Making Transformers - Core Size Considerations, Jan Roland

This is long article on making your own power transformers. It is divided into a series of steps, each in its own section.   The material is presented in pretty much the order you would follow through the design process. Jon's casual style makes this an enjoyable read!


Some of us may have built items many times with store-bought transformers, and even when a project demanded some odd size, not really a catalog item, never imagined it can be relatively straightforward to make one's own, so we may have gotten by with the nearest stock item. Perhaps with the following, a few of us might consider making their own, next time we need a 38 volt, 11 ampere secondary, designed to work from a 183 volt, 40 Hz. primary!

There are basically two metal parts to a transformer; the copper (electrical) windings, and the iron (magnetic) laminations. Silicon-steel, actually. Obviously, these two metallic components must be sized for the load at hand. That is the essential point of this article. Note that this discussion is taylored for the "E-I" core configuration shown at right.

To facilitate "shop use", I break the steps down by into the numbered sections that follow.

1 - Core Size

A transformer's electrical (and, yes, physical) size is determined by the Volt-Ampere (VA) requirement. No, VA is not quite the same as Watts, but this is an electrical engineering detail a bit off the nuts-and-bolts of the topic at hand. But, yes, one simply multiplies the Volts times the Amperes the secondary must deliver.

If more than one secondary on the same transformer, figure the VA of each, and add together, for a total VA rating. Then, using the VA - Core Area table or spreadsheet (link below), find a value in square inches. You might safely round-off to, say, no smaller than 90% of the actual value, and higher would always be OK, so long as installation space and funding are not considerations.

If you wish to calculate core-area for yourself, a polynomial, which gives you the more conservative (larger) core-size through VA = 1000, is provided:

CA = A + B * VA + C * VA2 + D * VA3 + E * VA4 + F * VA5 + G * VA6


A = 1.637579x10-2,  B = 3.01207595x10-2,  C = -1.40417912x10-4, 
D = 3.90274903x10-7,  E = -5.75137667x10-10,  F = 4.26123945x10-13, and
G = -1.24586857x10-16

A spreadsheet using the polynomial to calculate tranformer core area requirements is provided for your convenience. Note that it is not valid for VA above 1000; the formula was derived using a "curve fit" algorithm, and the curve only went to 1000VA. From 200VA to 1000VA, though, the "curve" is relatively linear, so using y=mx+b, an "extension" was created which should yield fairly representative results for values above 1000VA.

Most small transformer core lamination stacks are figured so that the core is close to square. Obviously, it is an easy matter to stack fewer or more of the laminations of a given size to make the core thinner or thicker than its width, and there may be electrical or mechanical reasons for this kind of variation, now and then. But for most small power-transformers, square is what to shoot for.

You can simply take the square root of the Core Area you have selected, and round this off to the next-wider stock lamination size. Or, if it is only barely larger than a stock size, it'd be OK to select the slightly narrower one.

Example: Say you need a core-area of 2.00 by the graph. For a perfectly square core, you would need a 1.414" wide center-leg. 1.375" (1-3/8") is the closest under, and this would be just fine. 1.50" (1-1/2") is the next over, and this is wider than really needed, considering you can "stack to area".

So, say you will use 1.375" wide center-leg laminations; 2" = 1.45+" You can then stack laminations to nearly exactly that thickness. Plus or minus several will make hardly any difference, but the conservative engineer will always go for the exact, or next larger number.

Core-Area Calculated from Polynomial

VA Sq.In. VA Sq.In. VA Sq.In. VA Sq.In. VA Sq.In.
10 0.3 60 1.4 150 2.4 400 3.7 650 4.8
20 0.6 70 1.6 200 2.8 450 3.9 700 5.0
30 0.8 80 1.7 250 3.0 500 4.2 800 5.5
40 1.0 90 1.8 300 3.2 550 4.4 900 6.0
50 1.2 100 2.0 350 3.5 600 4.6 1000 6.4
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The math that follows assumes a single primary. You may want a pair of identical primaries such as you'd have where you want a design to be useable with either 120 VAC or 240 VAC.

You would connect the two windings in series for the higher voltage, or parallel for the lower voltage.   Do the math as if the higher voltage would be used, and then simply divide the number of turns by two, giving the turns-count for each of the two smaller primaries. Simple logic.

The general formula for primary turns is:

N = (E 108) / (4.44 f A B)
N = Number of turns
E = Primary Voltage
f = line frequency
A = core cross-section Area
B = maximum flux, in lines.


Assuming 60,000 lines of flux, a bit of algebra, and we have:

N = (k E)/ A


k = 6.256 when f = 60 Hz. or k = 7.507 if f = 50 Hz.

2 - Primary Turns

Simple: TV = N / E, where E = Primary Voltage.

3 - Primary Current

Simple: I = VA / E, where I = Primary Current.

4 - Primary Wire Size

Copper wire must be thicker for greater current. Wire cross-section is measured in "Circular Mils" (CM), this value being approximately the Diameter of the wire in Mils (thousandths of an inch) squared (CM = D2).

From various tables, this is quite accurate for 10 AWG through 30 AWG. For sizes outside this range, values in the table below (included For your convenience) are as shown in copper wire tables. These charts give the diameters, area in CM's, gage-number, turns per inch and average turns per square-inch, etc. You can find copper wire tables in electrical handbooks, the famous ARRL manuals, etc.

For power-transformers of the size considered here, a value of 750 CM per ampere, or 0.75 CM / milliamp is about right. For rather cool-running transformers, especially at full-load, 100% duty-cycle, you might go on up to 1000 CM / amp (1 CM / milliamp).

5 - Secondary Turns

There will be a 4% to 6% loss in transformers of the size considered here. Part of this loss is due to copper losses, and part due to magnetic losses in the iron. The total can even vary a bit due to differences in workmanship. This loss "goes up" as heat, usually just some warming of the transformer.

All else being equal, the %-loss is inversely proportional to the size of the transformer in question. A good number to use for the size we are considering here is 5%. That is, with a 5% loss, one must figure for 1.05 times the ideal number of secondary turns given by multiplying the Secondary Voltage x TV (TV from Step 3, above). Or,

ST = SV 1.05 TV

If you have more than one secondary, you must have added the VA for each, then used this sum for total VA in Step 1 above. Then, figure the ST count for each, separately, using this formula each time, using the different SV for each.

6 - Secondary Wire Size

Go through the look-up as you did in Step 5, above. Same thing.

Solid Copper Wire, Diameter in Mils, Area in Circular Mils
AWG Size AWG Size AWG Size AWG Size
dia area dia area dia area dia area
4 204.3 42000 13 72.0 5184 20 32.0 1024 27 14.2 201.6
6 162.0 26600 14 64.1 4109 21 28.5 812.3 28 12.6 158.8
8 128.5 16384 15 57.1 3260 22 25.3 640.1 29 11.3 127.7
9 114.4 13138 16 50.8 2581 23 22.6 510.8 30 10.0 100.0
10 101.9 10384 17 45.3 2052 24 20.1 404.0 32 8.0 63.2
11 90.7 8226 18 40.3 1624 25 17.9 320.4 34 6.3 39.69
12 80.8 6529 19 35.9 1289 26 15.9 252.8 36 5.0 25.0

As an alternative, you could calculate wire diameter (D) in decimal inches from:

To make this calculation using the Windows Calculator ("Start" - "Programs" - "Accessories" - "Calculator"),
in Scientific mode (mode selected from calculator View menu), follow the steps below:

That is a bit tedious, so you see why the table!

7 - Windings

You now have core width (CW) and core thickness (T) values for the "center leg" in an "E" shaped piece of the laminations comprising the transformer core. You can now make a hardwood spool using dimensions shown in the sketches on this page.

In the drawings, CH = Core Height, CT = Core Thickness (of bobbin, after "cheat-factor" added), CF=Core Front (the width of the "hole" in the coil for CW. H is Height of coil from front to back of transformer, and F is Face width of coil.

By adding that 1% of size to the wooden spool core, you ensure that your finished winding will slip easily over the iron (or, that the iron laminations may be easily slipped into the winding's opening.)

If, however, you intend to spiral wrap the winding with cloth tape before final assembly, you will have had to allow for the tape. So, you must add another few percent to the CW and T of the wooden spool center, so that the opening of the coil, when slipped off the wooden spool, is a bit larger, yet, allowing for the cloth tape.

This is common sense, but one must remember such details, or waste much material and time before discovering what you did, after all the work!

The sketch at right shows the the wooden "core" of this spool. Common "allthread" is used as an axle as shown. This not only holds the end-caps on the core ends, it provides hardware to attach in the lathe chuck, and to the live-center.

Before the axle is bolted in, four tacks should be driven in as shown to secure that the end-caps will remain indexed with the core. That is, the allthread's two nuts and washers will not prevent rotary slippage.

Notes on the End View of Spool Core:  This drawing shows the dimensions of this core are to be 1% greater than the actual laminate stack, to insure it will fit thereover, once wound, taped, soaked, and properly dried. If you intend to spirally-tape around the winding, allow more space! Say, 5%!

The notches on all four sides are to provide space for string so you can temporarily tie the winding before you slip it off the core, before Formvar soaking. You may determine, with your own experience and habits, these are unnecessary. The 0.2" depth of these grooves is a suggestion only.

The sketch at left shows the the the 1/4" plywood "end-cap" of this spool. In the event a spool will be used for several identical transformer coils, it is a good idea to glue on the end-cap on the left (chuck end), and still use the four brads shown. But on the center end, (the end you see above), instead of brads, use #6-3/4" pan head SM screws to hold that end-cap, so it can be removed and put back easily and securely.

Notes on the End Caps:  It is suggested that these be made of 1/4" or 3/8" Baltic Birch plywood or at least hardwood veneered domestic hardwood. Or, for repeated and heavy duty use, perhaps linen impregnated phenolic.

It is also be a very good idea to strongly break the corners on the inside (core-side) with a sanding block, and even round off the four corners of each end-cap with about 1/4" to 1/2" radius, first.

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8a - Making the Windings - Using the Spool

The physical size of any transformer coil bobbin (spool) over, say, 50 to 100 VA is a bit large for winding with a kludge using a Variable Speed Ratio (VSR) drill and some kind of "live center" bearing arrangement, even if beautifully-made.

A VSR arrangement might do for small transformers, especially, say, a 1/2" VSR drill. Someone who does not have a lathe, does not anticipate ever getting one for financial reasons, or lack of space, or unwillingness to store such a large thing, if rarely used, anyway, might consider home-brewing a "Transformer-Winding Lathe".

It might take, say, a DC gear-motor, some sturdy plywood for mounting it all, a couple of good ball-bearings and a fitting axle, to act as a "live center". Then, add a DC speed-control. Dayton Manufacturing has a line of 90 VDC gearmotors with controls, which would do such a job just fine, with some mechanical wizardry and a few nuts-and-bolts tools. But, especially as I have made transformers on up there beyond 750 VA, I like a standard engine-lathe for this purpose. Two reasons for this: It's there, anyway, as I use it for "normal things", and I rarely have to "tie it up" for making transformers.

A wooden winding-spool such as illustrated herewith is easy to make with basic woodworking equipment Or, one who "doesn't do sawdust" can go next door to the ol' boy who does, with a sketch in hand. These sketches should indicate rather exactly what is needed, and tiny details are left out for the obvious reason that many will be making these "one-time-use" items of "whatever's on hand", or, will have their own opinions as to what is best, and will be doing it slightly different, anyway (perhaps only to find, later, that they would have been much better off to follow the sketches and instructions more exactly?).

A 3-jaw chuck in a lathe clamps easily onto a hex nut, so, the arrangement shown with a length of all-thread with a hex nut on either end of the spool, with one end of that all-thread center drilled as indicated to fit the live-center is wonderfully straightforward and nonsense free.

Whether an engine lathe, a home-brew lathe, or a "VSR on a board" is used, some means of turns counting is necessary. Thirty or more years ago, even very professional coil-winding machines had mechanical "odometers" for counting turns. These don't seem to be readily available as separate or replacement parts, and if they are, they are probably very expensive.

Besides, one must be something of a mechanical wizard to arrange a reliable cam and/or lever means of driving one of these mechanical counters reliably, especially UP and DOWN. But digital ICs make the brewing of one's own UP/DOWN counter rather straightforward, and readily available Hall-effect sensors which look like TO-92 transistors, plus a small magnet, make turns counting easy. Accompanying sketches showing how these Hall sensors and a magnet were applied to the left end of my lathe's spindle should indicate how one might do it for some other kludge, such as the home-brew coil winder, or even the "VSR on a board" kludgery.


Click on drawings (above) for a picture of a Hall Effect sensor installation.

Below is a schematic of electronics that provide a numeric turns counter that can be reset by push-button.

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8b - Wire Facts

The Formvar insulated wire (old term: "enameled wire") will be on spools. Some small quantities are sold in palm sized spools, and these quantities may do for small transformers, or where you have several separate windings. But it is a bad idea to splice magnet wire in a winding, whether professional or just hobby stuff!

Take advice from someone who has done it eight ways: Never, never plan on splicing, and if you break a winding in progress after fewer than 100 turns, or run out of wire at that point, UNwind it, and begin again, after you put that full spool up there!

Back to my point, here: You will want to rig some kind of support for a piece of 1/2" dia. steel rod, say, 10-12" long, between supports, onto which you can place the spool of wire you will be winding, next. When pulling that wire end over to start it onto your winding bobbin, make sure it is free and kink free, before you start. Don't forget to "Zero" the counter before you begin, with each successive winding!

But first, consider terminations! There are several ways to terminate transformer winding ends. If the winding wire is fairly hefty, you might just slip spaghetti insulation over the first/last few inches, and let the winding ends, themselves, be "lead wire" for the particular winding in question. You can surely do this for wire gage #20 or smaller number (larger wire).

For large, flat "wire", you can even sand off the Formvar on the last 1/2" or so, and drill a hole in the middle of the flat "wire", making a "solder lug" right on the end of the winding copper, itself.

But for tiny wire, say, thinner than #22, you would be well advised to carefully sand off and tin the last couple inches of winding wire, wrap that nicely around the tinned tip of a nice piece of hook-up wire of appropriate size, color, and insulation type, solder properly. Then, lay fiber tape under, and on top of the joint, making a flat taped up connection, and tape this in place on the bobbin paper.

9 - Insulation Facts

Professional transformers are done two ways, nowadays: One way, the "easy way", is with nylon molded bobbins, where the primaries and secondaries have separate "compartments" on the molded form, and the windings are "scramble wound" in their respective spaces. These are even infrequently Formvar soaked, once done.

The wire ends are then attached - yes, not even soldered! - to solder tags molded into the bottom edge of the bobbin form. If you can locate those molded bobbins for exactly the transformer size you need to make, and don't object to "scramble winding", go for it! Makes for an easy job! And, if you bother to Formvar soak and properly tape over the cured windings, the end result can be very electrically proper and "professional looking"!

The second way is with lots and lots of care and fussing around like the old boys always did it, where the windings are done in careful flat layers, with tissue between each layer, so that the "enamel" insulation never sees more than the potential between adjacent turns.

This winding method requires mechanical wire distribution as the bobbin spins, stopping, laydown of a tissue piece, resumption, etc. I never saw this being done, so I don't really have a proper picture of what steps of this old method were automatic, and which were manual. Yep, they actually had real humans with their fingers down in there, manually operating small soldering irons, tape dispensers, diagonal wire cutters, and such, years ago! Data would be amazed!

Well, if you are ready to go, say, on a 500 VA transformer, but know there is no such thing as a molded bobbin of that particular size you need, you can "build your own" insulative bobbin on the wooden spool, by cutting the parts shown herewith to suit, and carefully installing, folding, and taping.

There is a professional Mylar core insulation paper used for custom transformers, which has light blue paper like outer layers, but a very tough Mylar (plastic film) core. I have always managed to find more than enough scraps of this in my transformer-buddy's trashcans for my needs. He buys it on $500 rolls, I guess. It probably comes in several thicknesses.

In the old days, say, 40 years or more, ago, "Kraft paper" was used for such as transformer windings, and once this was finally soaked in Formvar, after final assembly, it was suitable insulation. But it required manual manipulation, so I am fairly sure this is the reason it fell from favor!

Kraft paper? The thicker, nicer grocery bags (not the plastic ones!) are made of similar stuff. This paper is usually amazingly sturdy stuff, and, when carefully cut with an industrial, single edged razor blade against a straight edge over a smooth board, into nice strips of the appropriate widths, it makes for transformer bobbin insulation which is every bit as good as a "professional" one of 1958!

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10 - Preparing Mylar or Paper for use as Bobbin Core Wrap

Install the "core wrap" shown at right over wooden core of spool before adding the end-cap insulation shown below. With this core wrap installed, the notches in the wooden spool will be covered.

Where you must exit with winding ends or leads, punch through the wrap with an awl, careful not to damage windings.

At left is insulation for installation on the end-caps. Install one at each end of spool, after placing the core wrap shown above on the bobbin.

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11 - Laminations and Core Construction

One should locate a small transformer shop in your own, or a very nearby town of population, say, 100K or so, and make friends with the owner/operator, so you can go in there during workday hours, and "buy 2-1/8" of 1-1/4"-leg #24 E-I laminations".

Some might sell such "by the E-I set", so, you might want to take a calculator with you, to figure how many times the 0.025" (#24) laminations fit into your req. 2-1/8", or the 0.0185 (#26). The latter is better, but might cost you more per inch of stack, and will take a bit longer to assemble.

But for some "important" transformers, it might be worth the small difference. I have been told there is little measurable difference, using the thicker #24 laminations. Some also have #29, which is only 0.014" thick. There is a manufacturer, National Lamination Corporation, Des Plaines, IL (312) 763-7000.

They will surely have at least a full box minimum; the boxes I have seen at my nearest small transformer shop are around 200 lb.each!

The "coil window" in the laminations is something about which there is little choice. Oh, there are a couple of sizes where there is a difference in ratio between the coil window and the center leg width, but not all ranges, nor do I have any idea how to specify.

I do know that it seems all tile transformer windings I have done for a given "square centerleg stack" have just fit, just fine, with little wasted space (and very rarely not enough space!) So, the ol' boys who came up with the ratio between the core width and the window size certainly did so after much empirical data initially determined those values.

Don't forget, when out "buying iron", be sure to get two pair of brackets (illustration at left) to fit whatever E-I set you are getting, to use as "feet" for your transformer. These also perform the more important function of holding the E-I stack together, once assembled.

It brings me to this: The dimensioned sketch of E-I laminations herewith shows the entire stack of "E's" and "I's" completely separate. Assembly of a transformer larger than, say, 10 VA this way is not ideal. It is much better, even essential in larger ones, to alternate the "lay" of the E and I.

Too, you might put in pairs of laminations, each time, or even threes, but better, alternate, one-for one! That is, shove an E into right side of the coil, then the next one from the left side. Then the third from the right, again. And so on, until your pre-figured number of laminations are "stacked".

Then, carefully push-in the "I" pieces between the E's, on both sides (or, top and bottom). Don't forget, one goes also "outside" on both sides!

Now, assemble those "L-brackets", using machine screws of the appropriate size and length, and washers and hex-nuts. Gently tap the "I" pieces down against the "feet" of the E-legs, until the faces of the stack are smooth (i.e., no gaps left between the E- and I-pieces, "inside".)

Tighten the bolts on the "L-brackets" nicely, but not so tight the bolts break or the threads strip!

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12 - Formvar

You are now ready to impregnate the finished transformer in Formvar varnish. You might buy a gallon or two from that local transformer shop, or, they might tell you who their supplier is, and you can get fresh stuff from them.

Formvar is special in that it takes forever to harden "in air", but when heated, it cures in half an hour. You might want to get the supplier to tell you how to handle the stuff you get.

You have wound the coil "dry" with only copper, insulation, and air "in there". You will want to insulate the windings, and fill in all the air holes, and basically stick it all together, not only for insulative purposes, but to reduce audible humming when the transformer is in use, if not wound well, nor the laminations stacked well.

Some shops will just hang their completed transformers by the leads, or by wires temporarily through unused holes in the laminations, in a vat of Formvar, at room temperature, for 24 hours, or even less. I was once told a 24 hour soak is just as good as a vacuum soaking, but I sawed-up a recently made transformer I had soaked for 48 hours before cooking, and it was DRY, deep inside!

I use a cumbersome vacuum box I made of 1/2" Lexan plastic, with an O-ring set into a groove routed along the bottom rim, and I can then place this airtight onto a sheet of Lexan or thick glass, onto which I have first placed a container large enough to accept the transformer, and into which has been poured fresh Formvar, to about 1/4" over the highest point on the lamination-stack (or coil), and generally, with the lead-wires protruding upwards, out of the goo.

Next I turn on a small vacuum pump which is pneumatically connected to this box. In several seconds, a vacuum of better than 27" Hg is measurable, and bubbles come out of the coil area. Rather violently at first, then "tiny" and slowly, after a moment.

I leave the pump and vacuum on for a few minutes, this withdrawing all the air from the transformer parts. I then pull the hose off, allowing the atmosphere back into the box. This is when the Formvar "gets in there".

One must leave it alone for several minutes after the vacuum is off. After you remember where you were, lift up the "soak", and hang it over the container of varnish by the leads for a while.

Let it drip! Then, "cook" the transformer in the family cooking oven! You can do this either by hanging it from the leads from a grill placed as high as you can, and put a scrap of aluminum foil under the transformer to catch drippings (it will drip a bit more for a few seconds, as it heats up!), or, you can set it on a small piece of hardboard covered with first a scrap of aluminum foil, then waxed paper (so you can get that off the transformer when cured!)

Do not set the heat beyond, say, 375. What I have gotten seems to cure in a 350 oven in 30 min. It's nasty and sticky when still hot, so, set the transformer down on Teflon or Delrin wedges, over newspaper, etc., and wait four hours before handling.

If you undercook it, it will be sticky-soft in places, once cooled to room temperature. If you overcook it, the color of the insulation and varnish will have darkened noticeably, and/or, the PVC insulation on some/all of the soldered on lead wires will have obviously melted off! Bad!

13 - Finished Transformer

Below is a side view and winding detail to indicate how the winding insulation separates the wire from the core laminations.

Note that F should be about 99% of the sum of 2W and CW. If it is 100%, it may have to "squeeze in", doing damage. After making the winding, insulating and Formvar-soaking and drying, CF should be about 101% of T. For the transformer assembly itself, there is no limit for H except the completed transformer must fit where it is to be mounted!


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