GROUND CONTROL PI CIRCUIT

[Davor]

t^-1 works in ideal world. It is generally not a quality of ground as much as quality of equipment that spoils the t^-1 relationship, but it is there, and one should provide for slight variations. A big contribution to the mismatch is a duration of Tx charging period, or better say the lack of it. The ground response skews from a perfect t^-1 after the same amount of time as the charging period.

[Teleno]

t^-1 works in ideal world. It is generally not a quality of ground as much as quality of equipment that spoils the t^-1 relationship, but it is there, and one should provide for slight variations. A big contribution to the mismatch is a duration of Tx charging period, or better say the lack of it. The ground response skews from a perfect t^-1 after the same amount of time as the charging period.

The mismatch is


Some ideal examples of the regression technique (times in us, normalized to the first sample):

Target signal : with tau = 4us.

Ground signal with delta t (on-period) = 50us:

Regression to 1/t of 10 samples:

1. ground signal:

---- 1/t - 1/(t + T) --
1    1
2    0.490384615384615
3    0.320754716981132
4    0.236111111111111
5    0.185454545454545
6    0.151785714285714
7    0.12781954887218
8    0.109913793103448
9    0.096045197740113

Best fit: 0.98 / t; rss error: 0.0019

2. target signal:

---- e^t/tau--
1    1
2    0.778800783071405
3    0.606530659712633
4    0.472366552741015
5    0.367879441171442
6    0.28650479686019
7    0.22313016014843
8    0.173773943450445
9    0.135335283236613

Best fit: 1.23 / t; rss error: 0.17

3. target + ground signal:

---- e^t/tau + 1/t - 1/(t + T) --
1    1
2    0.618067447748263
3    0.447268712649278
4    0.340702210114235
5    0.266214676086582
6    0.211426316872256
7    0.170013885270402
8    0.138184901955875
9    0.113439054125622

Best fit: 1.09 / t; rss error: 0.028

Conclusion:

error of pure target is 2 x orders of magnitude the error of pure ground.

error of ground + target (when signals are of the same order) is 1 x order of magnitude the error of pure ground.

I believe there's a basis for ground balance here.

[6666]

Good information, but how do we convert these mathematical formulas into practical working circuits ?

[Teleno]

Good information, but how do we convert these mathematical formulas into practical working circuits ?

The cirtuit should in principle remain the same, it's just how you process the samples.

[Davor]

...
Conclusion:

error of pure target is 2 x orders of magnitude the error of pure ground.

error of ground + target (when signals are of the same order) is 1 x order of magnitude the error of pure ground.

I believe there's a basis for ground balance here.

That's the general idea. However, the ground will almost certainly assume a bit different exponent which you may compensate. You can't simply dismiss the ground because there is literally 2 orders of magnitude more of it than a target.

[scrungy_doolittle]

A typical implementation is an H-bridge:
http://en.wikipedia.org/wiki/H_bridge

There is an Hbridge driver chip L9110 and another one that are cheap anc commonly found on simple ebay motor controllers for arduinl I think this might make a good Hbridge driver (even for the hbridge mod to the TGS

[6666]

Thanks for the heads up on the L9110

[basellafe]

Thanks a lot for this wonderful device
File Programming

[6666]

OK - now I've got it.

Your equation is not as I assumed. In fact, it is:

x = A1(S1) + A3(S3) - A2(S2)

where A2 = A1 + A3

In your case, you're using different sample pulse widths to achieve / adjust the gain, but the result is the same.

As a test, with TS1 = 10 and TS2 = 2, the gb gain (A2) needs to be 5 in order to cancel the ground signal, so we have:

TS1 = 10
TS2 = 2
EF = 2
S1 = 12
S2 = 4
S3 = 2
A1 = 1
A2 = 5
A3 = ?

Let's calculate the required value of A3 (EF gain) to set x to zero (ground balanced).

A3 = (x - A1(S1) + A2(S2)) / S3
A3 = (0 - 1(12) + 5(4)) / 2
A3 = (-12 + 20) / 2 = 4

If you try various values for EF, the value for x is always zero, and the detector remains ground balanced.

So the big question is - why does this technique work in the same way as equation 2?

Here's the answer:

Starting with equation 1 : x = A1(S1) + A3(S3) - A2(S2)

Since A2 = A1 + A3, then: A3 = A2 - A1, and substituting for A3 gives:

x = A1(S1) + (A2 - A1)(S3) - A2(S2)
x = A1(S1) + A2(S3) - A1(S3) - A2(S2)

and now I bet you can see what's coming ...

x = A1(S1 - S3) - A2(S2 - S3) ........................ Viola! Eq.2

So, x = A1(S1) + A3(S3) - A2(S2) = A1(S1 - S3) - A2(S2 - S3)
i.e. Eq.1 = Eq.2

How did you come up with this alternative scheme without working the numbers?

Hello George
do you remember back when you did all the maths in reply #27 for Mickstv GEB solution ?, which intergrator configuration does the maths apply to, was it this one attached , with the signal straight out of the preamp ?
Thanks.

[mickstv]

Hi 6666,

I'd use an inverting stage after the preamp then use a single ended integrator stage....

[Qiaozhi]

Hello George
do you remember back when you did all the maths in reply #27 for Mickstv GEB solution ?, which intergrator configuration does the maths apply to, was it this one attached , with the signal straight out of the preamp ?
Thanks.

I'm not sure it really matters which integrator configuration is used. The one you posted is similar to the Hammerhead, which I believe will work by adjusting pulse widths to change the gain.

[6666]

Hi 6666,

I'd use an inverting stage after the preamp then use a single ended integrator stage....

G'day Mick, good to hear from you, hows things ?

[mickstv]

I'm not sure it really matters which integrator configuration is used. The one you posted is similar to the Hammerhead, which I believe will work by adjusting pulse widths to change the gain.

Hi George, I spent plenty of time testing both options, but the best method for GB and EF cancel is to use the single ended integrator method. It works better for wide samples.

[mickstv]

G'day Mick, good to hear from you, hows things ?

Hi Bruce, yeah going good, spending time out detecting yellow stuff...

[6666]

I'm not sure it really matters which integrator configuration is used. The one you posted is similar to the Hammerhead, which I believe will work by adjusting pulse widths to change the gain.

Thanks George, maths is not my strong point in my ageing years, was trying to match the circuit to the maths.