained an incorrect explanation for the effect where an open round target, such as a ring, gives a stronger response than a solid target, like a coin. See post #128, and figure 1 below.

My first reaction was that mikebg's assumption (which I have termed "The Concentric Ring Theory") was incorrect. The main reason being that this theory would appear to predict a solid round target has a better response than an open round target. Now, as any metal detectorist knows, this is not the case, and (as stated previously by Carl) the ring can be detected 2 to 2.5 cm farther away than the coin. In order to prove "The Concentric Ring Theory" was indeed incorrect, I started a series of experiments, with some interesting results.

The Concentric Ring Experiment

This experiment was designed to confirm that a set of concentric rings would have an improved response as more rings were added, thus demonstrating that "The Concentric Ring Theory" predicts something different to reality. The rings were constructed from 22SWG (0.71 mm) tinned copper wire with diameters of 3.7cm, 3cm, 2,5cm and 1.5cm. They were arranged as shown in figure 2 below. The RX amplitude was recorded for different combinations of the rings. It was a simple matter to show the best response was obtained by using all 4 rings, whereas any other combination gave a lower response.

The Coin Experiment

The same measurements were then made using an original coin plus a number of modified coins. See figure 3 below.
Now this is where it gets interesting...

It is clear from the measurements that the ring (#2) has a lower amplitude than the original coin (#1). This was contrary to expectations, and raises the question as to why the ring is detectable at a greater distance from the coil. The answer can be found by measuring the phase-shift of the RX signal for these two targets. In this case it was discovered that the ring (#2) produced a greater phase-shift than the original coin (#1). Therefore, although the RX amplitude is lower, the phase-shift is greater.

It was also found that coins 3, 4 and 5 gave progressively lower responses than the original coin, and the cut ring gave an extremely poor response.

How can we explain these results?

Obviously there are other factors, apart from the RX amplitude, in operation here that cause the ring to have an enhanced response in the real world. For a VLF detector the ring produces the greatest phase-shift in the received signal. For a PI the ring allows the eddy currents to persist for a longer period of time. In the concentric ring experiment the combination of rings A+C actually provided the greatest phase-shift. This could be explained by considering the individual targets as a tuned circuit. As we know, slightly adjusting the value of either the RX inductor or capacitor will cause the initial TX-RX phase relationship to change. Much the same situation must also be occurring for the various targets. With reference to figure 4 below, let's now consider the cut coins.

Coin #3 gave a slightly reduced amplitude response when compared to the ring (#2) or the original coin (#1). This is consistent with the idea that the outer eddy current ring(s) have been cut. Also note how the responses of coin #4 and #5 are markedly reduced when compared to coin #3. This is consistent with all the rings being cut , thus forcing the eddy currents to form alternate paths within the two halves of the coin, as shown in figure 4 below.

Conclusion

Although the eddy currents are generated in the target object as a number of extremely small intersecting vortices, the superposition of these eddy currents results in cancellation, such that larger eddy current rings are formed. The experiments have shown that the overall shape of the target has a significant effect on the received signal for both magnitude and phase, and a dramatic demonstration is given by the cut ring (#6), where the eddy currents are restricted to moving in small circles defined by the thickness of the ring.

Unfortunately I am failing to understand mikebg's description (most likely due to the language barrier) but we do now seem to agree on the way the eddy currents are formed in the target. Initially I expected the eddy currents to almost completely cancel in the coin interior, leaving a single strong circulating current around the circumference, but the experiments indicate otherwise. I believe Carl's modified diagram, shown in figure 5 below, is correct. Note how the arrows get smaller as you move towards the center of the coin.

This was an interesting set of experiments, even if I did manage to blunt a number of drill bits in the process.

I hope everyone else found it as interesting.

[mikebg]

Using of Normalized Impedance

The attachment below contains two impedance diagrams. In the left diagram, which is normalized, are shown OM signal across a coin and signal ON from a piece of coin cut in half as case 2 above in posting. Phases of the signals are properly presented in the normalized diagram, but not amplitudes. For proper display of amplitudes, is given the right diagram in which the frequencies and amplitudes are not relative, and each point means KHz.
Suppose that a coin has a cutoff frequency fc = 5KHz and we have a CW (Sine Induction) TX illuminating it with f = 5KHz. Then the relative frequency is F = f / fc = 1 and we receive a signal 0M with phase lag 45 deg, as shown in normalized diagram.
When the coin is cut into two halves, as in case 2 of the upper posting, the eddy diameter is twice smaller. The cutoff frequency fc is inversely proportional to square of eddy diameter. That means the new cutoff frequency is 4 times higher, ie fc = 20KHz. But TX continue to illuminate it with f = 5KHz. Then the relative frequency of case 2 is F = f / fc = 5 / 20 = 0,25 and we receive a signal 0N having phase lag less than 45 deg. A small phase lag is good when you need to suppress the signal from ferrous ground, which has a phase advance almost 90 degrees. Synchronous demodulators discriminate best when the phase difference is close to quadrature.
However, the work LF region is a disadvantage when targets are buried in conductive nonferrous ground because the ground signal also has a phase lag instead phase lead. Therefore, in saline beach is better TX to work in HF region to get closer to quadrature phase difference between the target signal and ground signal.
When TX works in the LF region of targets, the RX receives considerably weaker target signal. The left figure shows that ON <OM, but in reality this difference is much greater. If you do not use normalized impedance, we get shown the right picture, where the frequencies and amplitudes are not relative, but real. The reason for the weaker signal from a small eddy diameter is in addition due to the fact that the received signal depends on the mutual inductance between the RX loop and eddy loop in target. As smaller the eddy loop, the less is the mutual inductance.
So far we have examined the case of cut coin, but the experiment does not need to cut coins. There are coins of different diameter, made of the same metal.
Everything said here for "eddy diameter of target", goes for gold nugget. In a large gold nugget, TX illuminates it in HF region, where small - in LF region. In what region must work TX, depends on EM properties of ground. So the next posting will contain an explanation of grond signal as normalized impedance.

[Qiaozhi]

The attachment below contains two impedance diagrams. In the left diagram, which is normalized, are shown OM signal across a coin and signal ON from a piece of coin cut in half as case 2 above in posting. Phases of the signals are properly presented in the normalized diagram, but not amplitudes. For proper display of amplitudes, is given the right diagram in which the frequencies and amplitudes are not relative, and each point means KHz.
Suppose that a coin has a cutoff frequency fc = 5KHz and we have a CW (Sine Induction) TX illuminating it with f = 5KHz. Then the relative frequency is F = f / fc = 1 and we receive a signal 0M with phase lag 45 deg, as shown in normalized diagram.
When the coin is cut into two halves, as in case 2 of the upper posting, the eddy diameter is twice smaller. The cutoff frequency fc is inversely proportional to square of eddy diameter. That means the new cutoff frequency is 4 times higher, ie fc = 20KHz. But TX continue to illuminate it with f = 5KHz. Then the relative frequency of case 2 is F = f / fc = 5 / 20 = 0,25 and we receive a signal 0N having phase lag less than 45 deg. A small phase lag is good when you need to suppress the signal from ferrous ground, which has a phase advance almost 90 degrees. Synchronous demodulators discriminate best when the phase difference is close to quadrature.
However, the work LF region is a disadvantage when targets are buried in conductive nonferrous ground because the ground signal also has a phase lag instead phase lead. Therefore, in saline beach is better TX to work in HF region to get closer to quadrature phase difference between the target signal and ground signal.
When TX works in the LF region of targets, the RX receives considerably weaker target signal. The left figure shows that ON <OM, but in reality this difference is much greater. If you do not use normalized impedance, we get shown the right picture, where the frequencies and amplitudes are not relative, but real. The reason for the weaker signal from a small eddy diameter is in addition due to the fact that the received signal depends on the mutual inductance between the RX loop and eddy loop in target. As smaller the eddy loop, the less is the mutual inductance.
So far we have examined the case of cut coin, but the experiment does not need to cut coins. There are coins of different diameter, made of the same metal.
Everything said here for "eddy diameter of target", goes for gold nugget. In a large gold nugget, TX illuminates it in HF region, where small - in LF region. In what region must work TX, depends on EM properties of ground. So the next posting will contain an explanation of grond signal as normalized impedance.

In short, I presume you are saying that you need to use a higher TX frequency in order to find small targets such as gold nuggets.

[Tinkerer]

Mikebg, Tinkerer and other Gurus

The purpose of this thread is to try to identify an unknown target by some response properties that may help deduce an unknown target's identity. Because targets may lay in the ground in many different orientations, it is possible that some target responses may be ambigious requiring the target to be dug up to actually see its identity.

I am mostly a beach hunter as I live near the New Jersey Shore. I want to share some experiences and ask the active members of this discussion thread to comment and independently verify by doing a few quick tests.

I have experienced the following. When I locate a target on the beach, I visually pinpoint the target location, then move the coil about 2 inches off to the side and sweep the coil slowly over the target listening for the sound level in my headphones. I increase the sweeep speed about 3 times faster than the slowest sweep speed and listen for an increase in signal level. Most of the time the increase in signal level indicates a ferrous target like a washer.

If this technique could be verified, it may provide another tool in using coil sweep speed changes to help better deduce the identity of an unknown ferrous target. This should be tried with and without Ground Balance methods being activated.

Thanks for the interesting discussion.

bbsailor

Hi bbsailor,

thanks for sharing your experience with us.

Magnetically permeable targets, concentrate the field lines of the earths magnetic field and also change the vector of the field.
Sweeping the coil through the earths magnetic field will generate a current in the coin. If the field lines are parallel to the coil sweep, this current is practically 0.
Near the equator, in an area without iron ore bodies, the earths magnetic field lines are practically parallel to the surface of the earth.
In higher latitudes the angle increases. Near iron ore bodies the angle can be near 90 degrees.
But if the field lines are perpendicular, the coil current can be appreciable.
The faster the coil is swept across the field, the stronger is the coil current.
Even an object as small as an iron washer can concentrate and distort the earths magnetic field lines by 90 degreed in it's immediate vicinity.
Therefore, an iron target can give an increased response when the sweep speed is increased.

The following post about nulling the earths magnetic field response, has some bearings to this phenomenon.
http://www.geotech1.com/forums/showp...0&postcount=22

All the best

Tinkerer

[pebe]

Hi Mikebg,

I understand the following sentence:"The fundamental time constant,
respectively, the fundamental cutoff frequency, depend on the square of the eddy diameter. "

In the time domain, like PI, we have a few test targets for testing the TIME CONSTANTS (TC) and the detector's ability to detect targets with these time constants.
A square of 1" of Aluminium foil, of the thin household kind, has a TC or time constant of about 10us. If we cut this square in half, the time constant is reduced to 5us.
The time constants are affected by the conductivity of the target. An example is nickel that is often used in alloys for modern coins and stainless steel, that shortens the TC.
High conductivity = long time constant, but the thickness of the target also affects the TC.
Targets with less that 0.5mm thickness show a short time constant. Example is an Aluminium soda can. It gives a high amplitude response because of it's large surface area, but the TC is very short compared to a Aluminium block of the same volume.
Magnetic targets have a longer TC. Some types of detector use this feature to differentiate or discriminate FE targets. However, thin rusty pieces of steel sheet, have short TC's, so this type of discrimination is not very good for these targets.
With the TINKERERS_V1 the TC of a target behaves much like a cutoff frequency in the frequency domain. This is why some degree of target identification can be gleaned.

Tinkerer

I am familiar with RC and LR time constants (TC), but don't see how they are relevant in your text. Are you referring to 'time delay' or am I missing something? And why 'fundamental'?

[Tinkerer]

I am familiar with RC and LR time constants (TC), but don't see how they are relevant in your text. Are you referring to 'time delay' or am I missing something? And why 'fundamental'?

Hi pebe,

the "fundamental part, blue text, is a quote from Mikebg, he may answer that.

The TC or time constants I refer to, are for one part the time constant or TC of the coil, which is the LR you mention.

The other time constant is of the target. With the PI type of detector, a target behaves much like a coil. It does take some time to induce the maximum eddy currents like a LR time constant.

Then it takes some time for the eddy currents to dissipate again. This time is what the traditional PI uses to read the magnetic field caused by the eddy currents. (Time Domain)

When we refer to a time constant of a target, we usually consider it to be the time that it takes for the amplitude of a target response to fall by about 63%.
To put it in numbers, if a target response signal has an amplitude of 100uV
10us after switch off of the TX pulse, and 10us later the signal amplitude is only about 37uV and still 10us later it will be about 15uV.
This means that probably, about 30 to 40us after switch off of the TX pulse, the target signal will be lost in the noise. S/N

Few PI detectors are capable of sensing a target that has a TC less than 5us.

Tinkerer

[pebe]

Hi Tinkerer,
Thanks for your most comprehensive reply. It makes sense to me now.

pebe

[mikebg]

Cutoff frequency and timeconstant of ground

Ground signal, TX frequency and diameter of TX loop

The conductive ground also has a cutoff frequency. It depends on the diameter of the TX loop.

What happens when you change diameter of TX coil, can be analyzed with a Normalized Impedance in complex plane.
Cutoff frequency of ground is inversely proportional to the square of the diameter according the formula below. However the attached figure and formula are valid for nonmagnetic ground only.
What happens when ground has mineralization (ferromagnetizm), is explained in the posting #18.
When synchronous demodulator is adjusted to eliminate the ground signal (ground balance), it must remain sensitive enough to target signal. The task of the designer is to select one TX frequency and such diameter of TX loop, to obtain an appropriate phase difference between the ground signal and target signal. The most relevant difference is quadrature phase, ie 90 degrees. But if you think about how to do this at the impedance of a mineralized ground shown in posting # 18, you'll understand why in Australia for metal detector is difficult to find gold nuggets.

[mikebg]

One year has passed since (R)EMI group ceased its activities in July morning.
Ex members of (R)EMI group felt that I have lack of knowledge. They were dissatisfied with my work as a spokesman, but I, in turn, was unhappy with their work organization because nobody helped me in compiling and editing postings. They only answered my questions. They stopped to answer me a year ago because they thought that in the 21st century

The learning process requires mostly student working, than work of teachers.

However, I have gained knowledge and skill to see the shortcomings of my postings.
For example, not even a brief explanation of the formulas to above figure. I had to point out that D is the diameter of the TX coil. The above formula is universally valid, but the below formula is simplified because it is assumed that no ferrite soil properties, ie ur = 1.
Not specified how by measurement of fc we can calculate timeconstants of soil.
Not specified how to design optimal D (TX coil diameter) by measuring phase lag of GND signal with a given TX coil.
However I know the answers

[mikebg]

Cutoff frequency and timeconstants of ground

Addition to post #206:
Conductive ground also has series of timeconstants as described above in post #98:
http://www.geotech1.com/forums/showt...9656#post99656
John Corbin measured enough exact two of ground timeconstants. Note that measured by him ratio is almost 9 times
http://www.geotech1.com/pages/metdet...byn/corbyn.pdf

[Qiaozhi]

Cutoff frequency and timeconstants of ground

Addition to post #206:
Conductive ground also has series of timeconstants as described above in post #98:
http://www.geotech1.com/forums/showt...9656#post99656
John Corbin measured enough exact two of ground timeconstants. Note that measured by him ratio is almost 9 times
http://www.geotech1.com/pages/metdet...byn/corbyn.pdf

Note:
In the Corbyn article, there is some text missing from the bottom of the first page.
The scanned document says "Fig. 2 shows the case where a magnetic flux of Weber is normal to a loop of radius a and ..."

It should go on to say "... effectively falls to zero in time . If L is ...". Which then continues on the second page.

[mikebg]

CORRECTIONS OF PAPERS

To say that there are metal detectors working in the frequency domain is nonsense. The frequency domain is only a poweful tool for analysis and design. Every metal detector (see connected to it oscilloscope :-) works in time domain.
According to frequency domain, metal detectors are only two types:

1. Narrow band metal detectors, in which the receiver processes spectral data from a narrow bandwidth of frequencies (for example 16Hz), and

2. Wideband (broad band) metal detectors, in which the receiver processes information from a wider bandwidth (for example an octave or more).

Note that this classification is subject to received frequency band only, not to the transmitted by own TX spectrum. If the spectrum radiated by transmitter contains frequencies that the receiver does not handle and does not need, it means that the TX wastes energy. Each ham designer of QRP amateur radio will tell you that such one transmitter is not created by member of this brotherhood.
Using Frequency domain, we can correct certain documents posted in this thread. Here is an example, but instead corrections, I recommend you to write papers again.
You can see the original of this document in post # 27:

http://www.geotech1.com/forums/showt...1424#post71424