detection depth

[green]

Hmmm.. you didn't say how you corrected it. So I can't assess your reasoning. But I have spent some (lots) time this evening on hyperphys trying to check your charts - including the constant inductance.
I concentrated on the Z = 0 points, as that's easier, mathematically speaking, and we seem to agree the general shape of the curves is correct.
It appears your 'reference' point on both charts is for the 200mm coil, at Z = 0, giving a reading of 12000 signal amplitude. I had to calculate this based on the Z = 25mm data point at 10000 amplitude.

For the fixed inductance curves, I calculated Z = 0 amplitudes of:
200mm coil: 12000
300mm coil: 3270
400mm coil: 1275
500mm coil: 709
These seem to match well with your figures. This assumes 'received voltage' is proportional to 'received current'. (due to fixed inductance).

For the Fixed number of turns chart, the reference curve is the 200mm coil, with 12000 amplitude at Z = 0, as before.
I multiplied the 'recieved current' by the calculated inductance L = 278 uH, then found a scaling factor to get 12000.
For the remaining larger coils, the transmit (current x turns) was kept constant, as turns is kept constant. The received voltage was multiplied by the coil inductance, then by the previously-determined scaling factor. Results are:
200mm coil; L = 278 uH; 12000 amplitude
300mm coil; L = 458 uH; 8787
400mm coil; L = 651 uH; 7025
500mm coil; L = 853 uH; 5892

Notice that these are much closer together - you're gaining with the larger coils because: you're transmitting a constant (Amp-turn) product, and because: the coil inductance goes up roughly in proportion to coil diameter, so the received voltage goes up too.

I would be interested in your thoughts.

For same inductance I think I followed your instructions reply#34. I=23.874*(200mm/coil mm)^.5, enter coil radius and target distance, record Gauss. Rx(chart amplitude)=Gauss^2*5331, (200mm coil with 25mm distance=10000)
added the zero distance points latter.

For same number of turns. Error chart, I=23.874 for all coils, enter coil radius and target distance, record Gauss. Rx(chart amplitude)=Gauss^2*5331.
Corrected chart, Rx(chart amplitude)=Gauss^2*5331/(coilmm/200mm)^.5.
Receive amplitude is proportional to inductance(Tx_Ampere turns, Rx_turns or turns squared) so I calculated what I thought a 300mm coil should be and played with squaring something until I got the same answer. Don't know if it makes sense. Should have checked with inductance increase the first time I charted same number of turns.

Trying to make sense of what I did, not sure it's correct.

[green]

Trying to make sense of what I did to correct it. Know I think the error chart might be correct. Eric's chart states a coil with a radius larger or smaller than selected coil would have less signal(coils with same number of turns). My corrected chart passed the test where the error chart didn't so I thought maybe I had corrected it. It's late and I'm more confused.

[Skippy]

Sure is confusing. I think I've spotted an error we've made, that affects both charts, and I think your correction to the fixed-turns chart is also incorrect.
Why the measured values for real fixed-inductance coils seemed to match up with theory is what was bothering me in my earlier post, where I questioned whether you used three correction factors for three curves... there should be just one, applied to all curves.
Let me sort out my ideas and I'll post later.

[green]

Trying to make sense of what I did to correct it. Know I think the error chart might be correct. Eric's chart states a coil with a radius larger or smaller than selected coil would have less signal(coils with same number of turns). My corrected chart passed the test where the error chart didn't so I thought maybe I had corrected it. It's late and I'm more confused.

Maybe I can make more sense this morning. (SI)same inductance, (ST)same turns. (ST)coils, inductance proportional to selected(coil mm/200mm). Signal strength proportional to inductance. 400mm(ST) coil has two times the inductance of the 400mm(SI) coil. 400mm(ST)coil should have two times the 400mm(SI)signal. It did with what I called the error curve. When I first posted some signal strength vs target distance charts a few years back, Monolith suggested I use Hyper physics to calculate it instead of measuring. Can't guess how many times I think I calculated wrong. Skippy suggested the (ST) curves might be wrong and they didn't pass Eric's constant turns test so I tried to correct them. Got confused again and probably made an error but they did pass Eric's (ST) test. I'm not sure any of the charts are correct. I think the(SI)chart might be because I think I followed Skippy's instructions correcting the way I was trying and it matches my measured curves. It also passes Eric's(ST)test. Couple possibility's, Eric's chart is(SI)not(ST). Neither of my charts is correct which is quite possible do to the number of times I've done them wrong. Other possibility's? Would like to see a set of correct charts.

See Skippy posted while I was typing, I'm slow with two fingers. Hope he figures it out.

[Skippy]

It's easy to get ONE set of theoretical and real data figures to match, because of the arbitrary fiddle-factor. If your theory has a flaw that creates a scale-factor error (eg. not adjusting for number of turns properly...) you just don't see it.
Only when you start changing things, like diameters, or turns, or current, do you realise the fiddle-factor was wrong, and you're left puzzling why.

[green]

For same inductance I think I followed your instructions reply#34. I=23.874*(200mm/coil mm)^.5, enter coil radius and target distance, record Gauss. Rx(chart amplitude)=Gauss^2*5331, (200mm coil with 25mm distance=10000)
added the zero distance points latter.

For same number of turns. Error chart, I=23.874 for all coils, enter coil radius and target distance, record Gauss. Rx(chart amplitude)=Gauss^2*5331.
Corrected chart, Rx(chart amplitude)=Gauss^2*5331/(coilmm/200mm)^.5.
Receive amplitude is proportional to inductance(Tx_Ampere turns, Rx_turns or turns squared) so I calculated what I thought a 300mm coil should be and played with squaring something until I got the same answer. Don't know if it makes sense. Should have checked with inductance increase the first time I charted same number of turns.

Trying to make sense of what I did, not sure it's correct.

Calculations for the first 275mm target distance. Makes it easy to compare which coil gives the highest reading at the selected coil radius, Eric's chart. Error chart(I think might be correct now) and same inductance chart. Error chart(same turns)calculations on left side, same inductance chart calculations on the right. Changed I for each coil diameter when calculating Gauss for same inductance chart, I=23.874*(200mm/coil mm)^.5

[Skippy]

OK, here's where I found the flaw in the 'Gauss-squared' bit of our simulation.
You will agree that if we doubled the transmit current in a PI coil, we would expect double the voltage back from the target (and the ground), this equally applies to running a VLF at double the coil TX voltage.
If you try this with our simulation model, it fails.
Example suppose 15 Amps produces 1 Gauss at Z = 0. We worked out G² * 12000 to plot signal strength = 12000.
If we doubled the current to 30A, we would get 2 Gauss at Z=0. We then get signal strength = 12000 * 2² = 48000, four times bigger. Obviously incorrect.
To correct for this, we need to modify the formula so current isn't squared, it's just proportional.
A revised formula is:

Output signal = 12000 * G² * ( 15 / I )

so if we used 3 times the current, we'd get 3 times the G, the G² would be 9 times, but the additional term produces (1/3), taking the output back to 3 times.

Getting this wrong gave us an offset on the Z=0 value, and hence on all the other points on that curve.

I think you've used a 'reference point' as 1 Gauss for the 133mm coil? (not sure about that). As the charts didn't have 133mm coil data, I recalculated my own, choosing 200mm coil, Z=0 as having 1.00 Gauss. This was for I = 15.916 A.

So my corrected formula is:

Output = 12000 * G² * (15.916 / I)

So my Z=0 outputs are:
200mm coil: 12000
300mm coil: 4178
400mm coil: 1955
500mm coil: 1164

These are closer together than previously. I did try and match them to the measured data for 133/200/300 coils, the match is a bit mehh, those test coils aren't really like the theoretical idea, they're not a single diameter, and I'm not sure how you've allowed for this.

Back later with 'Constant turns' thoughts.

[Skippy]

And for the 'constant turns' coils:
The current used in the simulation is constant, so the output current calculation is simply:

Output current = K * G²

To correct for the varying inductance, either calculate the true inductance with the 'Coil Calculator' javascript program on here, or use the approximation that:

Inductance = Constant * Diameter * Turns² , approx.

We're keeping Turns unchanged, so inductance is roughly proportional to the coil radius/diameter.

So using my figures:

Output voltage = 12000 * G² * ( coil diameter/200)

[green]

And for the 'constant turns' coils:
The current used in the simulation is constant, so the output current calculation is simply:

Output current = K * G²

To correct for the varying inductance, either calculate the true inductance with the 'Coil Calculator' javascript program on here, or use the approximation that:

Inductance = Constant * Diameter * Turns² , approx.

We're keeping Turns unchanged, so inductance is roughly proportional to the coil radius/diameter.

So using my figures:

Output voltage = 12000 * G² * ( coil diameter/200)

The current used in the calculation above is the total current, so for a coil of N turns, the current used is Ni where i is the current supplied to the coil statement at bottom of HyperPhysics(field at center of current loop)


I'm thinking if a current of 1amp is used I=turns. Tx=ampere turns, Rx=turns so squaring Gauss is correct for return signal for constant turns coils. For constant inductance coils, turns need to be adjusted for coil diameter change. Inductance is proportional to diameter so I=turns*(200mm/new coil mm)^2.
200mm is the start or reference coil. I=25 (turns)could be used for the 200mm coil, same inductance or same turns.

Why are you correcting for varying inductance with constant turn coils? Doesn't the HyperPhysics calculation do that when you enter a radius?

[green]

Woke up this morning wondering if I was changing the slope when calculating same turns or same inductance coils. Charted the 200mm and 500mm coils on the same chart. Does it make sense that slope doesn't change and the 500mm same turns Rx signal is 2.5 times the 500mm same inductance Rx signal?

[Skippy]

Quote:"Why are you correcting for varying inductance with constant turn coils? Doesn't the HyperPhysics calculation do that when you enter a radius?"
I'm working on the assumption that when we use hyperphys, we are putting a current in, and getting a current out. To 'translate' that output current into a voltage, we need to use the relationship:

V = -L * dI/dt

I hope this is correct.

Hence for the constant-inductance coils, we don't need to do any compensation, just assume "Voltage out = current out" and let the arbitrary correction factor take care of it.
But for the constant-turns/variable-diameter coils, the inductance varies, increasing roughly in proportion to the diameter of the coil, so I was suggesting that output voltage:

V = I * coil diameter * correction-factor

I wonder if there's an alternative way we could simulate, such as actually modelling the target, and using the receive coil as a voltage source. For double-checking purposes.

[Skippy]

Quote:"Charted the 200mm and 500mm coils on the same chart. Does it make sense that slope doesn't change and the 500mm same turns Rx signal is 2.5 times the 500mm same inductance Rx signal?"

The slope doesn't change because that is determined by geometry, just the radius of the coil, and the distance away on the Z axis. So a 500mm coils behaves like any other 500mm coil, shape-wise, it's just things like number of turns, and transmitted current that shift the whole curve up or down as appropriate.
Re: the 2.5:1 voltage ratio.
I calculated at Z = 0, the same-turns signal was down to 0.4 ( = 1 / 2.5) eg. 12000 down to 4800
... and the same-inductance signal was down to 0.101 ( = 0.4² * square-root(0.4) ) ( or 0.4^2.5 )
eg. 12000 down to 1212.
These two figures are pretty much 4:1 ratio.

I'm curious about the 133/200/300 test coils you made. Do you have more detailed dimensions, eg. outer diameter, inner diameter, of the windings? I'm thinking of how well their performance matches up to our theory ( or many theories..).

[green]

Quote:"Charted the 200mm and 500mm coils on the same chart. Does it make sense that slope doesn't change and the 500mm same turns Rx signal is 2.5 times the 500mm same inductance Rx signal?"

The slope doesn't change because that is determined by geometry, just the radius of the coil, and the distance away on the Z axis. So a 500mm coils behaves like any other 500mm coil, shape-wise, it's just things like number of turns, and transmitted current that shift the whole curve up or down as appropriate.
Re: the 2.5:1 voltage ratio.
I calculated at Z = 0, the same-turns signal was down to 0.4 ( = 1 / 2.5) eg. 12000 down to 4800
... and the same-inductance signal was down to 0.101 ( = 0.4² * square-root(0.4) ) ( or 0.4^2.5 )
eg. 12000 down to 1212.
These two figures are pretty much 4:1 ratio.

I'm curious about the 133/200/300 test coils you made. Do you have more detailed dimensions, eg. outer diameter, inner diameter, of the windings? I'm thinking of how well their performance matches up to our theory ( or many theories..).

Charted constant turns using your formula reply#159, I think. Chart doesn't pass Eric's constant turns test(signal strength is maximum at selected coil radius, a coil smaller or larger would have less signal).

I'll get the information for the three coils tomorrow.

[green]

I'm curious about the 133/200/300 test coils you made. Do you have more detailed dimensions, eg. outer diameter, inner diameter, of the windings? I'm thinking of how well their performance matches up to our theory ( or many theories..)

_____133mm coil 200mm coil 300mm coil
ID ___120mm___ 195mm____ 292mm
OD__ 146mm____ 205mm____ 307mm

including chart with turns, resistance, inductance and resonance for the coils + test data. Coils are spiral wound around tooth picks with awg28 magnet wire. Inductance wasn't exactly 300uH for each coil so measured date was multiplied by 300uH/coil inductance before charting.

After playing with the target response tester and seeing how much target orientation(flux lines crossing the target) effect target decay I wonder if the target data matching HyperPhysics means a whole lot.

[Skippy]

Thanks for the test-coil info. I think that assuming coil diameter is the mean of the inner and outer diameters is going to be OK. What is potentially the tricky thing with these flat coils is the lack of mutual inductance between each turn. Which means the inductance will be less than a tight bundle would be. This will affect the smallest 133mm coil the most.
I've been struggling to work out how to analyse the measured data, do I use the original or corrected data, can I correct it a different way etc. What I was trying to find out, in particular, was the Z = 0 figure. It would be nice to end up with a straight-line plot of real vs theoretical data, that I could just draw a straight-line through and get the best fit relationship, and hence calculate a good 'measured' Z = 0 value. In the end, I settled for a non-graphical estimation.

You will be pleased to know that I've cracked the problem, for both fixed-inductance and ( I hope ) fixed turns. The fixed-inductance analysis matches the 133/200/300 test data pretty well: 133 vs 200, 200 vs 300, and 133 vs 300.

Plenty of synapses were damaged in the process.

When I've cleaned up my maths, I'll post up the 'recipe', so you can assess it yourself.