PI TX Settling

[Carl-NC]

Introduction

When you turn on a standard PI transmitter, the coil current rises exponentially with a tau of L/R, where L is the coil inductance and R is the total equivalent series resistance. A typical setup is a TX width of 100us, L=300us, and R=1-3 ohms. This gives a tau of 100-300us, so if the TX width is only 100us then the coil current will still be rising at the turn-off point.

Eric Foster has long argued that the coil current should be flat-topped at turn-off; a still-rising TX current will continue to induce reverse-eddies in the target, and those reverse eddies will subtract from the forward eddies at turn-off and reduce the overall target signal. While I've never doubted that this happens, for years I've considered that the effect is not significant enough to worry about. My reasoning was that the dI/dt of the rising turn-on (typically 10mA/us) is far less than the dI/dt of the turn-off collapse (typically 1A/us). But I never spent any time doing an objective investigation.

Circuit Setup

The first stage of this investigation is in Spice. I concurrently ran 3 transmitters with 3 different turn-on characteristics. The first was with no series coil R other than the MOSFET switch (IRF740); therefore it has a coil current that is very close to a linear ramp. At 100us it peaks at 1.52A which is the peak used for the other transmitters. The second TX has a series R of 15 ohms to achieve a tau of about 20us, which means that at 100us is should be settled to 5 tau. Its drive voltage is set to 23.8V to give a flat-top current of 1.52A. The third TX has a series R of 150 ohms for a tau of 2us, and a drive voltage of 229V.

Each TX coil is coupled to its own target modeled by an inductor & resistor. The target tau is L/R; the L was fixed to 100uH and the R was adjusted for desired tau.

Each target is coupled to its own RX coil which drives a simple MAX410 non-inverting preamp stage.

The sim was run for target taus of 1, 10, 100, and 1000us. For each target tau sim, I plotted the TX current (always the same for each sim), the target eddy current response, and the preamp output voltage. Each plot shows the result for the ramp TX (blue), the 20us TX (green), and the 2us TX (red).

Sim Results

Target tau of 1us:



Target tau of 10us:



Target tau of 100us:



Target tau of 1000us:



To be continued...

[Qiaozhi]

From the results, it appears that flat-topping the coil current gives the most improvement for the 100us target tau. But even then the difference between the sets of results is not large. I will attempt to create a similar SPICE simulation for comparison.

[Carl-NC]

Yes, it appears the biggest improvement comes from a target tau that matches the TX width. I ran a few other taus to verify the peak seems to be 100us.

Here are the improvements between the fast (TX-2us) pulse and the slow (TX-ramp) pulse:

1us: 1%
10us: 10%
100us: 37%
1000us: 2.5%

Note that for the ramped TX current, the long-term target response is a steady-state eddy current. This is expected, as the eddy response is proportional to the derivative of the magnetic field. This creates an offset eddy that subtracts from the turn-off eddy, as people have correctly argued. For a 1us target, the steady-state eddy current is small because of the higher effective resistance of the material (and/or skin effect), so the offset is so small compared to the flat-top responses (TX-2us & TX-20us) that it makes no difference.

For the 10us target, all 3 eddy responses have flattened out but the higher conductivity yields a larger proportional offset for the TX-ramp response.

As the target taus approaches 100us, none of the target eddy responses have settled out, but TX-2us and TX-20us are clearly on a positive trajectory while TX-ramp is still heading south. This creates the largest relative offset between the fast and slow cases.

By the time the target tau hits 1000us, the eddy responses are so slow that all 3 are just following the TX current and all are close to the same offset eddy value, which happens to be an offset almost exactly equal to the turn-off eddy step. What this means is that such a target should have almost no detectable response.

[Ferric Toes]

Yes, it appears the biggest improvement comes from a target tau that matches the TX width. I ran a few other taus to verify the peak seems to be 100us.

Here are the improvements between the fast (TX-2us) pulse and the slow (TX-ramp) pulse:

1us: 1%
10us: 10%
100us: 37%
1000us: 2.5%

Note that for the ramped TX current, the long-term target response is a steady-state eddy current. This is expected, as the eddy response is proportional to the derivative of the magnetic field. This creates an offset eddy that subtracts from the turn-off eddy, as people have correctly argued. For a 1us target, the steady-state eddy current is small because of the higher effective resistance of the material (and/or skin effect), so the offset is so small compared to the flat-top responses (TX-2us & TX-20us) that it makes no difference.

For the 10us target, all 3 eddy responses have flattened out but the higher conductivity yields a larger proportional offset for the TX-ramp response.

As the target taus approaches 100us, none of the target eddy responses have settled out, but TX-2us and TX-20us are clearly on a positive trajectory while TX-ramp is still heading south. This creates the largest relative offset between the fast and slow cases.

By the time the target tau hits 1000us, the eddy responses are so slow that all 3 are just following the TX current and all are close to the same offset eddy value, which happens to be an offset almost exactly equal to the turn-off eddy step. What this means is that such a target should have almost no detectable response.

I wonder if the simulated results are a bit different to what happens in practice. From what I have both read and observed in tests with a logarithmic front end, the response of a solid target such as a sphere or cube only settles to a single exponential
after one Tau. Prior to that, it is a sum of exponentials (the skins of an onion effect). This I believe can be simulated by having additional inductors and resistors mutually coupled to the single one.

This effect reduces for thin flat objects, such as coins or rings. A medium to thin gold ring will display a single exponential, while a coin such as a silver dollar will display the sum of exponentials effect.

Invariably PI detectors sample well with the Tau of many objects, particularly higher conductivity ones where the TX pulse is too short to excite the primary Tau. What we then we see is only the skin effect response and we wonder why a big silver dollar has much less range than a nickel.

Fundamental theory states that that for 99% excitation the TX pulse should be 5 x the target Tau although 3 x is still 95%. Likewise for maximum current and a almost flat termination of the field before switch off the TX pulse should be 5, or at least 3, time the coil TC. The easy way of improving the coil TC is to add some series resistance.

Eric.

[Carl-NC]

I agree the simulation is not going to capture real-life nuances because of the over-simplified target model. But it does provide some good insight. Stage 2 of this investigation is to build a test circuit with a double-acting TX driver and 2 RX demods. I want to measure target responses for both TX cases exactly simultaneously.

[Ferric Toes]

Yes, it will be good to do some practical experiments to verify what is happening. I am going to repeat an experiment I did many years ago by having one TX, an RX preamp, and looking at the whole decay directly on a scope. I will have a pot, or switch, in the timing circuit that controls the TX width with a range say of 50uS to 500uS. I will also have a constant current TX that flat tops in 10uS for all widths. This is something I did not do previously but we need to keep the applied field constant so that the only variable is the pulse width. From previously, I remember seeing the waveform for a good conductive object (English copper penny or US quarter) 'fill out' as the width was increased until you reached a point when there was no increase in mid-time amplitude and then that was deemed to be the best TX width for that object. It was also good for anything smaller or less conductive except that you are wasting energy with an overlong pulse for that object.
I don't have one, but if anyone has a storage scope then you can hold the short TX width response and super-impose on it the following long TX responses. It is an easy experiment, but to be valid you need the flat top current. Otherwise the current will increase for each longer pulse width with the effect that you have two variables.

Eric.

[green]

A couple charts. I've been using the 1 amp peak 160usec ramp. Charted one with a flat top at 1/2 the peak current(same average current). Flat with 1 amp peak Tx, amplifier out would be 4 volts peak compared to 3 volts peak with the 1 amp peak ramp. Could chart some with flat top at 50, 100, 200, 300, 400 and 500usec Tx time if everything makes sense. I have a IB coil and could chart amplifier out during Tx on and off if that would be better. Used a 135mm diameter coil. Target spacing, quarter(34mm) nickel(65mm) 1 troy ounce 99.9% pure copper coin(56mm) for the ramp and flat recordings.

[green]

More charts with IB coil(Rx two 8inch round figure eight, Tx oval surrounding Rx). Targets(US quarters 1, 2 stacked, 4 stacked), Wire coil(12 turns bundle wound, 36mm I.D., AWG19 magnet wire, ends butted and soldered. Tried to get longer TC targets. Quarters were spaced 44mm from coil and wire coil was spaced 88mm from coil for the ramp and flat recordings. With the same average Tx current, amplifier out was a little higher with the ramp at decay times less than 100usec and about the same after 100usec. I started using the controlled ramp for testing to keep the same Tx waveform when I changed coils or when the battery volts changed. Thought the ramp might loose some signal strength but it doesn't seem to with a 160usec Tx time with average Tx current the same. Tried spice simulation with same average current, ramp gives higher target signal. Tried again with spice, first time increased coil resistance and volts to get 1 amp peak flat Tx. Second try left coil the same and varied fet gate for flat 1 amp peak Tx, ramp had lower target signal. Tried again with spice, ramp was higher when adjusting flat Tx at same average current when changing the coil or the fet gate volts.

[Qiaozhi]

Constant Current Simulation with Flat-Topping

Here's an interesting LTSpice simulation which limits the coil current and steps the TX pulse width from 50us to 800us. The Coil is 300uH with 3ohm series resistance, giving a of 100us. The target is 100us.

As you can see, the target eddy currents [I(L1)] are generated (in reverse) during TX-on. These eddy currents will take 5 target TCs to decay completely in order to gain full target response during TX-off. It can clearly be seen from the target plot that the reverse eddy currents need to be overcome first.

Interestingly, the current-limiting causes all the coil current waveforms to flat-top, but the full target response is only achieved after 5 target TCs. Hence, simply flat-topping by using current-limiting is not the answer. The original "you must let the current flat-top" statement is only applicable to the situation where the coil current is allowed to build up to maximum, and which is limited by the series resistance. Therefore Carl's simulation represents a situation where the 4 different TX pulse widths allow the coil current to rise to the same value, but with a different for each example. This tends to mask the effect of the reverse eddy currents in the target. Whereas the constant-current examples all have the same , and the loss of target response is primarily due to the time taken for the reverse eddy currents to die away.

It is interesting to play around with the of the coil to see what effect this has on the results.

Anyway, it's more food for thought.

[green]

More charts with IB coil(Rx two 8inch round figure eight, Tx oval surrounding Rx). Targets(US quarters 1, 2 stacked, 4 stacked), Wire coil(12 turns bundle wound, 36mm I.D., AWG19 magnet wire, ends butted and soldered. Tried to get longer TC targets. Quarters were spaced 44mm from coil and wire coil was spaced 88mm from coil for the ramp and flat recordings. With the same average Tx current, amplifier out was a little higher with the ramp at decay times less than 100usec and about the same after 100usec. I started using the controlled ramp for testing to keep the same Tx waveform when I changed coils or when the battery volts changed. Thought the ramp might loose some signal strength but it doesn't seem to with a 160usec Tx time with average Tx current the same. Tried spice simulation with same average current, ramp gives higher target signal. Tried again with spice, first time increased coil resistance and volts to get 1 amp peak flat Tx. Second try left coil the same and varied fet gate for flat 1 amp peak Tx, ramp had lower target signal. Tried again with spice, ramp was higher when adjusting flat Tx at same average current when changing the coil or the fet gate volts.

Increased the Tx time to 510usec. Above coil. Targets(US quarter, 1 troy ounce 99.9% copper coin and the 12 turn coil above reply). Ramp(1amp peak) flat top(.5 amp peak for same average Tx current). Thought the curves would straighten out down to 10usec but they didn't. Looking forward to other member measurements to see if I'm doing something wrong. For the same peak Tx current, flat Tx gives higher signal. For the same average Tx current, ramp Tx gives higher signal. Seems like a low resistance coil where the coil TC is longer than Tx on time would be the most efficient. US quarter spaced 40mm from coil, other targets spaced 80mm from coil.

[Teleno]

Here's an interesting LTSpice simulation which limits the coil current and steps the TX pulse width from 50us to 800us. The Coil is 300uH with 3ohm series resistance, giving a of 100us. The target is 100us.

As you can see, the target eddy currents [I(L1)] are generated (in reverse) during TX-on. These eddy currents will take 5 target TCs to decay completely in order to gain full target response during TX-off. It can clearly be seen from the target plot that the reverse eddy currents need to be overcome first.

It is clear from this simulation that sampling during on-time captures the strongest target response. Constant current excitation + on-time sampling is the way to go.

[Ferric Toes]

It is clear from this simulation that sampling during on-time captures the strongest target response. Constant current excitation + on-time sampling is the way to go.

If it were possible to have a TX pulse where the current rise at on-time was as fast as at the cut off, then the eddy currents generated in the target would be exactly the same, but in opposite polarities. It is not clear to me how the signal can be better in the on-time.

Eric.

[Teleno]

If it were possible to have a TX pulse where the current rise at on-time was as fast as at the cut off, then the eddy currents generated in the target would be exactly the same, but in opposite polarities. It is not clear to me how the signal can be better in the on-time.

Eric.

Eddy currents are induced at the transitions. Eddy currents decay between transitions.

Therefore, the on-time signal signal measured after an off-time of 1ms is the same as the off-time signal measured after an on-time of 1ms. Energy consumption in the first case is much lower though, because we don't need to maintain the on-current for 1ms, but only long enough to take a sample.

It is quite simple to create TX pulse where the current rise at on-time is faster than the cut off. It is called "boost converter".

[Qiaozhi]

It is clear from this simulation that sampling during on-time captures the strongest target response. Constant current excitation + on-time sampling is the way to go.

Run the simulation and set the plot to display only the 800us pulse width result, and then use the cursor facility to measure the peak of the eddy current response generated in the target during the on and off times. You will see that the target response following TX-off is stronger than at TX-on.

Also, with this particular setup, there is no target response at the preamp output during the TX on-time.

[Teleno]

Run the simulation and set the plot to display only the 800us pulse width result, and then use the cursor facility to measure the peak of the eddy current response generated in the target during the on and off times. You will see that the target response following TX-off is stronger than at TX-on.

The only reason for this is that the Tx rise time is somewhat slower. If you simulate with the same Tx rise and fall times you'll see that the signals will be the same.





Example for target with Tau=1ms, Tx period = 1ms, Ton = 50us. The on-time response captures the full amplitude of the target, while the off-time falls very short.

Also, with this particular setup, there is no target response at the preamp output during the TX on-time.

Certainly the on-time approach is not possible on a monocoil. A balanced Tx/Rx setup is a must.