electromagnetic transducer: twisted (fig.8) single coil vs. two series coils

[Paul R]

Hi, I make guitar pickups. I'm not an EE. I've applied for a patent, and the patent examiner is having a hard time distinguishing the difference between a single coil twisted into a figure 8 shape and a pair of coils connected in series. I need some help making the case that these are significantly different things.

The figure 8 coil shares some properties with a pair of coils in series, the most important one being hum cancellation when each loop of the figure 8 (or each coil in the series pair) goes around a magnet of opposing polarity to the other. But it does not share other properties: mutual inductance and mutual capacitance, for example, are undefined... they have no meaning in a single coil. In a coil twisted into a figure 8 shape, each turn of the coil goes clockwise, then counter-clockwise. In a pair of coils in series, the turns go around one way thousands of times, then the other way thousands of times.

The figure 8 coil has a tone (when used as a guitar pickup) that sounds like a single coil. Two coils in series give a different sound, even when side by side so that each coil "picks up" different strings. That's not something I know how to quantify, and will vary depending on any number of factors, so it's not a particularly useful argument.

Is there anything else you can think of that would help make the case that one coil twisted into a figure 8 shape is not the same as two coils in series? I'd love to have a simple, unrefutable scientific argument in clear electronic terms. I'd like something more "solid" than just that certain qualities are undefined.

Can you help? Thank you.

 

[MacGyverS2000]

Depends upon how you wrapped the figure-8... mutual inductance between the two coils can range from (nearly) zero (when the common sides are at 90 degrees to each other) to the (nearly) maximum calculable for two inductors. Two inductors in series (assuming no common core) would simply add their individual inductances. That's the math of it.

From a "sound" standpoint, you'll need to quantify what changes happen to audio frequencies (and possibly beyond if those higher frequencies have an affect on a typical amplifier, such as harmonic feedback/resonance that affects the audio frequencies... but I'm going to guess that is way beyond your current capabilities). This part is highly variable (based upon driven equipment) and likely has no place in your patent.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[Paul R]

Thanks... but in this case there is only one coil, so mutual inductance is undefined (in other words, it makes no sense). Twisting one coil into a fig 8 shape gives it some properties of two coils in series (e.g. hum cancellation) but that doesn't make it two coils. What I'm looking for is a clear technical explanation for why one coil in fig 8 is not the same thing as two coils in series. Geometrically they're fundamentally different (though in a two-dimensional representation they appear similar), but I need an electronics accounting of the difference.

I could do FFT analysis of the resulting sound, but there's so much variation between pickups of the same type (i.e. from single coil to single coil, humbucker to humbucker) due to variations in their design that this would not likely be convincing.

What properties does one coil have that a pair of coils in series does not have? If I could nail that down I think I'd be set. A pair of coils has properties a single coil does not, regardless of its shape: mutual inductance, mutual capacitance, mutual anything. But what about the other way around? What are some unique properties of a single coil? Are there any?

 

[waross]

Are these air cores? If a magnetic core, how is it configured?
If the figure 8 is placed on two arms of a "U" shaped core, there may be little difference compared to two coils except for more difficulty in winding the coils.
Can you post a sketch?
Some possible constructions may result in a non-inductive, wire wound resistor.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Paul R]

Thanks for your response. Each loop of the 8 is in proximity to a magnet; these magnets are arranged in opposite polarity to each other. There are other (proprietary) adjustments to account for the "dead spot" between the two magnetic fields. The arrangement is to cancel hum, the same way that occurs with two reverse-wound coils in series. The coils are easy to wind... they're wound as normal ovals, then twisted by hand to create the 8 shape. A loop of an 8 functions similar to a separate coil in some ways (hum cancellation) but is not itself a coil. Each turn of the coil contains a section from each loop; in contrast, in a pair of coils side-by-side, each turn is confined to the side containing the coil its a member of, and goes for thousands of turns before connecting to the other coil, where it goes for thousands of turns in the opposite direction. In the twisted coil, each turn reverses direction half-way through. A pair of coils in series can be "tapped" to function as two separate coils side-by-side, singly or in parallel. This can not be done with the figure 8 single coil... if you were to tap it somewhere in the middle, it would become two figure 8s, stacked on top of each other, not two coils side-by-side.
This is not theoretical... I've made many prototypes, which function as intended (cancel hum like a humbucker, sound like a single coil). I'm just searching for a statement I can make along the lines of "a single coil has X property that a pair of coils in series does not have. A single coil twisted into a fig. 8 shares this property". Or any other kind of definitional statement that clearly marks the difference. I can do this in the language of geometry, but I'd like to be able to do it in the language of electronics.

 

[MacGyverS2000]

Thanks... but in this case there is only one coil, so mutual inductance is undefined (in other words, it makes no sense).

It may be a single piece of wire, but a figure-8, by definition, splits it into two coils. How those two coils are intertwined/oriented will have a huge effect on their mutual inductance. Coils do not need a common core (e.g., transformer) for mutual inductance, a common core just increases existing mutuality. If you still believe it's a single coil, you're not looking at it from a proper perspective.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[Paul R]

What is your definition of a coil? I'm not arguing that a single piece of wire equals a coil... if you wind one coil and then wind another continuously with one wire, that's two coils. That's not what I'm describing. If you take an oval coil and twist it into a figure 8 shape, it does not magically make it into two coils. There is no way to take separate inductance measurements for each "lobe" of the coil. They have no independent current, voltage, resistance or capacitance. They are part of the same coil and cannot be separated. Two continuously wound coils can be separated down the middle to make two separate coils. A single coil twisted into fig. 8 cut down the middle will make thousands of C-shaped segments. They are not the same thing.

The direction of current flow will be entirely different... in two adjacent coils, left and right, the current flows in a circle through the left coil thousands of times, once for each turn, then into the second (right) coil, where it flows thousands of times in a circle the other way. In the fig. 8, it flows left, then right, then left, then right, and so on. There is no direct connection between each left-turning section and each other left-turning section. If reversing direction makes a new coil by definition, then we don't have two coils, we have 8000 (or so) one-turn coils per lobe.

 

[Paul R]

I've been looking up various definitions of "coil" in every dictionary I can find, and not one of them fits when applied to one lobe of the twisted coil. The only one that sort of fits, but only if you interpret it disingenuously, is "a series of loops". I think what is meant here is "a continuous series of loops", otherwise a pile of circles on a ring-toss game would constitute a coil, and I think no one would agree that it does. The "circles" of one lobe are not continuous with each other and do not create a spiral. Only taken as a whole does the fig. 8 constitute a coil. But this is geometry, and I'm looking for an argument from an electronics standpoint. What are the unique consequences of this geometry? If you want to argue that it functions the same as a pair of coils in series in every way, go ahead (it does me no good) but don't tell me they are the same thing, because by any definition, they're not. One lobe of the figure 8 may visually resemble a coil, it may function in some ways like a coil, but by no definition does it constitute a coil.

 

[waross]

You have hundreds of single turn coils connected in series with short jumpers.
If you designate the openings in the figure 8 as Left and Right,
Starting with one turn:
You can have 1 L in series with 1 R
Progressing
You can have 2 L in series with 2 R
You can have 3 L in series with 3 R
You can have 4 L in series with 4 R
You can have 5 L in series with 5 R
You can have 6 L in series with 6 R
You can have n L in series with n R
Because of the proximity of the turns on each side of the figure 8, each side will exhibit self induction, equal to the square of the number of paths or turns for relatively small spacings.
Taking it the other way, you may take two coils, an L and a R and cut both in half so as to make 4 coils in series.
You can continue cutting the coils in half for 8 coils, 16 coils, 32 coils, or n coils all in series.
I don't think that the electrons care nearly as much as you do.


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Paul R]

Thanks Bill,

That makes sense, though to me it's much simpler (and no less accurate) to think of it as a single coil twisted 180 degrees in the middle than as thousands of single turn coils in series. As you said, the electrons don't care. In terms of inductance, yes, that's how I expect (and observe) it to behave. What I'm after is concrete differences between this (whether you call it a twisted single coil or thousands of coils in series) and a pair of side-by-side coils in series. Any difference. The observed sound is like a single coil in tone. This is somewhat true of a pair of side-by-side coils in series, as each coil picks up different strings, so there's not the additive effect you'd get in a normal humbucker, in which the two coils are both under all the strings. But any two coil arrangement has an effect on the sound, whether it's side-by-side, stacked, a dummy coil located away from the strings, and so on. I'm looking for a technical reason to cite that causes the observed difference in sound. The current flows along a different path... could this cause some difference in behavior, in terms of capacitance, or resistance, or something else? While most behavior of electrons is well documented and predictable, they do exist in the realm of quantum mechanics and not classical physics, and have properties like "spin" that don't come into play in everyday electronics, but may have some audible effect on the signal and might possibly be affected by a different current path. Maybe I'm getting too esoteric here, but in my experience, electronics are never as cut and dried as most people think.