# One coil twisted in a figure 8 vs. two coils side-by-side

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1. Jun 5, 2017

### Thelonious Monk

The side by side coils are round or oval, and wired together in series. Let's say the side by side coils are wound opposite (one clockwise and one counterclockwise) to match the direction of travel of the twisted coil's loops. Each of the side by side coils has the same number of turns as the twisted coil. All other parameters (wire gauge, etc.) are the same. Are these functionally identical in every way, or would there be a difference? If there is a difference, what would it be? Would there be mutual inductance between the loops of the fig 8 even though they are not separate coils?

2. Jun 5, 2017

### marcusl

I don't understand your first two questions. For #3, if you were to calculate the inductance of the figure 8 you would sum the inductances of each loop plus the mutual inductance between them. Just like doing any inductance calculation.

3. Jun 5, 2017

### Thelonious Monk

How would you measure the inductance of one loop of a twisted coil? With two coils in series, it's easy enough to separate them into two circuits and test each one; with one coil in a figure 8, each loop can not be separated into its own circuit.

4. Jun 5, 2017

### marcusl

Read my post, I said calculate.
EDIT: On second thought, maybe you are asking how you would measure one coil to compare to a calculation. You would have to wind a coil that had the closest geometry possible to one half of the 8, and account for any errors or differences.

5. Jun 5, 2017

### Thelonious Monk

I read what you wrote... what I was asking was how I would get those figures to begin with (inductance of each loop and the mutual inductance) to be able to make the calculation. You didn't say to calculate those.

What I'm after, mainly, though is to find if the fig 8 would behave any differently than two opposite-direction coils side by side, in any way at all (capacitance, reactance, etc.). I expect they're nearly identical, but I imagine there would have to be some difference. The path of the electrons will be completely different-- in the 8, they go around one loop, then the other, back and forth, while in the coil pair, they go round and round one completely then round and round the other. In an AC signal, they'll go both directions, but it's still along a different path. I just wonder if that has any consequences, even subtle ones, that would be measurable. I'm sorry this is so vague.

6. Jun 5, 2017

### marcusl

The inductance of a circular loop is available in closed form (the formula includes elliptic integrals), which you can find through Google search. The mutual inductance of co-planar coils, on the other hand, is probably not available in closed form. Your best bet is to use a numerical simulation package, which has the benefit of including the effects of parasitic capacitance. HFSS and COMSOL are names of popular codes. How close you get to a figure 8 depends on details of the geometry (for example, exactly what the crossover region looks like) and, especially, what the frequency is. At high frequencies, small differences between model and actual become important. If you are doing numerical simulation, then your can input the exact geometry of the 8.