# Number of turns vs. wire length affecting voltage in coil

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1. Mar 21, 2017

### Thelonious Monk

When winding a coil around a magnetic core, if you wanted to tap the coil such that each half has the same AC voltage output, would you:

A) wind each part at the same RPM for the same amount of time, to get the same number of turns for each, or
B) wind the second part proportionally less, to compensate for the wider diameter of the coil as it grows

In A the DCR is greater in the second part, due to the longer length of wire needed to complete the wider turns.
In B DCR (and wire length) will be equal in both parts, but the second part will have fewer turns.

2. Mar 21, 2017

### BvU

Hello TM,

So the core question here is what determines the AC voltage output of one turn. Is it the area or is it mainly something else ?

Oh, and for homework, PF has a very useful template !

3. Mar 21, 2017

### Thelonious Monk

Thanks BvU.
My background is in music, and my electronics experience is more practical than theoretical. Unfortunately I have no idea what to plug into that template.
I make electromagnetic sensors. I have a line of products I make that people can order, but sometimes I get special requests. This question relates to one of those. The customer wants the coil tapped in the electrical center so that AC output is the same for both the inner and outer coil. All the formulas I've seen, and what my experience leads me to, is that A above is correct (same RPM, same time, for the same number of turns). This leads to larger DCR on the outer coil. The customer doesn't like that and wants the same DCR on each, thinking it will give the same voltage. I don't have a reliable way to measure AC millivolts, so I can't just test it empirically. To do it his way will take a lot more time and work, and if A is correct, will be a waste of time.

4. Mar 21, 2017

### Thelonious Monk

Another factor to consider is that the outer coil, while having greater length, is also a greater distance from the magnetic core in the center.

5. Mar 21, 2017

### BvU

Voltage induced is proportional to number of turns and also to change in flux and that's (almost completely) concentrated in the core. So area is less important. But you want to be careful: customer might not only want same voltage from the two halves but also the same impedance (depending on the application). If that is so, it would be much better to have two coils on the same core.

6. Mar 21, 2017

### Thelonious Monk

Thanks.
The two coils are on the same core; one is inner, the other is outer. They're two halves (more or less) of the same coil. Theoretically it would be possible to coil around one section (half the length) of the core at a time, so both parts would be "inner", but this a) is not practical in this case, and b) would put one coil farther from the vibrating steel that's inducing a current.
The customer has been very clear that what he wants is equal voltage. What his application is, who knows? Even with a non-disclosure agreement, he won't tell me a thing. It really inhibits my ability to help him.

7. Mar 21, 2017

### jim hardy

How much voltage ? If not very much, Why not wind two wires at same time instead of one at a time ? That way they lie adjacent and enclose the same area. It's called "Bifilar winding" . In our control rod drive system for the nuke plant, the precision voltage sensing transformers were wound so.
If the voltage is modest enough to not stress the insulating varnish between the windings that should give them a good match.

old jim

8. Mar 21, 2017

### Thelonious Monk

Thanks Jim. I've been considering that, and it should work. We're talking millivolts, so there's no danger of stressing the coating. It would mean reconfiguring my equipment, which will interfere with making my standard products. The wire is extremely thin (like spider webs) and passes through about 8 inches of 1mm diameter tube on the way to the core. The possibility of tangling the wires is just one of many possible problems. I'm going to have to think about this...

9. Mar 21, 2017

### Thelonious Monk

So is it safe to say that A in the original post is true? I made a set of three for this guy, and shipped them. I told him ahead of time how I was making them (same time, same RPM, two halves of one coil) and he had no objections. When I told him they had shipped, I told him about the resistance measurements, and the difference from one side to the other. That's when he said he wanted them compensated to be the same length, which he believes will give the same voltage. If A is true, I've fulfilled my obligation.
Even if the voltage is the same, it's no guarantee that his invention will work... that's not my responsibility. Of course if he would tell me what he was trying to achieve, I could offer my insight and experience. But now I feel like this guy is trying to take advantage by raising the bar after the fact, and that there's no end in sight. If B is true, I'm happy to give him a refund and be done with it.

10. Mar 21, 2017

### jim hardy

leakage flux would be your worry, ie flux that doesn't stay in the core.

You say millivolts which infers low flux which at first glance infers very little leakage, so the difference in area shouldn't matter . Virtually all the flux stays in the core of a well behaved machine.
You did not say how much current flows in these windings.
If they drive perhaps an amplifier with high input impedance then there's virtually no voltage drop along the resistance of your wires so some Δresistance is of no consequence.
If they drive something that draws current then ΔR will affect customer's balance. And that current will affect, however slightly, the leakage flux in region of each coil ..
Since you say it's such fine wire i can't imagine there's much current. Without appreciable current there's just not enough mmf to squeeze flux out into the leakage path, i'd say, unless this is some specialty core with an air gap..

I'd ask him to test your transformer for imbalance in his actual application.

Hmmmm, how much Δlength do you have? Moving by one wire gage changes resistance close to 26% . Might you wind the longer winding with one gage bigger wire?

old jim

11. Mar 21, 2017

### Thelonious Monk

I asked him to test the output voltage, but all he'll say is, "what you have supplied will not work properly". Since I don't know what work he wants it to do there's nothing I can do about that. He asked for equal voltage for each part, and from what people are saying that's what I gave him. It sounds like bifilar winding is the best solution.
Small size is important with these. Also 26% is too much of a difference. The difference in DCR of these is just under 18% if I'm calculating correctly.
Now he wants his money back without returning the original coils...