Time Constant (TC) of targets

[Tinkerer]

Time constant of targets, TCDifferent metals have different TC’s. Even different alloys of metals have different TC’s. Jewelry gold comes in hundreds of different alloys, each with a different TC.The shape of the targets, even of similar alloy, also generates a response of different TC’s. Yet, it is our desire to get some kind of information of the kind of target under the coil, before we start digging. With VLF detectors, the TC translates into a phase shift used to give some information about the target identity. Can we obtain something similar from a PI detector?Can we measure the TC of a target with a PI?The time constant (TC) of a Nickel is about 15us. This means that having a response signal of 100uV at a time, say 5us after the switch Off of the TX pulse, the signal will be 63.2uV less, at a time 15us later. (Actually there are ways to stretch the time we can measure short TC’s or shorten the time of long TC’s, but we leave that for later)However, the signal that we look at, is composed of the coil decay and the target decay, so to get some sense of our measurement, we must first measure the coil decay only, without target, and then subtract this number from our total signal. This TC is made up of several TC’s. The largest partial TC is from the skin eddy currents. Then there are eddy currents from a deeper level within the coin. The amplitude of the skin eddy currents is much affected by the surface area presented to the magnetic field lines of the coil. With the coin at an angle, the surface is less so the response amplitude is less. Taking only a single measurement of the target response amplitude gives us no information about the quality of the target.As we can see from the above,we need to take at least 3 measurements at different times to define the TC of a target.There are several different ways to obtain a lot more information about the targets under a PI coil. It would be time well spent discussing these possibilities.

[WM6]

The time constant (TC) of a Nickel is about 15us. This means that having a response signal of 100uV at a time, say 5us after the switch Off of the TX pulse, the signal will be 63.2uV less, at a time 15us later.

Thanks for explanation of TC, Tinkerer.
Please check at my Nickel TC drawing, if I understand your Nickel TC example correct.
If yes, is it not more correct to say that Nickel TC is 10us (15-5) than 15us?

[Tinkerer]

Thanks for explanation of TC, Tinkerer.
Please check at my Nickel TC drawing, if I understand your Nickel TC example correct.
If yes, is it not more correct to say that Nickel TC is 10us (15-5) than 15us?

Thank you for the nice graph. It helps explaining better than my words.
Now measure the target signal response at time 30us again. You will find that it is again 63.2% less than at time 15us. This is what TC means.

On your graph, you start measuring as soon as the opamp comes out of saturation. This is not a good spot, as the signal is still distorted by the saturation of the opamp.
In real life PI circuit there are other limitations. We measure by sampling. Our sample may be anywhere from 1us to 40us wide. This means that we are averaging the voltage during this time. The shorter the sample time, the more sensitivity we get for short TC targets, but we also get more susceptibility to HF noise. We counteract this by stacking or averaging many samples.

[green]

Interesting subject. I get a T.C. of 10 not 15 for a nickel. Was reading a thread in another forum that gave 17khz as the best frequency for detecting a nickel with a VLF detector. 1/(2*pi*17000)= 9.3usec. Should the best frequency for a VLF relate to the PI time constant? Maybe we need to list what we know or think we know. Stacking coins changes the T.C.. Side by side doesn't. With an IB coil a quarter has a higher response at coil turn on. A nickel has a higher response at coil turn off for a start. If any will be useful is another question.

[Tinkerer]

Interesting subject. I get a T.C. of 10 not 15 for a nickel. Was reading a thread in another forum that gave 17khz as the best frequency for detecting a nickel with a VLF detector. 1/(2*pi*17000)= 9.3usec. Should the best frequency for a VLF relate to the PI time constant? Maybe we need to list what we know or think we know. Stacking coins changes the T.C.. Side by side doesn't. With an IB coil a quarter has a higher response at coil turn on. A nickel has a higher response at coil turn off for a start. If any will be useful is another question.

Sorry about the discrepancy and thank you for correcting. It has been many years since I measured the TC Nickel, I just used a random number to explain what the TC of a target is.
When you say stacking coins, do you mean with isolator between?

I believe there is a relationship between the skin effect and eddy currents. In general the skin effect is measured with the frequency of a sine wave, but if we look closely at a sine wave, we see that the current is continuously changing, but not at the same rate of change. The current of a sine wave increases during some time, so do the eddy currents. When the current inverts, the existing eddy currents are reduced to 0 before the new eddy currents can be formed. The same happens with our PI TX current. The TX ON ramp corresponds to a much lower frequency than the switch OFF transient.

With a near linear ramp, during a long TX ON time, the short TC targets get "saturated", while the long TC target response keeps increasing.

If my explanations sound a bit garbled, it is because English is not my mother tongue, same as many here on the forum. My memory is not the best either, so I am glad when somebody points out mistakes or discrepancies.
Discussions help many people understand better.

[green]

First I'm just learning and not trying to correct anyone. I say what I think, might not be correct. THREE COINS IN THE P.I.FOUNTAIN 5/29/2013 has information on stacked coins.

[Tinkerer]

First I'm just learning and not trying to correct anyone. I say what I think, might not be correct. THREE COINS IN THE P.I.FOUNTAIN 5/29/2013 has information on stacked coins.

Thanks for the link. This is an interesting discussion. I think that many of the secrets of target response could be deciphered if we look at the interaction of the coil magnetic field and the target magnetic field and, not to forget, the earth's magnetic field surrounding all of this.

Maybe more urgent to resolve, is the definition of the relationship between the coil diameter and target diameter, or rather the surface areas. The target response amplitude seems to be mostly due to this relationship.