Torodial transformer winding calculator

[theoldwizard1]

Maybe I am too old for DIY electronics experimenting, or at least too many years away from doing any of it, but I need help.

In an earlier post I said I wanted to experiment with DIY inverters using some of the very inexpensive boards available on eBay.  I understand the basic "theory of operation" of these board enough that I am will to throw down some $$$.  I will likely be building a "low voltage" (i.e. transformer connected to Vbatt) design with a torodial transformer.  But this is where I am stuck.

There is probably more than a dozen YouTube video on calculating the windings, but I get lost.  I know the cross sectional area of the toroid and the turns/volt from the manufacturer.  It is a laminated core, made of grain-aligned magnetic steel.

The online calculators confuse me  .  The core I have chosen is for a 500VA transformer.  The input voltage will be from a 24V battery bank and I want the output to be 220V.  I know the turn ratio is approximately the voltage ratio.  I also know that too many turns of each will saturate the core and reduce efficiency.  My questions are simple.

• What size wire of the primary and secondary ?
• How many turns of each ?

Do I just "wing it" ?  Get some 20-24 AWG enamel magnet wire and throw a bunch of turns on the core for the secondary and then about 1/10th the number of 14-18 AWG windings for the primary and just leave an extra couple of feet and see what kind of numbers I get ?


(Ultimate goal is to run a 208V-240V inverter air conditioner from batteries.  Inverter A/C are "easy" on inverters because they have a built-in "soft starter" (current limit) so the starting current is much lower than a typical motor.)

[bob91343]

Wire size is usually determined by current flow.  Use at least 500 circular mils per Ampere.

More turns means more flux if current is constant.  More turns means less flux if voltage is constant.

Use the classic formula for turns.  It's in every book on transformers.  You put in the desired flux, the frequency, the cross section, etc.

[theoldwizard1]

Wire size is usually determined by current flow.  Use at least 500 circular mils per Ampere.

I am ASSUMING "circular mils" is "... CM is a unit of area used especially to denote cross-sectional size of a wire or cable."

So a 1kVA transformer with a 240V output would be capable of about 4A would use 2,000 CM wire which is about 18 AWG !!  That is for the secondary. 

The primary would have to handle at least 40A, so 20,000 CM or about 8 gauge.    For a 1 kVA transformer !!!

[Siwastaja]

I think this is a good reference:
https://ludens.cl/Electron/Magnet.html

[TimFox]

The "circular mil" is the area of a circle whose diameter is "one mil" = 0.001 inch.  When you get to very large wire sizes, past AWG 0000, the US standard is "MCM" for "thousand circular mils" (M as in Roman numeral), so "500 MCM" has a diameter of about 700 mils = 0.7 inch
I made a mistake once when working in UK when a colleague asked if "four millimeter" wire were large enough and I thought he meant 4 mm diameter, but wire there is sold by "real area", so he meant 4 mm², which is less than one-third the area.
18 AWG for 4 A agrees with the literature on transformer windings, so you do need heavy wire for the higher current primary.  Wire diameter is based on allowable temperature rise of the copper under load.

[Siwastaja]

I made a mistake once when working in UK when a colleague asked if "four millimeter" wire were large enough and I thought he meant 4 mm diameter, but wire there is sold by "real area", so he meant 4 mm²,

No, that colleague made the mistake and you were doing fine.

Because sometimes we deal with diameter, sometimes with area, the only thing you can do is to say what you mean, not something else. This is an easy situation because the unit makes it clear what it's about, the only thing left is to use the correct unit. Shouldn't be that difficult.

But there are, and always will be, "professionals" who talk about "watts" when they mean "watt-hours", or "amps" when they mean "amp-hours". Same thing with wire thickness. Avoid having to do any actual non-trivial work with these types if possible.

[themadhippy]

No, that colleague made the mistake and you were doing fine

nope,here in the uk csa is the normal way of describing  power  cables,so if someone said 4mm to me id assume they meant 4mm²of course we could go back to pre decimal days and start talking in 7/0.36.

[Siwastaja]

No, that colleague made the mistake and you were doing fine

so if someone said 4mm to me id assume they meant 4mm²

You are part of the problem. You are assuming, out of nowhere, that they don't mean what they said, but something else. You are likely right; but what if they really meant what they said? Yes, it happens! For example, enameled wire is referred in diameter normally, while PVC insulated wire is referred in cross-sectional area. So the harsh reality is, wire is sold in at least three different systems, AWG tables, diameter [mm] and cross-sectional area [mm^2]. In Europe, it's just the insulation type which decides what's the most usual unit is. But there is absolutely no problem because the units are clear and easy to understand, especially for professionals. All you need is a little bit of professionalism.

This is the classic type of miscommunication that causes space shuttles to self-destroy then become textbook examples of stupid miscommunication everybody laughs at in the classroom. "How could they do that mistake."

If you think they made a mistake and meant something else than they said, do not assume; ASK for clarification! Engineers need to be careful with numbers and units, it's the same thing that a pharmacist just isn't allowed to mix up micrograms and milligrams!

The added benefit: you asking a clarification and they noticing their mistake may make them think it and start communicating better in the future. Or, if they "don't see the point", you know whom to stay away from. Everybody wins

[TimFox]

My story dates back to maybe 12 years ago,  the first time I was working at a UK site.  Thinking back, he may have said "4 mils" to me, and I knew he didn't mean 38 AWG.  Being used to American AWG dimensions and current ratings, my logic went "4 mils -- he means 4 mm -- that's about 0.16 inch -- that's about 6 AWG -- OK".  6 AWG would have been conservative, and nothing blew up, so nobody complained.  4 mm ² is about 11 AWG.  The handy thing about AWG numbers is that they are decibel-like:  A 3 AWG difference is about twice the area and thereby twice the current capability.  My mnemonic is that 10 AWG is close to 1/10 inch diameter.

[themadhippy]

Being used to American AWG dimensions

And you had to be different when we already had the perfectly good SWG ,same  with  your pints and gallons.

[TimFox]

The difference between AWG and SWG is approximately one or two:  10 AWG is approximately 12 AWG, but 20 AWG is exactly 21 SWG.
The difference between British pints and gallons and American pints and gallons was that the old English gallon depended on what liquid you were measuring.  Thereafter, the Brits chose one standard liquid (ale) and the Americans chose another (wine).  Over the years, the exact definitions of these two gallons were tweaked, but the relationship between them is still approximately the same.

[Brumby]

No, that colleague made the mistake and you were doing fine

nope,here in the uk csa is the normal way of describing  power  cables,so if someone said 4mm to me id assume they meant 4mm²of course we could go back to pre decimal days and start talking in 7/0.36.

My experience in Australia is the same.

I had a conversation with an electrician last week about what cable to run for a circuit I had in mind.  The numbers mentioned were 2.5 and 4 ... and we both knew we were talking about actual conductor cross section area - without spelling that out.

It's also how these cables are sold.

[Jwillis]

The VA of the core is the answer. The current  in amps is equal to the apparent power in volt-amps, divided by the line voltage. So with a 500VA core with 24 volts on the primary is around  20 amps and the 220 on the secondary is around 2 amps  . That gives you your maximum current ratings for secondary and primary on a 500VA core . Current like volts is proportional to the winding ratio. So if your draw on the secondary side is 2 amps at 220V  it would require 20 amps on the primary side at 24V. Which is around a 10:1 ratio.   If you know what you want to draw in current on the secondary side you would use the appropriate wire gauge plus some over head . The number of windings is related to the flux density of your core ,core area and frequency . Fewer windings are required with higher frequency.  Typical steel core are around 1 T to 1.5 T. The core area of a toroidal is the cross section area . So in a lot of ways its much the same as an EI core in calculating the windings . 

[Vovk_Z]

I don't know about all Europe, but here in former-USSR we use cross section (mm²) for wiring, but line dimensions (diameter in mm) for solid winding wire (for motors, transformers ets).

[Siwastaja]

I don't know about all Europe, but here in former-USSR we use cross section (mm²) for wiring, but line dimensions (diameter in mm) for solid winding wire (for motors, transformers ets).

I think it's like this in most of the Europe.

The reason why I "nitpicked" in this thread because this very thread is about transformer winding, where you are very likely to shop using diameter [mm], so the potential for confusion is very real if someone means mm^2 but is saying mm instead.

The reason magnet wire is sold using diameter is because windings are made to tightly fit a certain winding window area available, thus calculations are needed to see how many wires fit in a "layer", and how many layers you can fit without making the winding too thick. Approximate idea about the physical dimensions is not enough.

Thermals are fairly difficult to numerically analyze anyway, so either complex thermal simulation, or just test&measure is needed.

[theoldwizard1]

The VA of the core is the answer. The current  in amps is equal to the apparent power in volt-amps, divided by the line voltage. So with a 500VA core with 24 volts on the primary is around  20 amps and the 220 on the secondary is around 2 amps  . That gives you your maximum current ratings for secondary and primary on a 500VA core . Current like volts is proportional to the winding ratio. So if your draw on the secondary side is 2 amps at 220V  it would require 20 amps on the primary side at 24V. Which is around a 10:1 ratio.   If you know what you want to draw in current on the secondary side you would use the appropriate wire gauge plus some over head . The number of windings is related to the flux density of your core ,core area and frequency . Fewer windings are required with higher frequency.  Typical steel core are around 1 T to 1.5 T. The core area of a toroidal is the cross section area . So in a lot of ways its much the same as an EI core in calculating the windings .

I understand all of this, but I am looking for more than just an "approximation".  Smaller wire has more resistance and would create more heat. For the primary side :

• What size wire, 14 AWG or 20 AWG (or the equivalent in mm²) ?
• How many turns ?  More turns of course is more resistance, but it also affects the magnetics of the transformer (saturation) ?

I do understand that you can "fudge" a little by winding the secondary first (at least 10 times more turns) and if the output is too low you can add a couple more turns on the primary (leave a long tail, just in case).

[Vovk_Z]

We choose wire to have about 3.5 A/mm2 (from 2.5 A/mm2 to 4.5-5.0A/mm2). It depends on rated power (transformers size) and others economical reasons. The higher the density of current - the higher the temperature under load.

[planet12]

I think this is a good reference:
https://ludens.cl/Electron/Magnet.html

I second this - it is the simplest, most sensible explanation of what's going on, done by a guy who has wound plenty of his own - including some chunky 10KVA ones.

For the OP: turns/volt from the manufacturer is being used as a proxy for the recommended magnetic flux density in the core - and the turns/volt will only apply for the specific frequency it has been specified for, and should be treated as a maximum (ie. the inverse is "minimum number of turns for a given voltage without saturating the core").

For example, if the specification is "4 turns per volt @ 50Hz", then for 24V chopped at 50Hz, you'd need 96 turns for the primary. You could use more than this, but not less. To get 220 volts out, you'd need 220/24 times more turns for the secondary - 220/24 * 96 = 880 turns.

I also know that too many turns of each will saturate the core and reduce efficiency.

It's the other way around - too few turns will generated too high a flux density and saturate the core. More turns will reduce the flux density, which in turn reduces core losses, but also means a longer length of copper, increasing resistive loss in the winding. You can increase the wire size to compensate, but at some point you end up running out of area for the windings. The normal design process looks at where core losses (reducing with more turns) and winding losses (increasing with more turns) intersect, to get the minimum total loss - and therefore heating - in the core.

[Jwillis]

The VA of the core is the answer. The current  in amps is equal to the apparent power in volt-amps, divided by the line voltage. So with a 500VA core with 24 volts on the primary is around  20 amps and the 220 on the secondary is around 2 amps  . That gives you your maximum current ratings for secondary and primary on a 500VA core . Current like volts is proportional to the winding ratio. So if your draw on the secondary side is 2 amps at 220V  it would require 20 amps on the primary side at 24V. Which is around a 10:1 ratio.   If you know what you want to draw in current on the secondary side you would use the appropriate wire gauge plus some over head . The number of windings is related to the flux density of your core ,core area and frequency . Fewer windings are required with higher frequency.  Typical steel core are around 1 T to 1.5 T. The core area of a toroidal is the cross section area . So in a lot of ways its much the same as an EI core in calculating the windings .

I understand all of this, but I am looking for more than just an "approximation".  Smaller wire has more resistance and would create more heat. For the primary side :

• What size wire, 14 AWG or 20 AWG (or the equivalent in mm²) ?
• How many turns ?  More turns of course is more resistance, but it also affects the magnetics of the transformer (saturation) ?

I do understand that you can "fudge" a little by winding the secondary first (at least 10 times more turns) and if the output is too low you can add a couple more turns on the primary (leave a long tail, just in case).

Your putting the cart before the horse. You need to know how many windings are required for a specific core based on certain factors .
As I said  the number of windings depends on the flux of the core , core area , frequency .ect. 

It doesn't matter what gauge of wire is used because the number of windings required will be the same. The VA of the core gives you the maximum current that size of core can handle at a specific voltage. It does not necessarily mean that you will be able to get that amount of current.  You size the wire according to the current required and the limitations of the dimensions of the core. Two cores can have the same VA but with different dimensions . This can limit the number of windings on one core at a certain voltage with a certain gauge of wire than the other core. This is more important on toroids than E cores because of the centre diameter. As more windings that are applied the centre will get smaller with every layer. On the out side of the core the windings will be spaced farther apart. So you can look at it as a cylinder inside of a cylinder with every layer.

The number of windings of the primary is determined by

N(p) = (V x 10⁸) / (4.44 B A f K)  for sine wave

N(p) = (V x 10⁸) / (4 B A f K)  for square wave.

B = Flux density in gauss    1 tesla is 10000 gauss     The flux of the windings must be less than or equal to the flux the core. Data sheet will show the flux density of a specific core.

A = Core area in centimeters squared

f = Frequency

K = Stacking factor     The ratio of the effective cross-sectional area of the transformer core to the physical cross-sectional area of the transformer core. The data sheet  may show this. Typically 0.95 or higher

Once you have the number of windings required for the core you have you can determine what size of wire will fit on that core , based on it dimensions , plus the number of windings of the secondary.

You also need to determine the losses . typically  losses on an EI core is 15- 20% and  toroids of 5 -10 % This will determine the how many extra windings you will require to give the desired secondary voltage.