Ground Balance

[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.

[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.

[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.

[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.

[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.

[WM6]

Going to alternating Tx pulses may be a great answer to this problem.

What mean here "alternating"? Changing in polarity in pulses?

[Davor]

Yup!
With a single pair EF pulse is duration 1, with 2 pairs EF pulse is duration 5, with 3 pairs EF pulse is duration 21, and so forth. It is simple only for a single pair of target/GB samples. EF pulse also needs additional time to prevent it from spoiling the rest of the math, and the only natural answer to this would be going for alternating Tx pulses to avoid EF altogether. It could make a whole process highly simplified as all the timing would remain in simple power of 2 counters ... including Tx.

I'm also considering constant current Tx, as it prevents diminishing target response of large tau targets, and keeps coil currents sane. I guess classic unregulated Tx also influences the effective ground response exponent, as for the longer delays these responses converge ... provided a flyback does not "reset" the previous viscous response "memory".

[Carl-NC]

OK, I found my round tooit so here are a few drawings to clarify. First, in a common non-GB PI (Hammerhead, SurfPI, etc) we often see the differential integrator:



Most of these designs have a target sample and an Earth-field sample:



The differential nature of the integrator subtracts the Earth field from the target signal. For best results you want good matching between the time constants, which usually means getting well-matched caps.

You can do the same thing with a non-diff integrator:



Now both samples use the same time constant. The gain of -1 is pretty easy to make sufficiently accurate. Timing is the same as above.

When we implement subtractive GB we normally sample shortly after the target, amplify the GB sample, and subtract from the target sample. This is usually done with a completely separate channel and its gain is the GB control. Again, matching the taus is critically important, and if the target sample has an Earth-field subtraction then so must the GB sample:



Timing is now:



Subtractive GB does not require diff integrators, you could use the non-diff integrator above for each channel (target & GB). You also don't have to use a variable gain stage. Instead, sample the ground with a variable sample width and now the width is the GB control. And since the ground channel no longer needs a different gain, there is no longer any need for a separate channel... you can do everything in the single non-diff integrator channel above using this timing:



Finally, I've mentioned before the benefits of bipolar pulsing, namely getting rid of the Earth-field samples:



This potentially allows for much faster pulse rates.

[Qiaozhi]

OK, I found my round tooit ...

If anyone else needs a "round tuit", you can buy them on eBay and Amazon.
A very useful device to have around when you need to get something finished..

[bbsailor]

OK, I found my round tooit so here are a few drawings to clarify. First, in a common non-GB PI (Hammerhead, SurfPI, etc) we often see the differential integrator:

[ATTACH]30586[/ATTACH]

Most of these designs have a target sample and an Earth-field sample:

[ATTACH]30587[/ATTACH]

The differential nature of the integrator subtracts the Earth field from the target signal. For best results you want good matching between the time constants, which usually means getting well-matched caps.

You can do the same thing with a non-diff integrator:

[ATTACH]30588[/ATTACH]

Now both samples use the same time constant. The gain of -1 is pretty easy to make sufficiently accurate. Timing is the same as above.

When we implement subtractive GB we normally sample shortly after the target, amplify the GB sample, and subtract from the target sample. This is usually done with a completely separate channel and its gain is the GB control. Again, matching the taus is critically important, and if the target sample has an Earth-field subtraction then so must the GB sample:

[ATTACH]30589[/ATTACH]

Timing is now:

[ATTACH]30590[/ATTACH]

Subtractive GB does not require diff integrators, you could use the non-diff integrator above for each channel (target & GB). You also don't have to use a variable gain stage. Instead, sample the ground with a variable sample width and now the width is the GB control. And since the ground channel no longer needs a different gain, there is no longer any need for a separate channel... you can do everything in the single non-diff integrator channel above using this timing:

[ATTACH]30591[/ATTACH]

Finally, I've mentioned before the benefits of bipolar pulsing, namely getting rid of the Earth-field samples:

[ATTACH]30592[/ATTACH]

This potentially allows for much faster pulse rates.

Carl,

One more thing that you may want to consider is the integration of from 500 to 1500 RX cycles such as what Eric Foster has introduced into the PI technology. This now puts the focus on methods to extract a meaningful signal from and within varying noise levels rather than increase the TX power. If you look at how lock-in amplifiers work you will see a similarity between the number of samples taken and Eric Foster 3,000 PPS PI machines with incresed RX sensitivity. Many PI machines have been using this technique but it is good to see how the lock-in technology has been adopted to PI machines beeing able to see very small target signals even in the presence of noise. Just do a web search on "lock-in amplifier" to begin to connect the dots.


bbsailor

[Carl-NC]

True, but generally you set the integrator tau to achieve a minimal target latency and then you get what you get in terms of how many cycles are integrated. At 3000 pps a 1500-cycle integration will probably give too much delay. By using bipolar pulsing and a short TX pulse width you could run the pulse rate upwards of 20,000 pps and, for a given integrator tau, integrate more samples. Since target signals correlate and noise does not, this could be a win-win solution.

[Davor]

I may have an addendum to this one:

Subtractive GB does not require diff integrators, you could use the non-diff integrator above for each channel (target & GB). You also don't have to use a variable gain stage. Instead, sample the ground with a variable sample width and now the width is the GB control. And since the ground channel no longer needs a different gain, there is no longer any need for a separate channel... you can do everything in the single non-diff integrator channel above using this timing:

[ATTACH]30591[/ATTACH]

You can also overlap Target and GB channels' EF samples, and notice that in a case of equal gain in positive and negative subchannel thea cancel each other while they overlap.So instead you may also use a single shorter EF to the same effect. That's basically what the scheme I proposed earlier would do, and the arithmetic is simple as all the samples are quantised.

[Carl-NC]

Yep, that's true, and pretty easy to do when you use PWM for the GB sample instead of variable gain. When you move to a 3-sample GB scheme this makes even more sense.

[greylourie]

I don't know about "round to-its" or "round tuits", but there appears to be more than one "fundi" posting here. (I will just quietly go off, and mindlessly drool at the images posted up by Carl and Davor - it will sink in...gradually)

Thanks for the round to-it, Carl.

[revmaster]

Did anyone tried PWM based GB, i tried but has been unable to find sweet spot.... If i try to balance soil the sensitivity is reduces a lot.

I am using differential integrator and have taken 3 samples: Target(+), GB(-) and EF(+). Width of Target + EF = GB Width.
Any inputs as where am i going wrong....