Ground Balance

[Davor]

Lets speak math

I previously mentioned that for successive samples with duration that keeps a constant ratio against the total period before it we have a GB solution in a single channel with constant but alternating gain (+,-,+,-,...) The simplest form is what I propose +1,-2,+4,-8,...
GB solution is achieved for each successive pair



That's because




and



keeping the successive durations at constant ratio will maintain GB condition satisfied, and in this case




and also



So subtracting these will eliminate ground.

Considering the target responds as



and substituting t/τ with x, and integrating such signal, for indefinite integral we get



but integrated at the above mentioned sample durations gives a bit different result



and



And these are most obviously not equal.

As for the hole, I inserted these formulas in Wolfram Alpha as it produces nice analisys and graphs. These results may be a little counter intuitive as x stands for t/tau, so for x=1 t is equal to tau but left of x=1 are the longer taus (I did not bother rectifying this):
http://www.wolframalpha.com/input/?i...++for+x%3D0..4

As mentioned before, introducing additional sample pairs will shift the zero more to the left to include longer taus without a hole:
http://www.wolframalpha.com/input/?i...++for+x%3D0..4

Adding sample pairs makes sense only up to a finite number of pairs, as this process takes a lot of time after, say, a second pair, and that may affect the pulse rate. There is also a problem of EF pulse and its constraints. Going to alternating Tx pulses may be a great answer to this problem.
In any case, these all possibilities are at hand, and I'll try some eventually. For the time being I'm happy with the minipulse PCB that arrived today, and it looks fabulous.

[Davor]

Thanks for noticing, that transistor can be just about any small signal PNP that you have. At Elektor magazine they used to designate such non-critical transistors as TUP for PNP and TUN for NPN. At this place it is only a clamp.

I mentioned some more complicated schemes based on this constant time ratio concept, but for classic implementation with non-programmable chips this is just about it. Widening a hole-free range of taus by means of introducing more sample pairs seem a perfect job for a micro.

[Thomas]

Advice for running the MinipulseGB sym, Assign a transistor to Q1 (2n3906) worked for me, spice chokes for me when it is left generic.
Davor that is a work of art. I just started running it, and it is really getting my idea machine going.

[sinclairuser]

thanks davor, very interesting and thankyou, aziz while quite brilliant in some aspects, was his own worst enemy in others, all he had to do was shut his trap(as carl has said before), on that one day, he could not do that and paid the price.
which is a shame as much for us as it is for him, this place is now poorer without him.
what we do is not all about practicalities, sometimes an excellent theorist with pin sharp maths is worth 10 nuts and bolts engineers, a fact lost on the minelab sycophants, its a shame but thats how it went, sometimes you have to button your lip and let things go, a fact lost on aziz, quite a few here suffer from the same affliction.

[Davor]

Not so much executive summary would be like this...

Assumption: gain is the same throughout.

GB condition is met when sum of integrated samples in target and GB samples is zero for 1/t stimulus.
Here we have timing: 1 delay, 1 sample, 2 GB
Because duration ratios 1delay:1sample = 1:1 = 1 and (1delay + 1sample):2GB = 2:2 = 1 -> subtractive integrating 1/t over such periods produces 0
Actually for 1/t stimulus, if you alternate samples at a constant ratio you also get GB, but binary sequence is a handy one for simple counters.

Because the ground may assume some value of exponent other than -1, for whatever reason, I'm varying initial delay a little to compensate.

EF condition is achieved when sum of positive pulses duration equals duration of the negative pulse duration, and counter-intuitive it is positive here. So 1sample-2GB+1EF=0. This is so because gain is the same throughout.

For targets the response varies with t/tau ratio, and there is a hole. I'll place some links to Wolfram Alpha to give some insight to this. It is even more interesting when additional pairs of sample&GB are added, 4 sample, 8GB, and 16 sample, 32 GB, as this shifts the hole in a favourable way and widens the response.

Polarity of the response is different below and above the hole. No surprise there.

[Qiaozhi]

As mentioned before, here is the solution with independent initial delay and the time base, by virtue of a clamp. Also is attached a LTspice project folder in a zip file.

For the time being I'm only concerned about GB for minipulse. This is not tested, but math says it should work. There is no practical reason why this approach would fail on other devices.

The math also implies a way of removing the problem of a "hole" in response typical to the PI machines with GB. It is only slightly more complicated. With increased number of samples in a geometric series duration and alternating polarity, the hole-less range of useful tau targets vs. sample duration becomes larger, and without harmful influence on target response. That would be point-on with Aziz' FFT solution, but to realise this one should go a bit deeper into FFT theory. In a way it truly is a WBGB system as he often advertised. Too bad he got banned.

It would be a good idea if you could provide a block diagram of your proposed GB method, plus a simplified (executive overview) explanation of how it's supposed to work. At the moment I'm failing to understand the concept, even though I've downloaded and successfully run the simulation.

[Davor]

At the FETs gates. Timing circuit must be powered with 0 and -5V for FETs to work properly, same as originaly in minipulse.

I'm considering scribbling an overview of ground balance with this approach in mind.

[6666]

As mentioned before, here is the solution with independent initial delay and the time base, by virtue of a clamp. Also is attached a LTspice project folder in a zip file.

For the time being I'm only concerned about GB for minipulse. This is not tested, but math says it should work. There is no practical reason why this approach would fail on other devices.

The math also implies a way of removing the problem of a "hole" in response typical to the PI machines with GB. It is only slightly more complicated. With increased number of samples in a geometric series duration and alternating polarity, the hole-less range of useful tau targets vs. sample duration becomes larger, and without harmful influence on target response. That would be point-on with Aziz' FFT solution, but to realise this one should go a bit deeper into FFT theory. In a way it truly is a WBGB system as he often advertised. Too bad he got banned.

Good work Davor, where do you plug it into the mini pulse ?

[greylourie]

The only thing you need to balance out is viscous soil. What remains are the targets, and perhaps a hot rock or two.

Your timing/generator circuit looks like a good candidate for experimentation with many platforms. Quite a list of possible projects could use this as a substitute or basis for their sampling regime. Very tempting. Thanks for taking the time to share. I'm going to study it.

[greylourie]

Thanks Carl.

Really interested in the single differential integrator, and adjusting the sample widths. Will have a closer look at the example equations Qiaozhi posted up in another thread here (http://www.geotech1.com/forums/showt...ROL-PI-CIRCUIT), and see if I can figure out how to plug in the original goldscan pulse widths/sequences to come up with an alternative.

[Carl-NC]

Cheers Carl,

I guessed I made a fundamental error. By using the expression (^-1), was trying to show the inverting opamp would multiply by a negative to what ever it sees on its input.
As a rule, what is coming out of the differential integrator (iron), before hitting the inverting opamp is a positive value ? As simple as that ? I complicated everything by assuming too much.

How could I translate the formula to use a single channel (with differential integrator at the front ), but continue to be able to exploit the means to see or balance to different metals like the original does ? Is it possible ?

As a rule, in a simple PI everything (ferrous, nonferrous, salt, ground) responds with a positive value. The difference is the curvature of the response (1/t vs exp) and the time constant of the exponential response.

A 2-sample subtractive GB can be adjusted to exactly cancel ground, but that setting will also exactly cancel a particular exponential tau. If you take 3 samples then you can exactly cancel a 1/t response but not cancel any exponential taus because they have a different curvature. Regardless of the method, subtractive GB on the decay always reduces target depth.

You can use a single differential integrator by appropriately sampling on the inverting and non-inverting sides and adjusting either the gains or the sample widths. You can also do all this with a non-differential integrator by running some of the sample switches off an inverted preamp signal.

When I get some time I'll try to post some drawings of all this. Work has me hopping right now.

[Davor]

The only thing you need to balance out is viscous soil. What remains are the targets, and perhaps a hot rock or two.

[greylourie]

As mentioned before, here is the solution with independent initial delay and the time base, by virtue of a clamp. Also is attached a LTspice project folder in a zip file.

For the time being I'm only concerned about GB for minipulse. This is not tested, but math says it should work. There is no practical reason why this approach would fail on other devices.

The math also implies a way of removing the problem of a "hole" in response typical to the PI machines with GB. It is only slightly more complicated. With increased number of samples in a geometric series duration and alternating polarity, the hole-less range of useful tau targets vs. sample duration becomes larger, and without harmful influence on target response. That would be point-on with Aziz' FFT solution, but to realise this one should go a bit deeper into FFT theory. In a way it truly is a WBGB system as he often advertised. Too bad he got banned.

Oh wow, another implementation. Thanks a lot Davor. Bet Aziz would like it.

I'm still trying to pick Carls brain. I frequently watch a downloaded copy of Jose's youtube video of his homemade goldscan4 facsimile. It would great to be able to implement (if possible), the traits of that type of balancing in a hammerhead/minipulse type machine. Imagine the hours spent balancing out various items. Fun ! Maybe I'm just being stupid again, and missing the obvious.

[greylourie]

Cheers Carl,

I guessed I made a fundamental error. By using the expression (^-1), was trying to show the inverting opamp would multiply by a negative to what ever it sees on its input.
As a rule, what is coming out of the differential integrator (iron), before hitting the inverting opamp is a positive value ? As simple as that ? I complicated everything by assuming too much.

How could I translate the formula to use a single channel (with differential integrator at the front ), but continue to be able to exploit the means to see or balance to different metals like the original does ? Is it possible ?

[Davor]

As mentioned before, here is the solution with independent initial delay and the time base, by virtue of a clamp. Also is attached a LTspice project folder in a zip file.

For the time being I'm only concerned about GB for minipulse. This is not tested, but math says it should work. There is no practical reason why this approach would fail on other devices.

The math also implies a way of removing the problem of a "hole" in response typical to the PI machines with GB. It is only slightly more complicated. With increased number of samples in a geometric series duration and alternating polarity, the hole-less range of useful tau targets vs. sample duration becomes larger, and without harmful influence on target response. That would be point-on with Aziz' FFT solution, but to realise this one should go a bit deeper into FFT theory. In a way it truly is a WBGB system as he often advertised. Too bad he got banned.