# Minimum number of turns on a transformer

I am trying to wind my own transformer for a power supply. How many turns do I need on my primary winding?

I know that the turn ratio determines the voltage ratio, but how do I determine the actual number of turns? I can imagine that for an air-core transformer, having many windings can help keep the flux from leaking. However, the more wire I use the more materially expensive and electrically inefficient it becomes.

If I'm using a toroidal core, can I get away with just one loop for the primary?

Thanks!

• Why do you prefer to wind your own transformer rather than buy a stock transformer? What power rating are you typing about anyway, what frequency? A one turn secondary works just fine ... but unless you are trying to melt aluminium probably not too practical. – jippie Mar 2 '15 at 19:01
• I have seen lots of programs and javascript tools etc. out there that allow you to input a few parameter and then get the turns – PlasmaHH Mar 2 '15 at 19:54
• I want to wind my own coil because I want to learn and I learn best by doing. – freefood89 Mar 2 '15 at 20:20
• I respect the desire to learn but shouldn't you experiment with commercial transformers instead of increasng your chances of killing yourself? Maybe build 20-30 power supplies, use them and learn before hand wrapping? Just saying.... – cbmeeks Mar 2 '15 at 21:21
• Thanks for the comments, but I'd like to clarify that I'm not a random kid plugging things into the wall. I studied analog integrated circuit design at a respected university and have nearly a decade of experience tinkering. I will take the necessary precautions to be safe. I just want to be more comfortable with magnetic devices because in IC design (especially in college) one does not use many inductive devices and as I've mentioned earlier I learn best by tinkering. – freefood89 Mar 2 '15 at 22:30

Here (from Wikipedia) is a fairly complete linear model of a transformer:

Note the magnetizing inductance Xm across the primary. If that inductance is too low, you'll get excessive current flowing even with no load on the secondary.

While a single-turn primary is certainly possible, with sensibly-sized cores it implies either a very low voltage (for example, a current transformer, which is typically toroidal) or a very high frequency (or both).

The inductance is proportional to the number of turns squared, and a small 120/240V 50/60Hz mains transformer primary might be some hundreds of turns, so you can see how far off a single turn is. At a fraction of a volt, or higher frequencies at relatively low voltage, a single-turn primary might make some sense.

• Thanks for giving me a starting point. I will go back to my college books to figure out how to actually determine X_m. I'll be back if I don't get hundreds of turns as I expect. – freefood89 Mar 2 '15 at 20:44

The calculations for the transformer are complex; however, since you want a toroid where windings are always on top of each other you can't just make something, measure and adjust - you want to know before laying out the coils so I suggest to just bite the bullet and start understanding the formulae.

If your power source is 120V and you want to get 12V then the smallest secondary is one turn and your primary can't have less than an integer multiple of 10 turns. This is only close to real life for high frequencies, for 50/60 Hz frequencies of typical household mains the number of turns in the primary will be in the thousands and the number of turns in the secondary must reflect that.

A workable shortcut will be to grab a ready-made toroid transformer that has its secondary on top, remove it, figure out the turns ratio by winding and measuring test coils, then wind the desired secondary - this can be done without calculations.

• Thanks. I am actually not afraid of math. I'm trying to get over my uneasiness with magnetic devices. – freefood89 Mar 2 '15 at 20:21
• the issue with magnetics is that fundamentals are quite trivial but you're restricted by tons of secondary factors. For example, when winding a transformer you will be concerned with how much wire you can actually pack in the gap of your core of choice. Smaller cores require more turns for given power and frequency, to keep the core from saturating (saturated core will "disappear" and your coils will act like they are in free air). Again, if you want to experiment, find a transformer in which the secondary can be easily removed, then remove it and wind your own. You'll learn much by doing it. – Oleg Mazurov Mar 2 '15 at 20:32
• hi, thanks again for the additional input. I went through my textbook again and realized that I totally forgot about phenomena like the skin effect and the proximity effect. I may need to follow advice from you and others and start from modifying a commercial transformer. – freefood89 Apr 19 '15 at 1:54

The minimum number of turns required for a 120 V, 60 Hz primary is a closely guarded secret. :-) Not really, but everyone always talks about turns ratios, but forgets to mention the minimum number of turns for the primary. Well, the iron/silicon/metal core of the transformer can accept only so much magnetic flux before it saturates and can't take more. If you go beyond this, the inductance drops a lot and you end up drawing a lot more current off the powerline and it will get really hot - not good.

A rule of thumb, for transformer laminations you may salvage from a junked 60 Hz transformer: Number of turns needed for the 120 V, 60 Hz primary = 800/(area of the core in square inches). You measure the height of the pile of laminations, and the width of the center leg of the E lamination. This width is measured along a line that would go vertical when looking at the E as the letter E appears here. In other words, imagine a single turn of wire tight on the center core, the area of the loop this single turn forms is the area. Do not include the outer legs of the E, or the I. A bigger area will make for a lower number of turns.

Once you have the number of primary turns, then you can do the turns ratio to get the number of turns for the secondary. Add a few more turns to make up for resistance of the wire voltage losses. If your powerline frequency is 50 Hz, you need 60/50 times the above result for your primary for 120 V, and twice that for 240 V.

https://en.wikipedia.org/wiki/Transformer gives the universal EMF equation as: E(rms) = 4.44fNaB(peak), where: E(rms) is the rms voltage that you are applying to the primary f = the operating frequency N = the number of turns a = the core cross sectional area in square meters B(peak) = the peak magnetic flux. This is a property of the core material, typically 1.2 - 2 for silicon steel and 0.7 for soft steel.