Fig 1.
 

(2) List all voltage and current in power requirements for the amplifier to
specify transformer VA rating.
The transformer must be able to easily provide total output operating power
needed for idle conditions, and have a capability of sustaining 50% higher
current load indefinitely. Calculations based on steady idle state for filaments,
driver -input tubes and bias, but with higher current for output tube HT for B+ to
allow for class AB and various working conditions.

NOTE. Allow for all possible output tubes including KT120 which need more
filament current than 6550, KT88 or KT90.

Vac Heater supplies from 4 x 6.3V windings to give two phases of 12.6Vrms.
4 x KT120. 12.6Vac x 2.1A x 2 = 53Watts,
4 x EL84, 12.6Vac x 0.8A x 2 = 21Watts.
Vdc Heater supplies.
2 x power amp input 6CG7, 17Vdc x 0.6A = 10Watts.
Phono preamp, 17Vdc x 0.9A = 15.3Watts.

Total heater power = 53W + 21W + 10W + 15.3W = 99.3Watts.
All 4 6.3 windings are in series, with CT to 0V.
Winding current = Iac = P / V = 99.3W / 25.2V = 3.94Arms, say 4.0Amps.

Wanted filament heater windings =  4 x 6.3Vac x 4.0A.

(4)  Output Stage B+ Anode Supply and HT winding.

State type of rectifier = Voltage Doubler with two silicon diodes.

Define ratio Vdc / Vac with Vdc measured at idle measured across 2 series
capacitors and Vac is HT winding voltage Vrms.
 
Ratio is approximately 2.6 : 1.

Choose Output Tubes, will be TWO PAIRS of KT88, KT90, KT120, EL34,
6CA7, 6L6GC, 5881, KT66, or could be TWO QUADS of EL34, 6L6GC,
5881, KT66.

Choose two pairs of KT120.

Choose Class of operation, to be variable, PP pure class A1 to class AB1.

List Range of B+ Vdc wanted = +360V, +400V, +440V, +480V, +520V,
from 5 taps on HT winding.

List Range of idle DC currents for maximum class A, and to to suit
safe Pda, and list maximum AB1 Idc.

Table 1. Class A conditions :-

NOTE. There are other circuit parts to be supplied with B+ power!!!

(5) Calculate maximum B+ current wanted for other uses :-

Max power is where B+ is highest, this example, = +520Vdc.

5A, Shunt resistances across electrolytic capacitors.
This case, 2 // 272 = 136k, get Idc = 520V / 136k = 3.8mA.

5B. Phono amp anode supply, estimate 2 channels at 15mA each = 30mA.

5C. Shunt regulator zener diodes for input stage = 6mA.

5D. Line level preamp input stage, 2 channels at 7mA = 14mA.

5E. Power amp input tubes, 2 channels at 8 mA = 16mA

5F. EL84 in triode in LTP,  2 channels at 24mA = 48mA.

Total Idc for other uses = 118madc.

Total DC POWER for other uses
= max Vdc x Idc = 520V x 0.118A = 62Watts ( nearest whole Watt ).

If the other use B+ currents are kept constant for all values of B+ Vdc,
then Iac is highest in HT winding where Vac is lowest at 140Vac.
Iac = Power / Vac = 62W / 140V = 0.44Amps rms.

Total Iac wanted from HT winding = Output tube Iac + other use Iac
= 1.2 Amps + 0.44Amps = 1.64Amps.

(7) Summary of secondary windings and VA.

Step 2. Filament Heater windings, 4 x 6.3V x 4.0A = 101VA. 

Step 3. Anode HT for output tubes, 200V x 1.2A, = 240VA.

Step 4. Anode HT for other inputs etc, 200V x 0.5A = 100VA

Step 5. Negative voltage bias 50V x 0.26A = 13VA.

Sub total of VA for all secondaries = 454VA.

(8)  Calculate primary input VA and the nominal rating for the transformer.
Allow 6% of the secondary power to be wasted as heat produced in the
winding resistance and GOSS core.
Note, losses depend on the Bmax, ie turns per volt and magnetic properties
of the core.
Bmax should NEVER BE HIGHER THAN 0.9 TESLA for any transformer
used in hi-fi amps, even when using GOSS. Keeping Bmax < 0.9 ensures
the transformer will be quiet and free of vibration and more likely to run cooler
even if the core is low grade, especially if it is re-cycled material from old
stocks made 50 years ago. If the core has max permeability µ < 3,500 at
50Hz and 0.9Tesla, it is low grade high loss material and total losses should
be assessed at 10%.

Calculate loss VA and Primary VA :-

Losses = 6% with GOSS. Loss VA = 6% of secondary VA = 0.06 x 454 =27VA.

Input primary VA = secondary VA + losses = 454 + 27 = 481VA.

(9)  Calculate the wanted pair of two mains primary windings with taps.

Primary windings should be suitable for use with mains voltages used
internationally and mains frequencies of 50Hz and 60Hz.
50Hz is the Australian and UK and European frequency, 60Hz is the USA frequency.
The design at this website is based on 50Hz, and will work OK where mains is 60Hz.
( If the design was based 60Hz, and the PT is used with 50Hz, the noise and core loss
heat increases.)

This design allows for use with mains of 110V, 117V, 125V, with 2 windings
paralleled, and 220V, 227V, 235V, 242V, 250V if windings are in series.
Many amplifiers such as made by Audio Research Corp ( who should know better! )
have only two mains windings of 110V each, which may suit USA conditions when
paralleled. But when used in series the mains should be 220V, which may suit China,
but here in Australia, mains is often measured at 255V even though nominal Australian
mains voltage should be 240V. Audio Research amps with 110V mains may have B+
at say +400Vdc, but when used in Australia with seriesed windings meant for 220V
but getting 255V, B+ becomes +464V, and this threatens the failure of electrolytic
capacitors rated for 450Vdc, and also raises bias currents in output tubes thus causing
the idle Pda of each tube to rise to very close to the 42W Pda rating for the tubes.
I have had to repair many ARC amps because of premature tube failure because tubes
run far too hot. VAC amps made in USA have similar problems. Multiple tubes in output
stages do not stay matched as they age, and because of variations some tubes will
exceed their Pda with mains if is too high. Audio Research make things worse by not
having grid bias voltage individually adjustable for each output tube.

Calculate current rating for mains windings when windings are used with minimum
expected mains voltages.

Minimum mains voltage = 110V.

Calculate Input current for calculated input VA, Iac = Input Va / mains voltage.
This case Iac = 481VA / 110Vac = 3.37 Amps rms.

Calculate current in each of the two primary windings:-
Two 110V windings are in parallel, then current in each = total input current / 2 = 4.37 / 2
= 2.2 Amps.

Wanted primary windings = 2 x 125V x 2.2 Amps, each with taps for 117V and 110V.

(10)  Calculating Afe size for the transformer so :-
10A.  PT will NOT heat up more than +10Cdegrees above ambient,
10B.  PT remains silent especially where we have a rectifier connected,
10C.  PT can sustain a fault condition for 4 hours or indefinitely with 50% higher than
normal current for any winding, and / or 20% higher than usual  mains voltages.

Calculate required transformer central core leg area, AFe, in square mm.
Afe = Tongue T x Stack S for E&I laminations, or could be build up thickness T x strip width
S for toroidal core or C-core. If the build up of one C-core = 20mm, then a double C-core
transformer with two C-cores side by side, 00, will have build up or T = 40mm.

For about 80 years, the most simple well known equation to determine core size for
mains transformers has  been :-

Afe = sq.root VA / 4.44,

For metric measurement with dimensions in millimetres,
the same old equation becomes :-

Afe in sq.mm = 145 x sq.root VA,
(( Because 1 square inch = 645 square millimetres, and,
645 x A in sq.inches = 645 x sq.rt VA / 4.44.
So constant 4.44 is changed to 645 / 4.44 = 145.))

Bmax =  26.2 x Vac x 10,000 
                    Afe x F x N

Where 26.2 and 10,000 are constants, Vac is Vrms applied across the winding
considered,
Afe = T x S in sq.mm, F is frequency Hz, N = winding turns.

Therefore N = 26.2 x Vac x 10,000 
                          F x Afe x Bmax

For this example, Theoretical Primary turns,
Th Np  = 26.2 x 250 x 10,000   = 447t
                  50 x 3,256 x 0.9

Select wire size required. From step 9 above, primary current = 2.2Amps.
Current density = 3Amps per sq.mm, so required wire section area =
working current / 3 = 2.2 / 3 = 0.733 sq.mm.
Round section area = pye x dia squared / 4 = 0.786 x d squared, therefore
dia d = square root ( Awire / 0.786 ) = sq.rt ( 0.733 / 0.786 ) = 0.967mm.

Examine wire tables for Grade2 wire for nearest Cu wire size and record the oa
diameter with enamel insulation :-
Table for wire sizes, Grade 2 wire, rated 200C max, polyester-imide enamel.

Select wire = 1.0mm Cu dia with oa dia = 1.093mm including enamel.

(13)  Calculate Primary turns per layer, TPL, With T = 51mm, H = 25mm,
L = 76mm :-
TPL = bobbin winding width / wire oa dia. 
Bobbin window L = 76mm, and most plastic bobbins for T51 have cheeks
1.6mm thick plus some clearance is needed of 0.5mm, so available winding width
= 76 - 3.7mm = 72.3mm
and TPL = 72.3 / 1.093 = 66.14.  Fractions of a turn are ignored,
so TPL = 66 turns.

th NLp = th Np / TPL = 447 / 66 = 6.77 Layers.
Fractions of a layer are best avoided, and round th NLp to nearest full layer,
this case, actual layers would be NLp = 7 layers.
( if thNLp calculated was say 6.35 layers, round down to 6 Layers. )
Possible primary turns Np = NLp x TPL = 7 x 66 = 462 turns.

TWO identical primary windings are required, so each 1/2 primary = Np / 2,
= 462 = 231t, less 2 turns for creepage between 1/2 layers, so each 1/2 Np
= 229t, thus

Np = 458t.

Calculate P winding height :-
Insulation layers for primary are 4 x 0.05, 2 x 0.5 = 1.2mm.
Wire = 7 layers, 1.093 high = 7.651mm.
Total P Ht = 8.851mm.

Total P + S Avail height
= Window H - ( bobbin bass thickness + clearances + 1.6mm
between P and S + clearance 1.6mm between last on winding and core )
= 25 - ( 1.7 + 1.6 + 1.6 ) = 25 - 4.9 = 20.1mm.
Calculated for P or S = Total avail ht / 2 = 20.1 / 2 = 10.05mm.

Is P winding wire + insulation height more than available height? yes or no?

No, calculated P + insulation height does NOT exceed available height,
and details of primary winding can be completed.

For the DIYer or small manufacturer there several choices for core material :-

19A. Grain Oriented Silicon Steel E&I laminations, known as "low loss GOSS lams."
It is also known as CRGO, Cold Rolled Grain Oriented, and also as M6.
This steel sheet material has about 4% silicon content, and has been cold rolled then
annealed to align the crystalline structure mainly in one direction to raise
permeability, µ.
E&I laminations using GOSS for most applications usually have thickness of 0.35mm.
Thinner laminations are made but not available in small quantities.
Wasteless pattern GOSS lams can give µ up to 17,000 when maximally interleaved,
and very low core losses when used for mains transformers. Distortion in audio output
transformers is usually much lower than produced by the tubes, even at low F where
distortion is maximum.
Bmax of power transformers using GOSS can be as high as 1.5Tesla but then distortion
currents become high and there is vibration, noise and increased stray field radiation
which may not matter for industrial applications but for hi-fi amps Bmax should not
exceed 0.9 Tesla.
I don't sell any transformer parts and GOSS E&I price may be $30 per Kg, if ever
you cab find someone able to sell say 15Kg for a typical 2 channel audio amp
project.

19B. Non grain Oriented Silicon Steel E&I laminations, known as "medium loss
NOSS" and as M19 has about 3% to 4% silicon content but has not had the additional
rolling and heat treatments to increase its µ which is seldom above 3,500.
The thickness of the sheet metal is more than GOSS and its losses are high compared to
GOSS and power transformers run hot. To minimize core heating the Bmax might be
0.7Tesla and should never exceed 0.9 Tesla which means the power transformer stack
may be 33% higher than if using GOSS. Distortion in OPTs with NOSS is also always
higher especially at low F but nevertheless still not higher than distortion in tubes and
reduced with negative feedback.
Price is about 1/2 the price of GOSS, but it may be found in old unwanted transformers
which may be heated in a small wood fire until all plastics and varnish are decomposed
and then dismantled easily and re-used. But beware, because some old material has
extremely poor quality, so you need to test a sample for its permeability before use.

19C. C-cores are made by winding a long strip of GOSS around a steel bar which has a
section size equal to the core winding window. While winding it, epoxy glue is applied
and after being wound to a wanted "build up" thickness, the core glue is allowed to
cure. The core is then removed from the bar former, and you have a rectangular
"ring" of coiled strip well glued together. This is then sawn in half and sawn surfaces
ground smooth. You then have two C shapes. These can be brought together after
inserting one leg into a winding, and you have a single C-core transformer. More
commonly, 4 such Cs are used to make a "double 00" type of transformer. The Afe
required for C-cores is the same as for any other GOSS transformer, but the ratio of
winding window size to Afe is higher than wasteless pattern E&I, so copper wire size can
be increased and overall heat losses reduced for a total weight of transformer.
Prices for GOSS C-cores can be $30 per Kg.

19D. Unicore made by AEM in Sth Aust, with GOSS sheet material.
This form of core is far more difficult for the DIY person to use successfully, and usually
unavailable in small quantities.
5. Toroidal cores. Toroidal cores are made by winding a circular spiral coil of GOSS material.
It is almost impossible for the DIY hobbyist to successfully use unless he has an expensive
special toroidal winding machine.
19E. Amorphous cores. These are strip wound C-cores using high falooting techniques with
special alloys. I can't find any raw data or samples except that it is said they saturate at a
low Bmax, but have heat losses less than 1/2 that of GOSS. They are becoming popular
in the heavy power industry where multi kW or MW are involved. No need to use them.
They are said to be very brittle, and dropping a transformer could ruin it.

19F. Nickel - iron alloys are very expensive, and difficult to source and use is not justified for
a power transformer.  

I base my design ideas on using GOSS E&I laminations or C-cores, or NOSS if you are
poverty stricken, and you don't mind wasted heat and high weight.

Where there was a temperature rise of 15 degrees C above ambient for a generously
designed power transformer with NOSS, the same sized core in GOSS with the same
winding will perhaps give a T rise of less than 5 degrees C after 4 hours. The T rise
for the GOSS will be mainly caused by the copper losses being far greater than the
core losses.
Toroidal transformers are nearly all spirally wound coils of GOSS which have an iron µ
of perhaps up to 40,000, because there is no change in direction to the crystalline grain
which happens in assembled E&I cores. The grain direction affects the magnetic
properties, and the more crossings of grain and joint gaps, the lower the effective µ
of the iron.

For most transformers in audio equipment the B should be kept below 0.9Tesla, and
not up at 1.3 Tesla which is typical for industrial/PA amp applications where the noise
and heat losses may be of little concern.
The audio amp power transformer needs to work silently and stay cool, and also be
well enough naturally regulated. The hi-fi audio gear E&I power transformer will thus be
larger and heavier than the mass market industrial grade transformer designed by
accountants with poor appreciation of hi-fi gear requirements.
_______________________________________________________________________

VA  =   4.44 x B x F x I x ff x Sf x T x S x L x H        
                               1,000,000

Where :-
VA = Input volts x amps, or watts rating of the completed transformer,
4.44 is a constant for all equations and minimum grades of iron.
B is the magnetic field strength in Tesla, and we should aim for B = 0.9 Tesla for quiet running,
F is the frequency of the mains,
I is the current density in the copper, and we will allow 3.0 amps per square mm ACu,
ff is the fill factor, ie, ff = Total cross sectional area of all copper wire in window / L x H,
which usually ranges from 0.25 to 0.45, where primary ACu = secondary ACu.
Sf is the stacking factor of the laminations, since there is a coating of insulation, so about 0.95,
L is the length of the core winding window, mm,
H is the height of the core winding window, mm,
T is the core tongue width, mm,
S is the core stack height, mm,
1,000,000 is a constant for all equations.

This equation was supposed to suit all types of cores, including those which are not
wasteless pattern E&I.
Toroidal cores are not included because the window sizes of L and H don't exist,
and some other formula for Toroidal cores must be used. I don't have one at this
website.

The above formula has problems, and I now suggest nobody use it.

20B. Let us go back to the basics from which the above formula was finalized in 1984.

A = sq.rt VA / 4.44, where A is Afe square section in sq.inches, 4.44 is the required constant,
VA is Watts, or Vrms input x Current Amps rms input.

Other factors affect VA rating.
For the old transformer formula to work about right a few assumptions must be made and
these are :- Sf = 0.95, F = 50Hz, Cu I density = 3A/sq.mm, ff = 0.30, and Bmax = 0.9 Tesla.

In older transformers, thick paper insulation was used between all layers, and wire was kept
further back from core on each side of traverse winding width so ff was rarely more than 0.3.
The ff could be 0.4 higher using polyester insulation polyester-imide coated and thin walled
plastic bobbins.
Just increasing the copper area x 1.33 times means current can be increased 1.33 times.
If VA = V x A so something built on old formula to give 480VA would have 638VA if the
ff can be increased x 1.33. Despite the same current density, There would be 1.33 times more
heat generated, but its offset by lower core heat using GOSS, so the overall T would not rise. 

One factor limiting VA is the heating expected in the core, but GOSS avoids the problem.
Therefore, if the ff is better and and GOSS core material is used, the 4.44 constant for low
grade iron could be increased to 5.0.
Therefore we get Afe = sq.rt VA / 5.0, so VA = 25 x A squared, in sq.in.

This becomes Afe = 129 x sq.rt VA if Afe is in square mm. But the Afe must have a square
section with selected T no less than theoretical T = square root Afe.
So VA = Afe squared / 129 squared = Afe squared / 16,641.
Where T = S, VA = T to 4th power / 16,641.

Now what if the equation included all 4 dimensions, T, S, L, H?

For wasteless E&I lams, T x S x L x H = 0.75 x T to 4th.
Therefore T to 4th = 1.333 x T x S x L x H which can be expressed as
T to 4th = 1.333 x Afe x L x H.

Therefore VA = 1.333 x Afe x L x H / 16,641 ie,
VA = Afe x L x H / 12,512.

Testing this with Afe = 3,180, T = 51, S = 62.5, L = 76, H = 25,
VA = 3,180 x 76 x 25 / 12,512 = 482, which is very close to VA calculated for design
example in steps 1 to18 above!

If all we knew was VA needed, and we wanted to know T

Now the original equation was Afe = 145 x sq.rt VA, and T = S so T = sq.rt ( 145 x sq.rt VA )
so T = 12.0 x 4th root VA.

Testing, VA = 480, then T = 12 x 4.68 = 56.2mm, which is what we calculated above,
where B = 0.9 Tesla, F = 50Hz, current density = 3.0 amps per square mm,
ff = 0.3, Sf = 0.95.

All these nominal items could be included in equation as divisors and actual values used
as factors, and Afe squared = 0.75 x T x S x L x H, so

VA  =   B x F x I x ff x Sf x 0.75 x T x S x L x H      
         0.9 x 50 x 3 x 0.3 x 0.95 x 12,512

=   B x F x I x ff x Sf x T x S x L x H 
                481,399.2
VA =   B x F x I x ff x Sf x T x S x L x H 
                         641,700

With B = 0.9, F = 50Hz, I = 3Amps, ff= 0.4, Sf = 0.4, T = 51, S = 62.5, L = 76, H = 25,
VA =   0.9 x 50 x 3 x 0.4 x 0.95 x 51 x 62.5 x 76 x 25  
                           641,700

= 484 also VERY close to what we calculated above.

Now, Electronics & Wireless World October 1984:- 

VA  =   4.44 x B x F x I x ff x Sf x T x S x L x H        
                               1,000,000

This IS wrong, and the constants 4.44 / 1,000,000 can be stated as 1 / 227,272,
and therefore if you calculated VA using B, F, I, ff, Sf as used just above, the VA would
be roughly 3 times 480. I think the magazine needed better proof reading, and it did
lead me astray when I included it in earlier versions of this page.

20C. So the correct full VA equation is :-

VA =   B x F x I x ff x Sf x T x S x L x H 
                               641,700

Now for those wanting B = 0.9, F = 50Hz, Id =3, ff = 0.4, Sf = 0.95, then
VA =   51.3 x T x S x L x H  
                  641,700

= T x S x L x H / 12,508, and 12,508 can be rounded to 12,500,

VA = T x S x L x H / 12,500.

Testing, if selected T = 44 for wasteless E&I, and VA = 480  and we wanted to know S,
then 480 = 44 x S x 66 x 22 / 12,500 = 5.11 x S, so S = 480 / 5.11 = 93.9mm, close
to what was calculated in step 11 - A above.

Calculating S for T = 62.5 we get 480 = 62.5 x S x 93.75 x 31.25 / 12,500
= 14.6 x S, so S = 480 / 14.6 = 32.8, also what we calculated above in step 11C above.

20D. What about C-cores? C-cores often have a larger window for a given Afe than
E&I wasteless pattern. For example, a double C-core might have build up of each C-core
= 16mm, so T = 2 x 20 = 40mm. The window in each C-core for the build up may be 76 x 25.
if we want VA = 480, then all we need to know is S, the strip width of the wound C-core.

VA = 480 = 40 x S x 76 x 25 / 12,500 = 6.08 x S, so S = 480 / 6.08 = 78.9mm.

Afe = 40 x 78.9 = 3,157, close to wanted Afe of 3,180 calculated in design example above!

You will find the C-cores are lighter than E&I lams, unless they had similar relative core
dimensions of T, S, L, and H.

Now GOSS can be made to run at higher Bmax than 0.9, and makers quote maybe
1.5Tesla and VA rating for C-cores is often based on this which simply means less turns per
volt are used, so wire can all be thicker to take more current, and you can
get say VA = 666 for the same core rated for 480 with B at 0.9Tesla. But I don't like
using such a high Bmax, so C-core manufacturer data is all best ignored,
and the transformer designed by first principles as outlined in the above example.

In mains transformers the core heating is mainly due to hysteresis losses in the core.
There is a formula which relates the "cosine of the current phase angle to losses" but
that's all too difficult  for you to remember, and all that is needed here is to focus on the
practical, and the above set of steps for design to give you a fairly cool transformer
even with relatively high iron losses if you have B < 0.9 Tesla.
The Radiotron Designer's Handbook, 4th Ed, page 234 gives some figures to use to
estimate core losses for various E&I laminations from an old maker's product called
Silcor which range as follows:-
4% Si steel,  :- 1.32 watts per Kg @  B = 1 Tesla,   2.34 watts per Kg @ 1.3Tesla.
1% Si steel,  :-  2.97 watts per Kg @ B = 1 Tesla,   5.04 watts per Kg @ 1.3Tesla.

So for the design example with core weighing 7.8Kg, and 4% Si, and Bmax 0.9Tesla,
expect losses = 1.2 Watts / Kg = 9.36Watts = 2% for VA = 480W, If the copper losses
were 5%, heat = 24W, and total losses = say 34Watts. 
If you work out the surface area of the transformer, then for the example above
it is about 600 sq.cm, and if the losses are 30Watts, then you have 20sq.cm per Watt.
One might say this should apply apply to all transformers you make. This area
per watt is only 1.75 inches square, not much, but an area of iron that large should
radiate 1 Watt OK without rising in Temp too much. Air flow around the core helps.
The chassis may not help much at all because the transformer may be mounted with
an air gap and rubber washers to reduce vibration and allow the air flow.

Some laminations I have re-cycled from old transformers obviously had high iron losses
because the iron had a low Si content and it was not rolled and heat treated much and
got hot after a few hours of use, ie, about 20C above ambient, which means that if
the room temp is 30C on a hot summer evening, the PT runs at 50C, and you cannot
keep a hand on the core.
The best E&I lams or C-cores have more Si content and better rolling and heat
treatments and have lower core loss figures than the best in the above list.

So if you wind a transformer to the above formula with the poorest of NOSS iron,
it will work quite OK but don't be surprised if the temperature rise is a bit too high.

Nothing except the tubes should be too hot to keep a hand on in any amp you build.
Using the same amount of GOSS with the methods above won't give you a smaller
transformer but it sure will be cooler. Before using some laminations taken from some
ancient transformer, the µ should be tested with Bmax at 0.9Tesla and it should be
above 3,500. if this is the case, the heating should not be severe. But so often some
old iron measures µ = 2,000, and its only good for a choke.

20E. Some facts.

Density of GOSS = 7.6 grams per cubic centimetre.

From my private data file on Sankey Laminations,
they list four types of  steel lamination sheet used for iron cored inductors and transformers,
and list them as follows, with the first 3 being non grain oriented cheapest grade steel.

20F. Magnetizing current, iron µ check.

The primary inductance can be calculated if one wants to predict what the
magnetizing current flow is in the core with no secondary loading,
or the µ of a sample of iron can be calculated if inductance is measured.

Lp =   1.26 x N x N x T x S x µ  
            1,000,000,000 x ML

Where
Lp = primary inductance in Henrys,
1.26 = a constant for all equations,
N = primary turns,
T = the tongue width,
S = stack height,
µ = the permeability of the core, not usually mentioned by manufacturers, but can be
measured. 1,000,000,000 = constant for all equations,
ML = magnetic path length in mm.

µ = core permeability, and is the number of times a given magnetic core increases
the magnetic field strength compared to the given winding wound without any core.
An air cored inductor has µ = 1.0

µ varies with the frequency of operation, reducing as F increases and varies with
the applied voltage, and always considered below voltages causing saturation,
and without any load currents.
The variations of µ with applied voltage and frequency are non linear.  

In the case of GOSS Sankey material, for 0.9Tesla, and 50Hz, µ = approx 17,000.

For 480VA in design example, Np = 458turns , Afe = 51 x 62.5, ML = 280mm, µ = 17,000. 

Lp =   1.26 x 458 x 458 x 51 x 62.5 x 17,000  
                     1,000,000,000 x 280
       =  51.15 Henrys.

At 50 Hz, this will be a reactance XLp = Lp x 6.28 x F,

Where
XL =  the reactance of the primary inductance, in ohms
6.28 = 2 x pye, a constant for all equations,
F = frequency of operation.

Design example, XLp = 51.15 x 6.28 x 50 = 16,060 ohms.

If there is 250Vrms at 50Hz applied to the primary, magnetizing current flow = 250 / 16.06k
= 15.6 mA, a tiny flow, and much better and lower than if we used lower grade iron
which may have µ = 3,500 thus giving 75mA.

20G. To find the µ for unknown quality iron for a given applied mains voltage at 50Hz, a small
test winding of say 200 turns with 0.5mm dia wire is made on a temporary bobbin to allow
a 12mm stack of sample lamination material inserted into the winding with maximal interleaving.
Taping the laminations together with masking tape is sufficient for the test.
Using a resistance in series with the coil of 1k0 x 5W, voltage is applied from a variac from
the mains through the coil + 1k0 while monitoring the wave form and distortion on an
oscilloscope.
One begins the test setting the variac low at say 2Vrms, and measuring Vac across the coil
and across the 1k0, and recording both in your exercise book.
The voltages are recorded at 4V, 6V, 8V, 12V, 16V and so on until distortion current
observed just exceeds an easily visible 20%, which appears as "wings" off + and - wave peaks.
Armed with the listed VR, and VL, the reactance of the coil can be worked out for each pair of
voltages, and a graph drawn of the coil reactance. XL = VL / IL.
Current in L = voltage across 1k0 / 1k0. Therefore
XL = 1,000 x VL / VR.
The graph will have XL marked along vertical axis and applied coil voltage on horizontal axis.

With GOSS, you should plot an arched shaped graph of XL. The graph will start from XL = 0.0
and VL = 0.0, rise rapidly, and then plateau, and begin to fall, as the iron begins to saturate.

From the test graph you can SEE where XL is at a maximum, because inductance is at a
maximum, and from the inductance you can find the µ because you have all other quantities for
insertion into the inductance equation.

You can also work out Field strength B in Tesla because you have applied Vac, Afe,
frequency and applied voltage and a known number of turns.
You should find that the B is between 0.6Tesla and 0.9Tesla at the top of the arched graph where
L is maximal, and distortion currents are low. If the test is done with low grade material the
distortion currents will appear to be far higher.

One can apply a similar test to any inductor or choke, with or without an air gap or DC flow in a
similar manner to unlock all the secrets of the inductor performance and qualities.

If some second hand laminations have become available for use there is no problem with their
re-use in newly made transformers or inductors providing the iron µ is high enough to allow
the use application without generating clouds of smoke. Hence with second hand iron,
the above testing is essential. The magnetic properties of iron from old transformers does
not change over time GOSS or NOSS. Roasting an old transformer in a wood fire to dull red
heat to get rid of plastics and varnish to make it easy to pull apart does not affect the µ.

(21) About winding.

21D. Fasten loose ends as you wind.
During wind up on the lathe, the emerging ends of windings should be secured around screws
placed in plywood plates clamping bobbins tight on their mandrel. Coordinate this carefully,
lest you end up in mess, or yank an end of a winding and break a wire, which utterly negates
your work.

21E. Label all taps and winding loose ends.
All winding taps and winding ends should be labeled with a piece of masking tape and felt pen
with numbers for mains voltages and letters for secondaries, as indicated on the winding diagram.
When winding is complete, the labelled wire ends make it easy to terminate the wires on a board.

21F. Minimizing bulge.
As you wind wire and insulation around a rectangular bobbin shape, neither wish to lay perfectly
flat and all will try to spring up, so that if the winding became say 200mm high, all windings would
become almost circular. Hence the need to allow some extra room in the bobbin to accommodate
some bulge.
If epoxy varnish is applied during bobbin winding work, then it is wise to cramp completed
windings between a pair of plywood blocks and a G-cramp to ensure the winding height will
fit in the core window during assembly. When the day's winding is done, blocks and clamp is
applied, and bobbin left to cure for 2 days before removing off the lathe. The whole winding
should harden and all appear well glued together. After clamping, excess epoxy will leak out
everywhere and make a mess. Its OK, clean up with lots of kitchen tissue paper.
If varnish is applied later after winding everything, the varnish will be electrical type requiring
soaking and maybe vacuum impregnation and heat baking.
The winding should be cramped up between plywood blocks fitting neatly between bobbin cheeks
and left over night. Usually some minute amount of "give" occurs in that time, and total winding
height is reduced when clamp is removed. You should find bulge is not enough to prevent
the winding fitting into the core window.

21G. Avoid tangled wires.
What can tangle, does tangle, and what can kink, does kink, and always its because wires being
unwound off the end of a spool resting on the floor become twisted as you go. Spools of wire
should always be placed under your bench on a greased dowel through a bench support leg
or on some sort of stand that allows wire to roll off the spool and not develop twist. Twist
causes loops, and loops pull tight as the wire goes though your hands, and you get a sharp
wire kink. Sometimes wire will just break. If so, unwind back to the start of the layer and chuck
out the unwound wire, solder a fresh wire end from spool, leave the join outside the bobbin,
and proceed, it can later be folded down out of the way. Kinks when straightened out can later
fatigue and that's where a wire might fuse open but kinks are not always bad enough to warrant
a wire join. Practice with winding chokes gets you use to winding without kinks, or using too
much wire tension. Practice will make what seems difficult at first seem easier later.
If you want to be a barbour, don't expect praise of payment for the first few haircuts.

21H. Sleeve again before soldering wires.
Before soldering wires to terminals, use sleeving from back of terminal to bobbin wire exit if wire
sleeving applied at in-out points isn't long enough to get to the terminal.

21O. Potting.
Potting is an additional process I sometimes use after varnishing to make a transformer or
choke mechanically quiet, and to add some magnetic shielding.
I make a sheet metal box with suitable 1mm thick sheet steel. I set up the tranny ( or choke )
inside the pot so it is bolted in but also with provision for bolting all to a chassis.
To bolt the potted transformer to chassis, bolts are screwed upwards into threads on yokes
because there is no access to nuts for bolts. Aluminium yokes on transformer should have
a strip of 3mm steel bar bolted onto topside of Al yoke flange and glued with silicone.
Pilot holes for M5 or M6 bolts are drilled through Al and steel so that the bolt is unlikely to
ever strip the thread in Al + steel. Al alone is just not good enough. Bolts used can in fact
be phillips head screws, and easily wound in or out.

I do not recommend that power transformers with low grade E&I cores ever be potted because
they run hot without any pot, and when in a pot they run even hotter because the pot acts as a
blanket around the transformer. Potted transformers should only have GOSS cores.

The best "potting compound" is a two pack mix of bulk liquid plus a small amount of hardening
agent. Its wanted properties are that it cures to a dense rubber like solid, and is not highly
exothermic, ie, the curing reaction does not cause it to heat up. It is wanted to bond well to all
metal and plastic and remain liquid long enough to allow air bubbles to escape.

The transformer with pot is placed on a level bench upside down. Place holding bolts into the
4 bolt holes with bolts turned in further than they ever will when bolted to a chassis. Mix a batch
of potting mix less than total required and pour in, avoiding any terminal boards. Mix and pour
additional batches until the pot is very nearly full.
Leave undisturbed for 24 hours. Then remove bolts. They should come out OK because the
potting mix bond isn't strong enough to lock the bolt in.

Once a transformer has been potted with proper potting mix, it is sealed in forever. If the
transformer fails later, it is extremely difficult to remove it from the pot without damaging the pot,
so don't even bother trying to save the pot, just chisel or saw off the metal pot, and then chisel
off potting mix where you can, remove Al yokes, remove bolts, terminal boards, and heat the
transformer to dull read heat so that all plastics will decompose and you can re-use the core
or whatever else you can. The copper goes to the recycle guy.

The next best potting method uses a small amount of spray-can varnish, epoxy casting resin,
and well washed and well dried fine sand. The transformer is bolted inside its pot, making sure
there is a gap at least 10mm between pot and any part pf transformer except where bolts and
spacing washers are used. Chassis bolts are wound in further than needed.

Sand can be plain "washed river sand" usually available where there is a concrete mixing
plant in an industrial area, or from a landscape material supplier. Just arrive with a couple of
20 litre buckets and offer the guy $10, he probably will say yes. Wash the sand again
at home and then dry in old electric fry-pan left on at 250C for a day. Allow to cool, and keep
sand dry. The washing removes organic muck and possible salt contamination.

Set up transformer on level bench and in pot with hold bolts turned in. If the pot has its finished
coat applied, use masking tape and paper to avoid damage on outside. Pour in dry sand to
about 1/4 full. Use a small hammer and block of wood held against outside of can at bottom
of sides to vibrate sand and make it compact under transformer. Add more sand and continue
hammer compacting with many little blows. When you get sand up to 15mm below the pot
top lip level, and you can't get it to settle any lower with vibration, then you have used the
required dry sand. Make sure you keep the level of sand just below bolt ends which you
screwed in. Adjust sand level at bolts with an old spoon, dowel, pencil etc.

Apply some varnish from spray can to wet the sand surface in the pot. Not too much, as this
varnish will soak into sand maybe 10mm. Leave to dry for a day. The idea is to seal the dry
sand surface and prevent subsequent penetration by liquids.

Once the sand surface is sealed, make some concrete using 50% epoxy resin with its hardener
plus 50% dry sand. This goopy stuff is then poured into the last 15mm of pot height. You will
find it messy to use, but it will find its own level, and the liquid epoxy won't seap out wet
concrete to dry sand below. This 15mm layer will form a very strong hard plug which helps to
hold transformer to pot, and ensure internal dry sand cannot run out later. The sand is very
cheap, and with the concrete, you don't use much resin. Leave to harden for 24 hours at least.
Bolts can be greased before use which aids their easy removal later.

If the transformer fails later, its usually possible to use an old 10mm carpenter's chisel to chop
out the 15mm "plug" and dry sand will just pour our, and pot holding bolts removed, and the
pot might be used again, although the varnished transformer is PIA to re-wind.

The next best potting method involves using hot molten roof pitch heated to about 200C.
The transformer is bolted to its pot, then heated to about 60C and placed on the bench upside
down. You need an old electric stove and pot. Using a gas ring could be deadly if you spill
the pitch and things catch fire. Have a water hose ready. But you need to begin heating the
bulk block pitch first. It begins to smoke when it has become very liquid. DO NOT do it indoors.
Smoke is not totally toxic though. Pouring liquids at over 150C is DANGEROUS so put two
pairs of trousers on, use two old long sleeved shirts, and leather gloves and face mask.
Don't blame me if you burn yourself.
With transformer nicely warmed up at 50C at least, you pour in the pitch and it should flow
well around the transformer. When it settles against cool surfaces it will begin hardening
immediately. Don't try to rush the process. The amount of pitch at 150C is far less than the
transformer weight so the transformer won't get much hotter when the pot appears to be full.

Roof pitch has a higher melting point than Road pitch. Both are known as tar, or emoleum
or by some trade name, and both are byproducts of petroleum refining or coal refining.
The Roof pitch becomes harder than road tar at room temp, and is unlikely to run out of
the pot unless temperature exceeds 60C. Buying roof pitch isn't easy, and it comes in 20 Kg
blocks which can be chopped into pieces with a tomahawk to suit a cook pot.
But Road pitch is quite liquid at 60C, and will drip at 30C, and thus will run out of a pot
if a transformer becomes hot which can occur on hot days in a hot climate area.
KNOW what are the properties of what you might use. Some might say that using a mix
of sand and road pitch is OK, but I've never tried it. I have no idea what might be added to
road pitch to raise its melting point. I have used the roof pitch on a couple of projects
but I now favor the sand fill method.

With small transformers, potting only with resin concrete is quite OK. Small pots are
easily made and pop riveted together. But silicon needs to be applied inside to stop
liquid potting mix leaking out. After a couple of failures and OOPS moments, you
will learn to think before doing anything.

21P. Bell Ends instead of potting?
Many amplifiers have their transformers fitted with "bell end" covers bolted over transformer
windings. They are not always easy to source. The die hard dedicated metalworker will
make his own, and others will rob them off old transformers. They don't lessen any noise
a transformer might make not reduce all stray magnetic fields. They do replace transformer
yokes though. Only one per transformer is needed if the one side of the winding with a
terminal board is allowed reach through a rectangular hole in the chassis, so that the
transformer is "flat mounted" Where transformers are "edge mounted", and maybe with
bell ends with lugs for bolting to a chassis, then all wires are brought below chassis top
level to a board. This method gives maximum real estate available to all the other stuff
under the chassis.

21Q. Open frame?
This method uses yokes for all wound items, and is easiest, and edge mounting gives
maximum under chassis space. Often there is room above chassis and near PT to place
diodes or caps as well. What is NEEDED is a sheet metal cover box, lest you wake up
one morning to find a child has been electrocuted.
Metal transformer covers MUST be well bolted or screwed into position in the same
manner as covers over vacuum tubes. There is a trend to use 4mm banana plugs
and recessed sockets to secure chassis cover boxes. Don't let me catch you doing it!
if a transformer is dropped, or being carried or moved when power has been left on,
and a cover comes off, someone might get electrocuted. Don't ever try to tell me shit
does not happen. Transformer cover boxes should have some ventilation holes 
placed high up in box sides and less than 5mm dia, and away from dangerous voltages
inside the box. Steel boxes near power transformers may vibrate with stray field, and
the only way to minimize it is to use 3mm aluminium, or drill lots of holes where most
noise is generated. Sometimes fixing fibre board to inside surfaces helps along with
rubber pads so the top of box sits tight on transformer when box is screwed tight.

22. Winding losses.
I could calculate the winding losses, but when all windings are rated for close to 3A/sq.mm,
there is no need because winding losses will always be OK.
Copper losses for each winding = DC resistance x I squared.

I suggest I leave that for you to check out, and if you come up with a better lower
loss transformer, itemize your findings to argue your case with me.

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