Table 1a. SE Pentode, Beam Tetrode, CFB, UL.
Tube type  Single
Ended Mode 
Max Pda at idle, Watts 
Ea +Vdc a to k 
Ia mA dc 
Max Audio Power Watts 
Effici ency % Max 
Eg2 g2 to k 
Ig2 mA dc 
RL for max PO 
EL84 and 6V6  P,
BT,
CFB, Eg2 < Ea. 
12 12 12 
300 275 250 
40 43 48 
5.0 4.8 4.5 
42 40 38 
270 235 200 
4 5 6 
6k7 5k7 4k7 
EL84 and 6V6  UL, Eg2 = Ea 
11 11 11 
300 275 250 
37 40 44 
4.4 4.2 4.0 
40 38 36 
300 275 250 
4 5 6 
7k3 6k2 5k1 
EL86  P,CFB, Eg2 < Ea. 
12 12 12 
250 225 200 
48 53 60 
5.0 4.8 4.5 
42 40 38 
200 200 200 
4 5 6 
4k7 3k9 3k0 
EL86  UL, Eg2 = Ea 
12 12 12 
250 225 200 
48 53 60 
4.8 4.5 4.3 
40 38 36 
250 225 200 
5 6 7 
4k7 3k9 3k0 
807,
6L6, KT66, 5881 
BT,
CFB, Eg2 < Ea. 
21 21 21 
400 350 300 
53 60 70 
9.2 8.8 8.4 
43 41 39 
300 270 250 
4 5 6 
6k8 5k3 3k8 
807,
6L6, KT66, 5881 
UL, Eg2 = Ea 
20 20 20 
400 350 300 
53 60 70 
8.6 8.4 8.0 
43 41 39 
400 350 300 
4 5 6 
6k8 5k3 3k9 
EL34, 6CA7  P,
BT, CFB, Eg2 < Ea 
24 24 24 
420 350 270 
57 68 88 
10.3 9.8 9.3 
43 41 39 
270 270 270 
7 8 9 
6k6 4k7 2k8 
EL34, 6CA7  UL, Eg2 = Ea 
23 23 23 
420 350 270 
54 65 85 
9.2 8.7 8.2 
40 38 36 
420 350 270 
8 9 10 
7k0 4k9 2k9 
6550, KT88  BT,
UL, CFB, Eg2 < Ea 
30 30 30 30 
450 390 330 270 
66 76 90 110 
12.9 12.3 11.7 10.5 
43 41 39 35 
300 270 270 270 
4 5 6 7 
6k2 4k7 3k3 2k2 
6550, KT88  UL, Eg2 = Ea 
30 30 30 30 
450 390 330 270 
66 76 90 110 
12.3 11.7 11.1 10.5 
41 39 37 35 
450 390 330 270 
4 5 6 7 
6k2 4k7 3k3 2k2 
KT90, KT120  BT,
UL, CFB, Eg2 > Ea 
35 35 35 35 
450 390 330 270 
77 89 106 129 
15.5 14.3 13.6 12.2 
43 41 39 35 
300 270 270 270 
5 6 7 8 
5k3 3k9 2k8 1k9 
KT90, KT120  UL, Eg2 = Ea 
35 35 35 35 
450 390 330 270 
77 89 106 129 
14.8 13.6 13.0 12.2 
41 39 37 35 
450 390 330 270 
5 6 7 8 
5k3 3k9 2k8 1k9 
13E1  BT,
CFB, Eg2 < Ea 
72 72 72 72 
550 460 380 300 
130 156 189 240 
31.0 30.0 28.1 25.2 
43 41 39 35 
220 200 180 160 
6 5 5 4 
3k2 2k7 1k9 1k2 
13E1  UL, Eg2 = Ea 
70 70 70 
375 350 325 
186 200 215 
27.3 25.9 22.1 
39 37 35 
375 350 325 
13 12 10 
1k8 1k6 1k4 
Tube
type 
Single
Ended Triode Mode 
Max Pda + Pg2 at idle, Watts 
Ea +Vdc a to k 
Ia
+ Ig2 mA dc 
Max Audio Power Watts 
Eff icient % Max 
Ra
at Eg1= 0Vdc 
RL for max PO 
EL84, 
Triode 
12 12 12 
330 300 280 
36 40 43 
3.1 2.5 2.0 
26 21 17 
2k2 2k2 2k2 
4k8 3k1 2k2 
EL86 
Triode 
12 12 12 
250 225 200 
48 53 60 
4.3 4.1 3.6 
36 34 30 
0k7 0k7 0k7 
3k8 2k9 2k0 
6V6 
Triode 
12 12 12 
370 340 317 
32 35 38 
3.1 2.5 2.0 
6 21 17 
k8 2k8 2k8 
k0 4k2 2k8 
807,
6L6, KT66, 5881 
Triode  22 22 22 22 
500 450 400 350 
44 49 55 63 
8.6 8.1 7.4 6.3 
39 37 33 28 
2k4 2k4 2k4 2k4 
9k0 6k8 4k9 3k2 
6CM5, EL36  Triode  18 18 18 
375 350 325 
48 51 55 
7.8 7.5 7.4 
43 41 40 
0k5 0k5 0k5 
6k8 5k8 4k9 
EL34, 6CA7  Triode  24 24 24 24 
450 420 390 360 
53 57 61 66 
9.1 8.7 8.1 7.6 
37 36 33 31 
1k0 1k0 1k0 1k0 
6k5 5k4 4k4 3k5 
6550, KT88  Triode  33 33 33 33 
500 450 400 350 
66 73 82 94 
13.0 12.0 11.0 9.6 
39 36 33 29 
0k8 0k8 0k8 0k8 
6k0 4k6 3k3 2k2 
KT90  Triode  37 37 37 37 
500 450 400 350 
74 82 92 105 
14.7 13.7 12.6 10.8 
39 37 34 29 
0k7 0k7 0k7 0k7 
5k4 4k1 3k0 2k0 
KT120  Triode  40 40 40 40 
500 450 400 350 
80 88 100 114 
15.6 14.7 13.5 11.0 
39 36 33 27 
0k7 0k7 0k7 0k7 
4k9 3k8 2k7 1k7 
45 
Triode  8 8 8 
270 240 210 
29 33 38 
2.4 2.0 1.4 
30 25 17 
1k8 1k8 1k8 
5k7 3k7 1k9 
2A3  Triode  12 12 12 
300 275 250 
40 43 48 
4.4 4.2 3.9 
36 35 32 
0k9 0k9 0k9 
5k6 4k6 3k4 
300B  Triode  28 28 28 
420 380 340 
65 73 82 
10.6 10.0 9.3 
37 35 33 
0k7 0k7 0k7 
5k1 3k8 2k8 
845  Triode  75 75 75 
1,100 950 800 
68 78 93 
27.1 23.7 18.2 
36 31 24 
2k2 2k2 2k2 
11k8 7k8 4k2 
GM70 
Triode 
75 75 75 
1,100 950 800 
68 78 93 
29.1 26.1 22.0 
38 34 29 
1k8 1k8 1k8 
12k6 8k6 5k1 
13E1 
Triode  70 70 70 
375 350 325 
186 200 215 
24.0 23.0 22.0 
34 32 31 
0k3 0k3 0k3 
1k4 1k2 1k0 
SINGLE
ENDED
OPT4
EXAMPLE.
Total PO = PO for one tube x number of paralleled tubes  will depend on mode.
OPT4, for 35W, List some
choices.
7 x EL84/6BQ5 in pentode mode, 10 for triode
operation.
3 x 6550/KT88 in beam tetrode, 5 for triode operation.
4 x 6L6GC, 5881, KT66, 807, EL34, 6CA7 in beam tetrode, pentode,
5 for triode.
Note.
An example of a real amp
already
exists this
website at SE35 monobloc.
Let OPT4 be the design example
for 4 x EL34/6CA7 in pentode
with
CFB, ( SE Acoustical ).
Nominate audio power required from 1 tube = Max PO / No of tubes
= 35W
/ 4
= 8.75 Watts.
Choose from above tables and
centre Ea values listed.
Tube 
SE
Pentode 
Pda  Ea  Ia  PO 
Eff 
Eg2  Ig2  RLa 
EL34 
CFB, Eg2 < Ea  24W  +350V  68mA  9.8W  41%  +270V  8mA 
4k7 
The choice will produce
9.8W from one tube so therefore
39.2W from 4 tubes and allowing
for winding losses there will probably be 35 Watts at the
secondary
speaker terminal.
Graph
1.
Graph
1 shows the
maximum power levels for various RLa loads
available from
ONE SE EL34 or 6CA7 in Pentode mode, UL or CFB mode. Everyone
should
consider what ONE tube will do before considering what 4 tubes
in
parallel may
do.
Fig 1 tells us we have an OPT with ZR = 1,285:1, and with 3.5
ohms at
the
secondary
the RLa will be 1,285 x 3.5 ohms = 4,495 ohms. The arrangement
would suit a
speaker with "nominal" Z = 4 ohms.
Maximum PO is only possible at one value of RL for a given set
of idle
conditions
for Ea, Ia and Eg2 and the graph curve is only valid for one
idle
condition.
Most SE amps are designed to give the maximum SE power to either
4, 8
or
perhaps 16
ohms. But if we consider the OPT is set up for max PO at 3.5
ohms
as in Fig1, in
fact the tube will drive a range of loads below and above 3.5
ohms
and produce useful
power. From the graph we see that 6 watts or more is available
at all RLa loads between
2k5 and 8k6 which corresponds to speaker loads between
about 2 ohms and 6.7 ohms.
All the power is pure class A so there is no THD
generated as a result of devices
switching on or off as with PP amps. So as long
as there is sufficient NFB the result is
listenable. If a horn loaded speaker
Z = 8 ohms with 100dB/W/M sensitivity and never
needed more
than 1 watt, then the amp will still give 5W into 8 ohms.
If the ZR of the OPT was 4,500 :
5.6ohms, ie, 803:1, then the
range of anode
RLa values would also be 2k5 and 8k6 and the speaker load could
be
between
3.1 ohms and 10.7 ohms for 6 watts of output. Most SE amps will
withstand
the load variations with ease because the power is still all
class A.
If there are
4 parallel tubes each making 6 useful Watts then you have 24
Watts
total
which is enough for most people.
So when considering SE PO, the
Center Value RLa for Maximum PO
is
worked out,
then the OPT ratio calculated for this and to give a range of
loads from below and above which are suitable.
Fig
1 below will introduce
everyone to the very basic pentode and triode
Ra curves for EL34. Only the Ra curves for Eg = 0V are shown
because
these are all that is needed for OPT design.
Fig 1.
Fig
1 shows the
EL34 Pentode Ra curves for Eg1=0V, Eg2 = 350V,
and for Eg1=0V, Eg2 = 250V.
Pda is shown at 25Watts for EL34
or 6CA7. The Pg2 is included.
EL34 data indicates max Pda = 28W, but I do not recommend that
any EL34 should ever have total Pda plus Pg2 idle power >
25W.
Ra curve for Eg1 = 0V for triode
connected EL34 or 6CA7 is also
shown.
There is also a straight line with slope of 280 ohms shown which
is the
Ea
swing "limiting line" value which may be used for all pentodes
and beam
power
tetrodes where the Ultralinear screen taps up to 60% taps or CFB
windings are
used.
The slope of the 280 ohm line is
"less steep" than the Ra
curves
for below
Ea = 50V which have been copied from old tube data sheets.
Ra for below Ea = 50V may be 140
ohms for EL34 in pentode mode, but
when UL connection or CFB is used there is some reduction of
possible Ea
swing and the line for 280 ohms is a conservative value which
may be
used
for all power pentodes and beam tetrodes.
The Ra curves for pentodes and
tetrodes seem strange because
between the
Ea swing between 0V to 50V, the Ra appears to be very low, only
140
ohms,
yet Ra increases to many thousands of ohms between 50V and say
500V.
Pentodes and beam tetrodes produce all their power in the region
where
Ra is many thousands of ohms, but their power is slightly
limited by
the
low Ra region where Ea < 50V.
Now if one assumes the pentode
Ra Limiting Line = 280 ohms, and
that the
knee of
Ra
curves will always be well above 2 x Ia at idle for an
appropriate
Eg2
value shown in the tables above, then one may calculate RLa
after
choosing Ea and Ia values without using any load line analysis
providing Ea is
within the
ranges shown in Table 1 above.
A. Pentodes and Beam
Tetrodes only
:
Calculate Center Value RLa for
maximum possible PO,
Formula 1: RLa = 0.9 x Ea / Ia ohms.
Formula
2 : RLa = Ea / Ia  (
2 x 280 ) ohms.
where 280 ohms is the limiting low Ra for where Eg = 0V,
and Ea < 50V, which prevents Ea swinging to a lower voltage
because
of
grid current.
NOTE. The curve data for most
power pentodes and tetrodes may
show the Ra
limiting line for Ea < 50V having a slope of say 150 ohms,
but when
such tubes
are used with UL taps or with CFB windings the Ra line may be
assumed
to be
280 ohms.
PO
at
clipping = 0.5 x RLa x Ia squared, where Ia = Iadc at
idle.
Example
1: EL34 with
Ea = 350V, Ia = 68mA.
Formula 1, RLa = 0.9 x 350/0.068
= 4,632 ohms.
Formula 2, RLa = ( 350/0.068 ) 
560 = 4,587 ohms.
Both formulas give near the same
answer.
PO at clipping = 0.5 x 4,600 x
0.068 x 0.068 = 10.6 Watts.
For
any selected
RLa Lower than Center Value for max possible PO,
PO = RLa x ( Ia squared / 2 ), RLa Lower
than Center
Value.
Example
2 : RLa =
3,000 ohms, Ea 350V, Ia 68mA,
PO = 0.5 x 3,000 x 0.068 x 0.068 = 6.94 Watts.
For
any selected RLa Higher than Center
Value
for
max
possible
PO,
PO = 0.5 x ( Ea 
[ 280 x
Ia
] ) squared
x RLa
Higher than Center Value.
(
280
+
RL
)
squared
Example 3 : RLa = 9,000 ohms, Ea 350V, Ia
68mA,
PO = 0.5 x ( 350 
[
280 x 0.068 ] ) squared x 9,000
(
280
+
9,000
)
squared
= 0.5 x ( 350  19 )
x ( 350
 19 ) x 9,000
(
9,280
x
9,280
)
= 5.72 Watts.
B.
Triodes only :
Calculate
Center Value RLa for
maximum possible PO,
RLa = ( Ea / Ia )  ( 2 x Ra
)
ohms.
Where Ra is the limiting Ra
value
where Eg = 0V which prevents Ea
reaching any lower voltage because of grid current.
If the above equation gives RLa less than twice Ra, the Ea
should be
raised
and Ia reduced so Pda stays constant or slightly less so RLa
will then
be a
preferred minimum of 3 x Ra, if not more.
Example
4 : Triode
connected EL34, Ra = 1,285ohms, Ea = 350V, Ia = 68mA.
RLa = ( 350 / 0.068 )  ( 2 x
1,285 ) = 5,147  2,570 = 2,577
ohms.
PO max = 0.5 x 2,577 x 0.068 x
0.068 = 5.9 Watts.
Example
5 : RLa =
1,500 ohms, Ea 350V, Ia 68mA,
PO = 0.5 x 1,500 x 0.068 x 0.068 = 3.5 Watts.
For
any selected RLa Higher than Center
Value
for
max
possible
PO,
PO = 0.5 x ( Ea 
[ Ra x
Ia
] ) squared
x RLa
Higher than Center Value.
(
Ra
+
RLa
)
squared
Example 6 : RLa = 4,600 ohms, Ea 350V, Ia
68mA,
PO = 0.5 x ( 350  [
1,285 x
0.068 ] ) squared x 4,600
(
1,285
+
4,600
)
squared
= 0.5 x ( 350  87 )
x ( 350
 87 ) x 4,600
(
5,885
x
5,885
)
= 4.6 Watts.
NOTE.
These sample calculations for EL34 pentode and triode are
for the same
Ea and Ia conditions, and Example 1 for pentode with Centre
Value RLa
gives
maximum PO = 10.6W and the same load for triode gives 4.6W. It
will
be found that the SEUL connected EL34 with 40% to 50% screen tap
or
with
15% CFB will give higher power and better sound than triode for
the Ea
and Ia
conditions. But when Ea Is raised and Ia reduced, the triode can
then
perform
much better.
Example
7 : Ea = 400V,
Ia+Ig2 = 57mA, Pda = 23W, Ra = 1,300 ohms.
Center Value RLa = ( 400 / 0.057 )  ( 2 x 1,300 ) = 4,417 ohms.
PO = 0.5 x 4,417 x 0.057 x 0.057
= 7.17 Watts.
Example
8 : RLa
= 2,557 ohms,
PO = 0.5 x 0.057 0.057 x 2,557 = 4.15 Watts.
Example
9 : RLa
= 9,000 ohms,
PO = 0.5 x (
400
 [ 1,300 x 0.057 ] ) squared x 9,000
(
1,285
+
4,600
)
squared
= 0.5 x ( 400  74 )
x ( 400
 74 ) x 9,000 = 4.78 Watts.
(
10,300
x
10,300
)
Fig 2 shows
the Ra
curve for EL34/6CA7 at Eg1 = 0V copied from tube
data
sheets in old data books. There are THREE Ra curves given for
Eg1
= 0V because there are THREE values of Eg2 also shown.
Fig 2 shows
that for SE operation the Eg2 does not have to be as high as Ea.
The ideal
Eg2 for many SE pentodes and beam tetrodes is well below Ea,
but not often
below 200V, which might be the minimum Ea anyone would
consider.
If Eg2 = 250V for EL34, the Ig2 is low, and the Eg1 needed for
biasing
is also
low so
little heat is wasted in a cathode resistor in cathode biasing.
This
means
that
where Ea = +350V, and Ek = +17V, and Vdc drop across OPT Rw =
+15V,
then total B+ supply rail to OPT would be +382Vdc, so 450Vdc
rated
electrolytics
may be used without fear of them being subject to too high a
voltage
when
no tubes were present in the amp. This assumes that Si diodes
and not
tube
diodes have been selected for the rectifier.
In Fig 2, the curves for Ra for many values of Eg1 have not been
shown
because they are not needed, and establishing the cathode bias
must be
done by
experiment when the amp is first tested, and with shunt
regulated
screen supply
established.
HOW
TO DRAW THE
LOADLINES.
The Fig 2 loadines are
shown
here
to save everyone the
trouble of
going to
another page on load
line
analysis, and this graph is relevant to the OPT4 design.
I have chosen idle
conditions with Ea
= +350Vdc, Ia dc = 68mA, Pda = 24W.
NOTE.
For UL use of
pentodes
or beam tetrodes, Eg2 = Ea. The knee of
the
Ra curve is high **if** the UL tapping point is less than 60% of
the total anode
turns in most pentodes or tetrodes. UL operation with UL tap up
to 60%
allows
max
class A1 PO up to the same as for pure pentode or beam tetrode,
but
distortion
will become similar to triode, mainly 2H. The best UL tap
position
for
SEUL operation
is that which is the closest to the anode terminal but which
still
allows PO to be close to full pentode or tetrode power.
B.
Draw the load line which will give maximum audio power. This
load line
is for the CENTER VALUE RLa = 4,853 ohms, shown as line AQB.
5. Calculate
the core tongue dimension, T.
For a square core centre leg section,
tongue width = stack height, ie T = S, and Afe = T x S, = T
squared.
Therefore theoretical T dimension = square root AFe, mm.
OPT4, thT = sq.rt 2,984 = 54.6mm.
Choose
nearest T
size
less than thT from list of available
wasteless
GOSS
E&I laminations or Ccores.
NOTE. T sizes commonly available for wasteless pattern E&I
laminations :
20mm, 25mm, 32mm, 38mm, 44mm, 51mm, 63.5mm.
NOTE. Ccores are normally
used to make a double C core,
and a wide variety
of strip build up heights and strip widths are available.
Usually the
Ccore
ratio of window area to a square section AFe is larger than for
E&I
laminations.
The T dimension for double Ccores is twice the strip build up
of one
Ccore
and the S dimension, or stack, is the strip width of the
Ccore.
NOTE.
Choosing a
standard T size above thT gives a larger window area and
lower copper winding losses and possibly a stack height less
than the
T.
Choosing T below thT gives a smaller window size and higher
winding
losses
but lower weight and
smaller overall size.
If T is chosen below thT, Afe may need to be increased so less
turns
may be used
to keep winding losses low and to maintain the wanted bass
response
NOTE.
In general, S
should not exceed 2 x T.
NOTE.
HF performance
depends entirely upon the interleaving
geometry and
insulation.
For OPT4, choose core T =
51mm
6. Calculate
theoretical stack height S for chosen T from step 5.
thS = Afe / T, then adjust to a larger height to suit nearest
standard
plastic bobbin
size if available.
NOTE, standard bobbin sizes are usually available for all square
core
leg shapes
for T = S. There are other S heights usually always greater than
the T
size, at
convenient larger sizes. For T = 51mm, S might be 51mm, 62.5mm,
76mm,
and
102mm. Sometimes it is
necessary to make the whole bobbin from fibreglass
sheeting cut neatly and glued
together.
OPT4. thS = 2,984 / 51 = 58.5mm, say
58mm,
not
a
standard
S
size.
Bobbin would be handmade at S =
58mm, but a premade bobbin
with S = 62.5mm
could be used.
S = 58mm will be used for OPT4.
7. Calculate usable Afe =
chosen T x
chosen
S.
OPT4. Confirm Afe = 51 x
58 =
2,958sq.mm.
NOTE.
Some constructors
will
be using non wasteless pattern E&I lams, or
Ccores 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.
For wasteless pattern E&I,
where the centre leg tongue
dimension =
T,
the
window Length L = 1.5T and window Height H = 0.5T.
Overall dimensions
of plan area of
assembled E&I lamination is 2.5T x 3T.
Plan area of assembled laminations =
6Tsquared, not including both windows.
From this the volume of the iron used in the wasteless core
= 6 x Tsquared x Stack height.
Core weight in Kg = Volume x 0.0084 where volume is in cubic
centimetres.
Some other E&I lamination
patterns
and most Ccores have a much larger
window area for their effective T dimension so that larger wire
sizes
for less
copper
loss may be employed or to give more room for more turns and
insulation layers. Regardless
of
the core type and pattern, the ratio of Afe
size relative to Bac max must be maintained. Some Ccored OPT
look very
impressive and physically large but Afe might be much too
small
for the
number of turns used to keep Fsat low enough.
If the Afe is reduced by 50% then Np must be increased by 50%.
Then
winding resistance rises unless thicker wire is used. If one
thing is
changed,
many other things will have to change to comply with all design
rules.
I prefer
wasteless E&I patterns, and most designs have an Afe aspect
ratio
where
S = 1.5T approximately. Suitable Ccores are rarely ever in
stock with
any
transformer parts suppliers and are more expensive than GOSS
E&I
lams.
The design process may be written out step by step using one
choice of
core and it is never too much trouble to repeat the design
process 4 or
five
times to choose alternative core sizes to compare results which
will
offer the
best result.
Table
of possible T and S for
output powers.
OPT Power Watts 
AFe sq.mm 
Theoretical T, mm. 
Choose T x S, mm. 
Choose T x S, mm. 
Wasteless E&I Core Weight Kilograms 

100 
4,500 
67.0 
62.5
T 
75
S 
50 T  100 S  14.8 
70 
3,764 
61.4 
50 
80 
44 
90 
10.1 
50 
3,181  56.4 
50 
65 
44 
80 
8.2 
35 
2,662 
51.6 
50 
52 
44 
62 
6.6 
28 
2,381 
48.8 
50 
47 
44 
55 
5.9 
20 
2,012 
44.9 
44 
46 
38 
55 
4.5 
14 
1,683 
41.0 
38 
45 
32 
57 
3.3 
10 
1,423 
37.7 
38 
38 
32 
48 
2.8 
7 
1,190 
34.4 
32 
38 
25 
60 
2.0 
5 
1,006 
31.7 
32 
32 
25 
50 
1.7 
9. Calculate
theoretical primary winding turns, thNp.
Th Np = Va max x 20,000 / Afe
or = square root of ( anode RL x PO) x ( 20,000 /
Afe ).
NOTE.
The
formula here is derived from more complex and complete formula
taking Bac max and F into account. For GOSS cores, maximum ac
magnetic
field
strength, Bac cannot be allowed above 0.8 Tesla at 14Hz. This is
based
on the
maximum dc magnetic field being 0.8 Tesla, so the combined
maximum
Bac and Bdc = 1.6T. For lesser grades of steel it is safer to
work with
Bac = Bdc
= 0.6T with totla of both = 1.2T.
Th Np = 231 x 20,000 /
2,958 = 1,562 turns.
10. Calculate
theoretical
Primary wire dia, thPdia.
NOTE. 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
most OPT.
Each turn of wire will occupy an area = oa dia squared. Overall
or oa
dia is the
copper dia PLUS enamel insulation. Therefore theoretical over
all dia
of
P,
thoaPdia, of wire including enamel insulation
= square root ( 0.28 x L x H / Th Np ), mm.
OPT4. Th oa dia P wire = sq.rt ( 0.28 x 76 x 25 / 1,562 ) = sq.rt 0.341
= 0.584mm.
11. Find nearest suitable theoretical oa wire size for Primary.
Wire
Size Table of available
wire sizes.
12.
Calculate the
bobbin
winding
traverse width, Bww.
NOTE.
Bobbin traverse
width is the distance between the cheek flanges and
varies depending on who made the bobbin, but 2mm for each flange
thickness
is
common but could be more or less, and this affects the number of
turns
per layer. Where bobbin flanges are not used, and interlayer
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.
So the winding will traverse a
distance = L  4mm.
OPT4. Bww = 76  4 = 72
mm.
13. Calculate no
of
theoretical P turns per layer.
Th Ptpl = 0.97 x Bww / oa dia from Step 11.
NOTE. The
constant
0.97
factor allows for imperfect layer filling with
such fine wire. Leave out fractions of a turn.
OPT4. Th P tpl = 0.97 x 72 / 0.569 =
122 turns
14. Calculate
theoretical
number of primary layers.
Theoretical Npl = thNp / Ptpl,
then round up/down.
OPT4. ThNpl = 1,562 / 122 = 12.8 layers; round up to
13 layers
NOTE. Rounding down to
12L may
reduce the Np needed for Fsat = 20 Hz.
NOTE.
Fsat for SE amps
at full PO may be allowed to be up to
20Hz and not
14Hz for PP OPT because it will be found the design size, weight
and
cost will
rapidly increase if Fsat is much below 20Hz.
Rounding up No of layers increases Np which gives Fsat
marginally lower
than
20
Hz, which is OK.
Fsat may be lowered if Afe is increased by increasing S from say
51 mm
to
62mm and be able to use a standard sized bobbin, and the change
lowers
Fsat
from 20Hz to 16Hz and only slightly extends low bass
response.
15. Calculate
actual
Np. Np = P layers x Ptpl, turns
OPT4. Np = 13 x 122 =
1,586turns.
16. Calculate
average
turn length.
TL
= ( 3.142 x H )
+ ( 2 x S )
+ ( 2 x T ), mm.
NOTE. 3.14 is pye, or
22/7.
OPT4. TL = ( 3.142 x 25 ) + ( 2 x 51 ) + ( 2 x 58 ) =
297mm.
17. Calculate
Primary
winding resistance.
Rwp = ( Np x TL ) / ( 44,000 x
Pdia x
Pdia ) ohms, where 44,000 is a constant,
P dia is the copper dia from the wire
tables.
OPT4, Rwp = 1,586 x 297 / ( 44,000 x 0.475 x 0.475 )
= 48 ohms.
18. Calculate
primary winding loss %.
P loss % = 100 x Rwp / ( PRL + Rwp ),
%.
OPT4 P loss = 100 x 48 / ( 1,213 + 48 )
= 3.80%.
19. Is
the
primary winding close to 3.5%?
If 15% more than 3.5%, the design calculations must be checked
and
perhaps
a larger
core stack or window size chosen. If no, proceed to Step 21.
P winding loss exceeds 3.5% by less than 15%, so proceed...
NOTE.
If the P
winding losses are less than 2.5%, there is a possibility that
the P
wire
size could be reduced to increase the turns per layer, and
possibly
reduce the
number of P
layers from say 14 to 13. However I rarely find SE
OPT P winding losses will be less
than 2.5%
with the
rated load, and one
must allow for where the speaker load used maybe is half
the RL used
for
the design. Where the load used = 1/2 the design RL, P
winding
losses
will double. It is better to have winding losses lower than
required so
that
the
windings are unlikely to
overheat if a tube malfunctions and draws
excessive Idc during a "bias failure
event".
20.
Is the Primary
wire
able to carry the intended Idc current?
Calculate copper
wire section area and allowed
Idc
based
on
maximum
current
density of 2A per sq.mm. Allowed Idc should be well above
intended
Idc.
OPT4. Primary wire section
area = ( 22/7 ) x ( Cu dia squared / 4 )
=
3.142 x ( 0.475 x 0.475 / 4 ) = 0.177 sq.mm.
Allowed Idc = Cu Area x 2A / sq.mm current density = 0.177 x 2A
= 0.354
amps.
Idle DC current from Step 4 = 272mA.
Allowed Idc is well above idle Idc.
NOTE.
The primary
wire heat
dissipation
=
Idc
squared
x
RwP
= 0.272 x 0272 x 48 = 3.55Watts.
This will cause a small temp rise but if the Idc was 1 Amp, the
Pd =
48Watts,
and wire will become too hot. The wire may even fuse open if
current
density
reached 30A per square mm, ie, 5.3 Amps. Therefore a fuse of
0.25Amps
should be used between each EL34 cathode and OPT connection.
Each
EL34 should have its own RC biasing network and series fuse.
Active
protection to guard against bias failure in one or more OP tubes
should
be used.
If a tube is allowed to seriously over heat the internal grid
wires may
melt
and a short circuit may develop between anode and cathode or
between
anode
and grid which can cause expensive damage.
21.
Choose the
winding interleaving pattern.
Search
the Tables 2, 3, 4, 5,
below for the output
power
rating
of
the
transformer.
In general, all OPT should
comply
with the following P&S layer number
relationships :
Where the first and last layer
of wire
wound onto the bobbin is in a primary
section, then these sections should have nearly 1/2 the layers
of the
inner
primary sections. So if there are 3 outer primary layers in a
Primary
section,
the inner P sections might be either 5p, 6p or 7p
layers. When this guide ensures
the best HF response because the
leakage inductance is evenly and symmetrically
distributed.
This rule applies so that the
winding section pattern is a
mirror image below and
above center of the bobbin, and should always be the case for PP
OPTs.
This
means that if the first on wire layer is a Primary, the last on
layer
will also be a
Primary.
However, for SE OPTs, it is possible to start with Primary layer
and
end with a
Secondary layer. The anode is usually connected to the innermost
end of
the
Primary where the average turn length is shortest hence giving
lowest
shunt
capacitance. This is aided by starting with a Primary layer so
that the
highest
anode signal voltage is not adjacent to earthy secondary
layers.
When starting and finishing with
a secondary layer section, all internal primary
sections should have the same number of layers but it is not
always
possible
because the total number of primary layers may not be exactly
divided
by the
number of wanted primary sections. So where there were a total
of 18
Primary
layers in 4 sections there may be 2 sections of 4
layers
and 2 sections of 5 layers.
The size of such inner sections located between secondary
sections should
not vary
more than 25%. Equal thickness of insulation should
used
between
all primary and secondary sections. This gives minimal
problems
with
resonances at HF. Alternatively, one might use an
interleaving pattern with
4P and 4S sections, with the sections being 3pS5pS5pS5pS,
starting in
that order from the bobbin bottom. But where possible I try to
start
and finish
with layers of either Pri or Sec.
Capacitance.
The
insulation thickness between primary and
secondary is
needed to prevent arcing between high primary voltages and
earthy
speaker
secondaries. As the tube amp primary load is reduced, the effect
of
shunt
capacitance diminishes, so insulation thickness can be reduced,
but
kept to
a minimum of about
0.4mm to prevent any arcing and help keep wire layers
neat and flat
as the bobbin is
wound.
Cathode
FB windings
will mostly comprise between 10% and 25% of all
primary turns. CFB windings should have only full layers of
primary
wire
and be distributed in the height of the bobbin winding and
located
between an
adjacent anode layer with the same thick insulation as used for
between
all
other primary layers and the speaker secondary layers.
For example, if there were 18p layers in a 4P + 5S pattern, and
3 P
layers
were devoted to the CFB winding then CFB % = 100% x 3/18 =
16.7%.
the ideal pattern of layers will be :
S4pcS4pSc4pSc4pS.
Such a pattern ensures the CFB winding is well coupled to all
other
windings.
However, I have seen a number of OPT with all layers used for a
CFB
winding
put into one central section, located with Secondary layers on
each
side.
An example for a pattern of 6S x 5P might be:
S4pS4pS3CS3pS4pS.
Because
the pattern has such a high number
of interleavings the coupling between CFB to S to anode P is
good.
but in all cases of CFB windings it is often necessary for Zobel
networks
to be placed to load the OPT at very HF at the best location for
damping
transients.
Transformers
for Electrostatic
Speakers, ESL :
These step up the amplifier voltage between 50 and 300
times.
Their primary winding resembles a tube amp secondary winding
meant for
amp output
voltages up up to about 30Vrms. Their secondary winding may
need to have greater
insulation
thickness for high voltages up to 6,000Vrms,
and to achieve lowest possible shunt capacitance. They resemble
PP tube
OPTs powered
"backwards" and can be designed with the
method here.
The design of ESL stepup transformers requires serious
additional
understanding of LCR modeling not within
this website.
Solid
State OPTs and speaker
load matching transformers :
For transformers to couple
mosfets or transistors to
loudspeakers, or to
couple a given amplifier output load outlet to suit a higher or
lower
load,
the
same amount of
interleaving is required for a given power level. When the
primary load
becomes similar to the secondary load the number of primary
layers will become
similar to number of secondary layers and wire size for
either will become
similar. An 8 ohm : 8 ohm OPT with very low dc voltage
differences between primary and secondary would have equal
numbers of
turns
for primary and
secondary and perhaps be simply
interleaved so each layer of
thick wire is alternatively devoted to
either primary or secondary.
The bandwidth can then be up to
250kHz.
Speaker matching transformers are useful where the amplifier has
an
outlet
labelled "8 ohms" but the loudspeaker is 4 ohms, and we wish to
allow
the
amp to
experience 8 ohms load or higher. Externally located speaker
matching
transformers
are very useful for use in OTL tube amplifiers which may have
been designed with
many parallel tubes to avoid an OPT, but which would
very much benefit the
use of a load of say 32 ohms instead of 8 ohms.
Speaker matching transformers
may be designed to be autotransformers
with ONE combined primary and secondary winding but they must
still be
interleaved to give wide bandwidth.
In
General :
But for matching tubes to normal
speaker loads between 3 and 9 ohms, the
interleaving list below will give at least 50
kHz of bandwidth, and where there
is a highest number of interleavings the bandwidth can
be 300kHz. Using more
interleaving than listed may lead to less available room on the
bobbin for wire
due to too many layers of insulation giving poorer high
frequency
response
due
to high shunt
capacitance, even though the leakage inductance has been made
very low. The designs here give both low leakage inductance and
low
shunt
capacitance which are both required for optimal high frequency
response
and
amplifier stability and freedom from overloading across the
widest
possible
bandwidth.
The higher the amplifier power
and the lower the primary RL
becomes, and 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.
Tables 2, 3, 4, 5, show interleaving pattern possibilities for SE OPTs.
TABLE 2. 
Total P layers 
Primary and
Secondary layer
distribution. 
P&S section pattern 
0 to 7W 
10p to 24p 
S  10p~24p  S 
2S + 1P 
7W to 15W  10p to 20p  S  5p~10p  S  5p~10p  S  3S + 2P 
7W to 15W 
10 to 20  2p~4p  S  4p~8p  S  4p~8p  S  2p~4p  3S + 4P 
TABLE 3. 
Total P layers 
Primary and Secondary layer distribution.  P&S section pattern 
15W to 30W  12p  2p  S  4p  S  4p  S  2p  3S + 4P 
12p  S  4p  S  4p  S  4p  S  4S + 3P  
13p 
2p  S  3p  S  3p  S  3p  S  2p  4S + 5P 

14p  2p  S  3p  S  4p  S  3p  S  2p  3S + 4P  
14p  S  5p  S  4p  S  5p  S  4S + 3P  
15p 
S  5p  S  5p  S  5p  S  4S + 3P 

16p  3p  S  5p  S  5p  S  3p  3S + 4P  
16p  S  4p  S  4p  S  4p  S  4p  S  5S + 4P  
16p  2p  S  4p  S  4p  S  4p  S  2p  4S + 5P  
18p  3p  S  6p  S  6p  S  3p  3S + 4P  
18p  S  4p  S  5p  S  5p  S  4p  S  5S + 4P  
20p  3p  S  7p  S  7p  S  3p  4S + 3P  
20p  S  5p  S  5p  S  5p  S  5p  S  5S + 4P  
20p  2p  S  5p  S  6p  S  5p  S  2p  4S + 5P 
TABLE 4. 
Total P layers 
Primary and Secondary layer distribution.  P&S section pattern 
30W to 100W  13p 
2p  S  3p  S  3p  S  3p  S  2p  4S + 5P 

14 p  S  3p  S  4p  S  4p  S  3p  S  5S + 4P 
14p 
2p  S  3p  S  4p  S  3p  S  2p  4S + 5P  
15p 
S  5p  S  5p  S  5p  S  4S + 3P 

15p 
2p  S  4p  S  3p  S  4p  S  2p  4S + 5P 

16p 
S  4p  S  4p  S  4p  S  4p  S  5S + 4P  
16p  2p  S  4p  S  4p  S  4p  S  2p  4S + 5P  
18p  S

4p
 S  5p  S  5p  S  4p 
S 
5S + 4P  
18p 
2p  S  5p  S  4p  S  5p  S  2p  4S + 5P  
19p 
2p  S  5p  S  5p  S  5p  S  2p  4S + 5P 

20 p  S  5p  S  5p  S  5p  S  5p  S  5S + 4P  
20p 
2p

S
 5p  S  6p  S  5p  S 
2p 
4S + 5P  
21p 
3p  S  5p  S  5p  S  5p  S  3p  4S + 5P 

22 p  S

5p
 S  6p  S  6p  S  5p 
S 
5S + 4P  
22p 
2p  S  6p  S  6p  S  6p  S  2p  4S + 5P 
TABLE 5. 
Total P layers 
Primary and Secondary layer distribution.  P&S section pattern 
100W to 250W  10p  2p  S  2p  S  2p  S  2p  S  2p  4S + 5P 
10p  S  2p  S  3p  S  3p  S  2p  S  5S + 4P  
10p  1p  S  2p  S  2p  S  2p  S  2p  S  1p  5S + 6P  
10p  S  2p  S  2p  S  2p  S  2p  S  2p  S  6S + 5P  
12p  2p  S  3p  S  2p  S  3p  S  2p  4S + 5P  
12p  S  3p  S  3p  S  3p  S  3p  S  5S + 4P  
12p  1p  S  2p  S  3p  S  3p  S  2p  S  1p  5S + 6P  
12p  S  2p  S  3p  S  2p  S  3p  S  2p  S  6S + 5P  
12p 
S  2p  S  2p  S  4p  S  2p  S  2p  S  6S + 5P  
13p 
2p  S  3p  S  3p  S  3p  S  2p  4S + 5P 

13p 
S  3p  S  4p  S  3p  S  3p  S  5S + 4P 

13p 
S  2p  S  3p  S  3p  S  3p  S  2p  S  6S + 5P 

14p 
2p  S  3p  S  4p  S  3p  S  2p  5S + 5P  
14p  S  3p  S  4p  S  4p  S  3p  S  5S + 4P  
14p  1p  S  3p  S  3p  S  3p  S  3p  S  1p  5S + 6P  
14p  S  2p  S  3p  S  4p  S  3p  S  2p  S  6S + 5P  
16p  2p

S
 4p  S  4p  S  4p  S 
2p 
4S + 5P  
16p  S  4p  S  4p  S  4p  S  4p  S  5S + 4P  
16p  2p  S  3p  S  3p  S  3p  S  3p  S  2p  5S + 6P  
16p  S

3p
 S  3p  S  4p  S  3p  S 
3p  S 
6S + 5P  
18p  2p

S
 5p  S  4p  S  5p  S 
2p 
4S + 5P  
18p  S

5p

S  4p  S  4p  S  5p 
S 
5S + 4P  
18p  2p  S  4p  S  3p  S  3p  S  4p  S  2p  5S + 6P  
18p  S  3p  S  4p  S  4p  S  4p  S  3p  S  6S + 5P  
19p 
S  3p  S  4p  S  5p  S  4p  S  3p  S  6S + 5P 

20p  3p  S  5p  S  4p  S  5p  S  3p  4S + 5P  
20p  S  5p  S  5p  S  5p  S  5p  S  5S + 4P  
20p  2p  S  4p  S  4p  S  4p  S  4p  S  2p  5S + 6P  
20p  S

4p
 S  4p  S  4p  S  4p  S 
4p 
S 
6S + 5P  
21p 
S  4p  S  4p  S  5p  S  4p  S  4p  S  6S + 5P 

21p 
3p  S  5p  S  4p  S  5p  S  3p  4S + 5P 

22p  3p  S  5p  S  6p  S  5p  S  3p  4S + 5P  
22p  S  5p  S  6p  S  6p  S  5p  S  5S + 4P  
22p  2p

S

5p  S  4p  S  4p  S  5p  S  2p 
5S + 6P  
22p  S

4p
 S  6p  S  4p  S  6p  S 
4p 
S 
6S + 5P 
30W to 100W  13p 
2p  S  3p  S  3p  S  3p  S  2p  4S
+
5P 
NOTE. Usually, p to p
insulation for all OPT needs to only be 0.05mm thick,
where Vdc between layers is the same, to avoid the risk of
shorted
turns.
OPT4. i =
0.05mm.
24. Choose
insulation
thickness used between Primary
and Secondary layers, or between primary Anode layers
and Cathode layers with full Vdc
potential difference.
NOTE.
For any
interleaved audio coupling transformer, there
will be
a
sum of
Vdc plus peak Vac between adjacent P and S windings and
insulation must
have
sufficient thickness and dielectric strength to prevent arcing
between
windings.
The insulation thickness
selected will always be far more than required to prevent
arcing because
low capacitance is so important. Insulation thicknesses should
be
selected from the insulation thickness
table 6 :
Table
6.
Total Vdc + Vac pk, working maximums 
Minimum
thickness, Polyester sheet. 
0Vdc to 100Vac pk 
0.1mm 
0Vdc to 400Vac pk 
0.2mm 
300Vdc to
600Vac pk 
0.4mm 
450Vdc to
900Vac pk 
0.45mm 
600Vdc to
1,200Vac pk 
0.5mm 
1,200Vdc to
2,400Vac pk 
0.7mm 
2,400Vdc to
4,800Vac pk 
1.4mm 
OPT4.
Calculate probable
peak Vac + Vdc between P&S
windings allowing
for unknown future OPT use.
500Vdc + 500Vpk ac = maximum working condition =
1,000V.
PS Insulation Minimum
Thickness, I
= 0.50mm
Confirm
the
interleaving
pattern
and
list
the
layers
of
insulation
which
will be used as calculated so
far.
OPT4.
Interleaving Pattern =
2p

S
 3p  S  3p  S  3p  S 
2p.
Show
CFB
windings
if
used
:
Fig 5.
Fig
5 bobbin diagram shows the OPT4 bobbin wire layers with
all
insulation
nominated.
OPT4
listed
Insulation
:
Between primary to primary layers, 8 x 0.05mm insulation =
0.40mm.
Between primary and secondary layers, 8 x 0.5mm = 4.0mm.
Total thickness of all 20 insulation
layers = 4.40mm.
NOTE.
The Fig 5 bobbin diagram has
4 secondary sections each with 2
layers of wire with double layer secondaries.
25.
Calculate
height
of
Primary
layers
plus
all
insulation.
OPT4.
13 layers of P wire at
oa dia of 0.569mm = 7.4mm,
Total height of all insulation
= 4.4mm,
Total
height of P wire + all
insulation = 11.80mm.
26. Calculate maximum theoretical oa dia of the secondary wire.
Calculate
available
height
for
layers
of
secondary
wire
:
Available Sec height = ( Available height in bobbin )  (
Height P + all Insulation ).
Available height in Bobbin = 0.8 x H window dimension.
OPT4. Avail Sec height = ( 0.8 x 25mm )  11.80mm = 8.2mm.
th Sec oa
dia = ( avail Sec
height ) / no of sec layers of wire,
OPT1A, Th oa dia sec = 8.2 / 4 = 2.05mm.
28. Calculate
theoretical
S
turns
per
layer,
thStpl.
Theoretical S
turns per layer, thStpl = Bww /
thSoadia from Step 27.
OPT4. ThStpl = 72 / 1.916 = 37.58, round down to 37
turns = 37tpl.
NOTE.
These
calculated
turns
per
layer
are
for
the
thickest
wire
possible, and
fewer turns per layer are forbidden because the increased wire
size to
fill a
layer
would make the winding height unable to fit onto the bobbin.
Wires
should never
be
wound on and spread apart so that the Tpl is reduced while
keeping wire
size
the
same, lest secondary winding resistance losses be increased too
much.
29.
Calculate
load
matches
with
Sec
turns
from
Step
28.
These
load
matches
will
be
theoretical
and
secondary
turns
and winding pattern will probably require adjustments.
Nominate
Ns, number of secondary
turns consisting of paralleled or seriesed
sec layers calculated in Step 27.
OPT4. Ns may be 4 x parallel windings of 37t =
37t.
2 x parallel windings of ( 37t + 37t in series ) = 78t.
4 x 37t all in series = 156t.
Primary
RLa
1,213
ohms Primary turns, Np 1,586t 
Ns  TR 
ZR 
Secondary RL ohms 
4 parallel layers  37t  42.86 
1,837  0.66
ohms 
2
parallel
x
(
2
series
layers
) 
78t 
21.43 
459 
2.64
ohms 
4 series layers  156t 
10.71 
115 
10.56
ohms 
3 series layers, with 2 parallel  111t 
TR
14.29 
ZR
204 
5.94
ohms 