(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 :
B+
supply Vdc Range Ea with Fixed bias, Ea = B+. 
360 
400 
440 
480 
520 
Idle
Pda each KT120, Watts 
40 
40 
40 
40 
40 
Idle
Pda, 4 x KT120, Watts 
160 
160 
160 
160 
160 
Idle
Idc = max Idc, ea KT120, mAdc 
110 
100 
90 
80 
70 
Idle
Idc all 4 x KT120, mA 
440 
400 
360 
320 
280 
Vac
for HT winding, Vrms approx 
140 
155 
170 
185 
200 
Pdc from PSU at max Idc, Watts  160 
160 
160 
160 
160 
Iac
for HT winding, Amps rms 
1.2 
1.1 
1.0 
0.9 
0.80 
Class
A PO max, One Channel, Watts 
34 
35 
36 
37 
37 
B+
supply Vdc Range Ea with Fixed bias, Ea = B+. 
360 
400 
440 
480 
520 
Idle Pda each KT120, Watts  28 
28 
28 
28 
28 
Idle Idc, each KT120 mAdc  77 
70 
63 
58 
53 
Max
Idc, AB1, each KT120, mAdc 
150 
150 
140 
130 
120 
Max Idc, 4 x KT120, mA  610 
600 
570 
540 
520 
Vac for HT winding, Vrms approx  140 
155 
170 
185 
200 
Pdc
from PSU at max Idc, Watts 
220 
240 
250 
260 
270 
Iac
for max Idc HT winding, Amps rms 
1.6 
1.5 
1.5 
1.4 
1.3 
Class AB PO max, 2 Channels, Watts  110 
120 
140 
160 
180 
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 hifi 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 recycled
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 Ccore. If the build up of one Ccore =
20mm, then a double Ccore
transformer with two Ccores 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.))
Standard
T mm 
62.5 
51 
44 
38 
32 
28 
19 
16 
Standard
T inches 
2.5

2.0 
1.75 
1.50 
1.25 
1.125 
0.75 
0.625 
Fe
plan area, sq.cms 
234 
150 
116 
87 
62 
47 
22 
16 
Lx H
sq.mm 
2,929 
1,950 
1,452 
1,083 
768 
588 
270 
192 
Bobbin
heights mm 
102, 75, 63  102,
75, 63, 50 
102,
75, 63, 50, 44 
102,
75, 63, 50, 38 
75,
63, 50, 38, 32 
50,
32, 28 
38,
32, 28, 19 
32,
28, 19, 16 
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, polyesterimide 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 hifi
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 reused. But beware, because some
old material has
extremely poor quality, so you need to test a sample for its
permeability before use.
19C. Ccores 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 Ccore
transformer. More
commonly, 4 such Cs are used to make a "double 00" type of
transformer. The Afe
required for Ccores 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 Ccores 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 Ccores 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 Ccores, 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 hifi 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 hifi 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
polyesterimide 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 Ccores? Ccores often have a larger
window for a given Afe than
E&I wasteless pattern. For example, a double Ccore might
have build up of each Ccore
= 16mm, so T = 2 x 20 = 40mm. The window in each Ccore 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 Ccore.
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 Ccores 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 Ccores 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 Ccore 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
recycled 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 Ccores 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.
Product name. 
Watts per Kg, 1.0 Tesla 
Watts per Kg, 1.5 Tesla 
Lycore 150 
1.5 
3.6 
Lycore 230 
2.3 
5.3 
Lycore 350 
3.5 
7.7 
35M5 ( GOSS ) 
not given, is low 
0.97 typical 
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
reuse 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 Gcramp 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 inout 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 reuse the core
or whatever else you can. The copper goes to the recycle guy.
The next best potting
method uses a small amount of spraycan 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 frypan 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 rewind.
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.