OUTPUT TRANSFORMER THEORY.
Content of this page :-
Function of the output transformer, ( OPT ).
How the OPT works.
Impedance and resistance transformation.
Fig1.  Equivalent model of Ultralinear output stage tubes and OPT.
Functions in the model and preferred OPT characteristics.
Test conditions for specifying OPT performance.
Description of OPT No1, wire and turns and insulation description.
Fig 2.  Cross section of bobbin winding details.
Fig 3.  Schematic of OPT No1 when used in UL with two impedance matching settings shown.
Fig 4.  Schematic of OPT No1 when used with 12.5% CFB windings and with two impedance
matching settings shown. Notes about recommended amounts of CFB to be used.
Impedance matching notes.
Table 1.  Impedance matchings available with OPT No1.
Table 2.  Recommended output tubes for OPT No1 with winding losses.
Comments about alternative tubes used with OPT No1.
Specification for OPT No1, notes re LF behaviour, power handling ability,
HF behaviour, HF resonances, distortion.
Description of PP OPT No2.
Description of SE OPT No3.
Brief note about SE OPT No4.
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In nearly all tube power amps there are transformers required to couple the output tubes to the
speaker load. Readers may wonder just what any transformer does; they see heavy box with
many terminals and there are no clues to what happens inside.

The tubes operate with large voltage and small current changes. The power they produce
in a load resistance, P RL = Volts rms x Amps rms = Watts. Conventional electro-magnetic
dynamic speakers require high current and low voltage. A typical pair of tubes may have an
output transformer, OPT, to produce 20 times the speaker voltage and 1/20 of the speaker
current needed for the speaker. Ribbon speakers require even lower voltage and higher current
and will have another transformer built into them. Electrostatic speakers also have transformers
built into them which transforms the amplifier output voltage upwards by perhaps 100 times,
and reduces the current in the ESL to be 100 times less than at the amplifier output terminals.
But we will always need an output transformer to get from the tubes which require a load of
thousands of ohms to the amplifier output terminals which have load range usually between 4
and 16 ohms.

The exception to the rule for needing an OPT is where a large number of "special" tubes are
used in what are called "OTL" amps, ie "output transformerless" amps. The vast majority of
tube amps use an OPT, and with an OTL amp I don't hear any better music. I have not ever
bothered to build any tube power amp without an OPT. Without an OPT, the load matching
in all OTL amps is quite appalling, and the tubes must work in their non linear near class
B region with high levels of NFB applied to correct the high levels of THD/IMD and very
high output resistance which exists without NFB use.

If you don't want to use an OPT, perhaps power mosfets are the best device to use. Tubes
were never designed to work in OTL amps. But people force them to do so with some risk to
reliability. And many people will end up finding that an external output transformer needs to be
used with an OTL amp; there are some companies making suitable "speaker load matching"
transformers, such as http://www.zeroimpedance.com  An impedance change of up to 8:1 is
available so that a 4 ohm speaker load is made to appear to the OTL amplifier as a 32 ohm
load which is far less likely to cause tube overheating and thermal run-away so prevalent in
OTL amps. 

So I will be discussing output transformers from my viewpoint that a well done OPT offers a
completely sonically transparent and neutral method to couple the energy from vacuum tubes
to speakers. With class A triode output stages it is possible to build amplifiers which do not
need any global NFB because the THD/IMD and Rout is all low enough, and the OPT
does not make significant contribution to THD/IMD.

The OPT works with two separate coils of wire wound around a core made of specially made
iron sheets called laminations. These laminations are usually made from 0.35mm thick sheet
iron which contains about 4% silicon and which has been repeatedly rolled and heat treated
to improve the magnetic qualities we seek that are suitable for use with any frequency from
very low F of say 3Hz to 10kHz. The iron core material has little function above 10kHz and
the OPT acts like an air cored transformer to perhaps 500kHz or more depending on the
winding interleaving and winding insulation and circuit loadings.
One of the two coils of wire consists of a primary winding which accepts incoming power from
the tubes which provide high voltage and low current, and has a lot of very fine wire turns using
insulated wire. The other winding is the output winding called the secondary and it has much
fewer turns but of much thicker wire to suit the higher current and lower voltage for a speaker.

When we apply a signal voltage to the primary, a varying magnetic field is set up in the iron core.
This magnetic field is shared by both primary and secondary. A strange and mysterious
electromagnetic phenomena occurs.

Consider this OPT example...
Suppose we have say 500Vrms applied to 2,000 primary turns. Suppose there is a secondary
of 64 turns. We will find that a voltmeter tells us there is only 16Vrms across the secondary.
This voltage is induced into the secondary by the shared and varying magnetic field produced
by the signal acting on the primary. In fact we would find that the primary to secondary
voltage ratio is proportional to the primary to secondary turn ratio. In this case we have
a 2,000 : 64 turn ratio, ie 31.25 : 1, called TR, so the secondary produces voltage
= ( 1 / TR ) x primary voltage, and current = TR x primary current.

Suppose we have an 8 ohm speaker load connected across the secondary with 2 Amps rms.
Spaker voltage = 16Vrms, and power = V squared / R  in Watts = 16 x 16 / 8 = 32 Watts.
Also from Ohm's Law, power = I squared x R = 2 x 2 x 8 = 32 watts.

We will find that the current in the primary winding = secondary current  / TR = 2 / 31.25
= 0.064Arms, or 64mArms.

We already know there is 500Vrms applied across the primary. This is reduced to 500 / TR
= 500 / 31.25 = 16Vrms. Primary input power = V x I = 500V x 0.064A = 32 watts.
Power liberated in a load = Voltage across the load x Current flow in through the load.

They should also see that where you have 500V applied to a load at the primary where
0.064 A flows, then from Ohm's Law, load, RL = E / I = 500V / 0.064A = 7,812 ohms.

The impedance ratio of the transformer is the ratio of the load "seen" at the primary winding
input and the load connected at the secondary. In this example 8 ohms is transformed to 7,812
ohms at the primary. The OPT is viewed as having no impedance or resistance itself , it is merely
a device to change the resistance or impedance of a secondary load to suit the tubes. The
change in impedance is the impedance ratio, ZR, and in this case ZR = 7,812 / 8 = 976.6 : 1
This is also always the square of the turns ratio and in this case the square root of the impedance
ratio = the turn ratio = 31.25 : 1.  ZR = TR squared.

Therefore the OPT transforms the secondary load from 8 ohms to 7.8k ohms "looking into"
the OPT primary terminals. The 7.8k load load could well suit a pair of 6550 or KT88 connected
with 40% Ultralinear taps or operating in triode mode.

Like any device used for power transformation there are technical imperfections. The winding
resistance of the wire used in the OPT may be 2.5% of the loads for each of the P and S
windings and so a total of 5% of power is lost as heat in the OPT, so that to get 32 watts at the
secondary output, 5% of 32 Watts, or 1.6 Watts of extra power must be applied to the primary,
ie, 33.6 Watts. The voltage supplied by the tubes must be higher for 33.6 Watts. Current will
remain the same 0.064Arms as for 32 Watts.
Primary input Vrms = ( Secondary output power + winding loss power ) / Primary Irms.
In this case, V Pri = 33.6 / 0.064 = 525Vrms.

Primary Load including Pri and Sec winding resistances = V / I = 525V / 0.064A = 8.2k ohms.

The load of 7.8k ohms still exists, but there 5% of this load, or 390 ohms of winding resistance,
Rw, which acts IN SERIES with the 7.8kohms to give a total load of 8.2k ohms.

During design analysis Rw may be neglected to keep calculations simple except for calculations
of amplifier output resistance.
Calculations are dealt with in my 'tube operation' and 'load matching pages'.

Here is a very basic Model of output tubes and output transformer with basic resistance,
capacitance, and leakage inductance.
Fig1.

Fig 1 shows an Equivalent Model of a PP output stage with a pair of class A UL 6550 tubes.
The OPT is considered without its centre tap and B+ supply because we are only interested here in
the ac working. So the OPT primary with CT can be considered here as one winding with one end
grounded. The Ra of 4k for each tube is summed to make Ra-a = 8k and this output anode resistance
of the 2 tubes and is shown in series between OPT primary winding input and the output of an
imaginary voltage generator.

The model generator has an imaginary output = µ x grid input voltage which in this case is the
summed grid to grid signal input voltage of 51.85Vrms. The µ of the tubes = 20, so the generator
produces the imaginary Vout = 1,037Vrms. There is 500Vrms across the the primary load and
the load is 7.8k, ( neglecting Rw ) so there is 64mA of load current which flows around the circuit
through Ra-a to the OPT input, through the leakage inductance which appears as a low value series
inductance, then through the winding resistance which also acts as a small series resistance and on to
the transformed secondary load which appears here as 7.8k at the primary winding input.
The actual two winding transformer is considered perfect with no losses due to Rw or L or C, but
here the imperfections are added as they behave in the real world and are depicted as

The Primary winding for anodes is 0.35 mm copper dia wire.
The overall dia including the coating of insulation will be 0.42 mm.
The traverse width of 62 mm of the bobbin will allow 145 turns per layer.
There are a total of 16 primary layers each with 145 turns, to make a total of 2,320 turns.
These layers are grouped into five sections, with two sections of two layers,
and three sections of four layers.
The HT is connected to a CT and UL screens can be connected to tappings at 37.5%
of the half primary windings to provide the UL screen feedback.
The central four layers are subdivided into four separately terminated windings to
allow tertiary cathode feedback use of either 12.5% or 25% of the total windings.

The Secondary winding for speaker connection consist of 6 windings in 4 layers using
1.0 mm copper dia wire. Three have 57 turns each between each side of the bobbin.
The uppermost secondary layer in the wind up is divided into three sections of 19 turns
each. These four layers are alternately placed between the 5 main primary sections.
It can be seen that there are 5 primary sections, and four secondary interleaved sections.
Thus 57, 76, and 114 secondary turns are available for matching purposes.

High temperature insulated best quality copper magnet winding wire
must be used, and neatly wound in even flat layers to fill the bobbin.

Insulation :-
Insulation can be Teflon, which is best, but it is very expensive and difficult to work with.
Polyester is quite OK and has sufficiently good temperature ratings and a dielectric constant
of under 3, and very similar to Teflon so the effective capacitance is not increased too much.
Don't use electrical paper. Nomex is another one which is also OK. I have used polyethylene
which gives a lower dielectric constant of less than 2, so capacitances are minimal with
polyethylene but the temperature rating is poor, so a short circuited tube may heat a primary
winding and melt the insulation unless there is active protection against excessive tube currents.
Polyethylene, also known more commonly as polythene does not allow the use of electrical
varnish and baking at 125C for 4 hours and the OPT must be impregnated by soaking in
molten wax at less than 90C. Alternatively use polyurethane two pack Estapol 7008 which
is applied while you wind and which avoids the whole process of varnish or wax or baking.
See the page on winding transformers.

The OPT described will not run hot under normal conditions.
The insulation is placed as noted on the bobbin winding guide. It should be pre cut from sheets
to tightly fit between the cheeks of the bobbin, but not so tight to causes wrinkling of the
sheet materials. The arrangement allows for 0.05 mm thick insulation is placed between
primary to primary layers with the same direct voltage potentials. 0.5 mm insulation is placed
between primary and secondary layers, with the exception of placing it between primary to
primary layers as shown on the winding guide within the four central layers to allow the use
of all these layers, or half of them for a tertiary cathode feedback winding.

All wires coming out of the wound bobbin through slots or holes are insulated with heat
resistant sleeving cut to 50 mm long, so 25mm of the sleeving extends into the winding area.
Outside the bobbin, this fine gauge sleeving extends 25 mm, and allow for slightly larger
sleeving to be fitted over the top between the bobbin and the termination boards,
following winding of the bobbin.

Fig 2. Bobbin details, OPT No1.

The schematic for the OPT No1 is shown below with probably the most common
and desirable load matching for the majority of push pull amplifiers world wide.
Fig 3.

The Fig 3 above shows the OPT connected for standard Ultralinear with 37.5% screen taps.

Fig 4.

The Fig 4 above shows the use of 12.5% of the primary windings used for cathode
feedback to the output tube cathodes. Its possible to use all primary layers from 6 to 13,
( see Fig 2 ) to have 25% of CFB. My website page describing the integrated 8585 amplifier
shows the details for using 12.5% CFB with KT90, KT88, 6550, with Ea = +480Vdc, screen
supply, Eg2 = +330Vdc. This gave the best power output, lowest THD, and biggest
effective anode resistance reduction compared to any other way of setting up an output
stage for multi-grid tubes. However, the maximum grid driving voltage Vg1-k at each
output tube is 56Vrms, and using 25% CFB increases Vg1-0V to about 87Vrms
and the distortion of the drive stage needs to be kept low by means of the circuit
shown in my 8585 amplifier.

There are 3 main turn ratios.
(1)  2,320 primary turns to 57 secondary turns, with four paralleled 57 turn windings.
This gives a TR = 40.7:1, which gives an impedance ratio, ZR, = 1,656:1.

(2)  2,320 primary turns to 76 secondary turns, made up from three paralleled 57 turn windings,
seriesed with three 19 turn windings in parallel.
This gives a TR = 30.5:1, which gives ZR = 930 to 1.

(3)  2,320 primary turns to 114 secondary turns, made up with two seriesed
pairs of 57 turn windings in parallel.
This gives a TR = 20.3:1, which gives ZR = 412:1.

Table 1.  Load matching and impedance ratios, OPT NO1.

The winding resistances are :-
Primary, 2,320 turns of 0.35 mm dia wire = 113 ohms.
Secondary, 4 x parallel 57 turn windings, 1.0mm dia wire = 0.085 ohms = 141 ohms reflected to the primary.
Total winding resistance looking into the primary = 113 + 141 = 254 ohms.

OPT Power Loss %  = 100 x Rw / ( Rw + RL ) %

Table 2. Recommended tubes for OPT No1 with approximate power output and winding losses :-

SPECIFICATIONS, OPT NO 1.

Low frequency behaviour.
The low frequency limit is due to core saturation which is voltage dependant, irrespective of load
currents. Frequency of saturation, Fsat = 13.2 Hz where Bmax = 1.8 Tesla at 547Vrms anode
to anode, which is 45 watts into 6.6k.

The primary inductance depends on the ac voltage and frequency applied and the permeability,
µ, of the iron laminations. At 50Hz maximum µ of the E&I GOSS laminations I purchased from
Sankey in Newcastle, NSW, reaches a maximum 17,000 when the lams are fully interleaved.
The resulting maximum primary inductance = 1,077 Henrys. At very low Va-a of 5Vrms,
LP is greater than 100H and the inductance is entirely sufficient so that with RL = 8ka-a
and Ra-a also 8k, the -3dB point at LF at levels below saturation = lower than 6 Hz.

Power handling ability is only restricted by to whatever saturation frequency and losses
are deemed acceptable, and limits on the DC input current. The primary wire size = 0.35mm
copper dia so the maximum dc current at 3amps/sq.mm = 288mA, or 577mA at the CT.
This is much more that whatever may be used for any of the tube listed in the
recommended tube table 2 above.

110 watts into 1.65k is only 426Vrms a-a, and the ac signal current = 258mA. This is
approaching the safe continuous ac power but with music signals there is never a
continuous maximum sine wave signal.

100 watts into 5k will be  707Vrms, and ac  signal current is well within the OPT safe
working area. However, as Va-a rises, the Fsat will rise, and at 800Va-a the Fsat =
19Hz, which is quite acceptable.

Winding losses rapidly increase as the RL is reduced. At RL = 5ka-a, Rw = 5% which is
excellent considering the OPT will most likely be used with loads above this figure where
winding losses become negligible.

High frequency cut off.
The leakage inductance, LL,  referred to the primary = 4.2 mH. The Ra-a + RLa-a
 = 8k + 8 k = 16k, so the cut off due to LL = 606 kHz. This figure will never be seen
since the shunt capacitance will cause the cut off at a lower frequency. Shunt C looking
into the end of each primary end with CT grounded and one end of the secondary
grounded will be approximately 1,000, so the equivalent Ca-a = 500pF. The HF cut off is
where the reactance of the shunt C = Ra-a and RLa-a in parallel = 4k. Therefore HC
cut off = 79.5 kHz, which is at a much lower F than than caused by the LL.

For much greater analysis of how to work out shunt capacitance see the
calculations for OPT No1 in the page on 'Push Pull Output Transformer calculations'

The leakage inductance and shunt capacitance will form an initial series resonant circuit
at 110 kHz when the response will show a dip due the reduced load impedance due to the
impedance of the series LC at resonance. The dip in impedance can be reduced by a zobel
network across the secondary of perhaps 8 ohms + 0.33uF. The critical damping load
required for a second order LC filter to prevent peaking in the response = 1.41 x ZC or
ZL at the resonant F. In this case, at 110kHz, 500pF has ZC = 2.9k so the damping
resistance load needed is 4k. Suppose we have the OPT set for 2,320 : 76 turns, giving
a 6.6k : 7 ohms match then ZR = 932:1 so the damping resistance theoretically should be
4k / 932 = 4.29 ohms. This is less than  the rated RL value of the amp but 4.7 ohms
could be tried with 0.47uF, thus loading the amp with a partially reactive load of 6.6 ohms
at 72kHz, and a mainly resistive load above 100kHz which should help prevent excessive
response undulations. One only needs just enough R&C for the zobel on the output to
prevent excessive square wave overshoot. The actual value of the zobel network across
the secondary must be confirmed experimentally and perhaps 0.27uF and 8.2 ohms will
be quite sufficient.
The phase shift and response sag at 20kHz will be negligible.

PP OUTPUT TRANSFORMER No2.

OPT 2 is larger transformer with an E&I wasteless core pattern with the same 44mm tongue
dimension as with OPT No 1. The size is simply increased by using a taller stack of laminations
up to 100 mm. The Primary turns are reduced to 2,080 total, but instead of 0.35mm Cu dia wire,
the wire diameter is 0.4 mm. The secondary wire diameter will remain 1.0 mm, and winding
arrangements equal to OPT No 1. The insulation size of 0.5mm between P&S layers and else
where may be reduced to 0.4mm and although this increases the Cshunt somewhat,
the RL likely to be used with such a transformer and the Ra-a will be lower so the capacitance
will not reduce the bandwidth greatly, and the slightly closer coupling distance between P&S
windings will reduce the leakage inductance. All other sizes and arrangements are kept the same.
The TR available will be 36.5:1, 27.4:1, and 18.2:1, and another comprehensive array of
impedance matches will be available and most likely to suit a quad or six pack of output tubes.
My 8585 integrated amplifier design uses a 62mm stack of 44 tongue core material with 2,080
primary turns. Four or more output tubes will be better suited to the No 2 OPT, and another
comprehensive set of impedance matches will be available. The plate current input rating
to the CT is 750mA, but 200 Ma would be the normal working current for 4 tubes.

For both OPT1 and OPT2 the frequency performance is similarly pleasing; No 2 will go
a couple of Hz lower than No1 if the stack height is 75 mm, and half an octave lower if
the stack height is 100 mm. 100mm stacks of iron would be excessive imho, and begin
to cause higher than wanted winding losses and lower HF cut off.

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SE OUTPUT TRANSFORMER No 3

Single Ended Output transformers can be made using the same winding details as
No1 or No2, but there is an air gapped core instead of the usual maximally interleaved
laminations.
Consider what the OPT No1 design may be useful for were it used for an SE amplifier.

We will consider the design when used for SE operation to be OPT No3.

The 0.35mm dia wire will take dc current = 288 mA, at a rated 3 amps per sq.mm.
But 140 mA would be a safer figure to allow for the occasional "oops" factor when
bias failure might occur. If the B+ voltage was +500Vdc, then PSU power input would be
70 Watts to the anode circuit. If Single Ended Ultralinear operation, SEUL, was called
for, and maximum efficiency was 35%, then we could expect 70 x 0.35 = 24.5 Watts of
maximum audio output power. Load line analysis will confirm this to be the case.
The load for 35% efficiency with SEUL will be one where at  clipping the peak change
in load current will be +/- approximately 0.9 x anode idle current, Iaq.

In this case it is 140mA x 0.9 = 126mA peak = 89mA rms.

ac Power in the load  = I squared x RL, where I =Amps rms.

We have PO = 24.5 watts = 0.089 x 0.089 x RL, therefore RL = 24.5 / ( 0.089 x 0.089 )
= 3,093 ohms.
The maximum load swing = 3,093 ohms x 0.089Arms = 275Vrms = + / -390V peak.

To accommodate 70watts of input power without causing undue heat stress in any
output tube, and be able to operate at Ea = +500Vdc, we could use two KT88 or
6550 in parallel so that each was dissipating 35 watts at idle which is below the
maximum Pda ratings of 42 watts. ( KT90 have Pda = 55 watts and would be
a better choice ). The ac load seen by each tube would therefore be 2 x 3,093 =
6.19k, and even triode operation would be quite excellent, although we would not
have quite such high audio power maximum, but the 15 watts from triode would be
quite OK. In triode, the Ra of 2 x 6550 in triode = approx 500 ohms, so the damping factor
with RL = 3.1 = about 7, so global NFB need not be applied. UL operation will require
global NFB.

With a maximum of 275Vrms signal voltage across the primary, the Bac at 14Hz = 0.85 Tesla.

This is a favourable result because it means that the iron could be magnetised by the dc so
that the dc magnetisation, Bdc, could be up to 0.75Tesla, leaving some headroom for LF
transients below 20Hz. The Core will be able to be air gapped so that the µ is reduced from
say 17,000 of the GOSS I am using to less than 1,000, and the dc magnetization reduced.
The golden rule for SE amps is :-
Reactance in ohms of the primary inductance, ZLp = RL at 20Hz or lower.
Since RL = 3.1k, Lp = 3,100 / ( 6.28 x 20 ) = 24.7H.

Experience tells me that the core could be gapped so that the measured Lp at 20 Hz = 24.7H
and the dc magnetization will not exceed 0.63Tesla.
The sum of ac and dc magnetization at 20 Hz at full power will be less than 1.63Tesla so
there is plenty of headroom. If the sum of Bac and Bdc < 1.6T at 14Hz, we are doing
even better, and careful adjustment of the gap will perhaps give this condition so that
distortion of the LF audio signals is negligible, and bass performance is blameless.

SE OUTPUT TRANSFORMER No4.

The use of 2,080 primary turns of 0.4mm dia wire with a taller stack of core material will
allow a higher Ia current of about 180mA. With Ea = 500V, the Pda = 90 watts from
which we might obtain 31 watts of SEUL power to a load of about 2.5k. So three
6550, KT88, KT90 could be used at 30 watts Pda per tube, or better still 4 output tubes
at Pda = 22.5 watts each. A quad of EL34, 6CA7, 6L6, 5881, KT66 could also be used
but with Ea = 420Vmax. Pda for the smaller tubes should be 20 watts max, so total = 80
watts, so Ia could be about 190mA, load will be about 2k.  But as RL is reduced and
power output increased, winding losses increase.

The reasoning used for SE OPT No3 can all be applied.