Target response tester

[green]

Green: Your log-amp calibration looks OK ( I assume -0.801mV is actually intended to read -0.801 V ).
Re:"What's different about the circuit?
Same circuit, Tx current in a control loop. Constant rate, 2780A/sec. It's all one recording, Tx damped and Rx damped separate."
I meant things like "a transistor is turned on , switching in a resistor" vs. "open-circuit".
I've never seen the circuit, and having trawled through this entire thread, I can't find it here either, so I can't say much at the moment.
There's a damping resistor on the RX coil all the time? There's a damping R on the TX all the time? And when the transmit fet(?) turns on, it's a perfect current source?
Is the circuit one of the standard 'project' ones on here?

Also: I too thought Eric's US 5c 'nickel' decay curve was odd. If that best-fit figure of 0.127 is reciprocated you get TC = 7.87 microsecs, ( f_c = 20.2kHz ) which is certainly different to what is generally measured ( about 9.5 usec ).

Yes, -.801V

Including the schematic of the TRT tester that was posted in another thread. I labeled the output off pin 14, am using output off pin 12. Schematic doesn't show Rx(2 round coils connected figure eight) and differential amplifier(Rx damping resistor connected across input)

Tx(on schematic surrounds Rx). The coil is balanced for zero signal at amplifier out when Tx on and off. Recorded the signal during Tx on and off. Normally don't record during Tx on, noisier and a PI uses decay Tx off.

[green]

Yes, I can do linear, log or semi-log plots' but opted for linear at the moment as the log compression limits the detail that can be seen at the 10 - 20uS start of the decay where signal levels are high and deviations are most likely to occur. I have included the data values so that others can re-plot if preferred.

I will plot a clad quarter, but I have a MK2 version of my equipment that would be better to use. The minimum delay on this is 20uS, but it will measure out to 1mS, which is good for larger and more highly conductive targets. Also, I can set the delay time spacings to give more resolution at the start of the decay as you suggest.

I will have a look at the noise on this MK2 unit which uses a single NE5534A as the first amplifier and followed by a NE5532 as a cross coupled phase inverter. This then feeds a single time constant integrator which give better low frequency noise rejection than a differential integrator with it's TC matching problems. Maybe my high front end noise is due to rf pickup from outside sources and the whole unit needs to be in a screened box, or at least the preamplifier. However, the noise I have seems to vanish in the subsequent filtering and dc amplification.

Eric.

Thanks, what ever you can do to test for the increase in slope at beginning of decay.
I'm just trying to understand the noise part. Was thinking shorting the 1k input to common would eliminate emi pickup at the input and allow testing for rti noise. A stable reading at integrator out is what matters. I'm recording amplifier out log scale, no integrator. Trying to minimize noise.

[Skippy]

Green: Your log-amp calibration looks OK ( I assume -0.801mV is actually intended to read -0.801 V ).
Re:"What's different about the circuit?
Same circuit, Tx current in a control loop. Constant rate, 2780A/sec. It's all one recording, Tx damped and Rx damped separate."
I meant things like "a transistor is turned on , switching in a resistor" vs. "open-circuit".
I've never seen the circuit, and having trawled through this entire thread, I can't find it here either, so I can't say much at the moment.
There's a damping resistor on the RX coil all the time? There's a damping R on the TX all the time? And when the transmit fet(?) turns on, it's a perfect current source?
Is the circuit one of the standard 'project' ones on here?

Also: I too thought Eric's US 5c 'nickel' decay curve was odd. If that best-fit figure of 0.127 is reciprocated you get TC = 7.87 microsecs, ( f_c = 20.2kHz ) which is certainly different to what is generally measured ( about 9.5 usec ).

[Ferric Toes]

Good tests. Charted your data linear-log to see how it looks the way I chart. Straight line decay except for one point, 3 instead of 4 would fix that. My decays usually chart straight line after one or two target time constants. Wondering if you could test a US clad quarter out to 600usec to see if you get something similar to what I get. Maybe every 10us starting at 10us out to 100us, every 20us to 200us, every 50us to 600us. What ever works for you. I tried 150us and 500us Tx, both had the same final slope. I could try something different if wanted. I get close to 10us time constant for a US nickel.

I'm guessing your 20mV is p-p. Seems high if I do the math right. .02/6/200000^.5/470=16nVrt Hz rti

Yes, I can do linear, log or semi-log plots' but opted for linear at the moment as the log compression limits the detail that can be seen at the 10 - 20uS start of the decay where signal levels are high and deviations are most likely to occur. I have included the data values so that others can re-plot if preferred.

I will plot a clad quarter, but I have a MK2 version of my equipment that would be better to use. The minimum delay on this is 20uS, but it will measure out to 1mS, which is good for larger and more highly conductive targets. Also, I can set the delay time spacings to give more resolution at the start of the decay as you suggest.

I will have a look at the noise on this MK2 unit which uses a single NE5534A as the first amplifier and followed by a NE5532 as a cross coupled phase inverter. This then feeds a single time constant integrator which give better low frequency noise rejection than a differential integrator with it's TC matching problems. Maybe my high front end noise is due to rf pickup from outside sources and the whole unit needs to be in a screened box, or at least the preamplifier. However, the noise I have seems to vanish in the subsequent filtering and dc amplification.

Eric.

[green]

I would suggest that 'skin effect' is visible and measurable on a PI detector. That is the time that elapses before the response settles down to a single time constant, i.e the late time referred to in Geonic's TN-7 report p-p 6-8. This is clearly seen in the case of a Victorian silver 3d coin I tested where an exponential fit was not obtained until measurement times exceeded 25uS. [ATTACH]45271[/ATTACH] Leaving out the first three data points shows the good fit. [ATTACH]45273[/ATTACH] Even a 25.4mm length of solid copper wire. 1.7mm diameter exhibits the effect by the deviation of the exponential fitting curve from the 10uS data point. [ATTACH]45274[/ATTACH]. The wire was mounted such that it was longitudinal in the coil i.e. parallel to the field lines.

However, a 10mm brass disc 2mm thick shows an almost perfect single exponential. (IACS% = 25) [ATTACH]45275[/ATTACH]

Relevant to this, and the threads on preamp noise and nugget responses, I have spent much time over the last two weeks checking my system for noise and linearity. I tried two other preamps as alternatives to the NE5532 IC; the LME49990 (dual on a SOIC - DIL adapter) and a MAX412. With preamp input shorted and 1k input resistor, wideband noise on all IC's appeared to be 20mV. Taking additional measures using extra ceramic 4.7uF caps on the supply pins and running from a battery supply rather than a linear regulated wall plug made little difference. The higher bandwidth and lower noise level of the LME49990 appeared not to make significant difference and it is more supply current hungry. The MAX412 worked OK but the slew rate was noticeably worse than the 5532, i.e. going from positive to negative saturation at the end of the TX pulse and then recovery to 0 volts took longer that the 5532. My dual preamp has a 1st stage gain of 10x, followed by 47x for the second stage. This being the only difference from Green's. Regarding the NE5532, there are differences in performance from the various manufacturers. This also applies the single NE5534. For the latter, I always used the A version which has a lower noise spec. The best devices were made by Philips with white printing and the Philips shield on the device. Bandwidth was also noticeably better than Texas devices. My current NE5532's are also Philips with the white lettering but not an A version, which I have been so far unable to find. Recovery of the preamp to 0V and full gain is achieved in 7uS with the start of the first sample at 10uS. It should be noted that Philips in Holland had a fire in their factory some years back which meant that they outsourced their production of 5534's and 5532's to another manufacturer. They were then re-badged as Philips but with brown lettering. These devices were not so good.

Some other relevant points to my measuring system:- I use a simple constant current method of putting a resistance in series with the solenoid coil that I use to measure target decay curves. The coil has an inductance of 200uH close wound in one layer with 0.25mm kynar insulated wire-wrap wire. The coil itself has a resistance of 4 ohms with an additional series resistance of 100 ohms. This gives a coil TC of 1.9uS with the result that the current flat tops in just under 10uS. This ensures that the TX field is the same for all measurements and is more than adequate to give sufficient signal from most objects when placed in the sensing chamber. Importantly, with the whole receiver chain there is no more than + or - 1mV noise on the LCD display for a maximum reading of 2000mV. I normally set the gain of the final amplifier such that 1000mV is the starting value at 10uS.

One minor source of 'early time' error was the 100 ohm resistor in series with the coil. Most through hole resistors that are available have steel caps at the ends to which the wires are attached, and between is a spiral track of resistive material. This track forms a small coil closely coupled to the steel caps, and carrying the TX current. Steel always has a long decay even with a short TX pulse, and can slightly distort the target signal within the sensing coil. This was replaced with an Arcol carbon composition resistor which has no steel end caps (tested with a magnet) and no spiral track. Available through RS Components and advertised as being very suitable for pulse work. Another cheaper option is to use a suitable wattage surface mount resistor. The same may apply to the damping resistor as it would have the same peak current on the high voltage flyback as the main coil. Anyway, I replaced both and appear to have a considerable cleaner and properly damped, with no glitches, recovery waveform on the 'scope'.

As a check on the accuracy and linearity of the system, I plotted the decay curve of 10gm of powdered volcanic tuff from Yucca Mountain in Nevada. This is regarded by experts in rock magnetism as an almost perfect natural example of magnetically mineralised rock material. Theory has it that non-interacting nano-metre size grains should exhibit a decay of t^-1.0 when a steady magnetic field is removed. My measurement gets close at t^-1.04 for this material, which is a good result. The important point is that there is no conductivity associated with this material, so 'skin effect' does not apply. [ATTACH]45276[/ATTACH]

Also for reference, here is the curve for the US Nickel coin which shows only a small deviation. [ATTACH]45277[/ATTACH]. IACS for the Nickel is 5.4%

Eric.

Good tests. Charted your data linear-log to see how it looks the way I chart. Straight line decay except for one point, 3 instead of 4 would fix that. My decays usually chart straight line after one or two target time constants. Wondering if you could test a US clad quarter out to 600usec to see if you get something similar to what I get. Maybe every 10us starting at 10us out to 100us, every 20us to 200us, every 50us to 600us. What ever works for you. I tried 150us and 500us Tx, both had the same final slope. I could try something different if wanted. I get close to 10us time constant for a US nickel.

I'm guessing your 20mV is p-p. Seems high if I do the math right. .02/6/200000^.5/470=16nVrt Hz rti

[green]

This initial rapid fall-off you see on your slopes -- it's not skin-effect. When you excite your target, circulating currents can flow in any which direction they like. Those that go in tight loops, because they are constrained by a thin sheet, or a wires' edge-profile etc, decay quicker. What's left later on are the 'big' circulating loops, whose size is related to the larger dimensions of the target. It's nothing to do with skin effect.
Remember that pdf Eric linked to, about the test jig that measured long rods of metal decaying ? The maths of that showed the multiple decays, and then stated that the 'big' one is the one they want to measure and analyse. It involved Bessell Functions, which are called upon when things happen in two (or three) dimensions ... vibrating drumskins? heat transfer through a solid? Digital filtering of images? I've little exposure to their intricacies ...

Skin effect is something really relevant to continuous AC signals, like a VLF detector, or 60Hz/50Hz power line currents. The currents only flow in the outermost layer of the item. At microwave freqs, it's just the skin, microns thick that conducts, nothing at all goes on in the core of a wire, it could be a tube, with no difference. You don't see 'the effect of the skin' , it's always there, it doesn't 'show itself' under any particular given circumstance.

[ I hope all that is correct, I don't want to have to ask Carl to edit/delete it..]

Re: your turn-on / off measurement differences. What's different about the circuit? An I correct in saying the damping is different between the two states, one is damped by a resistor, typically 500 Ohms, the other will be a near-zero Ohm turned-on Mosfet ?

your turn-on / off measurement differences. What's different about the circuit?

Same circuit, Tx current in a control loop. Constant rate, 2780A/sec. It's all one recording, Tx damped and Rx damped separate.
Still think skin effect effects the decay. Trying to figure out if it can effect as much as I record or it's what you suggest. Looked at some of the recordings I did before I made target response tester. Similar decay.

Checked calibration of log amplifier. .26mV in(-.801mV out) 25.1mV in(8.7mV out) 2.496V in(.800mV out) In test points on card maybe need to be trimmed closer?

[Ferric Toes]

This initial rapid fall-off you see on your slopes -- it's not skin-effect. When you excite your target, circulating currents can flow in any which direction they like. Those that go in tight loops, because they are constrained by a thin sheet, or a wires' edge-profile etc, decay quicker. What's left later on are the 'big' circulating loops, whose size is related to the larger dimensions of the target. It's nothing to do with skin effect.
Remember that pdf Eric linked to, about the test jig that measured long rods of metal decaying ? The maths of that showed the multiple decays, and then stated that the 'big' one is the one they want to measure and analyse. It involved Bessell Functions, which are called upon when things happen in two (or three) dimensions ... vibrating drumskins? heat transfer through a solid? Digital filtering of images? I've little exposure to their intricacies ...

Skin effect is something really relevant to continuous AC signals, like a VLF detector, or 60Hz/50Hz power line currents. The currents only flow in the outermost layer of the item. At microwave freqs, it's just the skin, microns thick that conducts, nothing at all goes on in the core of a wire, it could be a tube, with no difference. You don't see 'the effect of the skin' , it's always there, it doesn't 'show itself' under any particular given circumstance.

[ I hope all that is correct, I don't want to have to ask Carl to edit/delete it..]

Re: your turn-on / off measurement differences. What's different about the circuit? An I correct in saying the damping is different between the two states, one is damped by a resistor, typically 500 Ohms, the other will be a near-zero Ohm turned-on Mosfet ?

I would suggest that 'skin effect' is visible and measurable on a PI detector. That is the time that elapses before the response settles down to a single time constant, i.e the late time referred to in Geonic's TN-7 report p-p 6-8. This is clearly seen in the case of a Victorian silver 3d coin I tested where an exponential fit was not obtained until measurement times exceeded 25uS. Leaving out the first three data points shows the good fit. Even a 25.4mm length of solid copper wire. 1.7mm diameter exhibits the effect by the deviation of the exponential fitting curve from the 10uS data point. . The wire was mounted such that it was longitudinal in the coil i.e. parallel to the field lines.

However, a 10mm brass disc 2mm thick shows an almost perfect single exponential. (IACS% = 25)

Relevant to this, and the threads on preamp noise and nugget responses, I have spent much time over the last two weeks checking my system for noise and linearity. I tried two other preamps as alternatives to the NE5532 IC; the LME49990 (dual on a SOIC - DIL adapter) and a MAX412. With preamp input shorted and 1k input resistor, wideband noise on all IC's appeared to be 20mV. Taking additional measures using extra ceramic 4.7uF caps on the supply pins and running from a battery supply rather than a linear regulated wall plug made little difference. The higher bandwidth and lower noise level of the LME49990 appeared not to make significant difference and it is more supply current hungry. The MAX412 worked OK but the slew rate was noticeably worse than the 5532, i.e. going from positive to negative saturation at the end of the TX pulse and then recovery to 0 volts took longer that the 5532. My dual preamp has a 1st stage gain of 10x, followed by 47x for the second stage. This being the only difference from Green's. Regarding the NE5532, there are differences in performance from the various manufacturers. This also applies the single NE5534. For the latter, I always used the A version which has a lower noise spec. The best devices were made by Philips with white printing and the Philips shield on the device. Bandwidth was also noticeably better than Texas devices. My current NE5532's are also Philips with the white lettering but not an A version, which I have been so far unable to find. Recovery of the preamp to 0V and full gain is achieved in 7uS with the start of the first sample at 10uS. It should be noted that Philips in Holland had a fire in their factory some years back which meant that they outsourced their production of 5534's and 5532's to another manufacturer. They were then re-badged as Philips but with brown lettering. These devices were not so good.

Some other relevant points to my measuring system:- I use a simple constant current method of putting a resistance in series with the solenoid coil that I use to measure target decay curves. The coil has an inductance of 200uH close wound in one layer with 0.25mm kynar insulated wire-wrap wire. The coil itself has a resistance of 4 ohms with an additional series resistance of 100 ohms. This gives a coil TC of 1.9uS with the result that the current flat tops in just under 10uS. This ensures that the TX field is the same for all measurements and is more than adequate to give sufficient signal from most objects when placed in the sensing chamber. Importantly, with the whole receiver chain there is no more than + or - 1mV noise on the LCD display for a maximum reading of 2000mV. I normally set the gain of the final amplifier such that 1000mV is the starting value at 10uS.

One minor source of 'early time' error was the 100 ohm resistor in series with the coil. Most through hole resistors that are available have steel caps at the ends to which the wires are attached, and between is a spiral track of resistive material. This track forms a small coil closely coupled to the steel caps, and carrying the TX current. Steel always has a long decay even with a short TX pulse, and can slightly distort the target signal within the sensing coil. This was replaced with an Arcol carbon composition resistor which has no steel end caps (tested with a magnet) and no spiral track. Available through RS Components and advertised as being very suitable for pulse work. Another cheaper option is to use a suitable wattage surface mount resistor. The same may apply to the damping resistor as it would have the same peak current on the high voltage flyback as the main coil. Anyway, I replaced both and appear to have a considerable cleaner and properly damped, with no glitches, recovery waveform on the 'scope'.

As a check on the accuracy and linearity of the system, I plotted the decay curve of 10gm of powdered volcanic tuff from Yucca Mountain in Nevada. This is regarded by experts in rock magnetism as an almost perfect natural example of magnetically mineralised rock material. Theory has it that non-interacting nano-metre size grains should exhibit a decay of t^-1.0 when a steady magnetic field is removed. My measurement gets close at t^-1.04 for this material, which is a good result. The important point is that there is no conductivity associated with this material, so 'skin effect' does not apply.

Also for reference, here is the curve for the US Nickel coin which shows only a small deviation. . IACS for the Nickel is 5.4%

Eric.

[Skippy]

This initial rapid fall-off you see on your slopes -- it's not skin-effect. When you excite your target, circulating currents can flow in any which direction they like. Those that go in tight loops, because they are constrained by a thin sheet, or a wires' edge-profile etc, decay quicker. What's left later on are the 'big' circulating loops, whose size is related to the larger dimensions of the target. It's nothing to do with skin effect.
Remember that pdf Eric linked to, about the test jig that measured long rods of metal decaying ? The maths of that showed the multiple decays, and then stated that the 'big' one is the one they want to measure and analyse. It involved Bessell Functions, which are called upon when things happen in two (or three) dimensions ... vibrating drumskins? heat transfer through a solid? Digital filtering of images? I've little exposure to their intricacies ...

Skin effect is something really relevant to continuous AC signals, like a VLF detector, or 60Hz/50Hz power line currents. The currents only flow in the outermost layer of the item. At microwave freqs, it's just the skin, microns thick that conducts, nothing at all goes on in the core of a wire, it could be a tube, with no difference. You don't see 'the effect of the skin' , it's always there, it doesn't 'show itself' under any particular given circumstance.

[ I hope all that is correct, I don't want to have to ask Carl to edit/delete it..]

Re: your turn-on / off measurement differences. What's different about the circuit? An I correct in saying the damping is different between the two states, one is damped by a resistor, typically 500 Ohms, the other will be a near-zero Ohm turned-on Mosfet ?

[green]

Funny thing how the time-constant doesn't change much with ring size doubling, isn't it? Obviously resistance doubles, and a first-approximation is that inductance depends on the length of the wire in the loop, so L roughly doubles, too. Hence L/R is nearly the same.
It's not entirely a surprise to me from practical farmland detecting experience. I occasionally dig small washers, I assume brass, often 7 - 10mm diameter, that "fell off a tractor" , and they always seem to dupe you into thinking they must be some decent-size silver/copper coin. Then you eventually find the little blighter, shake your head and swear.

I've not been twiddlin' me thumbs, I've been trying to understand the modelling of loop inductance, but it sure is a minefield. Approximations everywhere, some of which are very dodgy, and other traps for the unwary. One model assumes 100% skin effect: no current flows inside the wire at all. Hmmm. Another assumes the wire is much smaller in diameter than the loop, not a good assumption. Another substitutes cos (x) with approximation ( 1 - 0.5 x² ).
Not good. Try it at 90 degrees (pi/2) and you'll see that Zero = -0.23, approximately. Kinda poor. Try cos(x) approx. = ( 1 - 0.405 x² ) , it's better.

One thing I did pick up on, though, which may be related to what you have seen: It seems that the theoretical L value assumes you are some distance away from the loop when you measure it. If you are too close, there can exist mutual inductance coupling between the loop and the 'test coil' , which effectively changes the L of the target loop. This may be what you are seeing when you suggested target distance mattered when you measured.
I haven't seen any such effect on my equipment, but everything I have is different ... a DD coil being the obvious one.

It's still looking like you're always getting higher TC's though. Can we scrutinise your circuit, and its calibration, to see if there's anything amiss ?

I'll write something for the calibration part tomorrow. Did a test, coil on and off. TC coil on less than coil off, same as I've seen in the past. Any idea why. Coil off doesn't show much skin effect for the 40mm diameter coil. Had to move 20mm coil closer to Rx to get an acceptable coil on recording.

[Skippy]

Funny thing how the time-constant doesn't change much with ring size doubling, isn't it? Obviously resistance doubles, and a first-approximation is that inductance depends on the length of the wire in the loop, so L roughly doubles, too. Hence L/R is nearly the same.
It's not entirely a surprise to me from practical farmland detecting experience. I occasionally dig small washers, I assume brass, often 7 - 10mm diameter, that "fell off a tractor" , and they always seem to dupe you into thinking they must be some decent-size silver/copper coin. Then you eventually find the little blighter, shake your head and swear.

I've not been twiddlin' me thumbs, I've been trying to understand the modelling of loop inductance, but it sure is a minefield. Approximations everywhere, some of which are very dodgy, and other traps for the unwary. One model assumes 100% skin effect: no current flows inside the wire at all. Hmmm. Another assumes the wire is much smaller in diameter than the loop, not a good assumption. Another substitutes cos (x) with approximation ( 1 - 0.5 x² ).
Not good. Try it at 90 degrees (pi/2) and you'll see that Zero = -0.23, approximately. Kinda poor. Try cos(x) approx. = ( 1 - 0.405 x² ) , it's better.

One thing I did pick up on, though, which may be related to what you have seen: It seems that the theoretical L value assumes you are some distance away from the loop when you measure it. If you are too close, there can exist mutual inductance coupling between the loop and the 'test coil' , which effectively changes the L of the target loop. This may be what you are seeing when you suggested target distance mattered when you measured.
I haven't seen any such effect on my equipment, but everything I have is different ... a DD coil being the obvious one.

It's still looking like you're always getting higher TC's though. Can we scrutinise your circuit, and its calibration, to see if there's anything amiss ?

[green]

We are making things a bit hard by using a 20mm diameter ring, the 40mm size is easier to work with, and any solder resistance errors also become less significant. I'm hoping the 20mm size proves useful when we get the 'finger ring' thread going.

I did wonder if the thicker wires could be bent by fitting the end into a snug fit hole drilled in metal. That is, make a 2.1mm hole, perhaps 6mm deep. Insert the 2.05mm wire, bend it a bit, remove the wire by 2mm, bend it a bit etc. Pliers tend to squash/deform the wire end, unsurprisingly.
I noticed my 2.44mm ring has the wire deformed into a slight oval - the inner diameter-outer diameter dimension reduced, but it got 'fatter'. Cross-sectional area will hopefully be unchanged.

Tried a 40mm ring with AWG10, 2.59mm diameter wire. Included another recording of the 20mm ring.

[Skippy]

We are making things a bit hard by using a 20mm diameter ring, the 40mm size is easier to work with, and any solder resistance errors also become less significant. I'm hoping the 20mm size proves useful when we get the 'finger ring' thread going.

I did wonder if the thicker wires could be bent by fitting the end into a snug fit hole drilled in metal. That is, make a 2.1mm hole, perhaps 6mm deep. Insert the 2.05mm wire, bend it a bit, remove the wire by 2mm, bend it a bit etc. Pliers tend to squash/deform the wire end, unsurprisingly.
I noticed my 2.44mm ring has the wire deformed into a slight oval - the inner diameter-outer diameter dimension reduced, but it got 'fatter'. Cross-sectional area will hopefully be unchanged.

[green]

I was thinking about the resistance of our 20mm loops, and wondered how good an approximation it really is to assume it's just a straight 63mm length of wire. Clearly with a fat wire , like 2mm diameter, the 'inside' of the 20mm loop presents a shorter path for the current to flow in, and the 'outside' create a longer path. These 'loops' all add up like resistors wired in parallel. The net result is the total resistance around the loop is less than that calculated by assuming a single 'equivalent' line in the centre of the wire.
I tried a (mathematically) simple model, assuming a flat sheet of metal cut into a ring.
For a 20mm ring made from 2mm width metal, it works out to have a loop resistance 0.42% lower than the 'central line' model. Hence a time-constant 0.42% greater.
So it's not that significant, but ... it is in the correct direction, making the model give a higher TC.
Whether it applies to round wire the same way, I'm doubtful. A computer simulation would be needed to sort that one out, not that hard, I think. Doing it in algebra is not viable, very tricky integration problems.

You might be correct. My guess would be the resistance doesn't change if bending strain is elastic. It's plastic strain, thinking resistance might increase. Interesting problem.

[Skippy]

I was thinking about the resistance of our 20mm loops, and wondered how good an approximation it really is to assume it's just a straight 63mm length of wire. Clearly with a fat wire , like 2mm diameter, the 'inside' of the 20mm loop presents a shorter path for the current to flow in, and the 'outside' create a longer path. These 'loops' all add up like resistors wired in parallel. The net result is the total resistance around the loop is less than that calculated by assuming a single 'equivalent' line in the centre of the wire.
I tried a (mathematically) simple model, assuming a flat sheet of metal cut into a ring.
For a 20mm ring made from 2mm width metal, it works out to have a loop resistance 0.42% lower than the 'central line' model. Hence a time-constant 0.42% greater.
So it's not that significant, but ... it is in the correct direction, making the model give a higher TC.
Whether it applies to round wire the same way, I'm doubtful. A computer simulation would be needed to sort that one out, not that hard, I think. Doing it in algebra is not viable, very tricky integration problems.

[green]

Skippy, thanks for the math.

Made some 20mm rings with AWG 10, 12 and 14. Not as good looking as yours but I'm getting better. Need to get the right size tubing to wrap wire around(cutting marks overlap slightly?). Starting with wire 30mm longer than desired, mark desired wire length before wrapping helps a lot. Spacing of target on coil seems to have an effect. First time Tx 160usec, did another test Tx 5msec. Measured greater than calculated time constant is one thing we have in common. I seem to be getting more scatter than you. Could try wrapping AWG 8 and 6 with a larger diameter.
Used average measured time constant, target on coil and spaced when calculating measured/calculated.