On this page I have collected some formulas for calculating transformers. So if anybody wants to "roll their own", here are some recipes. I have never tried to make output transformers myself, so I can't comment on the quality. I have, however, used the power transformer formulas. They work well.

Single-Ended Transformers

Power Transformers

Push-Pull Transformers

Originally by E.A.Schulze, Funkschau 1966, No.1, p.27f.

I will translate the most important parts of the original article.
I will use a 40W transformer with a primary imp. of 6k6 as an example.

Here we go:

First the sectional area of the core.

Fe in cm2

The original formula given in the magazine is:

Fe = 200P / min. frequency in Hz.

Fe is the area in square cm. P is the max. power.

However this formula gives an Fe than is way to big, and it must contain an error. I believe, judging from the example in the article, that the 200 should have been 20. If we use the 40W and 20Hz as an example, the Fe will be:

Fe = 20 * 40 / 20 = 40cm²

This is also a very big figure, but if you can afford such a big core it will guarantee that there is no phase shift at 20Hz, and it will give you a -3dB point of 5Hz (see Bild2.gif)

Using a rule of thumb that is mentioned in the text gives a smaller value. That formula is as follows:

Fe = Square root of (P * 20) = sqrt (40 * 20) = 28.3cm²

A third rule I know of simply states that the area should be twice the area of a mains transformer of the same power, for a 20Hz transformer. That gives the following formula:

Fe = (Square root of P) * 2 = (sqrt 40) * 2 = 12.65cm²

So you have three different numbers to work with. Which one you should choose depends on the space and the money available. But perhaps the 28.3 is the best compromise.

The next thing you do, is find the standard core that suits the calculated value best. You should use the effective area of the core, both for choosing the core and for the further calculations, and not simply the area. The core should be a standard EI core. The laminations should be made of grain-oriented silicon steel, and should be between 0.2 and 0.35mm thick.

Primary windings are calculated from voltage at max. power.
That gives the formula:

U = (Square root of P * Zp) = (sqrt of 40 * 6600) = 513.8V

The number of windings in the primary winding should be:

Np = 115 * U / Fe = 115 * 513.8 / 28.3 = 2088

The number 115 depends on the lower frequency limit. It should be 230 for 10Hz, 115 for 20Hz and 57.5 for 40Hz.

The secondary windings are calculated using the impedance relation:

Ns = Np / (Square root of Zp / Zs) = 2088 / (sqrt 6600 / 8) = 73

If you need outputs for more than one impedance it is not a good idea to make a tapped secondary. It is better to make four secondaries that can be connected in series or parallel. That way the entire transformer is always active, and not only half, as it is when you connect a 4 Ohm speaker to a transformer with 4, 8 and 16 Ohm taps. If you use four 0.8 Ohm secondaries, you can obtain the following outputs:

-->->->->     -->->     -->->     -->
  > > > >       > >       > >       >
  > > > >       > >       > >       >
-->->->->       >->       >->       >
                 |        |         |
                >->       >         >
                > >       >         >
                > >       >         >
              -->->       >         >
                          |         |
                          >         >
                          >         >
                          >         >
                        -->         >

  0.8 Ohm   3.2 Ohm   7.4 Ohm   12.5 Ohm

The reason I chose 7.4 instead of 8 and 3.2 instead of 4, is that the impedance of speakers is often lower than the rated impedance. You can of course also choose other values than 0.8 Ohm. If you choose 0.9 Ohm you can get an 8 Ohm output, if you know that the impedance of the speakers is in fact 8 Ohm.

Using the 0.8 Ohm secondaries the ns will be 23.


The transformer must be wound symmetrically to work best. A two-chamber bobbin should be used (see Bild1.gif). The windings must be split up in sections and interlieved. The primary should be split up in 10 sections of Np:10 windings, and the secondary must be split in 8 sections of Ns windings. One chamber of the bobbin is for tube one, and the other for tube two.

The wire must be isolated copperwire with a max. temperature of at least 110 degrees Celsius. The wire should be chosen so that the primary and secondary windings will have approx. the same winding height. The minimum thickness can be calculated using the max. current. The formulas are as follows:

Min. thickness: d = 0.65 * sqrt of max. I (mm)

The max. current in the secondary winding can be calculated with this formula:
Imax = sqrt of (P / R) = sqrt of (40 / 7.4) = 2.32A

As there is two windings for each secondary, the current should be divided by 2. So the min. diameters will be:

ds = 0.65 * sqrt 1.16 = 0.7mm

dp will probably be around 0.1mm

The wires should be chosen so that 80% of the chamber will be filled (including insulation). Thicker wire will give lower losses, so keep the wire as thick as possible. The thickness should also be chosen so that the windings will make full layers on the bobbin.
It is OK to change the number of windings a bit, to fill the layers, as long as the relation between the primary and secondary is maintained.

Start the winding with a primary winding. Start the primary winding at the center of the bobbin, and the secondaries at the edges. Between each layer of wire, put a layer of lacquered paper of teflon/mylar foil. Between the primaries and secondaries 3 or 4 layers are needed. Also remember to put flex on all the "ends" going in or out.

One of the chamber should be wound clockwise, and the other one anti-clockwise. That is done to make the magnetic fields of the DC-current of the primary-halves cancel-out each other.

The sectional view of the bobbin can be seen on Bild1.gif. The uneven numbers are beginnings, and the even ends.

After winding all the windings the bobbin should be sealed with glassfiber tape, or a similar strong heat-resistant tape.

After the winding is done, the windings should be connected as follows:

The primary windings should all be connected in series.
2-5, 6-9, 10-13, 14-17 and 20-23, 24-27, 28-31.

B+ is connected to 1 and 19. Plate 1 is connected to 18, and g2(1) is connected to 6. Plate 2 is connected to 36. and g2(2) is connected to 24. The g2 connections are for 40% taps. If you need 43% taps you will have to add some windings to the first two primary windings of each section.

The secondary connections should be crossed, because of the clockwise/anti-clockwise winding.

3+22 and 4+21 is the first secondary.
7+26 and 8+25, 11+30 and 12+29, 15+34 and 16+33 are the remaining three.

If you choose to make only one secondary winding, the connections are as follows:

- 3+7+11+15+22+26+30+34 and
- 4+8+12+16+21+25+29+33

The E's should be fitted first. The are fitted from both sides of the bobbin. First one from the right side, then one from the left side, and so on. The I's are then fitted afterwards. Be sure to keep the laminations the way they were when you got them, and fit them without flipping them, so that they are fitted the way they they were cut-out. That way you can stack them closer, making the efficiency higher. Be sure to fit as many laminations as possible (use a hammer for the last ones) to keep them from vibrating. Also remember to use non-magnetic bolts for assembling the transformers. After they are finished you can pot them if you like, and if you can find the necessary materials. I don't really think it is necessary though.

That should be all the information needed to make push-pull transformers. The frequency response of the transformer is shown in Bild2.gif. The author also writes that the phase-shift of the transformer is very low, and that if you limit the amp to 40kHz, there will be no high frequency instability - without any compensation in the feedback-loop. Stay tuned for the single-end formulas.

Single-ended transformers

Originally from the 1963 book "Funktechnik ohne Ballast" by Otto Limann

The sectional area (Fe) in cm² of the core is calculated with the same formulas as above.

The airgap (a) in mm is calculated as 0.4 times the square root of Fe.

The primary induction is calculated as follows:

L = 0.16 * (Zp in Ohm / low cut-off in Hz)

The primary winding number is calculated as follows:

Np = 1000 * sqrt of (10 * L * a / Fe)

The secondary windings are calculated using the relation m.

m = Np / Ns = sqrt of (Zp / Zs)

Ns = Np / (sqrt of (Zp / Zs))

The wire should be chosen using the same guidelines as above.

The transformers should be split up in 9 sections. 5 sections of Np / 5 and 4 section of Ns.

The airgap figure should be divided by two for an EI-core. For a single-ended OPT all the E's and all the I's should be stacked, and a piece of cardboard (or another isolator) with the thickness a/2 placed between them to form the airgap.

That should be all for now. Most of the materials should be easy to find. You should be able to find the wire, flex and tape in an electronics store. Teflon tape is used for plumbing (for tightening water pipes I think), so that should be available at a hardware store. If you can't get any mylar foil, just buy some frying bags. They are usually made of polyester/mylar.
The cores and bobbins can be harder to find. Try a transformer manufacturer. The ones I have tried in Denmark didn't mind selling a few loose cores and bobbins - just don't expect discount prices.

Power Transformers

Not ready yet ;-)


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