Object Decay Waveforms and Time Constants.

[Ferric Toes]

To start the ball rolling, here is a linear plot of a 3.5gm thin wedding band. A ring gives a virtually pure single exponential and all the plot numbers join up nicely.

Compare this with a US Nickel which is often used as a test target. In this plot you can see that the first three numbers deviate from the exponential and only from then on does the plot fit.

This is the effect of a solid centre which has the effect at early times of giving a faster initial decay; some call it a type of skin effect, others refer to it as diffusion. This behaviour is very evident in good conductors such as silver coins of which I will post some plots in due course.

The previous plots on the Vallon thread for 4mm square copper foil suffer from lack of data points as the lowest increment on my measuring instrument is 10uS. The instrument was designed for magnetic soil measurement where the signal decay persists for much longer. However, it can provide useful information on rings, coins, and all but the smallest gold nuggets.

The graph plotting is fairly basic but does provide a quick, hopefully accurate, and noise free, picture of the decay, although I agree that there seems to be a problem with the scaling of log plots. I will have a look at that.

Eric.

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To start the ball rolling, here is a linear plot of a 3.5gm thin wedding band. A ring gives a virtually pure single exponential and all the plot numbers join up nicely. [ATTACH]36349[/ATTACH]

Compare this with a US Nickel which is often used as a test target. In this plot you can see that the first three numbers deviate from the exponential and only from then on does the plot fit. [ATTACH]36350[/ATTACH]

This is the effect of a solid centre which has the effect at early times of giving a faster initial decay; some call it a type of skin effect, others refer to it as diffusion. This behaviour is very evident in good conductors such as silver coins of which I will post some plots in due course.

The previous plots on the Vallon thread for 4mm square copper foil suffer from lack of data points as the lowest increment on my measuring instrument is 10uS. The instrument was designed for magnetic soil measurement where the signal decay persists for much longer. However, it can provide useful information on rings, coins, and all but the smallest gold nuggets.

The graph plotting is fairly basic but does provide a quick, hopefully accurate, and noise free, picture of the decay, although I agree that there seems to be a problem with the scaling of log plots. I will have a look at that.

Eric.

Thanks for starting the thread. I've charted quite a few target TC's wondering if I'm right. I charted your data on a linear log chart the way I normally do to see what it looked like. Added a 10usec TC line to the chart, what I get for a US nickel. Need to find why the difference.

[Ferric Toes]

Thanks for starting the thread. I've charted quite a few target TC's wondering if I'm right. I charted your data on a linear log chart the way I normally do to see what it looked like. Added a 10usec TC line to the chart, what I get for a US nickel. Need to find why the difference.

I would first need to know how you arrive at the data that you plot. You can PM me if you prefer.
Eric.

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I would first need to know how you arrive at the data that you plot. You can PM me if you prefer.
Eric.

Had to rebuild the mono coil amplifier. Preamp gain_300, two post amplifiers gain_9 each. Charting procedure, Use a digital storage oscilloscope to record the no target signal at each amplifier output, Use the DSO to record the target signal at each amplifier output, dump the data into Excel, subtract the no target recording from the target recording for each amplifier output and chart. The curve for the nickel is similar to what I normally get, not quite straight with a TC close to 10usec. I'll work on the noise on the post amplifiers to try to get a longer decay. Looks like it might curve the same as your data after 50usec. Can't think what would cause the big difference we are seeing for TC, maybe instrument time base. Do you have any thoughts? TX(constant rate, 1 amp peak, 160usec). Scope triggers zero time when fet gate driver command goes low. The higher trace is the preamp output difference, the lower trace the x9 gain output difference(saturated the first 34usec) divided by 9 in Excel.

[Skippy]

I was thinking Eric's US Nickel data was unusual, too, the time-constant of 8.41 microsecs for the later part of the decay seems short, and it's clearly even shorter during the initial decay stage. (8.41 is the reciprocal of the b = 0.11884)
My measurements with a 13KHz VLF machine, which I believe to be accurate, show the Nickel has a time-constant of 9.9 usec ( f = 16.1 KHz).
( Random quotes from the web (attributed to George Payne / Troy G) put it at near 17kHz (approx 9.4 usec)).

[Ferric Toes]

Had to rebuild the mono coil amplifier. Preamp gain_300, two post amplifiers gain_9 each. Charting procedure, Use a digital storage oscilloscope to record the no target signal at each amplifier output, Use the DSO to record the target signal at each amplifier output, dump the data into Excel, subtract the no target recording from the target recording for each amplifier output and chart. The curve for the nickel is similar to what I normally get, not quite straight with a TC close to 10usec. I'll work on the noise on the post amplifiers to try to get a longer decay. Looks like it might curve the same as your data after 50usec. Can't think what would cause the big difference we are seeing for TC, maybe instrument time base. Do you have any thoughts? TX(constant rate, 1 amp peak, 160usec). Scope triggers zero time when fet gate driver command goes low. The higher trace is the preamp output difference, the lower trace the x9 gain output difference(saturated the first 34usec) divided by 9 in Excel.

My method is rather different. It uses a cylindrical coil 1.5in diameter and 2in long. Inside is a lifting platform on which a 10cc plastic container is placed and then the platform lowered so as to place the sample in the centre of the coil. The sample is usually soil or rock fragments. The TX pulse is 0.1A peak and fed to the coil such that the rise time of the current is fast compared to the TX width. This results in a flat top current pulse for all TX pulse widths. For coins, I have to use a spacer to bring the coin outside the coil, but still on axis, otherwise I get too much signal. The main control switch gives proportional control over all pulses, delays, and sample width. i.e. 10uS delay, 10uS sample width, 30uS TX. For 15uS delay, 15uS sample width, we have 45uS TX...................50uS delay, 50uS sample width, 150uS TX. There is also a x2 switch to continue to 100uS delay, 300uS TX, if needed. The amplified coil signal is integrated and the d.c. value displayed on a DVM module. These are the arbitrary readings I plot. With coins I usually adjust the d.c. gain to give a reading of 1000 or sometimes 500 for the first measurement at 10uS delay (which is really 15uS if you take the centre of the sample pulse rather than the start). For soils and rocks I have a calibration sample measured for magnetic susceptibility at two frequencies to give a viscosity figure. All readings of viscosity are then relative to the calibration sample.
The theoretical decay of magnetic viscosity is 1/t to -1(superscript). The log/log plot of soil and rock decay measured on this instrument gives a very close result to the theoretical i.e. -0.9 to -1.1 much of the time, so I assume the proportional pulse/delay/TX method to be valid. This gives me some measure of confidence that it is also valid for conductive metal targets. The fact that a gold ring gives a single exponential also suggests the validity. But, that is just my opinion. A mathematical analysis should be done, but that would take me well outside my comfort zone.
Attached is a linear plot of powdered volcanic tuff from Tiva Canyon. This was sent to me by a laboratory is the USA as a test standard adopted by other laboratories as a natural single domain non-conductive magnetic material. A log amplitude/log time plot should come out close to the theoretical 1/t/minus 1. My measurement was -1.05 which I thought was quite good. First the linear plot then the log/log plot

It would be nice to get the log scaling right so I might come back with some questions on alternative programs where I can enter the results table and do a better job. I will have a look at Excel first.

Eric.