behaviours, so the reading and learning experience will be very difficult for the novice.
Unfortunately, the associated reference material listed on pages 252 and 253 has mainly been lost or thrown out of many library archives to make way for the huge mountain of more modern knowledge within which there is very little on output transformers because mainstream development for tube OPTs stopped in about 1959 when the onslaught of transistor amps was well underway.
Not many folks will have RDH4 in their library nor will there be a nearby technical library with easy browsing access so I shall try to unfold the design method I have evolved based on information in the RDH or other sources I have collected over the last 10 years. After having wound many very fine PP output transformers with bandwidth as wide as 10 Hz to as high as 270 Khz, I feel well qualified to speak from experience.
The list of logic steps involved in producing the best possible OPT is based on designing for low winding losses,
core saturation at full power at 14Hz, and adequate interleaving to extend the HF response up to at least 70kHz
by keeping both the leakage inductance and shunt capacitances to low quantities. The end result gives a well filled winding window with several impedance matches possible without having wasted sections of any secondary winding
so the winding losses and response is the same for any of the chosen load matches.
Let us examine the output transformer No1 which was given as an a
recipe
for a good design for a push pull amp of approximately 60 watts in my
page
on 'Output Transformer Theory'.
First I will display the schematic of OPT No1 :-
Fig1
In the older 2002 edition of my website I list steps 1 to 10 to
design
OPT No1. The method was rather vague
and in February 2005 I rationalised the design process
to take all that RDH4 says about OPT design, plus create
a design flow that lists each step actually required to get to a
working design that any transformer winder can actually
use in his workshop without any further calculations to produce an OPT.
The main differences between the 2002 method and the 2006 method is
that winding resistance losses are
factored in early after calculating the primary turns. The
primary winding fill factor of the actual core window size is
limited to to 0.28 x S x T which appears to work with most OPTs.
Until May 2006, I have not seen any computer program which achieves
what
I attempt to achieve by following logic steps and using one's brain,
some intuitive imagination and
a pocket calculator with easy equations.
The design logic flow could be used to construct a computer program
where
one would enter the design requirements such as power, secondary load,
tube Ra, core dimensions, then with a click on a "design" button,
out would come a terrific
design including all the exact wire sizes and a cross sectional drawing
of the bobbin windup details that could be understood easily by
anyone with some winding experience.
Alas, I am not a computer expert, but i can give you the flow of logic
used to get a design finalised.
I invite anyone interested to
prepare a PC program to encompass all the horrible fiddly
details of
fitting the wire
that is available from the suppliers
into the cores available for superb
OPTs.
OUTPUT TRANSFORMER No1 DESIGN EXAMPLE
FOR 60 WATT PP OPT for 5,000 to 6
ohms.
1. Choose tubes,
operating conditions and primary
load for the tubes applied across the
full primary, known as the anode to anode load, PRL, ohms.
**Note. Careful loadline analysis is
required for accurate loading and
is
not in this list of steps.
OPT1, One pair of 6550, UL AB1,
Ea = 520V, Ia q = 60mA approx,
so allow for RL = 5ka-a...........................................................................5,000ohms
2. Choose the
secondary nominal speaker load value.
allow a default value of 5 ohms,
SRL, ohms.
OPT1.....................................................................................................5ohms
3. Choose the
maximum power at clipping for the
PRL chosen above. Max PO for any
class of operation, A1, AB1,
AB2, watts
**Note. The anode to anode voltage swings can be read off the PP
load line
analysis, and PO = ( Vrms anode to
anode ) squared / RL
OPT1. PO =
60w.....................................................................................60w
4. Calculate the minimum required
core centre leg cross sectional area, Afe,
for a nearly square core cross section.
Afe = 300 x
sq.rtPO sq.mm
**Note. This formula
has
been derived from a basic formula
for
core size used for mains transformers, Afe = sq.root power input / 4.4
where the Afe is in sq inches. This ancient formula is based on B being
about
1 Tesla at 50Hz but we would want B max < approx 0.5 Tesla for an
OPT.
After considerable trials the above formula is a good guide for audio
OPT.
OPT1, Afe = 300 x sq.rt 60 = 300 x 7.75 = 2,323
sq.mm........................2,323sq.mm
5. Calculate
the core tongue dimension, T.
For a square core section, tongue dimension = stack height, ie T = S.
T x S = Afe, sq.mm
Therefore theoretical T dimension =
sq.rt AFe = th T, mm
eg, thT = sq.rt 2,323 = 48.2
mm............................................................48.2mm
Choose suitable standard T size from list of available wasteless
E&I lamination core materials.
T sizes commonly available for OPTs :-
20mm, 25mm, 32mm, 38mm, 44mm, 51mm, 63.5mm
**Note. Choosing a
standard T size above thT gives lower copper winding
losses, higher weight,
and choosing T below thT gives higher losses and lower
weight. Afe will be the same for
either 44mm
or 51mm chosen from above so the LF response won't change with tongue
size. HF peformance
depends entirely upon the interleaving geometry and insulations.
OPT1 choose core T =
44mm..................................................................44mm
6. Calculate
theoretical stack height, thS using the chosen T
size.
thS = Afe / T, then adjust to a larger height to suit nearest standard
plastic bobbin size if
available, mm.
OPT1, S = 2,323 / 44 = 52.7mm, but choose
51mm........................................................51mm
7.
Adjusted Afe = chosen T x chosen
S, sq.mm
OPT1, Adjusted Afe = 44 x 51 =
2,244sq.mm.................................................................2,244sq.mm
**Note. Some constructors will
be using non wasteless E&I lams,
or
C cores which do not have the same relative dimensions as E&I
Wasteless Pattern cores.
The actual sizes of the T, S, H, & L of the core to be used
must be confirmed.
8. Confirm the
height of the winding window,
H, mm.
OPT1, 44T wasteless material has H =
22...........................................................................22mm
9. Confirm the
length of the winding widow,
L, mm.
OPT1, Wasteless material has L =
66mm............................................................................66mm
10. Calculate
the theoretical primary winding turns, thNp
Np = sq.rt( PRL x PO) x 10,000 /
Afe = thNp, no
of turns.
**Note.
The formula here is
derived from more complex and complete formula taking B and F
into account. If we assume magnetic field strength B = 1.6 Tesla, and F
= 14 Hz, which is a
suitably
low F for where saturation is commencing, and express V in terms of
load and power,
we get the above short easy equation for primary turns required.
The full formula for calculating B is in step 40 below. The V factor
can be expressed as
sq.root of ( Primary RL x power output ) as in the above simplified
equation.
OPT1, RL = 5,000 ohms, PO = 60w,
Afe = 2,244sq.mm from above,
thNp = sq.rt ( 5,000 x 60 ) x 10,000 / 2,244 = 2,440
turns..............................2,440 turns
11. Calculate
theoretical Primary wire dia, thPdia.
**Note 4. The Primary wire used
for the transformer will occupy a
portion
of the window area = 0.28 x L x
H. The constant of 0.28 works for 99% of OPT.
Each turn of wire will occupy an area = oa dia squared.
Overlall or oa dia is the dia including enamel insulation.
Therefore theoretical over all dia of
P wire including enamel
insulation
= sq.rt ( 0.28 x L x H / Np
),
mm.
OPT1, thoadia P wire = sq.rt ( 0.28 x 66 x 22 / 2,440 )
= sq.rt 0.167
= 0.4082
mm...............................................................................0.4082mm
12. Find nearest
suitable oa wire size from the
tables, oaPdia, mm
OPT1, try oa wire size = 0.414mm, ( for Cudia = 0.355 mm.
)..............................0.414mm
13. Establish
the
bobbin winding traverse
width, Bww, in mm.
**Note 5. Bobbin traverse
width is the distance between the cheek
flanges and varies depending
on who made the bobbin, but each flange thickness = 2mm maximum is
common but could be less.
Where bobbin flanges are not used, and insulation is simply extended to
the
full window length L,
the traverse width will be the same as in the case of of where bobbin does have flanges.
Ie, the winding will
traverse a distance = L - 4mm.
OPT1, Bww = 66 - 4 = 62
mm...........................................................................62mm
14. Calculate no of
theoretical P turns per layer,
thPtpl, turns.
thPtpl = 0.97 x Bww / oa dia from step
12.
**Note. The constant 0.97
factor allows for imperfect layer
filling.
Leave out fractions of a turn.
OPT1, thPtpl = 0.97 x 62 / 0.414 =
145.26.........................................................145
turns
15. Calculate
theoretical number of primary layers, thNpl,
then round down or up to convenient even
number of layers.
Theoretical Npl = thNp / Ptpl,
then round
up/down.
OPT1, thNpl = 2,440 / 145 = 16.68 layers; round down to
16................................16 layers
**Note. Rounding down may
reduce the Npl needed for Fs = 14 Hz.
But the actual turns used will still allow Fs = approximately 15 Hz,
which is ok.
For those wanting to maintain Fs, or have Fs marginally lower than 14
Hz,
the Afe can be increased by increasing S from say 51 mm to 62 mm, and
still use a standard
sized bobbin, and have Fs at 12Hz.
The calculated no of primary layers should be an even number to avoid a
CT in the middle of a layer,
and because each 1/2 primary winding must have an equal number of turns
and a symetrical geometric layout
either side of the CT.
16. Calculate actual
Np.
Np = P layers x thPtpl
OPT1, Np = 16 x 145 = 2,320
turns...............................................................2,320
turns
17. Calculate
average turn length, TL
TL = ( 3.14 x H ) + ( 2 x
S ) + ( 2 x T ), mm.
OPT1, TL = ( 3.14 x 22 ) + ( 2 x 51 ) + ( 2 x 44 ) = 259
mm............................259mm
18. Calculate
primary winding resistance, Rwp.
Rwp = ( Np x TL ) / ( 44,000 x Pdia x
Pdia ), ohms.
where 44,000 is a constant, and P dia is the copper dia from the wire
tables.
OPT1, Rwp = 2,320 x 267 / ( 44,000 x 0.355 x 0.355 ) = 111.7
ohms................112ohms
19. Calculate
primary winding loss %,
P loss % = 100 x Rwp / ( PRL + Rwp ),
%.
OPT1 P loss = 100 x 112 / ( 5,000 + 112 ) =
2.19%..............................................2.19%
20. Is the
winding loss more than 2.5%?
..................................................yes or no.
If yes, the design calcs must be checked again, if no, proceed to 21.
OPT1, P winding loss is less than 2.5%.
**Note. If the P
winding losses are less than 2%, there is a
possibility that the wire size could be reduced
to increase the turns per layer, and possibly reduce the number of P
layers by say 2.
However I rarely find P winding losses will be less than 2% with the
rated load, and one must allow for
where RL = 1/2 the design RL which will double P winding losses.
21. Choose the
interleaving pattern from the list below for
the wattage of the transformer.
All
OPT will have the secondary
sections containing only one layer of wire.
While this may be subdivided into further secondary sub sections, there
are no designs here which require
bifilar or trifilar winding or rectangular wire.
A
section of a winding is defined as a layer or group of layers devoted
solely to P or S.
The term "section" is not to be confused with "layer". For tube
OPT, most P sections will have
more than one layer of wire.
In general, all OPT should comply
with the following P&S layer number relationships :-
Where the first
and last winding on is a primary section, then these sections should
have near 1/2 the layers of the inner sections, hence
if there are 3 outer p layers in a P section, the inner sections might
be either 5, 6 or 7 p layers. When this
guide is adhered to there is the best HF response because the leakage
inductance is fairly evenly and
symetrically distributed.
When starting and finishing with
an S section all internal P sections
should have the same number of p layers
but it is not always possible and having say 2 sections of 4 p layers
and 2 sections of 5 p layers is OK.
The size of such "internal sections" should not vary more than 25%.
Where such guidelines are adhered to along
with equal thickness insulations between P and S sections, there are
minimal problems with resonances at HF.
For transformers to suit low
drive devices such as mosfets or transistors, the same amount of
interleaving is required for a
a given power level. The number of p layers will be reduced as Primary
RL becomes low, and wire dia will increase.
An 8 ohm : 8 ohm OPT with very low dc voltage differences between P and
S would have equal numbers of turns for P and S and perhaps be simply
interleaved so each layer of thick wire is alternatively devoted to
either P or S.
The bandwidth can then be very easily made to go up
to 500kHz. As the primary or secondary load is reduced, the effect of
shunt capacitance diminishes, so insulation thickness can be reduced.
Transformers for
electrostatic speakers which step up the
amplifier voltage between 50 and 100 times need to have good insulation
for voltages involved and need to have lower capacitance. They resemble
PP OPTs powered "backwards" and can be designed with the
method here.
But for matching tubes to normal
3 to 9 ohm speaker
loads, the interleaving list below with the number of primary layers
per section possible will give at
least 70 kHz of bandwidth, and where there is a highest number of
interleavings the bandwidth
can be 300kHz. Using more interleaving than listed leads to less
available room on the bobbin for wire due to too many layers of
insulation, and poor HF due to high shunt capacitances, and higher
winding
losses.
For lower Primary RL and higher amplifier power the larger the OPT
becomes and for a given number of interleavings the
HF response becomes less due to increasing leakage inductance so the
larger the OPT becomes, the number of interleaved sections increases.
So a small 15 watt OPT may only need
3S + 2P sections for 70kHz, but a 500 watt OPT may need 6S + 6P
sections.
LIST
OF PRIMARY AND SECONDARY WINDING SEQUENCE ON THE BOBBIN :-
Up
to 15W, 10 to 20 p
layers.....S - 5p to 10p - S - 5p to 10p -
S
3S + 2P sections
2p to 4p - S - 4p to 8p - S - 4p to 8p -
S -
2p to 4p 3S + 4P
15W to 35W, 12 p layers
.........2p - S - 4p - S - 4p - S -
2p
3S + 4P
S - 4p - S - 4p - S - 4p -
S
4S + 3P
16 p layers..........3p - S - 5p - S - 5p - S -
3p
3S + 4P
S - 4p - S - 4p - S - 4p - S - 4p -
S
5S + 4P
2p - S
- 4p - S - 4p - S - 4p - S -
2p
4S + 5P
18 p layers..........3p - S - 6p - S - 6p - S -
3p
3S + 4P
20 p layers.........3p - S - 7p - S - 7p - S -
3p
4S + 3P
S - 5p
- S - 5p - S - 5p - S - 5p - S
5S + 4P
2p - S
- 5p - S - 6p - S - 5p - S -
2p
4S + 5P
35W
to 120W, 14 p layers...........S
- 3p - S - 4p - S - 4p - S - 3p -
S
5S +
4P
2p - S - 3p - S - 4p - S - 3p - S -
2p
4S + 5P
16 p layers............S - 4p - S - 4p - S - 4p - S - 4p -
S
5S + 4P
2p - S - 4p - S - 4p - S - 4p - S -
2p
4S + 5P
18 p layers............S - 4p
- S - 5p - S - 5p - S - 4p -
S
5S + 4P
2p - S - 5p - S - 4p - S - 5p - S -
2p
4S + 5P
20 p layers............S - 5p
- S - 5p - S - 5p - S - 5p -
S
5S + 4P
2p - S - 5p - S - 6p - S - 5p - S -
2p
4S + 5P
22 p layers............S - 5p
- S - 6p - S - 6p - S - 5p -
S
5S + 4P
2p - S - 6p - S - 6p - S - 6p - S -
2p
4S + 5P
120W to 500W, 10 p
layers.........2p - S
- 2p - S - 2p - S - 2p - S -
2p
4S + 5P
S - 2p - S - 3p - S - 3p - S - 2p -
S
5S + 4P
1p - S - 2p - S - 2p - S - 2p - S - 2p -
S - 1p
5S + 6P
S - 2p - S - 2p - S - 2p - S - 2p -
S - 2p - S
6S + 5P
12 p layers...........2p - S - 3p - S - 2p - S - 3p - S -
2p
4S + 5P
S
- 3p - S - 3p - S - 3p - S - 3p -
S
5S + 4P
1p -
S - 2p - S - 3p - S - 3p - S - 2p - S - 1p
5S + 6P
S - 2p - S - 3p - S - 2p - S - 3p -
S - 2p -
S
6S + 5P
S - 2p - S - 2p - S - 4p - S - 2p - S -
2p - S
6S + 5P
14 p layers..........2p - S
- 3p - S - 4p - S - 3p - S -
2p
4S + 5P
S
- 3p - S - 4p - S - 4p - S - 3p -
S
5S + 4P
1p - S - 3p - S - 3p - S - 3p - S - 3p -
S - 1p
5S + 6P
S - 2p - S - 3p - S - 4p - S - 3p -
S - 2p - S
6S + 5P
16 p layers............2p -
S - 4p - S - 4p - S - 4p - S -
2p
4S + 5P
S
- 4p - S - 4p - S - 4p - S - 4p -
S
5S + 4P
2p - S
- 3p - S - 3p - S - 3p - S - 3p - S - 2p
5S + 6P
S - 3p - S - 3p - S - 4p - S - 3p -
S - 3p - S
6S + 5P
18 p layers............2p - S
- 5p - S - 4p - S - 5p - S -
2p
4S + 5P
S
- 5p - S - 4p - S - 4p - S - 5p -
S
5S + 4P
2p - S
- 4p - S - 3p - S - 3p - S - 4p - S - 2p
5S + 6P
S - 3p - S - 4p - S - 4p - S - 4p -
S - 3p - S
6S + 5P
20 p layers............3p - S - 5p - S - 4p - S - 5p - S -
3p
4S + 5P
S
- 5p - S - 5p - S - 5p - S - 5p -
S
5S + 4P
2p - S
- 4p - S - 4p - S - 4p - S - 4p - S - 2p
5S + 6P
S - 4p - S - 4p - S - 4p - S - 4p -
S - 4p -
S
6S + 5P
22 p layers.............3p - S - 5p - S - 6p - S - 5p - S -
3p
4S + 5P
S
- 5p - S - 6p - S - 6p - S - 5p -
S
5S + 4P
2p - S
- 5p - S - 4p - S - 4p - S - 5p - S - 2p
5S + 6P
S - 4p - S - 6p - S - 4p - S - 6p -
S - 4p -
S
6S + 5P
Record the choice of primary layers in
step 15.
choose a suitable P& S interleaving pattern from the above list.
OPT1, 16 primary layers, 60 watts, choose
...............................................................4S
+ 5P.
22. Choose
insulation, i, in
mm used between primary layers,
mm.
**Note. Usually p to p
insulation for all OPT needs to only be
0.05mm thick.
OPT1, i =
0.05mm....................................................................................................0.05mm
23. Choose
insulation, I, in
mm used between Primary and Secondary layers,
mm.
**Note. Usually,
for where Ea is above 450V, and
RL above 1k, the p to S
insulation is first reckoned = 0.6mm to keep shunt capacitance low with
good enough
insulation.
OPT1, I = 0.6 mm
...................................................................................................0.6mm
24. Calculate
portion of bobbin winding height comprising primary
wire layers, p to p insulation,
and p to S insulation.
height of P+I+i = ( no of layers x
oadia P wire ) + ( no x i ) + ( no x
I ), mm.
OPT1, P = 16 x 0.414 = 6.624 mm,
i ht = 11 x 0.05 = 0.55
mm,
I ht = 8 x 0.6 =
4.8 mm,
Total ht of above = 11.974
mm............................................................................11.98mm
25. Calculate
maximum total available height of all windings on bobbin.
Max wind ht = 0.8 x
H, mm.
**Note. The
constant of 0.8 will suit most OPT.
OPT1, Wht = 0.8 x 22 = 17.6
mm...................................................................................17.6mm
26. Calculate
the max theoretical oa dia of the the
secondary wire
in secondary layers, thSoadia.
max thSoadia = ( max wind ht - [
P+i+I ht ] ) / no of S
layers, mm
**Note. The available height for
secondary layers = maximum bobbin winding height - (
primary + all
insulations ).
OPT1, We have chosen 4 layers of secondary wires. Height from step
24
= 11.98mm
thSoadia = ( 17.6 - 11.98 ) / 4 = 5.62 / 4 = 1.405
mm..............................................1.406mm
27. Find
nearest oa dia wire size less than thSoadia calculated
in step 26.
OPT1, Try 1.351mm oa dia, which is 1.25 mm Cu dia
...............................................1.351mm
28.
Calculate the theoretical S turns per layer, to nearest
turn, thStpl.
Get the Bobbin winding width from step 13, Bww.
Theoretical S
turns per layer,
thStpl = Bww /
thSoadia from step 27
OPT1, thStpl = 62 / 1.351 = 45.89, choose
45...........................................................45 turns
per layer
**Note.
The calculated turns per layer are for the thickest wire possible but
could be more turns of a smaller dia
to obtain the wanted turn ratios to to give the wanted load matches.
No
less than 45 turns per S layer can be used if the traverse width is
kept full because the increase in wire size will give a total height of
the
winding which exceeds the allowable total winding height.
