TARGET TIME CONSTANT

[Tinkerer]

What is the Target Time Constant? Or target TC?
If a penny has a TC of 50uS, will it's signal diminish by 64% in 50uS?
Will the signal reach practically 0 after 300uS?

Will it take a TX of 5 TC's or 300uS to stimulate the penny to its maximum response?

What are the TC's of the Nickel? the Dime? the Quarter?

What is the TC of a silver dollar?

Tinkerer

[KingJL]

What is the Target Time Constant? Or target TC?

Good questions! But, are they "trick" questions? I think discussions of this are warranted and could prove to be highly interesting.

If a penny has a TC of 50uS, will it's signal diminish by 64% in 50uS?

If a penny, in a given environment, exhibits a TC of 50us then yes it's signal will diminish by 64% in 1 TC. I am not yet convinced that there is a fixed TC for a given target. The exhibited TC may be influenced by the TX signal.

Will the signal reach practically 0 after 300uS?

I haven't visited this lately, so I am not sure what the current thoughts are. But 47 years ago, it was accepted that with exponential discharge, 0 charge was, in all practicality, reached after 5 TC (or 250 usec in your stated case).

Will it take a TX of 5 TC's or 300uS to stimulate the penny to its maximum response?

What are the TC's of the Nickel? the Dime? the Quarter?

What is the TC of a silver dollar?

For these questions, I have yet to form an opinion. I hope to gain insight by further discussion and testing.

I have high regard for Eric Foster's views in this area.

[bbsailor]

What is the Target Time Constant? Or target TC?
If a penny has a TC of 50uS, will it's signal diminish by 64% in 50uS?
Will the signal reach practically 0 after 300uS?

Will it take a TX of 5 TC's or 300uS to stimulate the penny to its maximum response?

What are the TC's of the Nickel? the Dime? the Quarter?

What is the TC of a silver dollar?

Tinkerer

Tinkerer,

One thing you can do to see if a target had been saturated by a full pulse, based on the target's time constant (TC) is to start with a low pulse width (PW) about 25 uS and find the distance limit of detection. then, increase the PW and see if that target can be detected at a farther distance. If so, keep increasing the PW until there is no improvement in detection distance.

What you will find is that certain metals can be detected at low PW like U.S. nickels, small gold nuggets and gold rings. Other targets like copper, silver or clad coins need a longer PW to be detected at their full potential distance.

Unfortunately a PI coil, PPS rate, delay, and coil current is a compromise as beach hunters would be very happy just finding gold jewelry, but these targets are few and far between. To make the hunting more interesting it is always good to find coins and espicially when the coins are being thrown up on the beach (in the Spring) and being sorted by the wave action. Find a quarter and most coins along that parallel location to the water will be the same size coin.

So, even though gold is the primary target it is still desirable to find coins. Here is the design compromise. Any transmit pulse width beyond what fully stimulates a gold ring is wasted power from that ring's perspective but is under powered from the perspective of a copper penny that has a total discharge time of 350 uS (reported by Eric Foster on his web site). The copper penny TC is one fifth of the total decay time or 70 uS for the copper penny. A nickel is a good contrast as it has a total decay time of 100 uS with a TC of 20uS. Nickels are a substitute and a good indicator of a PI design/control settings to gold jewlery.

One design feature of PI detectors is the adjustment of the delay to favor certain types of targets. Low delay for low conductivity items like gold and nickels and higher delay for higher conductivity items like copper, silver, and clad coins. Set the delay too high and possibly miss a small gold target.

Getting the PI design to operate at the lowest possible delay requires a damping resistor value that is set at a particular range of PPS frequencies and pulse widths. Note that the new White's TDI, designed by Eric Foster operated in the 3,000 PPS range with a frequency control to vary the frequency a few hundred cycles to tune out local noise. This limited frequency range keeps the TX circuit adjusted and optimum for both gold as well as coins.

Compare this to the Hammerhead design, which has a wide PPS range, an independent PW adjustment and variable delay and sample window widths. If you set the Hammerhead damping resistor (Rd) to be optimum for a narrow PW, say 25 uS, the the flyback voltage will be higher when you increase the PW to 70 uS. Then, the value of Rd would need to be reduced slightly to optimumly damp that higher flyback. This suggests that if you use the Hammerhead or similar design with a wide range of TX pulse widths, that the value of Rd should be padded with a SPST switch with a center off position, allowing the operator to adjust the Rd value to be optimum for three ranges of PW.

As you raise the TX frequency the total battery power will increase as there are more duty cycles consuming battery power. Typically, when the TX PPS frequency is increased the PW is reduced to keep the battery draw to a practical value such as 8 hours of operating time.

The current rise TC of a coil is based on the traditional textbook current growth curve based on the TC of the TX coil circuit. This includes the coil inductance divided by the resistance of: the coil wire itself, any series resistance, MOSFET on-resistance, and the resistance of the coil coax lead.

The longer the TX PW the higher the TX current can rise. A 300 uH coil that is 5.4 ohms, with a .5 ohm MOSFET on-resistance and a lead resistance of .1 ohms has a total resistance of 6 ohms. 300/6 = 50uS.

If the max coil current is 12V/6ohms, 2 A is the maximum current. At a PW of 50 uS the current would grow to 63.2% of 2 amps or 1.264 A. In another 50 uS TC the current will grow 63.2% of the remaining difference to maximum current or 86.5% or maximum current or 1.706A. Add one more 50 uS PW and the current grows to 95% of maximum current or 1.9A. The last few TCs add less to the TX pulse power than the first few TCs. However, to fully saturate a copper penny the TX pulse would need to last about 350 uS. But, good performance on this target can be almost optimized with about 150 to 200 uS PW at the expense of less battery life or needing to carry around heavier batteries.

PI design starts with optimizing the TX on PW current rise and the turn-off current discharge to match the desired targets. Theory states that the optimum current turn-off time should be 5 times faster than the target TC. For a penny with a 70 uS TC a 14 us turn off is not a problem. A nickel with a 20 uS TC needs a 4 uS turn off time. A gold nugget that may have a TC of only 5 uS needs a 1 uS turn off. This current turn off slope, with vertical being fastest possible, is governed by the value of Rd as being the current discharge path.

The value of Rd is governed by the amount of capacitance in the TX circuit and is typically governed by the coil inductance, coil wire insulation dielectric constant, insulation thickness, coil diameter, shield, shield spacer, MOSFET COSS, and coax cable capacitance. In mono coils, the situation is further made a little more comples because the input resistor to the op amp Rin is attached to the coil through a resistor with a typical value of 1K ohms. This resistor is effectivly in parallel with Rd while the flyback pulse is causing the clamping diodes to conduct and this has the effect of lowering the effective value of Rd and lengthening the coil discharge TC. That is why DD coils or induction balanced PI coils are balanced to minimize RX flyback response and are potentially about 2 uS quicker in sampling for more sensitivity on smaller, lower conductive items. This is assuming that the DD coil or IB PI coil has the potential to operate at a lower delay by good construction techniques to minimize capacitance.

As the above discussion shows, the design of a PI detector, starts with knowing the characteristics of the desired targets and by working backwards, key circuit parameters can be identified as PI design parameters that include.

Coil inductance
Coil resistance
Damping resistor value
Main delay
Mono or DD coil
Coil diameter
Coax cable length
Maximum coil current
Battery voltage
Battery life
Pulse width
TX Pulse Per Second (PPS) rate

Beach hunters typically have one given that keeps the minimim delay to about 10 uS for hunting in wet salt sand. Any delay less than 10 us will start detecting the wet sand. Delays lower than 10 uS can be used on the dry portions of the upper beach.

Anyone who has constructed the Hammerhead can try some of the PW and target type experiments (above) for themselves. The Hammerhead is a wide range design that spans the capabilities of many common PI designs from lower frequency larger coil designs to small coil higher frequency nugget/jewlery hunting.

I hope this kicks off some interesting discussions. As PI designs are moving more into software control, knowing the characteristics of the desired targets will tell you the optimum pulse characteristics for your desired targets coded in software.

bbsailor

[Tinkerer]

Target TC

bbsailor, thank you for the extensive explanation.

Do you have any other target TC's available that could be used as reference? Like maybe alu foil? or other fast target TC's that could be used as an universal standard reference?

Do I understand right, that in order to measure the target TC, the TX pulse has to reach the steady state or Flattop as sometimes called? meaning at least 5 coil TC?

One last question: considering that the target signal decay/discharge curve, is exponential, does this make the target excitation /charge curve the same way exponential?

Tinkerer

[bbsailor]

bbsailor, thank you for the extensive explanation.

Do you have any other target TC's available that could be used as reference? Like maybe alu foil? or other fast target TC's that could be used as an universal standard reference?

Do I understand right, that in order to measure the target TC, the TX pulse has to reach the steady state or Flattop as sometimes called? meaning at least 5 coil TC?

One last question: considering that the target signal decay/discharge curve, is exponential, does this make the target excitation /charge curve the same way exponential?

Tinkerer

Tinkerer,

One square inch of household aluminum foil has a total discharge time of 50 uS and a 10 uS TC. Eric Foster mentioned, in one of his posts, that his Goldqust PI can detect this 1 sq inch foil at 12" using an 11" coil at 10 uS.

Eric also measured a common gum foil wrapper delay times a while ago based on a web conversation we were having.

Full gum foil wrapper: 25 uS
Cut in half: 20 uS
Cut in half again (1/4): 15 uS
Cut in half again (1/8: 10 uS

This series would suggest that if you cut the remaining piece in half again (1/16) that is should be detected at 5 uS delay, although I have not tried it.
Try this on your 5 uS delay design.

Steady state is the theoritical maximum current growth in 5 TCs but the last two TCs only add the last 5% of additional current. 95% occurs in 3 TCs and 85% occurs in 2 TCs.

When the current rises and stays on, even that last flatter section of the charge curve, the current is moving into the inner volume of a target from the earlier portion of the charge curve just forming on the target surface. When the target is only charges on it's surface it will discharge more quickly. If the targets has been more deeply stimulated, it's decay time will extend to a maximum defined by the maximum energy that can potentially be stored in any one piece or metal of the target full discharge time. Thicker metals require longer PWs to fully saturate.

The charge curve and discharge curves are both exponential but there is a difference. The current growth is relativly slow as it is governed by the coil charge TC as measure by coil inductance divided by coil resistance, including MOSFET on-resistance, coil wire resistance, any series resistor used, coax wire resistance. The discharge curve looks like a vertical cliff but it too is still exponential as this curve is governed by the coil inductance divided by values of Rd and Rin in parallel. Low conductor targets may take on a charge faster and when sampled very soon, may exhibit a stronger signal than a better conductor item. The low conductivity target needs to be sampled very quickly as the signal drops very quickly. It has a more vertical slope while the high conductivity targets tend to have a more horizontal slope to the discharge curve.

When the current grows, all targets within the pulse field have their charge also grow. Then suddenly, the current is turned off. A flyback pulse occurs as an artifact of the current change and needs to be damped as quickly as possible to turn on the RX circuit to have the coil see the eddy currents in the charged target decaying based on the TC of the target itself.

Obtain some fractional ohm resistor values (example: 0.1, 0.2, 0.3, 0.4 ohms) and solder them into a 1.5" diameter loop, 1" loop, .75" loop and .5" loop and you can simulate some targets. You can even use small loops of different gauge wire as a loop of the same size will have about the same inductance below 1 uH but the wire diameter will affect the resistance and ultimately the wire loop simulator target TC. You should be able to simulate any common target by using a wire loop of a particular diameter and wire gauge size. These should be easily replicatable by those needing references other than copper pennies, nickels or 1" square foil samples.

I hope this helps.

bbsailor

[allan.au]

target in intensive care

hey bbsailor, have u tried hooking your cro up to the resistor of these pseudo-targets to see what happens with various pulse widths and coils...there may be something to be learnt by monitoring the patient.....cheers, al

[bbsailor]

hey bbsailor, have u tried hooking your cro up to the resistor of these pseudo-targets to see what happens with various pulse widths and coils...there may be something to be learnt by monitoring the patient.....cheers, al

Al,

To do this, you would need to use a clamp on current transformer probe around the simulated target loop going through an external amplifier in either a picoamp range or microamp range depending on the total decay time of the target to see the full range of the target decay.

bbsailor

[Tinkerer]

Target Time Constants

A 1/2" square alu foil has a target time constant of about 5uS. I can still detect it at a distance of 15cm when sampling at 3.5uS. I guess that is as sensitive as I want to go.
Alu foil targets have the special characteristic of lots of surface for small mass.
A ring responds very well too. My tests show that at 3.5uS a 0.35 gram gold ring can be easily detected at 20cm.

Unfortunately, gold nuggets fall into an entirely different category.
They have a very small surface area for their mass.

So this means a lot more experimenting, if only I had a gold nugget.

Tinkerer

[bbsailor]

A 1/2" square alu foil has a target time constant of about 5uS. I can still detect it at a distance of 15cm when sampling at 3.5uS. I guess that is as sensitive as I want to go.
Alu foil targets have the special characteristic of lots of surface for small mass.
A ring responds very well too. My tests show that at 3.5uS a 0.35 gram gold ring can be easily detected at 20cm.

Unfortunately, gold nuggets fall into an entirely different category.
They have a very small surface area for their mass.

So this means a lot more experimenting, if only I had a gold nugget.

Tinkerer

Tinkerer,

Compare your household aluminum foil that is about .002" thick to the same size chewing gum foil wrapper that has a thinner aluminum foil mounted on a paper backing. Try different pulse widths to see where the response falls off with the thicker and thinner foil pieces.

Also, try puching a hole in the center of the foil and see what happens to the response. Try it again while enlarging the hole until you only have a thin edge making a complete ring around the perimeter.

These experiments will give you some data on target mass versus area and help you better understand the relationship of target characteristics to pulse characteristics.

Gold nuggets come in many variations. Some nuggets are solid, some have many pores while others are mixed with non-gold material making large nuggets look like smaller nuggets relative to their TC characteristics.

Getting your sampling down to 3.5uS is very good. Nice job!!!

bbsailor

[Tinkerer]

Corrections

Tinkerer,

Compare your household aluminum foil that is about .002" thick to the same size chewing gum foil wrapper that has a thinner aluminum foil mounted on a paper backing. Try different pulse widths to see where the response falls off with the thicker and thinner foil pieces.

Also, try puching a hole in the center of the foil and see what happens to the response. Try it again while enlarging the hole until you only have a thin edge making a complete ring around the perimeter.

These experiments will give you some data on target mass versus area and help you better understand the relationship of target characteristics to pulse characteristics.

Gold nuggets come in many variations. Some nuggets are solid, some have many pores while others are mixed with non-gold material making large nuggets look like smaller nuggets relative to their TC characteristics.

Getting your sampling down to 3.5uS is very good. Nice job!!!

bbsailor

bbsailor,
thanks for the feedback. I will try the alu foils with holes.

There are some corrections: The foil I am using has been measured by a watchmaker, using a micrometer. He says that it is 0.022mm thick. this corresponds to 22 micrometers.
A foil that is 0.02" (Inches) thick, would correspond to 0.05mm thickness.

Also I made a mistake with the sampling time. The actual time as shown by the scope, is 2.6uS, (two point six microseconds) after switch OFF.

This might present a record. I have not heard of such a short delay. It also might be somewhat academic, I can not think offhand of any use for so much detecting sensitivity.

Tinkerer

[garyq]

Aluminium is supposed to be a close surrogate for gold so I wonder by rolling a sheet of aluminium foil tightly in the palm of your hand as I tired with a 1" square piece and ended up with a 1/8" diameter ball than maybe this would be close copy of a gold nugget of similar size for test purposes?

You could also flatten the ball into whatever shape for comparisons as well use large pieces of foil into larger targets.

Just a thought and if worthwhile.

Gary

[green]

( One square inch of household aluminum foil has a total discharge time of 50 uS and a 10 uS TC. Eric Foster mentioned, in one of his posts, that his Goldqust PI can detect this 1 sq inch foil at 12" using an 11" coil at 10 uS.)
(So, even though gold is the primary target it is still desirable to find coins. Here is the design compromise. Any transmit pulse width beyond what fully stimulates a gold ring is wasted power from that ring's perspective but is under powered from the perspective of a copper penny that has a total discharge time of 350 uS (reported by Eric Foster on his web site). The copper penny TC is one fifth of the total decay time or 70 uS for the copper penny. A nickel is a good contrast as it has a total decay time of 100 uS with a TC of 20uS. Nickels are a substitute and a good indicator of a PI design/control settings to gold jewlery.)
I tried measuring some (Target Signals) awhile back. The time constants weren't correct. I don't have access to the equipment used then. I've been trying again at home. I get different answers but are still different than the time constants listed in the above posts. Can some one suggest what might cause my measurements to be different? I am buying (Inside the Metal Detector) hoping to answer some questions.

[baum7154]

What an interesting and useful thread! This can really help us to develop a recipe for a standardized set of targets. I would like a bit of clarification though on the foil. The standard Reynolds Aluminum foil I just measured is 0.001" thick. The Heavy Duty Reynolds foil is 0.002" thick.

Did Eric use the standard 0.001' thick X 1" square foil when he determined it had a 10us TC or was it the 0.002 thick stuff? In my mind doubling the thickness has the same effect as doubling the square inches of area.

A 1/2" X 1/2" square is 1/4 square inch and if Eric's standard is based on 0.001" thick material this should represent a 2.5usTC. However if the material is made of the Heavy Duty 0.002" thick foil wouldn't it have a TC of 5us, effectively mimicking a 1/2 square inch piece of the 0.001" foil?

Thanks for help,

Dan

[green]

I tried some Heavy Duty Reynolds foil. Different foil and equipment from above. Foil was 1 inch wide. Layers were made by folding a longer piece. Each target was the same distance out.

[Carl-NC]

In my mind doubling the thickness has the same effect as doubling the square inches of area.

Nope, area has a much smaller effect on TC than does thickness. In most targets TC is dominated by skin depth effects, which depends on thickness. Area mostly affects signal strength.

I use a set of 1" square aluminum foil targets for standards, with thicknesses of 1x,2x,4x,8x,16x, and 32x. I also have a 1/2" square of 1x and a 2" square of 1x, which has about the same TC as the 1" square 1x.

Green's plot exactly illustrates.