X2Ns

[Mike Sulzer]

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.

Yes, that sounds like a good size. I am planning on making one using an empty (and cleaned) bucket of the kind that many liquids come in (paint, etc. like you get from Home depot, I think they are 5 gallons). I will cut it off to give the right aspect ratio for an HC. I plan to use between 50 and 100 turns of #30 magnet wire wound compactly so it acts almost like a single turn.

[Joe Gwinn]

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

I certainly find the colors easier to grasp, albeit less precise. Plotting deviation from constant in decibels with a heatmap colorscale would also be quite illuminating, I suspect.

[Mike Sulzer]

I made my "field bucket" pretty much as described above. The coils are 11 inches in diameter. I sawed the bucket off to a convenient height and then sawed off a ring from the left over piece at the cut and slipped that over the bucket at the bottom so that the two coils would have almost the same diameter.

It is not wound with compact coils as described above. It is not necessary, and I found it more convenient to wind single layer coils right on the bucket.

Why is is not necessary?

Consider the solenoid with its length equal to its diameter. You can think of this as composed of many Helmholtz coils. Start with a Helmholtz pair, axis vertical; put a coil just above the lower one, and another one just above the upper coil. If you continue doing this until you fill the gap you have the solenoid, and we know it has essentially the same field as the HC except near the coils, where it is more constant.

Does this work if you only partly fill the gap? Yes, it is easy to show this with a calculation.

Repeating the same measurements as before made with the smaller coil gave nearly the same answers. The two coils are driven in parallel to keep the electric field across the coils down. (Actually, I drive each with one channel from the headphone output.) A measurement on my twelve coil pickup which fits into a strat cover (six series pairs, one for each string) gave good results. The measurement compared two coils in series with the voltage across one since it is not convenient to rewire the pair in phase in series. The ratio is 27 db. This is equivalent to 33 db if the two coils were put in phase in series.

With reference to our discussion on the quality of pc (or mac) FFT processors, I made a measurement of a humbucker coil with a very long FFT and a Hanning window. The measurement was at 100 Hz; the coil voltage is more than one volt at the fundamental. The lines (fundamental, harmonics and hum) hit the noise 100 db down with negligible width. Note that the harmonics do not decrease with frequency because the sensitivity of the pickup coil increases with frquency. (The law of magnetic induction depends on the change in time of the magnetic field.)
Plot: http://www.naic.edu/~sulzer/HCwithHBcoil.png.

[Steve Conner]

When was the last time you guys came across a uniform hum field at a gig?

One of my first jobs in DSP was to make a lock-in amp. The results are really not that different to a really long FFT, or better still, a bunch of FFTs with averaging. (The lock-in amp algorithm is nothing more than a FFT that calculates just one bin and throws the others away.)

[Mike Sulzer]

When was the last time you guys came across a uniform hum field at a gig?

One of my first jobs in DSP was to make a lock-in amp. The results are really not that different to a really long FFT, or better still, a bunch of FFTs with averaging. (The lock-in amp algorithm is nothing more than a FFT that calculates just one bin and throws the others away.)

We discussed that above. The field of the hum source is nearly uniform because you are not that close to it. The idea is to make a test device that is not too big, but similarly constant in space.

The FFT is better than a lock-in because it is so easy to optimize windowing, etc. One long FFT is always better, but not always practical. If you have to average to pull a stochastic signal out of the noise, you can do it across frequency if you have a single long FFT. If you take multiple short FFTs and average across time, the narrowness of the line is limited by their length. If you have a narrow deterministic signal, then you get the best SNR by making the coherent measurement over as long a time as possible, or as long as you need.

This is a trivial application here. I just took the long FFT to show what can be done.