Where :

- Pout is the output power in VA /Watt/

- Q - core size in sq. cm. /For square inches divide the result by 6.5./

Now increase Q with 10 % and choose a standard E-I size lamination. /For cheeper Hi-FI /with feedback/ or guitar amps you may reduce the size twice/. For longer equation - look here. Now lets calculate number of primary Turns/Volt - n1. /for feedback guitar amps you may reduce **n**1 twice/ Basic longer equation for Turns/Volt - look here.The AC voltage on **R**L in the primary is**N**1 - number of primary turns we need to wound is**N**1 =**n**1.**U**1Next we have to to match the loudspeaker impedance to tube impedance look again here /or to determine reflected impedance ratio/ and the basic formulae for transformer without losses is: - Where:

- n1; n2 - number of Turns/Volt for primary and secondary

- **N**1;
**N**2 - total
number of turns for primary and secondary

- **U**1 -
AC voltage on primary

- **Z** is loudspeaker impedance
in Ohm

- **d** - wire diameter in millimeters

- **I** - current in Amperes

Now calculate **N**2 and to reflect the losses in copper and iron we need to increase number of secondary turns -**N**2 with 5% to 15 % (the lower the power - the higher the percentage). Now the transformer is almost ready to be wound.Wire diameters depends mainly on Is A/sq.mm. you choose. To calculate the diameter in mm we use the equation: - Where:
- I is higher tube current in Amperes
- t = 0.7 when Is = 2.5 A/sq.mm;
- t = 0.8 when Is = 2 A/sq. mm;
- t = 0.9 when Is = 1.5 A/sq.mm
The thicker the wire the less power is lost and less heat is produced in both windings /primary and secondary/. So if possible choose wire thicker than calculated above, but keep in mind that physically you may not be able to fit all the numbers of turns when you start winding the coil. Now we have to calculate how our transformer can be made in the real world with the calculated parameters or we have to go back and choose different core or wire size. We choose square stack with following sizes: **h**- that the longest side of the coil former in millimeters.**H = / h - 2**mm**h**size and have to reduce it with 2-5 mm. /In Millimeters/**b**- shortest side /usually 1/4 of the flange size/ in mm. /Only one flange shown here/.**B =0.5 - 0.9 .**(**b - 1**mm)**D**- wire diameter with lacquer insulation in millimeters/a bit thicker 5% - 10% aprox. more than calculated/.**N**11;**N**22 - number of turns per layer**M**11 - number of layersNow we have to calculate if the number of turns we have calculated will fit our design: **N**11**= H/D**for number of turns per layer we take closest smaller number /example if calculated 29.47 = 29/ **M**11 =**B**/**D**for number of layers we take closest bigger number /example if calculated 9.47 = 10/. That the calculation for primary. The same way you calculate secondary **N**22**= H/D**;**M**22=**B**/**D**if it calculation does not fit the coil former - select thinner wire and insulation or bigger core size and start over. We may well split primary in series /high voltage side/ and split secondary in parallels /high current side/ in at least three or four equal parts each and interleave them for best frequency response - result from lower leakage induction. Start winding - secure leads tightly with glue or insulation tape and remember You may start with the secondary and finish again with it - that interleaving is good for reducing overall leakage induction; parasitic capacity to ground and also increases safety - low voltage side is on top. That's four secondaries and three primary windings. This design method is proven over times and gives extremely good results for Ultra - Fi SE amps. Finally you have to complete you transformer stacking the iron on the coil /for SE amps adding "air gap" between E and I sections of the iron is a must/. Air - gap is introducing an increased resistance in the magnetic path which shows increase in iron losses. There's complicated formulas for calculating "air-gaps" but in practice it boils down to the following:*turns nave to be very tight and as close as possible to each other.*The "air gap" is not usually "air" but precut piece of non magnetic material such as thick paper or "shoe box cardboard" /0.2 - 0.5 mm/ for reducing DC magnetic saturation of the iron and linearizing the magnetic hysteresys curve. Insert 0.3 mm thick material between E part and I part of the iron for best results /up to 15W SE output/. That is practical way to do a output transformer for SE amplifier. After completing the transformer test it the simplest way - connect the primary to the mains - if does not go out in smoke or burn in flames it is ready to be connected to the tubes in your schematics. If buzzing occurs tight the screws and look at the coil former - the transformer may need few more laminations. For Push-pull stages you may use same methods and equations and use the reduced core size since there is no standing current in the primary. Plate resistance here is: **R**pp = 2**R**p.Reflected impedance per tube is 1/4 of total impedance plate to plate. No unbalanced DC flowing so no "air gap" is used here E-I laminations piece by piece is inserted from both sides of the coil former/some folks may like to use air-gap for more linear response - that may create other problems with the low level induction and somewhat increased losses/. For Class AB or B you may need to split the coil former in two "disks" and wind first one of the "disks" interleaving primary and secondary and later take the coil out, turn it over and put it back for winding the second "disk". Here is how coil former looks in that case: There are equations to check induction of primary; frequency response and other parameters - that's no object of our practical transformer calculations. and it also difficult to do without exact iron parameters /such as magnetic permeability, flux density, exact B-H curve, iron per kilo/pound/ losses which varies from steel to steel/ specified by the silicon grade steel manufacturers. - Regards P.G.
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