Announcement

**dougAEGPF** · 12-06-2012, 09:36 PM

I have 13 pages of links to papers on EM here:
http://australianelectronicgoldprosp...and-em-fields/
dougAEGPF

**moodz** · 12-07-2012, 05:04 AM

Hi Eric ... was the work done by John ever in the public domain or was it under trade secrets or patents. Just curious.

thanks. Moodz.

**Ferric Toes** · 12-07-2012, 09:38 AM

Originally posted by moodz View Post

Hi Eric ... was the work done by John ever in the public domain or was it under trade secrets or patents. Just curious.

thanks. Moodz.

The work was done as part of a contract we had in 1976 - 77 to develop a vehicle mounted UXO detector, to clear tracts of land in southern England that had been used for Army training. Much of the theoretical side came from a 1956 paper By F.B. Johnson entitled A Pulsed Bomb Locator. This was done at the Signals Research and Development Establishment of the Army. Again there was a previous paper by J. H. Wescott in 1955 which Johnson built on. Wescott was from Imperial College, London. I was given the latter two papers when I joined the Research Laboratory for Archaeology, Oxford, as groundwork for the PI method. After Johnson's paper nothing much happened as the Army considered the method too active in that magnetic fuzes could be triggered. Mind you, Johnson was advocating a peak current of 25A in a coil of 2 Henrys to detect a 100lb bomb at 45ft! I was given the latter two papers as groundwork for PI when I joined the Research Laboratory for Archaeology, Oxford, in 1966. Articles on PI were published in "Archaeometry", the journal of RLA between 1965 and 1970 by Colani and Aitken, myself, and J. Green who is now Curator of the Maritime Museum, Freemantle, WA. John Alldred was also at RLA working on Thermoluminescent Dating equipment having gained his Masters Degree researching fluxgate magnetometers. I left RLA in 1970 and started my own business, Geoelectronics Ltd, and snapped John up a year later when he left.

PI has a longer history than is generally realised although much of the earlier stuff is not easily accessed. I have traced it back at least to 1914 -18 War in a primitive form.

Eric.

**moodz** · 12-07-2012, 11:08 AM

Thanks Eric ... the history is fascinating and I get the feeling some it will be lost if not already.

Regards,

Moodz

**Ferric Toes** · 12-07-2012, 01:52 PM

I have many of the historical documents still, and will post extracts from them when appropriate. The information may be useful to others who have more recently entered the PI camp and can apply cutting edge techniques to advance the technology further. Here is the cover page of Johnson's paper.

Eric.

**Davor** · 12-07-2012, 06:02 PM

More, more ....

**dougAEGPF** · 12-07-2012, 09:49 PM

Originally posted by moodz View Post

Thanks Eric ... the history is fascinating and I get the feeling some it will be lost if not already.

Regards,

Moodz

Another old but interesting one 1971
ON CALCULATING TRANSIENT ELECTROMAGNETIC FIELDS OF A SMALL CURRENT-CARRYING LOOP OVER A HOMOGENEOUS EARTH
James R. Wait and Randolph H. Ott
Institute for Telecommunication Sciences
Office of Telecommunications
U. S. Department of Commerce
Boulder, Colorado 80302

Contract No. PRO-Y-71-87Z
Project No. 5635
Task No. 563506

Work Unit No. 56350601
Scientific Report No. 53
July 14, 1971
http://australianelectronicgoldprospectingforum.com/electromagnetics-and-em-fields/on-calculating-transient-em-fields-of-a-small-current-carrying-loop/msg26520/?topicseen#msg26520
dougAEGPF

**Aziz** · 12-08-2012, 12:12 PM

Hi all,

has anyone made the interesting proof yet?
You know, it will be only a theory until someone proves it to be true (or false).

I'm not going to bite the bullet...
Cheers,
Aziz

**Qiaozhi** · 12-09-2012, 08:48 AM

Originally posted by Ferric Toes View Post

Well this is what I have. Not by me but by John Alldred, employed by myself in the 1970's. He had a Masters Degree in physics and was one of those rare persons who could work out all the maths and theory and then build something that worked.

Hi Eric,

This is a very interesting extract from the document you posted:
"In the present application, high efficiency was required over a wide range of τ values, a self-conflicting requirement which was met in the experimental model by having two receiver channels operating in parallel per coil, with different values of t1 t2 and t3, and hence different values of optimum τ. Not only does this mean that an efficient response will be obtained over a wider range of object time constants, but also that an immediate indication of approximate τ is shown which gives an idea of object size."

Then it goes on to say:
"The relative signal output as a function of object time constant is shown in Fig. 3 for the examples (a) t1 = t2 = 50us, t2 = 150us, (b) t1 = 100us, t2 = 200us, t3 = 400us. The vertical scale is arbitrary, as the factor R/rT needs to be incorporated."

Please note that there is small error in the above, as it should read "(a) t1 = t2 = 50us, t3 = 150us"

However, the figure shown below this text only appears to be the first part of figure 3.
Would it be possible for you to scan and post the whole of figure 3?

Lastly ... (perhaps this is generally known, and I'm just being slow) ... although everyone is aware that "ferric toes" is actually Eric Foster, I've only just noticed that it was also an anagram.

**sido** · 12-09-2012, 05:53 PM

Qiaozhi

"Lastly ... (perhaps this is generally known, and I'm just being slow) ... although everyone is aware that "ferric toes" is actually Eric Foster, I've only just noticed that it was also an anagram."

Great observation there, sure is a anagram.

Sid

**Ferric Toes** · 12-09-2012, 10:31 PM

Yup, erotic serf, is another possibility but ferric toes is more appropriate having tramped around a few times on Australian ironstone. Have a look at http://www.wordsmith.org/anagram/advanced.html and have fun with names.

Qiaozhi, should be t3 = 150uS as you say. I drew in the part of fig.3 that was relevant to the sampling, and the other part of fig. 3 has to to with coil size/object distance. That will appear when I post the page on coil calculations, which will be soon.

Would it be best to start a new thread on PI History and Theory so that the older information is all in one place?

Ferric.

**Qiaozhi** · 12-10-2012, 11:57 AM

I have examined the 3 pages of the paper by John Alldred, that were posted by Eric.
Here are my comments, starting from the section entitled "Electronic Signal Processing":

Firstly, please note that I have replaced $r\ \ with\ \ R_s,\ \ and\ \ R\ \ with\ \ R_l,\ \ as\ \ r\ \ and\ \ \tau$ look too similar in latex, and may cause confusion.

The input signal $V = v_0\exp^{-t/\tau}$ .......... (Eq. 9)

where:
V = value of the target signal due to eddy currents induced by the transmit pulse. This cannot be observed directly due to being swamped by the reverse voltage from the coil.
t = elapsed time after the transmit pulse is switched off.
$\tau$ = decay constant of the target.

It is stated that the transmission (sample) gate and associated integrator cannot be considered as a simple sample-and-hold unit.

At t = $t_1$ , the sample gate is closed for a time $t_2$ . Hence $t_1$ is the main sample delay and $t_2$ is the main sample pulse width. Note (at the bottom of page 1) it states "At time t = $t_1$ the transmission gate is opened". Of course, this should read "... the transmission gate is closed", since the gate needs to be closed to take the sample.

Charge builds up on the capacitor (C) according to:

$\Delta Q = \frac{1}{R_sC}\int_{t_1}^{t_1+t_2}v\ dt$ .......... (first part of Eq. 10)

$\Delta Q$ is the incremental charge transferred to the capacitor during each sample. There is also a scale factor ( $R_s$ ) which represents the resistance in series with the sample gate, plus the resistance of the sample gate itself (although this is small in comparison). The capacitor charging period occurs during the time period between $t_1$ (gate closes) and $t_1+t_2$ (gate opens). Which simply means that the capacitor (C) is charged via the series resistor ( $R_s$ ) when the main sample occurs, and this charge increments exponentially over time in the presence of a metal target as more samples are taken.

If we substitute equation 9 into equation 10, we have:

$\Delta Q = \frac{1}{R_sC} \int_{t_1}^{t_1+t_2}v_0\ \exp^{-t/\tau}\ \ dt$

Then:

$\Delta Q = \frac{v_0}{R_sC}\int_{t_1}^{t_1+t_2}\exp^{-t/\tau}\ \ dt \ \ = \ \ -\frac{v_0}{R_sC} \ \ \frac{\exp^{-t/\tau}}{1/\tau} \ \ = \ \ -\frac{v_0\tau}{R_sC}\ \ \exp^{-t/\tau}$

Plugging in the limits for the integral ( $t_1\ \ and\ \ t_1 + t_2$ ) gives:

$\Delta Q = \left (-\frac{v_0\tau}{R_sC}\ \ \exp^{-t_1/\tau}\right )\ \ -\ \ \left (-\frac{v_0\tau}{R_sC}\ \ \exp^{-(t_1+t_2)/\tau}\right )$

$\ \ =\ \ \left ( \frac{v_0\tau}{R_sC}\ \ \exp^{-(t_1+t_2)/\tau}\right )\ \ -\ \ \left (\frac{v_0\tau}{R_sC}\ \ \exp^{-t_1/\tau}\right )$

$\ \ =\ \ \frac{v_0\tau}{R_sC}\ \ \left (\exp^{-(t_1+t_2)/\tau} -\ \ \exp^{-t_1/\tau}\right )$

Hence:
$\Delta Q =\ \ -\frac{v_0 \tau\ \ \exp^{-t_1/\tau}}{R_sC}\left (1 - \exp^{-t_2/\tau}\right )$ .......... (Eq. 10)

Note that this equation has a negative sign (not shown in the paper).

In between samples the capacitor (C) loses some of its charge by:

$-\Delta Q = \frac{VT}{R_lC}$ where $R_l$ >> $R_s$ )

$R_l$ represents the leakage resistance for the charge on the capacitor.

Re-arranging for V gives:

$V = -\frac{R_lC}{T} \Delta Q$

Then subsititute equation 10 into the equation above, to eliminate $\Delta Q$ and C:

$V = \frac{R_l}{R_sT}\ \ \frac{v_0\exp^{-t_1/\tau}}{R_s}\ \ \tau\left (1 - \exp^{-t_2/\tau}\right )$

Note that the previous negative sign in equation 10 has been cancelled to reveal a positive voltage.

Hence we have arrived at equation 11:

$V = \frac{R_l}{R_s}\ \ v_0\exp^{-t_1/\tau}\ \ \frac{\tau}{T} \left (1 - \exp^{-t_2/\tau}\right )$ .......... (Eq. 11)

In order to show that this DC equilibrium signal can be approximated by $V \approx v_0\exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\ \ \frac{t_2}{T}$ for the case where $t_2\ \ <<\ \ \tau$ , we can try a simple example:

The question can be reduced to determining whether $t_2 \approx \tau \left (1 - \exp^{-t_2/\tau}\right )$ . In this case let us set $t_2 = 1\mu s$ and $\tau = 100\mu s$ .

Therefore: $\tau \left (1 - \exp^{-t_2/\tau} \right )\ \ = \ \ 100\mu s\ \ \left ( 1 - \exp^{-1/100} \right )\ \ = \ \ 1\mu s\ \ = \ \ t_2$

Confirming that $V \approx v_0\exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\ \ \frac{t_2}{T}$ for the case where $t_2\ \ <<\ \ \tau$ .......... (Eq. 12)

An alternative approach is to make $t_2$ >> $\tau$ , and the approximate equation then becomes:

$V = v_0 \exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\frac{\tau}{T}$ where $t_2$ >> $\tau$ .......... (Eq. 13)

This approximation assumes that $\left (1 - \exp^{-t_2/\tau}\right )$ is close to unity, which is true for $t_2$ >> $\tau$ .
Note that equation 13 in the paper incorrectly shows $v_0\exp^{-t/\tau}$ , which should of course be $v_0\exp^{-t_1/\tau}$ .

The result is that the transfer function $V/v_0$ increases with $\tau$ . In other words, the gain of the sample gate / inverter varies depending on the decay constant of the target, but is balanced somewhat by the fact that V itself is inversely proportional to $\tau$ .

The 3rd page of the paper discusses the use of a second later sample to remove the signal generated when the coil is moved through the Earth's magnetic field. I haven't studied that section in detail just yet.

The conclusion so far is:

For $t_2$ << $\tau$ , the amplitude of the received signal is largely independent of the target time constant. However, using a very small sample pulse width has the disadvantage of producing a very low amplitude signal.
For $t_2$ >> $\tau$ , the amplitude of the received signal is largely independent of the sample pulse width, as the exponential term containing $t_2$ tends to unity.

Hopefully I didn't make any errors with the latex syntax.

**ApBerg** · 12-10-2012, 12:41 PM

Originally posted by Qiaozhi View Post

I have examined the 3 pages of the paper by John Alldred, that were posted by Eric.
Here are my comments, starting from the section entitled "Electronic Signal Processing":

Firstly, please note that I have replaced $r\ \ with\ \ R_s,\ \ and\ \ R\ \ with\ \ R_l,\ \ as\ \ r\ \ and\ \ \tau$ look too similar in latex, and may cause confusion.

The input signal $V = v_0\exp^{-t/\tau}$ .......... (Eq. 9)

where:
V = value of the target signal due to eddy currents induced by the transmit pulse. This cannot be observed directly due to being swamped by the reverse voltage from the coil.
t = elapsed time after the transmit pulse is switched off.
$\tau$ = decay constant of the target.

It is stated that the transmission (sample) gate and associated integrator cannot be considered as a simple sample-and-hold unit.

At t = $t_1$ , the sample gate is closed for a time $t_2$ . Hence $t_1$ is the main sample delay and $t_2$ is the main sample pulse width. Note (at the bottom of page 1) it states "At time t = $t_1$ the transmission gate is opened". Of course, this should read "... the transmission gate is closed", since the gate needs to be closed to take the sample.

Charge builds up on the capacitor (C) according to:

$\Delta Q = \frac{1}{R_sC}\int_{t_1}^{t_1+t_2}v\ dt$ .......... (first part of Eq. 10)

$\Delta Q$ is the incremental charge transferred to the capacitor during each sample. There is also a scale factor ( $R_s$ ) which represents the resistance in series with the sample gate, plus the resistance of the sample gate itself (although this is small in comparison). The capacitor charging period occurs during the time period between $t_1$ (gate closes) and $t_1+t_2$ (gate opens). Which simply means that the capacitor (C) is charged via the series resistor ( $R_s$ ) when the main sample occurs, and this charge increments exponentially over time in the presence of a metal target as more samples are taken.

If we substitute equation 9 into equation 10, we have:

$\Delta Q = \frac{1}{R_sC} \int_{t_1}^{t_1+t_2}v_0\ \exp^{-t/\tau}\ \ dt$

Then:

$\Delta Q = \frac{v_0}{R_sC}\int_{t_1}^{t_1+t_2}\exp^{-t/\tau}\ \ dt \ \ = \ \ -\frac{v_0}{R_sC} \ \ \frac{\exp^{-t/\tau}}{1/\tau} \ \ = \ \ -\frac{v_0\tau}{R_sC}\ \ \exp^{-t/\tau}$

Plugging in the limits for the integral ( $t_1\ \ and\ \ t_1 + t_2$ ) gives:

$\Delta Q = \left (-\frac{v_0\tau}{R_sC}\ \ \exp^{-t_1/\tau}\right )\ \ -\ \ \left (-\frac{v_0\tau}{R_sC}\ \ \exp^{-(t_1+t_2)/\tau}\right )$

$\ \ =\ \ \left ( \frac{v_0\tau}{R_sC}\ \ \exp^{-(t_1+t_2)/\tau}\right )\ \ -\ \ \left (\frac{v_0\tau}{R_sC}\ \ \exp^{-t_1/\tau}\right )$

$\ \ =\ \ \frac{v_0\tau}{R_sC}\ \ \left (\exp^{-(t_1+t_2)/\tau} -\ \ \exp^{-t_1/\tau}\right )$

Hence:
$\Delta Q =\ \ -\frac{v_0 \tau\ \ \exp^{-t_1/\tau}}{R_sC}\left (1 - \exp^{-t_2/\tau}\right )$ .......... (Eq. 10)

Note that this equation has a negative sign (not shown in the paper).

In between samples the capacitor (C) loses some of its charge by:

$-\Delta Q = \frac{VT}{R_lC}$ where $R_l$ >> $R_s$ )

$R_l$ represents the leakage resistance for the charge on the capacitor.

Re-arranging for V gives:

$V = -\frac{R_lC}{T} \Delta Q$

Then subsititute equation 10 into the equation above, to eliminate $\Delta Q$ and C:

$V = \frac{R_l}{R_sT}\ \ \frac{v_0\exp^{-t_1/\tau}}{R_s}\ \ \tau\left (1 - \exp^{-t_2/\tau}\right )$

Note that the previous negative sign in equation 10 has been cancelled to reveal a positive voltage.

Hence we have arrived at equation 11:

$V = \frac{R_l}{R_s}\ \ v_0\exp^{-t_1/\tau}\ \ \frac{\tau}{T} \left (1 - \exp^{-t_2/\tau}\right )$ .......... (Eq. 11)

In order to show that this DC equilibrium signal can be approximated by $V \approx v_0\exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\ \ \frac{t_2}{T}$ for the case where $t_2\ \ <<\ \ \tau$ , we can try a simple example:

The question can be reduced to determining whether $t_2 \approx \tau \left (1 - \exp^{-t_2/\tau}\right )$ . In this case let us set $t_2 = 1\mu s$ and $\tau = 100\mu s$ .

Therefore: $\tau \left (1 - \exp^{-t_2/\tau} \right )\ \ = \ \ 100\mu s\ \ \left ( 1 - \exp^{-1/100} \right )\ \ = \ \ 1\mu s\ \ = \ \ t_2$

Confirming that $V \approx v_0\exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\ \ \frac{t_2}{T}$ for the case where $t_2\ \ <<\ \ \tau$ .......... (Eq. 12)

An alternative approach is to make $t_2$ >> $\tau$ , and the approximate equation then becomes:

$V = v_0 \exp^{-t_1/\tau}\ \ \frac{R_l}{R_s}\frac{\tau}{T}$ where $t_2$ >> $\tau$ .......... (Eq. 13)

This approximation assumes that $\left (1 - \exp^{-t_2/\tau}\right )$ is close to unity, which is true for $t_2$ >> $\tau$ .
Note that equation 13 in the paper incorrectly shows $v_0\exp^{-t/\tau}$ , which should of course be $v_0\exp^{-t_1/\tau}$ .

The result is that the transfer function $V/v_0$ increases with $\tau$ . In other words, the gain of the sample gate / inverter varies depending on the decay constant of the target, but is balanced somewhat by the fact that V itself is inversely proportional to $\tau$ .

The 3rd page of the paper discusses the use of a second later sample to remove the signal generated when the coil is moved through the Earth's magnetic field. I haven't studied that section in detail just yet.

The conclusion so far is:

For $t_2$ << $\tau$ , the amplitude of the received signal is largely independent of the target time constant. However, using a very small sample pulse width has the disadvantage of producing a very low amplitude signal.
For $t_2$ >> $\tau$ , the amplitude of the received signal is largely independent of the sample pulse width, as the exponential term containing $t_2$ tends to unity.

Hopefully I didn't make any errors with the latex syntax.

Oooo..., yes now I understand....

Thanks !

**Midas** · 12-10-2012, 01:30 PM

Originally posted by Ferric Toes View Post

Yup, erotic serf, is another possibility but ferric toes is more appropriate having tramped around a few times on Australian ironstone. Have a look at http://www.wordsmith.org/anagram/advanced.html and have fun with names.

Qiaozhi, should be t3 = 150uS as you say. I drew in the part of fig.3 that was relevant to the sampling, and the other part of fig. 3 has to to with coil size/object distance. That will appear when I post the page on coil calculations, which will be soon.

Would it be best to start a new thread on PI History and Theory so that the older information is all in one place?

Ferric.

You also don't seem like the fierce sort. But you could well be an if secretor, all good inventors are.

**Davor** · 12-10-2012, 01:31 PM

Now explain how you did it

Announcement

field test unit no 001 "model T"

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment

Comment