Design of OPT-1A continued....

14. Calculate minimum centre leg cross sectional area, Afe.

15. Calculate the core tongue dimension, T.

Fig 8. Wasteless E&I lamination details.

Fig 9. C-core details.

17. Confirm sizes for core.

18. Calculate the theoretical primary turns, thNp.

19. Calculate theoretical Primary wire dia, thPdia.

20. Find nearest suitable overall dia wire size from

the wire size table.

Table 1. Available Wire Sizes.

21. Caculate maximum safe working Idc.

22. Calculate the bobbin winding traverse width.

23. Calculate no of theoretical P turns per layer.

24. Calculate theoretical number of primary layers.

25. Calculate actual Np.

26. Calculate average turn length, TL.

27. Calculate primary winding resistance, Rwp.

28. Calculate pri winding loss % with minimum RLa-a,

29. Is the winding loss more than 3.0%?

------------------------------------------------------------------------------------

14. Calculate minimum centre leg cross sectional area, Afe.

Confirm RLa-a minimum and maximum power at clipping.

OPT-1A. From Previous Steps, RLa-a min = 4,500 ohms,

Max PO = 72 Watts.

Afe = 300 x sq.rt ( audio power, Watts ), in 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 old formula is based on B being
about 1 Tesla, or 10,000 gauss at 50Hz

but for audio hi-fi Bac max should be less than 0.5 Tesla for an
OPT at 50Hz.

After considerable trials I found the above formula is a good guide for
PP audio

OPT.

OPT-1A1, Theoretical Afe, thAfe =
300 x sq.rt 72

=
300 x 8.49 = 2,547
sq.mm

For a square core section,
Tongue
dimension = Stack height, ie, T = S.

Theoretical T x Theoretical S = th
Afe, sq.mm.

Therefore theoretical T dimension =
square root th AFe = Th T, mm

OPT-1A, thT = sq.rt 2,547 = 50.46mm.

Choose suitable standard T size from list of available wasteless
E&I lamination

core materials with assembled E&I plan sizes of :-

Fig
8.

T sizes commonly available for
wasteless OPTs :-

20mm, 25mm, 32mm, 38mm, 44mm, 50mm, 62.5mm

NOTE.
The thT calculated =
50.45mm, which indicates the standard size
of

T = 50mm may possibly be best.

But using one size smaller should be tried because it has been found
that the

weight may be slightly less if the aspect ratio gives a Stack height
more than

Tongue dimension. If it is found to be difficult to get low
winding losses

with the slightly lower T size, the stack height may be increased to
reduce the

number of primary and secondary turns so thicker wire with less
resistance

may be used.

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 must be the same for either T = 44mm or 50mm so the LF response and

Fsat does not change with tongue
size. HF peformance depends entirely upon

the interleaving geometry and
insulations.

OPT-1A, choose core T =
44mm

Fig
9.

NOTE.
Some constructors will
be using non wasteless pattern 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

carefully considered.

Other lamination
patterns or C-cores 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 pattern, the ratio of Afe size relative to

Bac max must be maintained.

16.
Calculate
theoretical
Stack
height.

thS = Afe / T,
then adjust to a larger height to suit nearest standard

plastic bobbin size if available, mm.

OPT-1A, S = 2,547 / 44 = 57.8mm. This is more than 10% above

a standard size bobbin allowing stack height of 50mm, so a hand

made bobbin should be used, say 45mm x 60mm maximum hole

size, with stack = 59mm.

Adjusted Afe = chosen T x chosen S, sq.mm

OPT-1A.
Adjusted
Afe
=
44
x
59
=
2,596sq.mm

T = 44mm, H = 22mm, L = 66mm, S = 59mm.

thNp
=
square
root
(
PRL
x
PO)
x
10,000
/
Afe
=
thNp,
no
of
turns.

NOTE.
The
formula
here
is
derived
from
more
complex
and
complete
formula

taking Bac max and F into account. If we want magnetic field strength
Bac

=
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

steps below where
the design is checked. The V factor
can be expressed as

sq.root of ( Primary RL x power output ) as in the above simplified
equation.

RL = 4,500 ohms, PO = 71,
Afe = 2,244sq.mm from previous steps,

OPT-1A. ThNp = sq.rt( 4,500 x 72 ) x 10,000 / 2,596 = 2,192 turns.

NOTE.
The
Primary
wire
used
for
the
transformer
will
occupy
a
portion

of the window area approximately = 0.28 x L x H. The constant of 0.28

works for
most OPT.

Each turn of wire will occupy an area = overall dia
squared.

Overall or oa dia is the dia including enamel insulation.

Therefore theoretical over all dia of
P, thoaPdia, of wire including enamel

insulation = square root (
0.28 x L x H / thNp ), mm.

OPT-1A, th oa dia P wire = sq.rt (
0.28
x 66 x 22 / 2,192 )

=
sq.rt
0.185 =
0.430
mm

20. Find nearest
suitable overall dia wire size from

the wire size table.
oaPdia, mm

Table
1.
Available
Wire
Sizes.

OPT-1A,
Want
oa
dia
not
exceeding
0.43mm
calculated
in
Step
19.

Try
oa
wire
size
=
0.414mm,
with bare copper dia =
0.335
mm.

21.
Caculate
maximum
safe
working
Idc.

Safe working direct
current density
rating for most OPTs

= 2Amps per square
millimetre of copper cross sectional area for the wire.

This results in OPTs running cool.

Safe dc current, Idc = Ia rating x pye
x ( d squared / 4 ) Amps.

where Ia rating is Amps per sq.mm, pye = 22/7, d is copper wire dia in
mm.

OPT-1A, Cu dia wire = 0.355mm, Rating 2A/sq.mm.

Safe Idc = 2 x 3.143 x 0.355 x 0.355 /
4 = 0.198 Amps dc.

Is this current rating more than 2 x idle current proposed?

Idle current = 50mAdc; 2 x Ia = 100mA, and well below wire rating;

Primary wire size is OK.

NOTE. If the Idc current
density is kept below 2A/sq.mm, the heat
dissipated

in a winding is usually very low so winding heating does not need to be

calculated. With 50mA Idc flow in 1/2 the primaryRwp of 57 ohms, heat
in

the wire = I squared x R = 0.1425 Watts. It must be remembered the primary

wire may seriously over heat if bias failure occurs and with a
saturated 6550

the Idc may reach 0.5 Amps, so heat in the P wire = 14.25 Watts, and
the

wire may get so hot it melts the OPT insulation, and insulation failure

may occur. It is important to
have active protection circuitry preventing Ia

ever reaching more than about 150mA dc for longer than 4 seconds.

22. Calculate
the bobbin winding traverse width.

NOTE. Bobbin traverse
width, Bww, is the distance between the cheek

flanges and varies depending on who made the bobbin, but it is common

for each flange thickness to be about 2mm for many bobbins with T
between

32mm and 62.5mm.

The winding traverese width affects the number of turns
per layer.

Some tradesmen or women do not use moulded bobbins but use a simple

rectangular tube former made with cut peices of 2mm fibre glass sheet

and then use interlayer insulation extending to the full window length
L.

The winding layers start and stop at about 2mm short of the window

size so Bww ends up being the same as for where a pre-moulded bobbin

with 2mm cheek flanges is used. The advantage is minor, but for OPTs

with HV, there is better "creepage distance" between each layer of wire

as the path for an arc is much longer with "cheekless bobbins". Much

more skill is needed for cheekless windings and so it is rarely ever
used

except by old guys who learnt their trade 60 years ago.

So, for design purposes, the
winding will traverse a
distance = L - 4mm.

OPT-1A, For core window L = 66mm, Bww
= 66 - 4 = 62
mm.

23. Calculate no of
theoretical P turns per layer.

ThPtpl = 0.97 x Bww / oa dia from Step
20.

NOTE. The constant 0.97
factor allows for imperfect layer filling.

Ignore fractions of a turn.

thPtpl = 0.97 x 62 / 0.414 =
145 Primary turns per layer.

24. Calculate
theoretical number of primary layers.

Then round down or
up to convenient even
number of layers.

Theoretical N pL = ( Theoretical Np
from step 18 ) / PtpL from step 23,

then round up/down.

OPT-1A, thNpL = 2,192 / 145 = 15.11 layers; round UP to 16 layers.

NOTE. Rounding down may
reduce Np and raise Fs above wanted 14 Hz.

But the actual turns used will give low enough Fs, in this case 14.4Hz,
less

than a 15% rise above design aim and OK. For those wanting to maintain

Fs = 14Hz, or have Fs marginally lower than 14
Hz, the Afe can be

increased by increasing S from say 59 mm to 62.5 mm or more and
then be

able to use a standard size of pre-made moulded bobbin 44mm x 62.5mm,

and have Fs slightly lower.

The calculated number of
primary layers should be an even
number to avoid

a
primary winding CT in the middle of a layer which is awkward to wind,

and because each
1/2 primary winding should have an equal
number of

turns
and a symetrical geometric layout either side of the
CT.

25. Calculate actual
Np.

Np = Number of P layers from Step 23 x thPtpl from Step 23.

OPT-1A,
Np
=
16
x
145
=
2,320
turns.

26. Calculate
average turn length, TL.

TL = ( 3.14 x H ) + ( 2 x
S ) + ( 2 x T ), mm.

where 3.14 is pye, or 22/7, and 2 are constants.

OPT-1A, TL = ( 3.14 x 22 ) +
( 2 x
59 ) + ( 2 x 44 ) = 275
mm.

27. Calculate
primary winding resistance, Rwp.

Rwp = 2.26 x ( Np x TL ) / ( 100,000 x
Pdia x
Pdia ), ohms.

where 2.26 is the resistance of 100 metres of 1.0mm dia wire and a
constant,

and 100,000 is a constant, and P dia is the copper dia from the wire
tables.

OPT-1A, PRwp = 2.26 x 2,320 x 275
/ ( 100,000 x 0.355 x 0.355 ) = 114
ohms.

28. Calculate
pri winding loss % with minimum RLa-a,

P loss % = 100% x Rwp / ( PRL + Rwp ),
%.

OPT-1A, P loss = 100% x 114 / ( 4,500 + 114 ) =
2.47%.

29.
Is
the
winding
loss
more
than
3.0%?

If YES the design calculations must be checked and perhaps a larger
core stack

or window size chosen.

If NO, proceed to Step 30.

OPT-1A, P winding loss is less than 3.0%.

NOTE.
The calculations so far
are based on using the lowest
likely RLa-a.

Under optimal normal operation, RLa-a will be higher than the mimimum

RLa-a for class AB1 and pure class A and give lower winding losses.

Typical Middle Value RLa-a would be 2 x min
RLa-a, or 9k0 in this case,

and if so, winding losses will be 1/2 those for
the 4k5. But for best design

the OPT should have low winding losses even were RLa-a is a minimum

value.

It is better to have low winding
losses so that the primary windings are unlikely

to
overheat if a tube malfunctions and draws excessive Idc during a

"bias failure
event". Such occurences were a main reason why so many

OPTs of the past failed so easily after being designed by accountants

rather than engineers who know "shit happens" :-)

Forward to PP OPT Calc page 3.

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to
PP
OPT
Calc Main Page 1.