Output Transformer: Refers to ability to match tube impedance (reverses flow resistance)
to speaker loadings in different voltage and amperage required force and flow rates.
When vintage tube amplifiers are modified or upgraded to higher power tubes, noteable is the
Chinese 100 watt KT-100, the voltage to each tube is doubled by replacing the transformer.
That input transformer would have to be 800 volts instead of 400 and 120 milliamperes.
This then can extend the tube backflow impedance from standard 4000 ohms to 5000 ohms.
However that is for the more simple 2 tube push pull type. For full quadrature class-A
the hypothesis is - you can reduce primary coil backflow to tube impedance back
down to half the KT-100's push pull backflow resistance because each tube is only
active for 1/4 of a sine wave as opposed to half a full wave. This halves the
amount of wire neededd on the primary coil and reduces the sizes of secondaries.
This also allow tube substitution with KT-88. (4k ohm output impedances.)
Tha Voltage split between the first tube and a second getting inverted signal then
requres a change in the output transformers to take more wattage (now 100 not 50), allowing
for either a pair (stereo) or a single output transformer to have output to approximately 8 ohms.

A KT-100 Audio Transformer Turns Ratio is used to accomplish this match. For simplicity lets assume the DC resistance
of our hypothetical transformer is a perfect 8 or 6.2 ohms. Then for a standard 50 watt tube,
we look for a primary impedance of 8 times 22.7 which is 182 DC ohms. The square root of 182
divided by the square root of 8 ohm coil is 4.78 turns ratio. This is not the 8 ohm out
which is usually 6.4 in practice, but it was considered close enough because 4000/516 = 7.75

Now we need to buy something heavier, more rubust, yet we want to overdrive it to get distortion sound.
I need to make special note here that this context is about the POWER AMPLIFIER section only.
That is to say, if you look at older vintage tube amplifiers, many have a built-in preamplifier.
That constant voltage pre-amp accounts for why output transformers are much smaller than calculated.
Their calculation is derived from less then maximum output from the power section, usually half power.
With a seperate pre-amp with it's own controls, assume here I want to drive the power tubes full power.

Marshall amplifiers used low impedance, tiny output transformers that distort at less than half volume.
But, the old standard is to begin distortion at half volume to allow for clean sounding amplification.
It turns out that it is hard to find such ideal transformers. All older ones never anticipated a 100 watts RMS.
We could look for a turns ratio of 10 to 15 to one however, in miliary or other transformers.
But, we have to work differently than just that because we need an efficient match to 8000 ohms.
Lets say we find an 8K ohm DC primary coil. What should the secondary be? Ideal is a 14 ratio.
Then sqr(8000)/sqr(40) is 14 turns ratio. Now we know turns ratio squared divides the tube Z.
For a full KT-100 output transformer, in push-pull 2 tube style, you need 8K ohms, not 5K Z.
Thus 8000 / 200 is the 40 ohm output to load. Now, this higher output load allows the wire to
take more milliamps without slowly burning the coating of the fine wire. 8K needs twice 4K lengths.
If we had a 1200 to 1500 ohm primary, for instance, we could match up the turns ratio with 8 ohms,
then we give up the efficiency of the match between the high voltage tube plate and the primary.
This mismatch also can result in degrading the transformer, even if it saturates sooner.
Saturation results in pleasant distortion with iron transformer plates. Audiophile is Nickel alloy.
There are some studies that have shown that the square root of the frequency is too high.
However, because we are normally using the lowest DC resistance and not the AC impedance,
we only use the square root of one impedance divided by another, so that they average out.
In any case, the tendency is for technicians and engineers to reduce output T sizes.
If the secondaries are wound to 8 ohms instead of assuming that 8 ohms is reflected
(measured with a reflectometer) impedance, the turns ratio gets compromised, along with performance.

I wrote in COcalc.htm that to find the current needed from

Ipeak = SQR(2 x Watts x Min Resistance)
     Min Resistance

Again, it is important that we use this formula at minumum resistance only.
The factor of 2 is used due to harmonic frequencies which have higher AC
impedances than the root frequency, but have small musical effect beyond 5th harmonic order,
unless the speaker load has a capacitor introduced into the circuit as a filter.
A more complete explanation of the increased relative loading known as 'power factor'
can be found on the page dealing with crossover types. kennedyaudio.com/cotypes.htm

This is a reason why a few newer tube desigs maximize for more even harmonics.
Some use the formula that substitutes the power 0.63 for square root, but in
any case, a 2 ohm tap on a transformer will require twice the current as compared
with a 4 ohm tap. That can mean using a center tapped common, which reduces the
voltage on the common wire at the same time current is equal, or if a seperate
winding is used, then a longer wire, (different turns ratio), keeps wattage at 'rated' power.
This would give us about 45 volts possible on the output to speakers at 2.25 amps without degradation.
If the step down transformer is 78 percent efficient, then the 45 volts is OK from 800 volts.(57V*.78)
As a general rule, the voltage rating for an inductor is equal to it's number of turns.(primary)
For Ohm's law E=I*R then 800 = I * 8000 ohms and I is about .1 amperes, the KT-100 input of .120 amps.
When looking at tube amp specifications, especially vintage tubes, remember that there are two tubes
and each could draw 120 milliamps alternatively at full volume. For a full Class-A balanced 4 tube
drivens sytem, you need a transformer 4-1/2 by 4 by 5 tall. It will supply .250 milliamps.
Most vintage push-pull chassis do not have room for that, much less the output transformer.
Furthermore, the secondary coils should meet a much higher standard - power wiring, not chassis. milliampers in rated capacity if that same current were wired into the speaker 'line' tap.
Full audio band output transformers require that there be one winding of at least 25 AWG wire,
collecting magnetic field flux without distorting the wave forms. A tube or valve is like a switch.
It makes a 400 or 800 volt hot plate, puts the musical wave on a screen that modulates voltage.
Then the collector plate passes gated pulsing energy to the transformer that converts to more current.
The size of the output coils at 100 watts becomes large due to the 'skin effect' of large diameter
wire, so that it saves weight and cost to make several parallel secondaries. Some 2, 4, 8 and if
there is space or the wattage of the tube set is low enough, a 16 ohm optimal secondary. (highest
amperage collected and thickest wire. There is not any extra 'load' by using these, so tag on more
speakers to get better sound - one of the reasons so many audiophiles still stick with valves.
Many transformers skip this redundance and wire one end to [C]ommon and then center tap the same
wire for the 4 ohm tap, and the other end goes to the 8 ohm tap. Professional taps are seperate.

Using logic, the Resistance of the output secondary must be less than 8 ohms, because 8 ohms is in parallel.
This is called reflected impedance, and depends somewhat on the distance and ratio which here is 40 to 8.
E=I * R and we said 44 volts = I times 8 - so that I is approximately five and a half amperes, compared to 2.5
This tells us that we should probably try to keep our speaker impedance at 16 ohms to run properly.
We could do that by putting several speakers in parallel, but actually, all speaker impedance are complex.
It depends mostly on the frequencies, the magnet weights, outside temperature, duration of use and so forth.
In any case, selecting such low transformer taps as 4 or 2 ohms reduces the power we get and is our last restort.
Remember too that all transformer drive systems have limited bandwidth. They are not full range audio.
This is why, along with the fact that you would get the full 57 volts, not 44 in a solid state amp, we
sell on the web page the Kennedy Audio single channel 500 watt RMS general purpose amplifier. It does the job.
It may be a pipe dream, but building a true stereo tube amplifier with proper transformer would be an
interesting, although heavy and bulky, experiment. Some efforts to eliminate the output transformer
have resulted in OTL amplifier - output transformerless - that have 4 ohm tube output impedances.
That is 1/1000 of the power tube's normal or 1/2000 of a KT-100, a derating of 200,000 percent.

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