FOR PP TRIODE CLASS

A1 AND AB1, OPT-2A

55. Understanding Ra curves for triodes.

Fig 29. Ra curves for 6550 and 300B.

56. Understanding Ra curves for triodes.

Fig 30. Ra curves for 6550 in triode.

57. Calculate the minimum PP Triode RLa-a for

maximum class AB1 power for OPT-2A.

Fig 31. Graph for Po vs RLa-a 6550 PP triodes.

58. Calculate maximum AB1 power for minimum RLa-a.

59. Calculate RLa-a for maximum pure class A1 power.

60. Calculate maximum class A1 PP triode power output.

61. Calculate the Middle RLa-a for triode PP operation.

62. Calculate PO for Middle RLa-a,

63. Conclusions about PP triode OPT design.

14T. Calculate minimum centre leg cross sectional area, Afe, triode PP amp.

15T. Calculate the core tongue dimension, T.

16T. Calculate theoretical Stack height.

17T. Confirm sizes for core.

18T. Calculate the theoretical primary turns, thNp.

19T. Calculate theoretical Primary wire dia, thPdia.

20T. Find nearest suitable overall dia wire size from wire tables.

21T. Calculate the bobbin winding traverse width.

22T. Calculate no of theoretical P turns per layer.

23T. Calculate theoretical number of primary layers.

24T. Calculate actual Np.

25T. Calculate average turn length, TL.

26T. Calculate primary winding resistance, Rwp.

27T. Calculate pri winding loss % with MIDDLE RLa-a.

28T. Is the winding loss more than 3.0%?

29T. Choose the interleaving pattern.

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55. Triode PP class A1, AB1.

The example title for Triode OPT will be OPT-2A,

and will be used for 2 x 6550 or KT88 with Ea = +500V,

Ia dc = 50mA in each tube at idle, and tube conditions are the same

as OPT-1A.

Before any calculations for triode PP OPTs begin it will be necessary

to inspect a copy of the Triode Ra curves for any triode chosen in a project,

or for triode connected pentode or tetrode, even if load line analysis is not

done.

Fig 29.

The above Fig 29 shows the triode Ra curves for Ea vs Ia for 6550 and 300B

on the same scale size allowing comparison of the two very differently

constructed tubes. Notice that the curves are substantially similar, and any

OPT designed specifically for 300B may be used for the following tubes

strapped as triodes :- 6550, KT88, KT90, KT120, or vice versa.

56. Understanding Ra curves for triodes.

Fig 30.

Fig 30 shows 6550 triode curves with curve for Pda limit = 42 Watts.

There are also two load lines, and although is not really necessary to draw

load lines for the OPT calculations, I have included them anyway and all is

explained :-

Inspect the anode Ra curve for where Eg1 = 0V.

Find the Ea and Ia point on this Ra line for Eg1 = 0V where it is intersected

by the 42 Watt Pda limit curve for the 6550 triode.

Plot this point on the Ra curve as POINT X.

Calculate the approximate Ra for the triode for where Eg1 = 0.0V.

Ra = Ea / Ia = 188V / 0.222A = 846 ohms.

This is the approximtae resistance value of the line between Point O

and Point X.

57. Calculate the minimum PP Triode RLa-a for

maximum class AB1 power for OPT-2A.

The minimum RLa-a for triodes should not be less than 4 x Ra, where Ra

is calculated between point O and point X, seen in Fig 30 above.

This means the class B RLa for each tube during AB1 operation should not

be less than Ra for the Eg1 = 0.0V curve. This applies for all values of Ea

used in triode amps.

Pda maximum with continuous sine wave signals should not exceed the

Pda rating for the tube, For triodes in class AB1 with restricted Ea swing

compared to tetrode operation, the Pda max is usually at clipping with the

low RLa-a values.

One might be tempted to use a B RLa-a of less than Ra which means

RLa-a will be very low, and tube Pda may exceed the data limit, class A1

portion of total power very low, THD very high, and damping factor

very low.

The Pda with sine wave operation up to clipping is dealt with in my page

anode-dissipation+waveforms.html

OPT-2A, Ea = +500V, Idle Ia per tube = 50mA,

Minimum RLa-a = 6 x 846 ohms = 5,076 ohms.

Fig 29 above shows the B RLa = RLa-a min / 4,

= 5,076 ohms / 4 = 1,269 ohms.

The amount of output power for PP 6550 triode operation is shown here :-

Fig 31.

Fig 31 shows the range of loads and output power for PP triodes using 6550.

The graph is only valid for Ea = 500V, and would need completely re-calculating

for other values of Ea and different tubes.

Values of Ea for various PP triodes may be chosen within ranges as follows,

with Ra values for calculations :-

2A3, Ea = +200 to +300V, Ra at Eg1=0V, 700 ohms approx.

300B, Ea = +300V to +420V, Ra = 680 ohms,

845, Ea = +800V to +1,250V, Ra = 2,200 ohms,

211, Ea = +800V to +1,500V, 3,500 ohms.

6CM5/EL36, Ea = +300V to +375V, Ra = 475 ohms,

13E1, Ea = +300 to +375V, Ra = 300 ohms,

6550, KT88, KT90, Ea = +350V to +520V, Ra = 850 ohms,

KT66, 6L6GC, 807, 5881, Ea = +300V to +430V, Ra = 1,600 ohms,

EL34, 6CA7, Ea = +300V to +430V, Ra = 1,250 ohms,

6V6, Ea = +250V to +350V, Ra = 2,600 ohms,

EL84, Ea = +250V to +350V, Ra = 2,100 ohms.

NOTE. Ra values are all at Eg1 = 0.0V, to enable minimum RLa-a

calculations. Ra will be higher at the idle position, and will vary

depending on Ia at idle, and is high for where Idle Ia is low and Ea is high.

Ra is lowest where Ia is highest and Ea lowest.

Designers MUST NOT assume anything.

58. Calculate maximum AB1 power for minimum RLa-a.

Maximum safe class AB1 Power,

PO
= 0.125 x
RLa-a
x
Ea
squared

(
[
RLa-a
/
4
]
+
Ra
)
squared

OPT-2A, RLa-a minimum
= 5,076 ohms, Ea = +500V,

Ra at Eg1 = 0V = 846 ohms,

Max class AB PO = 0.125 x
5,076 x 500
squared

( [ 5,076 / 4
] + 846 ) squared

= 0.125 x 5,076 x 250,000 / (
1,269 + 846 ) = 35.45 Watts.

the RLa-a for pure class A, the same formula may be used for where the limiting

Ra line slope is for Eg1 = 0.0V, and between Point O to Point X on curves.

For those needing to draw loadlines, the line D to C for B RLa = 1,269 ohms

intersects Ra limiting curve at Ea = 199V = Ea peak minimum V.

PO = 2 x ( Vpeak swing squared ) / RLa-a

RLa-a = 5,076 ohms from above, Vpeak swing, one triode = 500V - 199V

= 301V.

OPT-2A, PO max = 2 x 301 x 301 / 5,076 = 35.7 Watts

NOTE. This seems about correct for max PO shown in Fig 31 above.

59. Calculate RLa-a for maximum pure class A1 power.

RLa-a for 1 pair of output tubes in class A1 = 2 x [ ( Ea / Iadc ) - ( 2 x Ra ) ].

OPT-2A, RLa-a class A1 = 2 x [ ( 500 / 0.05 ) - ( 2 x 846 ) ]

=
16,616 ohms.

NOTE.
For more than one pair of output
tubes divide above by
the

number of
pairs, for example, if there were 4 x 6550, RL = 16k6 / 2 = 8k3.

60.
Calculate
maximum
class
A1
PP
triode
power
output.

PO = 0.5 x Ia squared x RLa-a
where Ia is the Idle Ia dc for one tube.

OPT-2A, Pure class A1 PO max = 0.5
x 0.05 x 0.05 x 16,616 = 20.77 Watts.

Middle RLa-a =

Minimum RLa-a x square root ( RLa-a for Max class A1 / RLa-a safe
minimum. ).

OPT-2A,
Middle
RLa-a

= 5k1 x sq root ( 16k6 / 5k1 ) = 5k1 x
sq root 3.25 = 9k2.

NOTE.
It is coincidental that
Middle RLa-a for 6550 Beam Tetrode and

Triode have been found to be so close to each other.

62. Calculate PO for Middle RLa-a,

Max class AB PO = 0.125
x
9,200 x 500
squared

( [ 9,200 / 4
] + 846 ) squared

=
29 Watts.

NOTE.
This result agrees with Fig 31 above.

63.
Conclusions
about
PP
triode
OPT
design.

OPT-2A,
For
2
x
6550,
Steps
55
to
63 can be summarized as listed :-

RLa-a Minimum AB1 = 5,076 ohms, PO
= 35W, Va-a = 421Vrms.

RLa-a Middle AB1= 9,200 ohms, PO = 29Watts, Va-a = 516Vrms.

RLa-a Max Class A1 = 16,600 ohms, PO = 21Watts, Va-a = 590Vrms.

The core size can be designed
according to the Middle RLaa PO and Va-a,

and for that the triode OPT is designed by following all the steps
after

Step 14, but labelled 14T to 19T :-

14T.
Calculate minimum centre leg
cross sectional area,

Afe, for triode PP amp.

NOTE. I have left out references and
diagrams from

steps 14 to 19 above.

Confirm MIDDLE RLa-a and
maximum power at clipping, 2 x 6550.

OPT-2A. From Steps above, Middle RLa-a
min = 9,200 ohms,

Max PO = 29 Watts.

Afe = 300 x sq.rt ( audio power,
Watts ), in sq.mm.

OPT-2A Theoretical Afe, thAfe =
300 x sq.rt 29

=
300 x 5.385 = 1,615
sq.mm

15T.
Calculate
the
core
tongue
dimension,
T.

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-2A, thT = sq.rt 1,615 = 40.2mm.

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

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

T sizes commonly available for
wasteless OPTs :-

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

NOTE.
The thT calculated =
40.2mm, which indicates the standard T size
of

38mm may possibly be best, because it is closest to 40.2mm.

But with triode there is
inefficient operation compared to UL or CFB operation.

So T should ALWAYS be larger than the theoretical T calculated.

Therefore T = 44mm should be
trialed.

If a smaller T is tried, 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-2A, choose core T =
44mm

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.

16T.
Calculate
theoretical
Stack
height.

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

plastic bobbin size if available, mm.

OPT-2A, S = 1,615 / 44 = 36.7mm. This may be increased to suit

a standard size bobbin allowing stack height of 38mm. A hand made

bobbin need not be used.

OPT-2A Stack height = 38mm.

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

OPT-1A.
Adjusted
Afe
=
44
x
38
=
1,672sq.mm

T = 44mm, H = 22mm, L = 66mm, S = 38mm.

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

OPT-2A,
RL
=
9,200
ohms,
PO
=
29,
Afe
=
1,672sq.mm
from above,

OPT-2A. ThNp = sq.rt( 9,200 x 29 ) x 10,000 / 1,672 = 3,089 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-2A, th oa dia P wire = sq.rt (
0.28
x 66 x 22 / 3,089 )

=
sq.rt
0.132 =
0.362
mm

20T. Find nearest
suitable overall dia wire size from

the wire size table.
oaPdia, mm.

Table
1.
Available
Wire
Sizes.

Choices are :-

0.334mm oa dia for Cu dia = 0.28mm,

0.371mm oa dia for Cu dia = 0.30mm.

NOTE. It will be found that working with wire less than 0.4mm is very difficult.

So the wire size immediately above 0.362 might be tried. The core stack

may always be increased to reduce the Np needed.

Try oa wire size = 0.371mm, with bare copper dia = 0.30 mm.

21T. Calculate the bobbin winding traverse width.

OPT-2A, For design purposes, the winding will traverse a distance = L - 4mm.

OPT-2A, For core window L = 66mm, Bww = 66 - 4 = 62 mm.

22T. Calculate no of
theoretical P turns per layer.

ThPtpl = 0.97 x Bww / oa dia from step
12.

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

Ignore fractions of a turn.

OPT-2A, thPtpl = 0.97 x 62 / 0.371 =
162 Primary turns per layer.

23T. Calculate
theoretical number of primary layers.

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

Theoretical N pL = ( Theoretical Np
from step 18T ) / PtpL from step 22T,

then round up/down.

OPT-2A, thNpL = 3,089 / 162 = 19.067 layers; round UP to 20 layers

or down to 18 layers.

Let
us
try
P
layers
=
18.

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 38mm to 44mm or more and
still be

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

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.

24T. Calculate actual
Np.

Np = Number of P layers from Step 23 x thPtpl from Step 22.

OPT-1A,
Np
=
18
x
162
=
2,916
turns.

25T. 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-2A, TL = ( 3.14 x 22 ) +
( 2 x
38 ) + ( 2 x 44 ) = 233
mm.

26T. 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-2A, PRwp = 2.26 x 2,916 x 233
/ ( 100,000 x 0.30 x 0.30 ) = 170
ohms.

27T. Calculate
pri winding loss % with MIDDLE RLa-a,

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

OPT-2A, P loss = 100% x 170 / ( 9,200 + 170 ) =
1.81%.

28T.
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 29.

OPT-2A, P winding loss is less than 3.0%.

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

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

MIDDLE RLa-a for class AB1. The winding losses for RLa-a of 5k0

are nearly double at about 3.3% and for pure class A of 16k6, losses
will

be less at about 1%, and in all cases losses are low enough.

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" :-).

29T. Choose the
interleaving pattern.

Inspect tables 2, 3, 4, 5 ABOVE for the power from the
transformer.

Choosing an interlaving pattern
may entirely bamboozle many readers

or designers who have not much experience with winding audio frequency

transformers for wide bandwidth between about 14Hz and at least 70kHz.

At this
point in the design process for PP triode OPTs,

I will now abandon you all and leave you to proceed

through all steps to a final design.