Ground Balance Theory

[Aziz]

I've wondered how a time shift effects the curve. Generated a slope of -1 at t=0. Plotted the same data starting at t=0+2, t=0+5, t=0+10. I hope I did it right, maybe not.

Hi green,

Yep! If you subtract a phase shift, then the log/log-curve should go down in the early times in your example.

That is the main problem here. If you don't know the real time code of the measurement data and make a best fit curve with Excel solver, you don't get reliable model parameters. Phase shift p is altering the exponent and other parameters.

Nevertheless, we have learned to be careful.

Cheers,
Aziz

[Aziz]

Thanks Thomas,

it is clearly now where your t0 is. No wonder, that it has confused me when I looked at your original data with original time code 0.
Nevertheless, I don't like your t0 position. I like the t0=switch-off time position no matter how long the coil damping takes place (t0 = 0 time code).
Aziz

[green]

I've wondered how a time shift effects the curve. Generated a slope of -1 at t=0. Plotted the same data starting at t=0+2, t=0+5, t=0+10. I hope I did it right, maybe not.

[PiTec]

Hi Aziz,

I thought the description in my previous post was clear enough Below is a timing diagram with 4 time marks (1) … (4).

The scope is triggered by the falling edge (2) of the microcontroller TX drive pin. There is a delay of maybe 100 ns (driver, MOSFET as you said), but this is negligible.

With the scope timebase set to 1 µs / div, I measure the time between trigger (2) and the end of the flyback pulse (3) directly at the TX coil. The end of the flyback pulse is t=0 (t0). The error should be quite small, maybe +/- 0.25 µs. Any delay in the driver and MOSFET would not be added.

Then I look at the RX signal at the OPAMP output (i.e. after 200x amplification) and select (4) as the earliest possible acquisition point, i.e. the RX signal should be almost zero without any ringing or over/undershoot. The time difference (4) – (3) is the first time code for the first acquired sample, i.e. 7 to 9 µs for the latest measurements I made.

The scope is then set to 20 µs/div and the trigger position is moved off screen by exactly the sum of the two measured times, i.e. flyback pulse duration plus necessary delay for the first acquisition. This time is displayed by the scope as trigger position delay, so it is accurate. Now (4) is exactly at the left side of the scope screen, and this will be the first acquired sample.

Finally, the air signal is stored and subtracted from the acquisition channel.

Thomas

[Aziz]

Hi all,

here is the math proof why the exponential target response Tgt(t) = a*e^(-t/TC) remains a straight line in the log/lin-t plot, if you even change your time base.

Correct time code:
Signal Tgt(t) = a*e^(-t/TC)
log/lin-t plot display:
y-axis: log10 (log base 10), x-axis linear (unchanged t-axis)

y = log10(Tgt(t))
y = log10(a*e^(-t/TC))
y = ln(a*e^(-t/TC))/ln(10), where ln is the natural log (base e = 2.71828..)
y = (ln(a) + (-t/TC) ) / ln(10)
y = ln(a)/ln(10) -1/(TC*ln(10)) * t
substitution for simplicity
c = ln(a)/ln(10),
m = -1/(TC*ln(10))
y = m*t + c (this is the linear equation for a straight line function with the slope of m and y=c at t=0)
-> A straight line response in the log/lin-t plot.
QED.

Now phase shifted time code: t = t+p, p unknown time later
We substitute the time variable t with t+p
-t -> -(t) -> -(t+p) = -t-p
Tgt(t+p) = a*e^((-t-p)/TC)
y = log10(Tgt(t+p))
y = log10(a*e^((-t-p)/TC))
y = ln(a*e^((-t-p)/TC))/ln(10), where ln() is the natural log (base e = 2.71828..)
y = (ln(a) + ((-t-p)/TC) ) / ln(10)
y = ln(a)/ln(10) -p/(TC*ln(10)) -1/(TC*ln(10)) * t
substitution for simplicity
c = ln(a)/ln(10) - p/(TC*ln(10)),
m = -1/(TC*ln(10))
y = m*t + c (this is the linear equation for a straight line function with the slope of m and y=c at t=0)
-> A straight line response in the log/lin-t plot.
QED.

If you compare both slopes m, they should be totally equal. Are they? QED.
So phase shifting (or time base shifting or plotting at unknown time position start) does produce the same straight line in the log/lin-t plot. This feature can be used to look at the early times, whether the amplifier is in the linear region when we look at the single time constant (TC) target reponse. We can determine a correction table for the early times to correct the data due to amplifier non-linearity (caused by limitted bandwidth for instance).

This simple logic can't be applied to the log/log-plot for VRM response however. If you have a phase shift in the time base, you are modifiying the shape of response in the log/log-plot. You simply don't get exact decay rates (exponents) and other parameters. This is the reason, why I need a consistent and known time base t0 (=TX switch-off time).

Cheers,
Aziz

PS: Don't blame me if there are missing brackets or minor bugs. I'm totally confused.

[Aziz]

Hi Thomas,

Ok, I have recognized, that you have corrected your time base manually.
Measurement 3: t0 +7 µs
Measurement 4: t0 +8 µs
Measurement 5: t0 +9 µs
t0: acquisition data time code t=0, not to confuse with your corrected time code

What I didn't understand is, when is your t0? Where have you hooked the trigger input? I hope not at the decay curve. This would be worthless. We need a stable & consistent time code and that should be at switch-off. The logic signal for switching the TX mosfet should trigger the oscilloscope at switch-off. That should be t=0. But not directly at the TX mosfet gate as this would be quite noisy I think. We can add some delay time due to mosfet driver, mosfet switch-off delay and amplifier delay.

I'm totally confused now.

Cheers,
Aziz

[Aziz]

Hi Aziz,

just a few notes on my test setup and the magnetic viscosity document.

Test setup:

• Preamp: Two NE5534 with x10 and x20 amplification, i.e. x200 total
• TX timing: 50 µs TXon (10 volts), 2 µs TXoff (flyback, determined by 250 volts avalanche breakdown of the MOSFET).
• 10 µs TXoff are achieved by clamping the flyback voltage to 50 volts. 500 µs TXon consist of 50 µs current ramp followed by 450 µs constant current to keep dI/dt at zero.
• Scope trigger is falling edge of TX drive, but t=0 is defined to be exactly at the end of the flyback pulse with an error of maybe +/- 0.25 µs. This error is the same for all 4 soil samples within a set of measurements, so if you add 'p', it should be the same for all 4 measurements.
• The OPAMPS will add some time lag and some frequency dependent phase shift, but these effects should be quite small considering the low amplification and band width requirement.

Magnetic viscosity document:
http://www.eos.ubc.ca/research/ubcgi..._eudem2003.pdf

This publication is not new to me. I have some problems with their definitions of the TX waveforms which seem to be impractical in real metal detectors ...

On page 2 it says:



Assuming that we add a constant current period of a few hundred µs to a standard PI timing, this would effectively be close enough to ∞ for most targets. But it is not possible to switch off the H-field instantly – there is always a ramp down which takes a few µs, depending on how high the flyback voltage is allowed to climb.

Same issue on page 3:



Well … a linear ramp is actually the usual shape of the coil current and hence the H-field for both TXon and TXoff times in most PI detectors. Some may have a flat top (resistive limited) coil current, but it is impossible to have a rectangular shaped coil current resp. H-field with for example 10 volts TXon and 250 or even 1000 volts TXoff.

They continue to assume a practically impossible rectangular H-field pulse that starts at t = −Δt and stops at t = 0 when they derive equation 15. Then they state that the ratio of Δt and the Néel relaxation time τ affects the response of the ferrites. In a real metal detector we have two H-field pulses, a linear ramp up followed by a linear ramp down. These two could be separated in time by adding a constant current period between them as described above and in post #519, so that only the ramp down (flyback pulse) would effectively cause a change of magnetization of the ferrites.

Now, what about the above defined Δt in a real metal detector? If the pulses are time separated, Δt is from a pulse that is too long ago to affect the magnetization considerably. If not time separated, then Δt will affect the response, but the second pulse (ramp down, with a second, usually very short Δt) will affect it much stronger and with opposite polarity. So it looks like as if equation 17 is not applicable for real metal detectors, and your 1/(t+p+w) term would make no sense.

Thomas

Thanks Thomas,

now this is a better description of your measurement. I can look at your latest measurements and can check the consistency of the model parameters.
G(t) = a*(t+p)^b is for 0 < t < 1 ms is quite good, but it needs a correction term in the early times.
So something like G(t) = a*( (t+p)^b - XXXX) is required. p can be set to zero, if the time code is accurate enough. Or it can be set for all measurements with a constant time code correction value. The 1/(t+p+w) term seems to produce inconsistent model parameters.

If you look at the log/log-plot, the decay rate (b) seems to be relative constant for late times. So we need a better correction term in the early timings and can take the late time decay rate.

Any further suggestions???

Cheers,
Aziz

[PiTec]

Hi Aziz,

just a few notes on my test setup and the magnetic viscosity document.

Test setup:

• Preamp: Two NE5534 with x10 and x20 amplification, i.e. x200 total
• TX timing: 50 µs TXon (10 volts), 2 µs TXoff (flyback, determined by 250 volts avalanche breakdown of the MOSFET).
• 10 µs TXoff are achieved by clamping the flyback voltage to 50 volts. 500 µs TXon consist of 50 µs current ramp followed by 450 µs constant current to keep dI/dt at zero.
• Scope trigger is falling edge of TX drive, but t=0 is defined to be exactly at the end of the flyback pulse with an error of maybe +/- 0.25 µs. This error is the same for all 4 soil samples within a set of measurements, so if you add 'p', it should be the same for all 4 measurements.
• The OPAMPS will add some time lag and some frequency dependent phase shift, but these effects should be quite small considering the low amplification and band width requirement.

Magnetic viscosity document:
http://www.eos.ubc.ca/research/ubcgi..._eudem2003.pdf

This publication is not new to me. I have some problems with their definitions of the TX waveforms which seem to be impractical in real metal detectors ...

On page 2 it says:

Consider the situation where a small DC field, H, which has been applied to a system at time t = −∞ is instantly switched off at t = 0.

Assuming that we add a constant current period of a few hundred µs to a standard PI timing, this would effectively be close enough to ∞ for most targets. But it is not possible to switch off the H-field instantly – there is always a ramp down which takes a few µs, depending on how high the flyback voltage is allowed to climb.

Same issue on page 3:

Candy [2] describes a metal detector that utilizes different pulse lengths to differentiate the response of a metal target from the ferrite response. The transmitter waveform used in the Candy system is a linear on ramp (as opposed to a rectangular pulse).

Well … a linear ramp is actually the usual shape of the coil current and hence the H-field for both TXon and TXoff times in most PI detectors. Some may have a flat top (resistive limited) coil current, but it is impossible to have a rectangular shaped coil current resp. H-field with for example 10 volts TXon and 250 or even 1000 volts TXoff.

They continue to assume a practically impossible rectangular H-field pulse that starts at t = −Δt and stops at t = 0 when they derive equation 15. Then they state that the ratio of Δt and the Néel relaxation time τ affects the response of the ferrites. In a real metal detector we have two H-field pulses, a linear ramp up followed by a linear ramp down. These two could be separated in time by adding a constant current period between them as described above and in post #519, so that only the ramp down (flyback pulse) would effectively cause a change of magnetization of the ferrites.

Now, what about the above defined Δt in a real metal detector? If the pulses are time separated, Δt is from a pulse that is too long ago to affect the magnetization considerably. If not time separated, then Δt will affect the response, but the second pulse (ramp down, with a second, usually very short Δt) will affect it much stronger and with opposite polarity. So it looks like as if equation 17 is not applicable for real metal detectors, and your 1/(t+p+w) term would make no sense.

Thomas

[Aziz]

Ok guys,

another trial.
Just imagine, I'm totally blind and don't see, what you are really making during the measurements.

1.

I want to see the TX gate signal curve in the measurement data (additional channel required). So I can see, when the f'nk mosfet switches off and all the time code for the measurements are correct & consistent (You know, I don't trust you and your measurements anymore! *LOL*). All the measurements must have the TX gate channel parallel to the signal channel. The time code must be consistent for all measurements. The measurement trigger must be hooked on the TX gate and it should trigger the measurement at the switch-off time (may not be the TX mosfet gate pin; it's noisy, but an earlier stable digital source is best).

2.
I want to see the AIR signal. This is the standard flyback measurement without any targets and soils and will be my reference signal. Coil up in the air! So I can remove DC voltages, residual flyback process signals and so on. This measurement must be repeatable and the time code must be consistent.
I'll subtract this reference from the soil measurements. You know, what's going to happen, if you screw this important measurement.

3.
Specify your pre-amp gain. Don't amplify much. A gain 10x - 100x would be enough. To model the transfer characteristics of the pre-amp (for early time non-linearity), we would require a purely single time constant (TC) target response measurement. The test target may not be magnetic (better thin copper or Al wire). TC of 20-50 µs would be enough. We should get a nice straight line in the log/lin-t plot and this is independent of variable time (time code). We can make either a correction look-up-table (LUT) for the early time non-linearity of the pre-amp or can directly see, when the pre-amp is producing a linear gain behaviour.


4.
Keep the temperature consistent for all measurements. And record the temperature.

5.
Fresh batteries? Use stable and noise free power source.

6.
Use a low noise amplifier. Use a high bandwidth (=fast) amplifier.

7.
Specify the measured entities. Unit (example: s, ms, µs, V, mV, ..), range (example: -2V..2V, 0V..5V). When the data gets clipped? Coil current type, coil current magnitude before switch-off, coil inductance and resistance (or at least the coil model name).

and so on.., which haven't been mentioned right now


You see the vague conditions and complexity of the measurements.


And here is an example for a measurement strategy:
Imagine we are going to test the VRM response strength consistency (parameter a in our example) for a given VRM model formula. We would require 2-5 measurements with different strength of response for the same soil sample. So we would vary either the sample to coil distance or would vary the sample amount.

And then we could easily check, whether parameter a is a direct proportional factor or whether it is depending on other (unknown) variables a(p1,p2..). If the latter one happens, the shape of response would differ for each measurements slightly.

You see that one have to be very accurate in making measurements.

Oh man!, I give up!
I make my own measurements and will bust all the scientists and gurus. *LOL*

Aziz

[Aziz]

Which admirably demonstrates why you shouldn't make wild claims before you've confirmed the basic science is correct.

Hi Mr. Q,

I'm looking for perfection & beauty in the VRM science & math.
You can bet, that the 1/t law isn't valid in the scope of usual PI timings (0 < t < 1 ms). There isn't any decay rate (exponent) of -1. Null, Nada, Nix, Nil, Yok, Nothing,..
A lot of b.$. were written by the scientists as well.
(I can see the obvious inconsistence in my nice numerical simulations. )

Better I make my own & correct measurements to avoid a lot of mistakes. Trusty, but verify.
I can't even trust in the time code I get from the different measurements. The crucial point is, that the time code must be at least consistent for all measurements. Even the soil sample temperature must be consistent. There are many many variables, that affect obviously the VRM response (pulse width, pulse shape, flyback decay shape until we can make measurements, coil current peak, sample distance to coil, ... )

We need dozens of consistent & accurate & repeatable measurements. The measurements must be exactly documented as well. I often have to ask for the measurement conditions. Well, I can't work under these vague conditions.. *LOL*


I'm open for suggestions... So Mr. Q, what do you suggest.

Cheers,
Aziz

[Qiaozhi]

Hi guys,

I made more numerical simulations and tested different VRM soil formulas again. And checked the consistency of the best fit soil model parameters. We can obviously forget all and everything about VRM science.
Inconsistencies everywhere.


So back to the roots.
Anyone a good idea?

Cheers,
Aziz

Which admirably demonstrates why you shouldn't make wild claims before you've confirmed the basic science is correct.

[Aziz]

Back to the roots!

Hi guys,

I made more numerical simulations and tested different VRM soil formulas again. And checked the consistency of the best fit soil model parameters. We can obviously forget all and everything about VRM science.
Inconsistencies everywhere.


So back to the roots.
Anyone a good idea?

Cheers,
Aziz

[Aziz]

So what?!? What is the point ? We figured out things, known for many years, soil is about 1\t, closest approximation, good enough. Ferrite, as expected, is nearly ideal 1\t, perfect consistency and grain size controlled in manufacturing process (some types may behave differently, but this is about ferrite properties, out of scope here), soil is less ideal. No new, interesting or useful data generated about any irregularity that can be exploited for some new GB design, or for improvement of existing methods. No data about, for example, influence of different pulse width, flyback shape and duration, breakdown period, bias field, effect of bipolar pulsing etc in different situations, all useful design parameters. Well documented, this can be far more interesting reading for anyone building PI, unveiling many “mysteries” and wrong interpretations still wide in circulation. Let's do something more funny, like, how many components need to be changed in Surf PI to achieve GB condition, or something similar?

Tepco,

if you are taking the 1/t law as an approximation function, you should be able to make the GB for the Surf PI. But you would require a good manual ground balancing potentiometer. You have to tweak always your GB pot.
The math and algorithm for 1/t GB is quite simple and trivial.

I see, you're not really interested in WBGB.
Cheers,
Aziz

[Tepco]

Uploads are now displayed as a file name, rather than displaying the image embedded in the post. The previous embedded method took up too much bandwidth on the server, and we had a complaint from the hosting company.

Nice for slower connections or mobile device access too. I occasionally use 3G modem on the field, prepaid, so when data limit is reached it basically drops to dial up speed, making forum with attachments almost unreadable.

[Tepco]

So what?!? What is the point ? We figured out things, known for many years, soil is about 1\t, closest approximation, good enough. Ferrite, as expected, is nearly ideal 1\t, perfect consistency and grain size controlled in manufacturing process (some types may behave differently, but this is about ferrite properties, out of scope here), soil is less ideal. No new, interesting or useful data generated about any irregularity that can be exploited for some new GB design, or for improvement of existing methods. No data about, for example, influence of different pulse width, flyback shape and duration, breakdown period, bias field, effect of bipolar pulsing etc in different situations, all useful design parameters. Well documented, this can be far more interesting reading for anyone building PI, unveiling many “mysteries” and wrong interpretations still wide in circulation. Let's do something more funny, like, how many components need to be changed in Surf PI to achieve GB condition, or something similar?