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Is there any formula to calculate number of windings to get a 50 Watts voice coil of a speaker?

let's say, I want to wind a 20mm diameter voice coil for a speaker. And my coil is made out of copper wire which is 1 mm thick (diameter) and has a resistance of 13 ohms per 1000 meters. And I want the voice coil to use 50 Watts. How do I calculate the number of windings required?

P.S: I'm developing a new speaker design, so, I'll experiment with overheating issues. Just ignore all other parameters and let me understand the relationships between given parameters to initially wind the voice coil. I'm stuck in finding out the number of windings to experiment with, so if some formula gives 50 turns, I'll initially wind it and experiment with all other parameters one by one (eg: overheating).

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  • \$\begingroup\$ Problem with that is 13 Ohms/km = resistivity of 1.02x10^-8, but the actual resistivity of copper is 1.68x10^-8. Perhaps if your wire had a square section? \$\endgroup\$ – Bruce Abbott Jan 19 '18 at 9:23
  • \$\begingroup\$ Square or hexagonal wire is not unknown in speaker design, for exactly this reason. I have no idea if that's what the questioner is using though. \$\endgroup\$ – Brian Drummond Jan 19 '18 at 11:42
  • \$\begingroup\$ just take it as an example :) I need to know the relationships between parameters to calculate how much turns does it require to withstand 50 Watts from the power amp. \$\endgroup\$ – Pretty_Girl100 Jan 19 '18 at 13:17
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No, you cannot calculate that with only these parameters.

Think about the relations between the parameters of the voice coil you list:

  • coil diameter
  • wire diameter
  • wire resistance
  • number of turns

And how that relates to the maximum power handling capability.

Suppose a certain voice coil can handle 50 W, what happens when I put 100 W into it? I think it will get hotter compared to the 50 W situation.

But how hot is OK? That isn't listed anywhere in the parameters for the voice coil. The coil itself is OK until the copper starts to melt. But I'm sure that at much lower temperatures other things had heat issues already like the material we're winding the coil onto. Some voice coils are wound on an aluminium tube which will help in dissipating the heat. That would increase the power handling capability of voice coil. But hey, you didn't list which material is used for winding the voice coil onto.

Also, if the voice coil is allowed some movement (like in long-throw speakers) that moves the air around the speaker which also helps in cooling.

If you're using the speaker in a free air, a closed enclosure or a bass reflex enclosure that will also have a significant impact on voice coil movement and therefore cooling and therefore power handling.

See how I got from just the voice coil to the complete design of a speaker?

That is because it is not only the voice coil which determines the maximum power handling capability, it is the complete design.

If you look up datasheets of loudspeaker drivers (so the speaker themselves, not a finished box with a speaker in it) then in a proper datasheet you should find the maximum power handling capability listed with a note saying how that's measured like what volume of enclosed box the driver was mounted in.

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  • \$\begingroup\$ At high temperatures you'd likely also damage the insulation on the coil, causing adjacent turns to short together. \$\endgroup\$ – immibis Jan 19 '18 at 9:37
  • \$\begingroup\$ Speaker assembly can use insulation and adhesive selected to survive 240C - (in the 1980s, maybe higher today). \$\endgroup\$ – Brian Drummond Jan 19 '18 at 11:46
  • \$\begingroup\$ Thank you for the answer. just forget all the other parameters of coil burning because of heat etc :) I just want to make the coil use the 50W power, so how many turns does it requires to use all 50W power? \$\endgroup\$ – Pretty_Girl100 Jan 19 '18 at 13:21
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    \$\begingroup\$ If you put 50W into a speaker it'll use 50W regardless of the number of turns. \$\endgroup\$ – Finbarr Jan 19 '18 at 14:18
  • \$\begingroup\$ I just want to make the coil use the 50W power, so how many turns does it requires to use all 50W power? Hmm, so please explain to me, after reading my answer, how you can still think that anyone can tell you how many turns you need for that 50W. \$\endgroup\$ – Bimpelrekkie Jan 19 '18 at 14:46
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interesting question... first you need to decide what tupe of amp you will use. then you will know 4 or 8 ohm speaker it will be. normal 100 watt amp will give you 20 volts into 4 ohms. to do that you firstly need to make coil that can withstand that conditions. mainly it will be coil the same 4 ohms in free air (in speaker it will change depending on magnetic system parameters). to make it just search for inductance coil calculating program. remember P=IU so as example for 4 ohm speaker ordinary will be used low woltage (+/-24V power supply) amp that can give about 30V max with no load. you need about 15V. to get 50W now you know that you need wire that can handle ~3.33Amps. wire for transformer windings has secure working point about 2.5 A per aquare millimeter. during fact that speaker has poor but better cooling than transformer 1 mm2 will be okay. remember 8 ohm version will requre 2 times smaller wire. now you can calculate the first coil with software and start experiments.

next one 4 OHM will be the lowest point of impedance of speaker. read about Thiele and Small parameters and you will understand difference between DC resistance and impedance - its not the same thing. so in resonance point impedance will rise up to several dozens ohm. of course in resonanse point speaker will give maximum output at the same conditions. But if you in surprising manner (industrial amp in supermarkets or similar) will feed real 50W at resonance poin (that can be 100 V or more) you will blow up the speaker :) to try out physics of T-S parameters just grab some speaker and amp give a sweep signal from 20Hz to 20 KHz (frequency generator software) and see how changes voltage in multimeter or what you have from measuring devices

P.S. remember this is calculation for sine wave signal. audio signal is mixed type signal and 50W RMS are huge power for audio system. as example many of high grade home stereo systems have just 10-20W RMS and sounds enough for large room.

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    \$\begingroup\$ Welcome to EE.SE. I tried to read your answer but gave up due to lack of capitalisation and punctuation. Please see Write to the best of your ability. \$\endgroup\$ – Transistor Dec 5 '18 at 21:49

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