Ground Balance Theory

[kt315]

Eric, why you do not begin to write a book with all PI matter? your posting in forums is good but it is so ephemeral and inanimate IMO.

[Aziz]

Hi All,

Round and round the wheel turns. The timing on my Viscosity Meter is initiated by the cessation of the drive pulse to the TX mosfet. This is t 0. The start of the measurement period is 10uS after t 0, then in 5uS steps. The flyback pulse occurs well within the delay period and can be considered as non existent at the start of the measurement period. However it is very difficult to achieve a completely flat response from the coil/cable/Tx/Rx front end in the absence of a target sample. That is why I first integrate and do a bit of dc filtering and amplification before the zeroing circuit. In other words the post integrator circuit is zeroed to 0000 before each sample measurement down the decay curve, which eliminates any spurious low level response all the way to the maximum delay. The result is that you get much closer to a true 1/t response and any variation is due to the nature (particle size distribution) of the target. Later times also then appear relatively noise free as the sample width increases proportionally as the delay.

Eric.

Hi Eric,

you have to be more clear, that your measurements can't be compared to the blokes voltage decay measurements.
You are using the integration of the VRM decay (sampling of the integral) rather than sampling the VRM voltage level.
It would be interesting to see the basic math involved in your measurement (I am aware of it but the blokes here would love to see it.)

Anyway, the integration-method would be quite well destined for modelling the VRM decay correction term, which domintes in the early times.

Cheers,
Aziz

[Aziz]

Hi all,

I hoped to see the math proof of the integration method. Nobody obviously likes math. Me too. I have to take a blue pill to be able to love it.

1. Assumption:
The VRM decay obeys the 1/t law. G(t) = a*(1/t), G(t) = a/t, where a = VRM response strength, t= time variable, t0=t=0 is at switch-off.

2. Integrator:
We are using an ideal integrator (ideal = no voltage errors, super linearity, super bandwidth, no phase delay... ) . We integrate from time t1 to t2, where the integration time period width is w = t2 - t1.
The indefinite integral of G(t) is = a*log(t) + constant

Integral (G(t)dt) = a*log(t)
(We don't need the constant term in definite integrals as they subtract to zero.)

log(t) = natural log (base e=2.71.

3. Condition:
The integration period width w is direct proportional to time t.

w = k*t, where k = proportionality constant.
So we get the integration timings:
t1 = t
t2 = t1+w = t+k*t = t*(1+k)

3. Integration (t1 .. t2):
We are going to integrate the VRM response G(t) from time t1 to t2. This is what our ideal integrator will get at the output.
Integral (G(t)dt)|t1-t2 = a*log(t2) - a*log(t1) =
= a * ( log(t2) - log(t1) ) , where t2 = t*(1+k), t1 = t
= a * ( log(t*(1+k)) - log(t) )
= a * ( log(t) + log(1+k) - log(t))
= a * log(1+k)

That's it.

We should get always the same VRM intergrator output voltage if we integrate anywhere in the time-axis. If the integrator output differs in time (not same, not constant), the VRM response doesn't obey to the 1/t law. We should observe this in the early timings however. No wonder, G(t)=a/t doesn't have any correction term for the early timings.

4. Special case for k=1
t1 = t
w = k*t = 1*t = t
t2 = t1+w = t+k*t = 2*t

t(=t1), w
=========
10 µs, 10 µs (t2=20 µs)
20 µs, 20 µs (t2=40 µs)
30 µs, 30 µs (t2=60 µs)
and so on...

The integrator output should be in this case for k=1:
Integral (G(t)dt)|t1-t2 = a*log(k+1) = a*log(2)
BTW, this timing scheme can be easily generated by the electronics.


You see the benefit of the VRM response integration method now. If the VRM decay doesn't obey the 1/t law, the integrator won't deliver a constant voltage over the full measurable time axis (t > flyback decay duration of course and t << noise floor level reached in time). Due to the large integration time w, the noise gets averaged into 0 and improving the SNR of the measurement therefore.

Cheers,
Aziz

[Aziz]

Anybody still doubting my claim to own the WBGB?

You don't have to understand the VRM science to make a good GB.
You can use your own pattern recognition ability to make a good GB (recognizing the response patterns).
You can use data mining principles to make a good GB (if your own pattern recognition feature fails).
You can use some nice and elegant math to make a good GB.

(Or take more blue pills to increase your MQ level. )

Cheers,
Aziz

[Aziz]

Hi all,

we haven't finished the thread yet.
I want the math proof of the linear combination factors related to this integrating method now. We still assume G(t) = a/t for simplicity (no correction term involved). We want to see the relationship of the two integrated windows (w1, w2).
(I have made this on the other forum. You may look up there and repeat it here.)

BTW, in the above proof, we have made all the linear combination factors = 1 for all t.
For instance: k=1
w1: t1=10 µs, t2=20 µs
w2: t1=20 µs, t2=40 µs
c = (Integral G(t) dt|for w1) / (Integral G(t) dt|for w2) = a*log(2)/a*log(2) = 1

Cheers,
Aziz

PS: I'm too busy to process the latest measurements made by Thomas. Sorry, it will delay.

[ivconic]

Poor man, under such horrible pressure!
Take one 10kg apaurin and relax, breathe slowly... breathe slowly... breathe slowly...

[Aziz]

Poor man, under such horrible pressure!
Take one 10kg apaurin and relax, breathe slowly... breathe slowly... breathe slowly...

No I can't. My MQ level would rise up to the moon and I would overtake the MD genius with lightspeed. *LOL*


BTW, we are talking about very trivial things & math.
log log log log log log log log ...

Cheers,
Aziz

[ivconic]

That's what i am talking about man!

[Davor]

So log gain and time, from such set take first+last sample, second+one before the last ... and if it is not a straight line at constant value - we have a target. Trivial.

[bbsailor]

Hi Eric,

you have to be more clear, that your measurements can't be compared to the blokes voltage decay measurements.
You are using the integration of the VRM decay (sampling of the integral) rather than sampling the VRM voltage level.
It would be interesting to see the basic math involved in your measurement (I am aware of it but the blokes here would love to see it.)

Anyway, the integration-method would be quite well destined for modelling the VRM decay correction term, which domintes in the early times.

Cheers,
Aziz

Aziz,

Note the Eric designs his PI machines to have a very high PPS rate from 3,000 PPS to 10,000 PPS so that he obtains a better target signal to noise ratio by integrating many samples of lower TX power to behave near what a high power TX pulse would have. Using a lower power TX pulse tends to stimulate bad ground less. By subtracting the ground response he can reduce the effect of ground as it's signal is more constant than a target which is only under the coil for a very short time. See this link to incorporate into your math analysis of the benefits of using many integrated signals. http://www.thinksrs.com/downloads/PD.../AboutLIAs.pdf The amount of signals that are integrated are based on the coil diameter, target size and sweep speed.

bbsailor

[Aziz]

Oh well,

it seems that it isn't as trivial as some of you would think of. Nobody is putting some trivial math here...
I'm quite disappointed..
4212

[kt315]

hard to seek... Ferric Toes is Eric Foster. for future search in forum.