X2Ns

[Mike Sulzer]

Practicality. While one can find the center, why bother? Use a big enough sweet volume, and you don't need to be that careful.

I agree it is more practical to have a larger sweet spot. I understood you to mean that it could not be done the way I did it.

I used your estimate.

Not really. You said it would drop of quickly farther away. It does not.

Ten percent? That's 20*Log10[0.1/2.1]= -26.4 dBc, which will interfere with clean measurements of pickups with hum rejections of 20 to 30 dBc..

Yes, 10%. This is at the same point where the H coil is down 6%. I am simply comparing the H. coil and my solenoid at the location of the H coil plane, not where the pickup would be, in order to show that they are not very different.

You were seeing a 2 dB effect at most.

Yes, that is what I measured. I do not understand what you are saying.

Umm. Lock-in amps can pull signals 100 dB down; FFTs cannot do this, because there is too much spectral leakage. A FFT plus a FIR or IIR prefilter can dig that deep. Lock-in amps are far simpler. But suit yourself.

I am not trying to pull out signals buried deep in noise, just avoid the effect of hum located 40 Hz away. It is a trivial application of spectral analysis, and a natural thing to do once you have the pc, sound card and software, all of which have many other uses.

A lock-in does not have any better inherent rejection of strong signals than an FFT does. How could it? Both are based on multiplying by a sine wave and accumulating.

Astronomy FFT machines use a computationally simple pre-filter which is locked to the FFT length. Simple windowing can be useful in many cases.

Yes, but what's the point? Bateman was not trying to pull a signal out of massive interference.

Nor am I, but what I am doing is far easier than what Bateman did.

[Joe Gwinn]

I agree it is more practical to have a larger sweet spot. I understood you to mean that it could not be done the way I did it.

My instinct is that trying to hit such a small sweet volume day after day is too fiddly to be practical, not that it's impossible.

Not really. You said it would drop of quickly farther away. It does not.

Your statement was that with a 13x13 cm solenoid, the field was uniformn to within 2% at 0.5 cm from the center, which I translated into a "sweet volume" being roughly a sphere 1 cm in diameter.

Yes, 10%. This is at the same point where the H coil is down 6%. I am simply comparing the H. coil and my solenoid at the location of the H coil plane, not where the pickup would be, in order to show that they are not very different.

OK. But it did grow from 2% to 10%, a factor of five.

But given that the construction effort is the same, it's better to build the Helmholtz coil versus the finite solenoid. This is why Helmholtz coils are still current technology, at least a century after invention.

Or, we can go one better: Maxwell coil - Wikipedia, the free encyclopedia.

Yes, that is what I measured. I do not understand what you are saying.

That 2 dB may be a bit too close to the error floor of the setup to yield reliable measurements.

I am not trying to pull out signals buried deep in noise, just avoid the effect of hum located 40 Hz away. It is a trivial application of spectral analysis, and a natural thing to do once you have the pc, sound card and software, all of which have many other uses.

A lock-in does not have any better inherent rejection of strong signals than an FFT does. How could it? Both are based on multiplying by a sine wave and accumulating.

Astronomy FFT machines use a computationally simple pre-filter which is locked to the FFT length. Simple windowing can be useful in many cases.

I build large radars by day, and we always have the prefilters and windows as well, but they serve different purposes.

As I recall the mathematical rationale for the prefilter, the issue is growth of numerical errors causing smearing of input signals into all frequency bins. Two things contribute to numerical noise, finite word length and the total number of arithmetic operations. FFTs, especially if one has many narrow frequency bins, require far more operations than a simple FIR filter. As for word length, this is the lesser of the digitizer width and the arithmetic width. In current systems, digitizer width is the determinant. Now, sound cards usually have far longer words than radar digitizers, and there isn't so much data that one cannot do the FFTs using 64-bit floats, so these may be the key. I'll have to look more deeply into what is causing the limit in radars, to see what does and does not carry over. Handling large out-of-band interference signals may also be involved, which would be the 60 Hz interference case as well.

As for the window functions, this is done simply to control the sidelobes in time and space, so the radar can see small thing near to large things without being blinded by the reflection from the large thing.

The advantage of lock-in amps is that they follow the test frequency, and they are simple. While the original models were all analog inside, current models are digital inside.

Nor am I, but what I am doing is far easier than what Bateman did.

True enough, but it's apples versus oranges. Anyway, for those wondering what this is about, here is a link to Cryil Bateman's 4-part article: Capacitor Sound.

[Mike Sulzer]

Based solely on the performance on axis, I agree that the H. coil pair is better. I have not found any evaluations of the performances off axis. Have you? I would like to understand that before proceeding, but I am reluctant to start evaluating elliptical integrals and summing up the responses of many current loops.

In spectral analysis, both prefilters (for example, the polyphase filter) and windowing can be used to reduce spectral leakage of strong lines with different costs and benefits.

Yes, FFTs using integer arithmetic and short words are a problem. But we should not blame the problem on the algorithm, but on the implementation. This is not a problem with pc based FFT machines using floating point, even if only 32 bit.

I am aware of windowing as applied in radar pulse compression. For example, when using a linear chirp as a waveform, it can be applied to the de-chirped signal to reduce the side lobes, which are large close to the main lobe. This is not an optimum method. A non-linear chirp can be used to reduce this problem instead. Good binary phase codes (Barker) also do not have this problem since all the side lobes are small or zero, but they are less convenient to use in some applications.

[Joe Gwinn]

Based solely on the performance on axis, I agree that the H. coil pair is better. I have not found any evaluations of the performances off axis. Have you? I would like to understand that before proceeding, but I am reluctant to start evaluating elliptical integrals and summing up the responses of many current loops.

I would explore this numerically. Actually, FEMM will solve this problem directly. Unlike a pickup coil, a Helmholtz coil is rotationally symmetric, a case the FEMM does well.

In spectral analysis, both prefilters (for example, the polyphase filter) and windowing can be used to reduce spectral leakage of strong lines with different costs and benefits.

Yes, FFTs using integer arithmetic and short words are a problem. But we should not blame the problem on the algorithm, but on the implementation. This is not a problem with pc based FFT machines using floating point, even if only 32 bit.

If and only if that's the whole problem. I'll have to ask the old-timers, the ones with all the scars.

I am aware of windowing as applied in radar pulse compression. For example, when using a linear chirp as a waveform, it can be applied to the de-chirped signal to reduce the side lobes, which are large close to the main lobe. This is not an optimum method. A non-linear chirp can be used to reduce this problem instead. Good binary phase codes (Barker) also do not have this problem since all the side lobes are small or zero, but they are less convenient to use in some applications.

Use of non-linear chirps is in all the radar textbooks, but very few radars do this, because nonlinear chirps very much complicate things, and one can get more radar for the money in other ways. What is also not often done is amplitude shaping the transmit pulse (except at the start and stop edges, to keep the splatter within regulatory limits.

[Mike Sulzer]

I would explore this numerically. Actually, FEMM will solve this problem directly. Unlike a pickup coil, a Helmholtz coil is rotationally symmetric, a case the FEMM does well.

If and only if that's the whole problem. I'll have to ask the old-timers, the ones with all the scars.

Use of non-linear chirps is in all the radar textbooks, but very few radars do this, because nonlinear chirps very much complicate things, and one can get more radar for the money in other ways. What is also not often done is amplitude shaping the transmit pulse (except at the start and stop edges, to keep the splatter within regulatory limits.

I am going to work with the equation for the field of a loop using elliptic integrals in this case. You tend to learn more by building things up out of the pieces. There is a loop calculator here: Field Calculator for Off-Axis Fields Due to a Current Loop, and I have spent some time copy/pasting values from it into another program to make a primitive look at the Helmholtz coil pair. But you really need too many values. C routines for computing elliptic integrals are available here, for example: Elliptic Integrals. I will write a small program to put a table of the necessary values in a file that I can read into another program for computing Helmholtz, solenoid, and maybe Maxwell.

I believe that there is a Raytheon product using a non-linear chirp. It is not that hard to do these days. Twenty years ago I had the capability built into our radar controller in a very general form: any waveform can be constructed with digital samples fed to two DACs to make an I/Q base band pair of signals which are then mixed to the radar IF frequency. I have only used this for chirp once; we usually use binary phase codes. Mostly this capability is used for digitally controlled frequency shifts for a topside ionosphere program.

[Joe Gwinn]

I am going to work with the equation for the field of a loop using elliptic integrals in this case. You tend to learn more by building things up out of the pieces. There is a loop calculator here: Field Calculator for Off-Axis Fields Due to a Current Loop, and I have spent some time copy/pasting values from it into another program to make a primitive look at the Helmholtz coil pair. But you really need too many values. C routines for computing elliptic integrals are available here, for example: Elliptic Integrals. I will write a small program to put a table of the necessary values in a file that I can read into another program for computing Helmholtz, solenoid, and maybe Maxwell.

It might be simpler to use the vector Biot-Savart law directly, integrating around the loop numerically by approximating the loop with ~100 little straight-line segments, applying the BS law segment by segment, and then summing the resulting ~100 vectors.

Biot-Savart law

I believe that there is a Raytheon product using a non-linear chirp. It is not that hard to do these days. Twenty years ago I had the capability built into our radar controller in a very general form: any waveform can be constructed with digital samples fed to two DACs to make an I/Q base band pair of signals which are then mixed to the radar IF frequency. I have only used this for chirp once; we usually use binary phase codes. Mostly this capability is used for digitally controlled frequency shifts for a topside ionosphere program.

I'm sure there are such radars; it's a very big place. However, for the large radars I work on, nonlinear chirps are always considered but rarely used. The problem is not that it's hard to do this in the digital domain. The problem is that better than half the cost of a radar is in the high-power but wideband analog components of the transmitter, and the tradeoff almost always favors simplicity.

Another issue is that the digital waveform generators of nonlinear chirps are more complicated than those for linear chirps, which can be a big issue if one is generating chirps a very high frequencies, as one can outrun the then semiconductor technology. Usually the approach with the lowest phase noise wins.

[Mike Sulzer]

http://www.naic.edu/~sulzer/HCsol.png
(Helmholtz coil versus solenoid with length equal to diameter)
The Helmholtz coil is somewhat better, except near the outside where the fluctuations get pretty dramatic. I think that which one you build depends on practical considerations. For a bigger one, space matters, and the HC takes up less.

This was done by making the loop field using elliptical integrals. The solenoid consists of 99 loops spaced by .01 r. (r = radius)

[Joe Gwinn]

http://www.naic.edu/~sulzer/HCsol.png
(Helmholtz coil versus solenoid with length equal to diameter)
The Helmholtz coil is somewhat better, except near the outside where the fluctuations get pretty dramatic. I think that which one you build depends on practical considerations. For a bigger one, space matters, and the HC takes up less.

This was done by making the loop field using elliptical integrals. The solenoid consists of 99 loops spaced by .01 r. (r = radius)

I wasn't quite sure what I was looking at. For one thing, what is the color code of traces?

Would it be difficult to do a contour or color plot of a longitudinal cross-section (the centerline is embedded in the cut plane)? This would be easier for all to grasp.

I would be tempted us use FEMM as a cross-check.

[Mike Sulzer]

I wasn't quite sure what I was looking at. For one thing, what is the color code of traces?

Would it be difficult to do a contour or color plot of a longitudinal cross-section (the centerline is embedded in the cut plane)? This would be easier for all to grasp.

I would be tempted us use FEMM as a cross-check.

The color just makes it easier to see which lines are which. The results along the axis pretty much agree with results presented earlier from the Jackson problem, etc. These results have been checked against less complete ones derived from loop fields computed with the web calculator referred to above above. (Some differ in the third decimal place, which surprises me.) I have spot checked the elliptical integrals against results from a web calculator and they are good to at least eight decimal places.

The top plots are the axial component of the field. The bottom line is this component along the central axis. The next line follows the same direction; it is field values .1r from the center axis. Each line is .1r farther from the center. If the axial field were perfectly constant (as we want as the ideal), then all the lines would be straight and lie on top of each other. Since the first few lines nearly do this, we know that the field is close to constant near the axis near the center..

The bottom two plots show the radial component in an analogous way. Ideally all values of the radial component would be zero as they are along the axis.

I do not know if I can make a contour or color plot that shows this nearly as accurately, but I will try.

[Joe Gwinn]

The color just makes it easier to see which lines are which. The results along the axis pretty much agree with results presented earlier from the Jackson problem, etc. These results have been checked against less complete ones derived from loop fields computed with the web calculator referred to above above. (Some differ in the third decimal place, which surprises me.) I have spot checked the elliptical integrals against results from a web calculator and they are good to at least eight decimal places.

So it does seem that the calculation is correct; always a worry.

The top plots are the axial component of the field. The bottom line is this component along the central axis. The next line follows the same direction; it is field values 0.1r from the center axis. Each line is 0.1r farther from the center. If the axial field were perfectly constant (as we want as the ideal), then all the lines would be straight and lie on top of each other. Since the first few lines nearly do this, we know that the field is close to constant near the axis near the center.

The bottom two plots show the radial component in an analogous way. Ideally all values of the radial component would be zero as they are along the axis.

This would be a good explanation to include with the plots.

I do not know if I can make a contour or color plot that shows this nearly as accurately, but I will try.

The classic approach is to subtract the ideal constant field and plot the difference as colors, this being the deviation.

A pickup-specific approach would be to plot 20*Log10(deviation from constant) in colors, as this will be the hum cancellation floor for measurements made with such a coil.

[fieldwrangler]

Fellas -

Just got back from a week or so away from most things; this X2N thing sure has taken an interesting turn or two.

Must admit, this radar stuff is pretty fascinating, although there are at least a half-dozen concepts here that are quite new to me. Last year my wife & I went to Panama to chase some birds and stayed in an old radar tower; I just had to shoot a couple of the antennae (late 50's-early 60's arrays I would guess) with a digicam while we were there.

'Meantime, back in the trenches, I found a box that's about 11" x 11" x 6" around which I intend to wind a coupla coils. By the way, Mike, you were right that I quickly tired of wasting a bunch of my nice 40 gauge wire on this; I'm gonna track down a few hundred feet or so of something more manageable within a week.

Thanks again for the education.

[Mike Sulzer]

So it does seem that the calculation is correct; always a worry.




This would be a good explanation to include with the plots.


The classic approach is to subtract the ideal constant field and plot the difference as colors, this being the deviation.

A pickup-specific approach would be to plot 20*Log10(deviation from constant) in colors, as this will be the hum cancellation floor for measurements made with such a coil.

This is about the best I can do with a linear scale. I think the lines (previous plot) are more sensitive to differences, but this gives a better picture.

http://www.naic.edu/~sulzer/HCSolImage.png

[Mike Sulzer]

Fellas -

Just got back from a week or so away from most things; this X2N thing sure has taken an interesting turn or two.

Must admit, this radar stuff is pretty fascinating, although there are at least a half-dozen concepts here that are quite new to me. Last year my wife & I went to Panama to chase some birds and stayed in an old radar tower; I just had to shoot a couple of the antennae (late 50's-early 60's arrays I would guess) with a digicam while we were there.

'Meantime, back in the trenches, I found a box that's about 11" x 11" x 6" around which I intend to wind a coupla coils. By the way, Mike, you were right that I quickly tired of wasting a bunch of my nice 40 gauge wire on this; I'm gonna track down a few hundred feet or so of something more manageable within a week.

Thanks again for the education.

Bob,

I am glad you find this useful. I think that 6" is a bit small and plan on making a bigger one.

[fieldwrangler]

Bob,

I am glad you find this useful. I think that 6" is a bit small and plan on making a bigger one.

I was thinking about winding 2 coils about a foot in circumference about 6" apart onto this box.

Does this seem like a viable test chamber? How big should I get with the wire gauge? I was thinking 20-something and 50 turns per coil.

[RedHouse]

...Here's the Greatful Dead's rig in 1974:

Wow what a memory, I was at the Seattle concert (a week before or after) the Vancouver one in the picture, I soooo remember the wall of sound.