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Andre Jute
 
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Default KISS 113 by Andre Jute

KISS 113 by Andre Jute

THE VOLTAGES IN THIS AMP WILL KILL YOU. GET EXPERIENCED SUPERVISION IF
IT IS YOUR FIRST TUBE AMP.

This text is copyright Andre Jute 2004 and may not be reproduced
except in the thread KISS xxx on rec.audio.tubes 211104

DESIGNING A REALLY GOOD 300B POWER STAGE

To design your own amplifier from scratch or seriously to modify a
design by someone else you have already built or bought, you need a
few methods and a little mathematics. The techniques are not
onerous—working in the flesh with high voltages should be far more
frightening—and the math to design a resistor-capacitor coupled or
transformer coupled amplifier is also pretty simple once you discover
a few shortcuts, which I shall shortly demonstrate for you. There are
of course esoteric complications with which the truly knowledgeable
may, if meanspirited, humiliate the aspirant. But as long as you stay
within the widely accepted margins of good design, you can ignore many
of them.

If you intend to take up amp design as the consuming hobby of the rest
of your life, the one indispensible book is Langford-Smith's The
Radiotron Designer's Handbook, 4th edition, which runs to 1500 pages
and can get pretty heavy but does not overlook any of the minutae.

The method of tube amp design offered in this chapter will, I hope, be
more accessible to the modern amateur designer and DIYer.

This chapter and the next two offer the minimum amount of information
required to design your own complete resistance-capacitance (RC)
coupled SE amplifier from scratch.

Design procedure
A tube amplifier consists of a signal chain and a power supply chain
which act as one unit to amplify a signal of a few millivolts to such
a level that the output transformer can convert the resulting much
larger voltage into enough current to drive a loudspeaker
satisfactorily. How this amplification function is performed is called
the "transfer function" of the amplifier and is evaluated in frequency
and power bandwidth, in flatness of response, and of course in
decibels of gain.

The amplifier is designed backwards from the interface of the output
transformer with the loudspeaker and, unless you can afford custom
transformers, is designed around output transformers, mains
transformers and chokes (collectively the "the transformers" or "the
iron") known to be available.

Describing the power supply of a hi-fidelity amplifier as part of its
transfer function means precisely what it says: everything is
connected; that also applies to every single other part. Since all
parts of the amp interact with all other parts of the amp, the design
may have to be done iteratively by cut and fit methods until you have
gained a good deal of experience. Designing an amp is also much more
of an art than a mere engineering exercise, so experience counts
double or treble.

If you design an amp for yourself, you should design it to suit your
favourite speakers or some speakers you know you will buy or build.
There is no point in building an amp in isolation from the rest of
your chain just because it is the fashionable topology of the week.

Let us say that the speakers you want to drive have a nominal
impedance rating of 8 ohms and that you have calculated that they
require a maximum of 3W to drive them. Refer to Section 102 The Myth
of the Watt for several mutually reinforcing methods of determining
how much power your speakers really need, as distinct from what the
manufacturers say they need, often a grotesquely inflated number.

Output tube and load
With the power requirement and the speaker load known, you can start
designing the signal cascade. A cascade is a series of tubes each
amplifying a signal a little more, or even a lot more. Each tube and
its surrounding components from its grid resistor to just before the
grid resistor of the next tube is called a "stage" in the cascade.
Confusingly many important calculations take the grid resistor of the
next stage into account rather than the grid resistor of the stage
being calculated.

A 3W single-ended output requirement is a doddle. We could do it with
2A3 but I like the 300B so that is what we choose.

At this point it helps, unless you can afford to have custom output
transformers made, to know what primary impedances are available over
the counter. For most power tubes you want an output transformer (OPT)
with a primary impedance (Zpri) of about four to ten times the plate
resistance (Rp) of the chosen power tube, which you also find on the
tube spec sheet. Lower Zpri multiples of the plate resistance deliver
more power but also more distortion; the higher multiples offer less
distortion but also less power. Aapproximately four times plate
resistance is chosen because at this multiple there is a reasonable
balance between distortion and power output. Load multiples of plate
resistance higher than four pay a substantial price in power for an
increasingly marginal improvement in the distortion figure. Most
audiophiles call a halt to the search for lower distortion at a
multiple between five and eight.

The plate resistance of a 300B and its eponymous imitators is usually
around 680-720 ohms. We are thus looking for an OPT with Zpri in the
region of 2.5Kohm to 7.2Kohm. Those of us who are not power hogs or
utterly obsessed with chasing irrelevantly vanishing transistor-land
distortion numbers will usually find happiness when loading 300B
somewhere from 3Kohm to 6Kohm.

The Lundahl 1623-SE can be wired on the secondary to reflect
impedances of 1.6-3.0-5.6Kohm onto the primary. (This is the correct
way to make a multi-use output transformer; actually tapping the
primary is an egregious practice for reasons we don't have the space
to go into here.) The two useful ones for SE 300B are 3.0Kohm, which
is pretty much a default 300B load, and 5.6Kohm, which is near enough
the upper limit of 8x plate resistance. It has different power ratings
at these impedances ranging from 13W to 50W, so our desired 3W will
never drive it into saturation.

Power tube operating points
There are several ways you can choose operating points for the power
tube.

You can apply Ohm's Law to calculate operating points from knowledge
of the tube's maximum power dissipation, within the envelope of its
maximum plate current and voltage, all of which is information usually
found on the spec sheets.

Or many tubes have one or more sets of suggested operating conditions
on the spec sheets, and you could choose one of those without doing
any calculations of your own.

Or you could do it visually, on the diagram published for the tube
which shows the plate current drawn against the plate voltage at any
level of grid bias. Such a set of curves allows you to determine all
the operating conditions of a tube with the aid only of a ruler, a
pencil and a very little mental arithmetic. I strongly recommend this
method, not least because it helps the amateur visualize what is
happening inside his precious tube.

For the 300B Western Electric published a huge numerical table of many
operating conditions, which also applies to the modern
productionWE300B. STC published another for the 4300, their version of
the 300B, of which the modern Chinese 300B is a copy. Study these
tables until you grasp the relationship between impedance and
distortion, and also the relationship between voltage/current and
output power.

Now forget the tables, and forget whatever you've read about other
people's operating points; some of them parrot these old tables
without any investigation or thought. Those tables are based on
measurements made under assumptions common at the time, one of which
was that 5% distortion would be acceptable to everyone. (The same
applies to almost all tubes, not just 300B!) The 5% is no longer true,
and hasn't been since 1947 when Olson discovered that critical
listeners found distortion objectionable when it reached 2.5% in an
amp with a bandwidth stretching only up to 15kHz. Today, with a more
sophisticated audience and a wider bandwidth by at least a third, the
discrepancy between the tube producers' wishful thinking and consumer
reality might be much larger than it was in 1947.

The curves are the only true authority!

Drawing the maximum dissipation curve
Refer to the 300B Ep-Ia (plate voltage-plate current) curves you
downloaded from the internet after reading Section 112. Work with me
on the transfer curves.

First, recollect that power (W) is voltage multiplied by current (VA).
Therefore current in amps is power in watts divided by voltage. This
knowledge permits you to draw a maximum power dissipation curve as VA
(volt-ampere) points. For the 300B the maximum permissable dissipation
(Pw or Pdmax) is 40W. Thus at 300V on the plate (Eb) it must not draw
more than 40W/300V = 0.133A or 133mA of current (Ia).

If you calculate Pw/Eb = Ia (eg. 40W/400V= 100mA) for every 50 or 100V
across the bottom of the page (the plate voltage, Eb) and draw it
directly on the sheet, that is accurate enough because you won't in
any event go near max dissipation. Just to be absolutely clear: You
must not operate any tube above its maximum dissipation rating. The
entire signal swing (we'll come to it) must fall under the maximum
dissipation curve, besides not causing any other limitation from the
spec sheet to be exceeded.

In fact, operating the tube at maximum dissipation is not recommended
either. It may be build like the proverbial Australian brick outhouse
and give years of service at maximum dissipation. Or it may not. In
any event, it is good engineering practice to derate components from
their maker's proudest claim in order to ensure the minimum of
breakages. Anywhere from 60% to 80% of the permitted maximum seems to
me conservative. For a 300B that is 25W-32W.

Perhaps you want to draw your chosen dissipation curve as well. You do
this by picking a percentage of full dissipation, say 80%, translating
it into power (32W out of a 300B's maximum of 40W for instance), and
repeating the process described above to draw a curve parallel to and
below the maximum dissipation curve.

Whoa! You may now wonder what is all this talk of 25W-32W when we are
talking about getting much less than 10W of amp-driving power. That is
because a power tube used in single-ended applications (by definition
Class A operation) is only 25% efficient. The other three-quarters of
the power in the maximum dissipation you will permit it will be
consumed as heat, quite literally dissipated. In practice other
losses, compromises and design decisions usually result in realized,
usable power in the order of nearer 20 per cent of dissipation.

The loadline
The load angle of your output transformer is the change in plate
voltage divided by the corresponding change in plate current or
-RL=?Eb/Ia. All the minus sign means is that the slope is negative,
i.e. that the line falls from top left to bottom right. Since our
standard schematic on which we will draw it comes only one way, the
loadline we draw will always have a negative slope, so you can ignore
such hairsplitting niceties. Another one is that transconductance (gm)
is usually given with a negative sign preceding it; that too is
irrelevant for our purposes though rendering these things shows
respect for the language of electrical engineers.

Okay, back to business. Since your OPT primary Z is normally fixed by
what is available, the formula is more conveniently written as
RL*?Ia=?Eb, which in English reads as: multiply the output transformer
primary impedance in ohms by an arbitrary amount of current in amps to
discover how much the plate voltage will move because of it. Thus if
your OPT primary Z is 3000 ohms, multiplying it by 150mA or 0.15A
tells you the plate voltage will move 450V because of the 150mA change
in its current.

Lay a ruler on the Ia-Eb lines at the load angle of your output
transformer. In our example the ruler would cut the vertical current
or Ia zero line at 150mA and the horizontal voltage Eb zero line at
450V. Anywhere along this line the load will be 3000 ohms. Even
better, at any point on any line precisely parallel to this arbitrary
loadline the load will also be 3000 ohms.

Grid bias and design centre values
Note that there are also diagonal lines on the table, curved at their
bottoms. These represent the negative grid bias voltage, which must be
as large or larger than the signal we shall put on the grid of the
300B to keep the tube operating in class A1 by preventing it ever
going into the positive grid bias region and drawing current on the
grid.

Along the loadline represented by your ruler you may choose any
operating point of voltage/current/grid bias at which the dissipation
is not more than 40W (max for the 300B; cf the spec sheet) or such
lower level you have chosen to ensure long tube life. I repeat: 60% to
80% of maximum dissipation or 25W to 32W is a good choice.

The operating point is a design centre value. When WE says the maximum
plate V is 450, they mean at quiescence i.e. no signal, which is
usually near or on the halfway mark along the negative grid bias, and
it follows that in fact the tube is theoretically good to 900V at
maximum swing (zero current) even if you may not put more than 450V
into it at the no signal condition. There is an unspoken practical
qualification to the last sentence: "as long as you do not exceed any
of the other maximum ratings." It is generally assumed that you will
not operate the tube at more than one maximum rating at any one time.

Zero current means the tube "cuts off". You don't want to go that far.
Serious distortion will result.

Note that the response curves for each negative bias condition curl at
their bottoms.

You don't want to go there either if you don't have to: non-linear
distortion.

Also, the zero negative bias voltage line is not a good place to be
too near to, as many valves start drawing grid current well into the
negative grid area. That too makes an unacceptable sound at the
extreme, though the overload condition is gradual and some listeners
are more sensitive to it than others.

Choosing your operating point
You now have a trapezoidal box outside which you should not, cannot or
do not want to operate the power tube. You can draw horizontal,
vertical and diagonal lines on the schematic to represent these
limits.

You want to start operating your tube on the loadline a little to the
right of the 0V grid bias line to ensure class A1 output. You want to
stop operating it at a point before the response becomes non-linear in
the region of a curved section of a grid bias line, or, worse, cuts
off because it can draw no current.

This current cut-off point can be extended by sliding your ruler up
while holding it at the same angle so that at any plate voltage you
are using higher current and somewhat lower bias into the same load.
Slide the ruler, still standing in for your loadline, until it touches
your chosen dissipation level and note that at this point the distance
between the zero bias line (or some line you have drawn to the right
of it and parallel to it to distance your ears from grid current) and
the furthest portion of straight, equidistant bias curve the loadline
crosses is longer than it can possibly be at any lower point.

Now choose the negative grid bias voltage which represents half the
bias voltage change between the peak to peak signal swing end points,
and there is your voltage at the plate (350V) and plate current
(72mA), and negative grid bias (-72V), all ready to be read off.

Choosing a specific output transformer
We now know that of the three current capabilities in the Lundahl
LL1623-SE OPT group we want the Lundahl LL1623-SE/90mA, the nearest
higher capability to the 72mA at the operating point. The alternatives
available, 120mA and 180mA would be too much. If you choose too little
current capability the OPT will saturate with DC current before
maximum power; if you choose too much the OPT will be operated
outside its most linear region.

The true power output
VA is only apparent power, of which about three-quarters will be
dissipated as heat: that is the price of class A sound! We need to
discover the true power the tube will deliver via the transformer to
the speaker. We also need to know if our operating point will deliver
more distortion than we can tolerate.

Calculate the true power output and distortion by measuring on the
curves, extending them upwards as required because their truncation at
the top of tube diagrams includes another implied and untrue
assumption, viz that the tube is perfectly and symmetrically linear
about its design centre.

The output power is the product of voltage swing and the current swing
(in whole amps!—72mA is 0.072A) divided by 8. The voltage swing is
540V-120V = 420V. The current swing is 150ma - 10mA = 0.140A. Thus we
can calculate 420*0.14/8 = 7.35W. The output transformer should be
rated for at least twice this power so that it offers an instantaneous
100% overload capability. At 3Kohm the Lundahl OPT we have chosen is
rated at 25W, so it embraces us with a huge safe margin.

Distortion
The 2nd harmonic distortion, as a percentage, is

((((Imax + Imin)/2)-Io)*100)/ (Imax-Imin)

where Io is the current at your chosen design centre operating point;
it is known as the quiescent current, sometimes rendered Iq. In Class
A single-ended operation we usually disregard third harmonic
distortion. With this method third harmonic is not likely ever to get
into your aural threshold because you will be able to see something is
wrong on the curves long before you hear it in a built amp.

In this case the formula works out to 1.43% second harmonic
distortion. Don't let it worry you. We cannot drive the amplifier (as
conceived, two stages total and with the transformer settings above)
to full output even if we wish to.

But even that is irrelevant. What really counts in any amp is whether
the first watt is good. In a low-powered tube amp, matched to suitable
speakers as we intend to do here, that first watt walks ten feet tall
because it falls in the most linear region of the tube's transfer
function, where the distortion is much less.

The 300B cathode resistor and humbuster
While we are here, we may as well calculate the rest of the network
around the 300B. The cathode bias resistor should put a negative
voltage of -72V on the cathode to prevent the signal ever swinging
into the positive grid area. The plate current determined above is
72mA. By Ohm's Law, the resistance required is the voltage drop
desired divided by the plate current (R=Vd/I) or -72V/0.072A=1000
ohms, a convenient value!

The power dissipated in this resistor will be, also by Ohm's handy
Law, W=I*I*R or 0.072x0.072x1000=5.184W and for safety we normally
specify a rating twice or three times that: 15W will do anywhere else
but the cathode resistor for a power valve is such a critical
component that 25W or even 50W would be a superior choice.

The resistors and the potentiometer in the humbuster network have
their ratings calculated by the same formula but with normal
multipliers of 2x or 3x for a safety margin. Thus the 100 ohm
potentiometer will dissipate 0.5184W and should be rated at 2W, and
the 100 ohm resistors branching out from it, splitting the current
between them, can be 2W for convenience.

The 300B cathode bypass capacitor
We'll bypass the cathode resistor with a capacitor. The larger the
capacitor is, the deeper the bass. I don't bother with the math,
because multiplying by pi (3.142-something) is beyond my mental
arithmetic after too many years of computers. (When I sit in boring
concerts I design amps on the screen of my Apple Newton - - I am an
old-fashioned sort of guy - - and do the arithmetic on the slide rule
bezel of my watch.) Anyway, I have long since had it imprinted on my
consciousness that if the product of the resistor in ohms and the
capacitor in microfarads (uF) is around 50,000, the stage will be flat
down to 32Hz, and if the RC product is around 100,000, the stage will
be flat down to 16Hz. Thus, for a 1Kohm resistor setting the cathode
bias, choose a 47uF (or 50uF) or 100uF bypass cap according to whether
you want to bypass to 32Hz or 16Hz, and be done with it.

The rule of thumb is that the reactance (Xc) of the cathode bypass
capacitor must not be more than 10% of the resistance of the cathode
resistor. Reactance is merely the resistance to electromagnetic flow
of a capacitor; it is frequency-dependent. Capacitive reactance is
easily calculated as Xc= 1/(2*pi*f*C) where pi is 3.142, f is the
lowest frequency you want to pass without attenuation, and C is the
capacitor in farads (one microfarad = one-millionth of a farad). The
reactance of a 50uF cap at 32Hz is 99.5 ohms, and the reactance of a
100uF cap at 16Hz is also 99.5 ohms, in each case less than 10% of the
1Kohm cathode resistor.

The reason for rolling the power tube off quite high at low frequency
(LF) end is that a driver in a horn speaker is unloaded below its
nominal resonance in free air. Feeding a Lowther horn driver a lot of
power at much under 30-36Hz is ill-advised.

The more uptight among electrical engineers can become pretty hot
under the collar about this sort of shortcut. They would prefer to
make a complicated dynamic model in which the various resistances with
an influence, such as for instance the cathode's internal resistance,
are all taken into account. That is interesting if one has the time
and a powerful computer, but we once did all the math for over 90
stages in cascades for over thirty amps consecutively through our
proto shop, and the shortcut in 95% of cases was closer than 5% to the
dynamic model prediction; the actual empirical choice after testing
was predicted by the shortcut in the same 95% of cases. A tube
amplifier is not rocket science so those margins of error fall well
within the margins of even the best available caps. Don't waste your
time with the heavy math where it doesn't matter, unless of course you
like heavy math for its own sake.

From plate voltage to supply voltage
The voltage to be supplied to the OPT by the power supply is the
design centre plate voltage (Ep or Eb) we have read off the diagram,
plus the voltage drop for the negative bias, plus the voltage drop
over the DC resistance (164 ohms for the chosen transformer) of the
OPT primary. The latter voltage drop is the product of the primary DC
resistance and the plate current draw, 164x0.072 or near enough 12V,
so the B+ for the power tube circuit must be 350+72+12V or 434V.

All that remains is the 300B's grid resistor, and that we can set at a
conservative 100Kohm though we may have to alter it when we design the
previous stage in the cascade, called the driver.

Compromise and iteration
We have now arrived at the sort of 300B output stage for which when
built into an amp you can pay a lot of money in a boutique or a bit
less but still substantial sums by mailorder from Taiwan or China.
It's an impressive amplifier and with the right speakers does its job
superbly. Only one person in perhaps a hundred thousand will ever hear
an amplifier this good.

At this point you have had a go on your own after the last section and
in this section you and I have worked out way through the design of a
good standard 300B power stage. (By standard you will of course
understand that the elite prefers not to attract attention to
themselves for fear that the government will tax their innocent
pleasures.) This output stage is in fact from a design I published in
the mid-1990s which was built with a two-stage 6SN7 voltage chain by
quite a few audiophiles of widely varying skill levels. Their speakers
were reported to require half a watt to 6W after generous allowance
for transient peaks, a breeze for this design which with the 3K load
is good for 7W.

Amplifier design doesn't in real life proceed in the tidy steps I have
just shown you. Experience, desire and your junk box put bits of the
amp in place out of order and you know before you reach, for instance,
the power supply, that you will have to redesign the output stage
because the supply won't make the voltage at the current required.
That is what happened here. The amp designed above was usually built
as two self-powered monoblocs or as a complete dual mono on the same
chassis. You and I are designing something much simpler, much cheaper,
a stereo integrated amplifier, everything on one chassis with only one
power supply and one voltage gain stage which will double as the
driver stage. Besides reducing the bulk and the real estate demands of
the amp, another design parameter is that I want to use a matching
power supply to the Lundahl OPTs because I have good experience with
it and have one sitting on my bench already.

In a process I shall show you later when we design the power supply, I
determined that what would be available for the 300B was about 396V
and 65mA each, which after the copper drop of about 11V in the primary
of the OPT would be 385V delivered to the plate, split as –65V
negative grid bias and 320V quiescent plate voltage. The same 1K
cathode resistor and cap would do well. Output power would decline a
little and distortion would increase but I didn't bother to calculate
either because I have no intention of using a 3K primary on a 300B to
drive 100dB horns with a fraction of watt.

The back-and-forth iteration of discovering that in an already-chosen
power tranny you don't have the juice is another difficulty you have
to overcome quite regularly unless you are rich and can just order up
custom transformers or unless you wind your own. And in this case I
would at a still later date discover a way of making precisely the
voltage I finally decided I wanted.

But good design though it may be, it isn't what we set out to do. What
we set out to design was an ultra-fi 300B amplifier, something much
more uncompromising than the near universal 300B for all seasons
above.

That requires a boost into lateral thinking mode.

NEXT: KISS 114: PUTTING NUMBERS ON THE REALLY IMPORTANT PARAMETERS OF
ULTRA-FI

211104
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